HalbachRectangular De
Date Mar 3, 2016 1:02:40 PM
Contents
1. Global
1.1. Definitions
2. Component 1
2.1. Definitions
2.2. Geometry 1
2.3. Materials
2.4. Magnetic Fields, No Currents
2.5. Mesh 1
3. Study 1
3.1. Stationary
3.2. Solver Configurations
4. Results
4.1. Data Sets
4.2. Tables
4.3. Plot Groups

1. Global

Date Dec 2, 2014 3:24:49 PM
Global settings
Name HalbachRectangular_de.mph
Path C:\2_UQ folder\1_Project\Journal Paper 2 Halbach Array\SPMA Rectangular Magnets\HalbachRectangular_de.mph
Program COMSOL 5.0 (Build: 244)
Unit system SI
Used products
COMSOL Multiphysics
AC/DC Module

1.1. Definitions

1.1.1. Parameters 1

Parameters
Name Expression Value Description
RC 0.075[m] 0.075000 m
RB 0.105[m] 0.10500 m
RA 0.15[m] 0.15000 m
BC 0.39[T] 0.39000 T
BB -0.39[T] -0.39000 T
corr_c 0 0.0000
corr_b 0 0.0000
BA 0.39[T] 0.39000 T

2. Component 1

Date Dec 2, 2014 3:24:49 PM
Component settings
Unit system SI
Geometry shape order automatic

2.1. Definitions

2.1.1. Coordinate Systems

Boundary System 1
Coordinate system type Boundary system
Tag sys1
Settings
First (t1) Second (t2) Third (n)
t1 t2 n
Settings
Name Value
Create first tangent direction from Global Cartesian

2.2. Geometry 1

geom_geom1.png

Geometry 1

Units
Length unit m
Angular unit deg
Geometry statistics
Property Value
Space dimension 3
Number of domains 32
Number of boundaries 312
Number of edges 744
Number of vertices 496

2.2.1. Work Plane 1 (Wp1)

Unite objects
Name Value
Unite objects On
Plane Geometry (Wp1)

geom_geom1_wp1.png

Plane Geometry

ArrayCMagnet1 (R1)
Position
Name Value
Position {RC, 0}
Base Center
Rotation angle
Name Value
Rotation 90
Size
Name Value
Width 0.012
Height 0.006
ArrayCMagnet3 (R3)
Position
Name Value
Position {RC*cos(2*pi*60/360), RC*sin(2*pi*60/360)}
Base Center
Rotation angle
Name Value
Rotation 210
Size
Name Value
Width 0.012
Height 0.006
ArrayCMagnet5 (R5)
Position
Name Value
Position {RC*cos(2*pi*120/360), RC*sin(2*pi*120/360)}
Base Center
Rotation angle
Name Value
Rotation 330
Size
Name Value
Width 0.012
Height 0.006
ArrayCMagnet7 (R7)
Position
Name Value
Position {RC*cos(2*pi*180/360), RC*sin(2*pi*180/360)}
Base Center
Rotation angle
Name Value
Rotation 450
Size
Name Value
Width 0.012
Height 0.006
ArrayCMagnet9 (R9)
Position
Name Value
Position {RC*cos(2*pi*240/360), RC*sin(2*pi*240/360)}
Base Center
Rotation angle
Name Value
Rotation 570
Size
Name Value
Width 0.012
Height 0.006
ArrayCMagnet11 (R11)
Position
Name Value
Position {RC*cos(2*pi*300/360), RC*sin(2*pi*300/360)}
Base Center
Rotation angle
Name Value
Rotation 690
Size
Name Value
Width 0.012
Height 0.006
Rotate 1 (Rot1)
Settings
Name Value
Rotation 0
Point on axis of rotation {0, 0}
ArrayBMagnet1 (R13)
Position
Name Value
Position {RB, 0}
Base Center
Rotation angle
Name Value
Rotation 90
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet2 (R14)
Position
Name Value
Position {RB*cos(2*pi*30/360), RB*sin(2*pi*30/360)}
Base Center
Rotation angle
Name Value
Rotation 150
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet3 (R15)
Position
Name Value
Position {RB*cos(2*pi*60/360), RB*sin(2*pi*60/360)}
Base Center
Rotation angle
Name Value
Rotation 210
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet4 (R16)
Position
Name Value
Position {RB*cos(2*pi*90/360), RB*sin(2*pi*90/360)}
Base Center
Rotation angle
Name Value
Rotation 270
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet5 (R17)
Position
Name Value
Position {RB*cos(2*pi*120/360), RB*sin(2*pi*120/360)}
Base Center
Rotation angle
Name Value
Rotation 330
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet6 (R18)
Position
Name Value
Position {RB*cos(2*pi*150/360), RB*sin(2*pi*150/360)}
Base Center
Rotation angle
Name Value
Rotation 390
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet7 (R19)
Position
Name Value
Position {RB*cos(2*pi*180/360), RB*sin(2*pi*180/360)}
Base Center
Rotation angle
Name Value
Rotation 450
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet8 (R20)
Position
Name Value
Position {RB*cos(2*pi*210/360), RB*sin(2*pi*210/360)}
Base Center
Rotation angle
Name Value
Rotation 510
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet9 (R21)
Position
Name Value
Position {RB*cos(2*pi*240/360), RB*sin(2*pi*240/360)}
Base Center
Rotation angle
Name Value
Rotation 570
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet10 (R22)
Position
Name Value
Position {RB*cos(2*pi*270/360), RB*sin(2*pi*270/360)}
Base Center
Rotation angle
Name Value
Rotation 630
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet11 (R23)
Position
Name Value
Position {RB*cos(2*pi*300/360), RB*sin(2*pi*300/360)}
Base Center
Rotation angle
Name Value
Rotation 690
Size
Name Value
Width 0.012
Height 0.006
ArrayBMagnet12 (R24)
Position
Name Value
Position {RB*cos(2*pi*330/360), RB*sin(2*pi*330/360)}
Base Center
Rotation angle
Name Value
Rotation 750
Size
Name Value
Width 0.012
Height 0.006
Rotate 2 (Rot2)
Settings
Name Value
Rotation 0
Point on axis of rotation {0, 0}
Fillet 1 (Fil1)
Settings
Name Value
Radius 0.0002
ArrayAMagnet1 (R25)
Position
Name Value
Position {RA, 0}
Base Center
Rotation angle
Name Value
Rotation 90
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet2 (R26)
Position
Name Value
Position {RA*cos(2*pi*30/360), RA*sin(2*pi*30/360)}
Base Center
Rotation angle
Name Value
Rotation 150
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet3 (R27)
Position
Name Value
Position {RA*cos(2*pi*60/360), RA*sin(2*pi*60/360)}
Base Center
Rotation angle
Name Value
Rotation 210
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet4 (R28)
Position
Name Value
Position {RA*cos(2*pi*90/360), RA*sin(2*pi*90/360)}
Base Center
Rotation angle
Name Value
Rotation 270
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet5 (R29)
Position
Name Value
Position {RA*cos(2*pi*120/360), RA*sin(2*pi*120/360)}
Base Center
Rotation angle
Name Value
Rotation 330
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet6 (R30)
Position
Name Value
Position {RA*cos(2*pi*150/360), RA*sin(2*pi*150/360)}
Base Center
Rotation angle
Name Value
Rotation 390
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet7 (R31)
Position
Name Value
Position {RA*cos(2*pi*180/360), RA*sin(2*pi*180/360)}
Base Center
Rotation angle
Name Value
Rotation 450
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet8 (R32)
Position
Name Value
Position {RA*cos(2*pi*210/360), RA*sin(2*pi*210/360)}
Base Center
Rotation angle
Name Value
Rotation 510
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet9 (R33)
Position
Name Value
Position {RA*cos(2*pi*240/360), RA*sin(2*pi*240/360)}
Base Center
Rotation angle
Name Value
Rotation 570
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet10 (R34)
Position
Name Value
Position {RA*cos(2*pi*270/360), RA*sin(2*pi*270/360)}
Base Center
Rotation angle
Name Value
Rotation 629
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet11 (R35)
Position
Name Value
Position {RA*cos(2*pi*300/360), RA*sin(2*pi*300/360)}
Base Center
Rotation angle
Name Value
Rotation 690
Size
Name Value
Width 0.0254
Height 0.025
ArrayAMagnet12 (R36)
Position
Name Value
Position {RA*cos(2*pi*330/360), RA*sin(2*pi*330/360)}
Base Center
Rotation angle
Name Value
Rotation 750
Size
Name Value
Width 0.0254
Height 0.025
Fillet 2 (Fil2)
Settings
Name Value
Radius 0.0002
Circle 1 (C1)
Position
Name Value
Position {0, 0}
Size and shape
Name Value
Radius 0.02

2.2.2. Extrude 1 (Ext1)

Settings
Name Value
Work plane Work Plane 1
Distances from plane
Name Value
Distances 0.15
Scales
Scales xw Scales yw
1 1
Displacements
Displacements xw (m) Displacements yw (m)
0 0
Twist angles
Name Value
Twist_angles 0

2.2.3. Block 1 (Blk1)

Position
Name Value
Position {0, 0, 0.075}
Base Center
Axis
Name Value
Axis type z - axis
Size and shape
Name Value
Width 0.6
Depth 0.6
Height 0.6

2.3. Materials

2.3.1. Soft Iron (Without Losses)

material_mat1.png

Soft Iron (without losses)

Selection
Geometric entity level Domain
Selection Domains 2–14, 16–32
Material parameters
Name Value Unit
Relative permeability 1.05 1
Basic Settings
Description Value
Electrical conductivity {{0.666e6[S/m], 0, 0}, {0, 0.666e6[S/m], 0}, {0, 0, 0.666e6[S/m]}}
Relative permittivity {{1.05, 0, 0}, {0, 1.05, 0}, {0, 0, 1.05}}
Relative permeability {{1.05, 0, 0}, {0, 1.05, 0}, {0, 0, 1.05}}
BH curve Settings
Description Value
Magnetic flux density norm BH(normH[m/A])[T]
normH sqrt(H1^2 + H2^2 + H3^2)
Functions
Function name Type
BH Interpolation

material_mat1_BHCurve_BH.png

BH

HB curve Settings
Description Value
Magnetic field norm HB(normB[1/T])[A/m]
normB sqrt(B1^2 + B2^2 + B3^2)
Functions
Function name Type
HB Interpolation

material_mat1_HBCurve_HB.png

HB

2.3.2. Air

material_mat2.png

Air

Selection
Geometric entity level Domain
Selection Domains 1, 15
Material parameters
Name Value Unit
Relative permeability 1 1
Basic Settings
Description Value
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Relative permittivity {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Dynamic viscosity eta(T[1/K])[Pa*s]
Ratio of specific heats 1.4
Electrical conductivity {{0[S/m], 0, 0}, {0, 0[S/m], 0}, {0, 0, 0[S/m]}}
Heat capacity at constant pressure Cp(T[1/K])[J/(kg*K)]
Density rho(pA[1/Pa], T[1/K])[kg/m^3]
Thermal conductivity {{k(T[1/K])[W/(m*K)], 0, 0}, {0, k(T[1/K])[W/(m*K)], 0}, {0, 0, k(T[1/K])[W/(m*K)]}}
Speed of sound cs(T[1/K])[m/s]
Functions
Function name Type
eta Piecewise
Cp Piecewise
rho Analytic
k Piecewise
cs Analytic

material_mat2_def_eta.png

eta

material_mat2_def_Cp.png

Cp

material_mat2_def_k.png

k

material_mat2_def_cs.png

cs

Refractive index Settings
Description Value
Refractive index {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Refractive index, imaginary part {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}

2.4. Magnetic Fields, No Currents

physics_mfnc.png

Magnetic Fields, No Currents

Selection
Geometric entity level Domain
Selection Domains 1–32
Equations

equ_mfnc_1.png

equ_mfnc_2.png

Settings
Description Value
Magnetic scalar potential Quadratic
Value type when using splitting of complex variables Complex
Used products
COMSOL Multiphysics
AC/DC Module
Variables
Name Expression Unit Description Selection
mfnc.Bbx 0 T Background magnetic flux density, x component Domains 1–32
mfnc.Bby 0 T Background magnetic flux density, y component Domains 1–32
mfnc.Bbz 0 T Background magnetic flux density, z component Domains 1–32
mfnc.Hbx 0 A/m Background magnetic field, x component Domains 1–32
mfnc.Hby 0 A/m Background magnetic field, y component Domains 1–32
mfnc.Hbz 0 A/m Background magnetic field, z component Domains 1–32
mfnc.nx nx Normal vector, x component Boundaries 6–311
mfnc.ny ny Normal vector, y component Boundaries 6–311
mfnc.nz nz Normal vector, z component Boundaries 6–311
mfnc.nx dnx Normal vector, x component Boundaries 1–5, 312
mfnc.ny dny Normal vector, y component Boundaries 1–5, 312
mfnc.nz dnz Normal vector, z component Boundaries 1–5, 312
mfnc.nmeshx nxmesh Mesh normal vector, x component Boundaries 6–311
mfnc.nmeshy nymesh Mesh normal vector, y component Boundaries 6–311
mfnc.nmeshz nzmesh Mesh normal vector, z component Boundaries 6–311
mfnc.nmeshx dnxmesh Mesh normal vector, x component Boundaries 1–5, 312
mfnc.nmeshy dnymesh Mesh normal vector, y component Boundaries 1–5, 312
mfnc.nmeshz dnzmesh Mesh normal vector, z component Boundaries 1–5, 312
mfnc.unmeshx unxmesh Mesh normal vector, upside, x component Boundaries 6–311
mfnc.unmeshy unymesh Mesh normal vector, upside, y component Boundaries 6–311
mfnc.unmeshz unzmesh Mesh normal vector, upside, z component Boundaries 6–311
mfnc.dnmeshx dnxmesh Mesh normal vector, downside, x component Boundaries 6–311
mfnc.dnmeshy dnymesh Mesh normal vector, downside, y component Boundaries 6–311
mfnc.dnmeshz dnzmesh Mesh normal vector, downside, z component Boundaries 6–311
mfnc.intWm mfnc.int_Wm(mfnc.d*mfnc.dWm) J Total magnetic energy Global
mfnc.d 1 1 Contribution Domains 1–32
mfnc.unTmx 0 Pa Maxwell upward magnetic surface stress tensor, x component Boundaries 1–312
mfnc.unTmy 0 Pa Maxwell upward magnetic surface stress tensor, y component Boundaries 1–312
mfnc.unTmz 0 Pa Maxwell upward magnetic surface stress tensor, z component Boundaries 1–312
mfnc.dnTmx 0 Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 1–312
mfnc.dnTmy 0 Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 1–312
mfnc.dnTmz 0 Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 1–312

2.4.1. Magnetic Flux Conservation 1

physics_mfnc_mfc1.png

Magnetic Flux Conservation 1

Selection
Geometric entity level Domain
Selection Domains 1, 15
Equations

equ_mfnc_mfc1_1.png

equ_mfnc_mfc1_2.png

Settings
Description Value
Constitutive relation Relative permeability
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Air Basic
Variables
Name Expression Unit Description Selection
mfnc.unTmx -0.5*mfnc.dnx*(real(up(mfnc.Bx))*real(up(mfnc.Hx))+real(up(mfnc.By))*real(up(mfnc.Hy))+real(up(mfnc.Bz))*real(up(mfnc.Hz)))+real(up(mfnc.Bx))*(real(up(mfnc.Hx))*mfnc.dnx+real(up(mfnc.Hy))*mfnc.dny+real(up(mfnc.Hz))*mfnc.dnz) Pa Maxwell upward magnetic surface stress tensor, x component Boundaries 136–139, 168–169
mfnc.unTmy -0.5*mfnc.dny*(real(up(mfnc.Bx))*real(up(mfnc.Hx))+real(up(mfnc.By))*real(up(mfnc.Hy))+real(up(mfnc.Bz))*real(up(mfnc.Hz)))+real(up(mfnc.By))*(real(up(mfnc.Hx))*mfnc.dnx+real(up(mfnc.Hy))*mfnc.dny+real(up(mfnc.Hz))*mfnc.dnz) Pa Maxwell upward magnetic surface stress tensor, y component Boundaries 136–139, 168–169
mfnc.unTmz -0.5*mfnc.dnz*(real(up(mfnc.Bx))*real(up(mfnc.Hx))+real(up(mfnc.By))*real(up(mfnc.Hy))+real(up(mfnc.Bz))*real(up(mfnc.Hz)))+real(up(mfnc.Bz))*(real(up(mfnc.Hx))*mfnc.dnx+real(up(mfnc.Hy))*mfnc.dny+real(up(mfnc.Hz))*mfnc.dnz) Pa Maxwell upward magnetic surface stress tensor, z component Boundaries 136–139, 168–169
mfnc.unTmx -0.5*mfnc.dnx*(real(up(mfnc.Bx))*real(up(mfnc.Hx))+real(up(mfnc.By))*real(up(mfnc.Hy))+real(up(mfnc.Bz))*real(up(mfnc.Hz)))+real(up(mfnc.Bx))*(real(up(mfnc.Hx))*mfnc.dnx+real(up(mfnc.Hy))*mfnc.dny+real(up(mfnc.Hz))*mfnc.dnz) Pa Maxwell upward magnetic surface stress tensor, x component Boundaries 6–135, 140–167, 170–311
mfnc.unTmy -0.5*mfnc.dny*(real(up(mfnc.Bx))*real(up(mfnc.Hx))+real(up(mfnc.By))*real(up(mfnc.Hy))+real(up(mfnc.Bz))*real(up(mfnc.Hz)))+real(up(mfnc.By))*(real(up(mfnc.Hx))*mfnc.dnx+real(up(mfnc.Hy))*mfnc.dny+real(up(mfnc.Hz))*mfnc.dnz) Pa Maxwell upward magnetic surface stress tensor, y component Boundaries 6–135, 140–167, 170–311
mfnc.unTmz -0.5*mfnc.dnz*(real(up(mfnc.Bx))*real(up(mfnc.Hx))+real(up(mfnc.By))*real(up(mfnc.Hy))+real(up(mfnc.Bz))*real(up(mfnc.Hz)))+real(up(mfnc.Bz))*(real(up(mfnc.Hx))*mfnc.dnx+real(up(mfnc.Hy))*mfnc.dny+real(up(mfnc.Hz))*mfnc.dnz) Pa Maxwell upward magnetic surface stress tensor, z component Boundaries 6–135, 140–167, 170–311
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 136–139, 168–169
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 136–139, 168–169
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 136–139, 168–169
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 1–5, 312
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 1–5, 312
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 1–5, 312
mfnc.Hx -Vmx A/m Magnetic field, x component Domains 1, 15
mfnc.Hy -Vmy A/m Magnetic field, y component Domains 1, 15
mfnc.Hz -Vmz A/m Magnetic field, z component Domains 1, 15
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 1–312
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 1–312
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 1–312
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domains 1, 15
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domains 1, 15
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domains 1, 15
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domains 1, 15
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domains 1, 15
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domains 1, 15
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domains 1, 15
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domains 1, 15
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domains 1, 15
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domains 1, 15
mfnc.Bx mu0_const*(mfnc.Ixx*mfnc.Hx+mfnc.Ixy*mfnc.Hy+mfnc.Ixz*mfnc.Hz+mfnc.Mx) T Magnetic flux density, x component Domains 1, 15
mfnc.By mu0_const*(mfnc.Iyx*mfnc.Hx+mfnc.Iyy*mfnc.Hy+mfnc.Iyz*mfnc.Hz+mfnc.My) T Magnetic flux density, y component Domains 1, 15
mfnc.Bz mu0_const*(mfnc.Izx*mfnc.Hx+mfnc.Izy*mfnc.Hy+mfnc.Izz*mfnc.Hz+mfnc.Mz) T Magnetic flux density, z component Domains 1, 15
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domains 1, 15
mfnc.Mx mfnc.chimxx*mfnc.Hx+mfnc.chimxy*mfnc.Hy+mfnc.chimxz*mfnc.Hz A/m Magnetization, x component Domains 1, 15
mfnc.My mfnc.chimyx*mfnc.Hx+mfnc.chimyy*mfnc.Hy+mfnc.chimyz*mfnc.Hz A/m Magnetization, y component Domains 1, 15
mfnc.Mz mfnc.chimzx*mfnc.Hx+mfnc.chimzy*mfnc.Hy+mfnc.chimzz*mfnc.Hz A/m Magnetization, z component Domains 1, 15
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domains 1, 15
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domains 1, 15
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domains 1, 15
mfnc.Izx 0 1 Spatial identity matrix, zx component Domains 1, 15
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domains 1, 15
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domains 1, 15
mfnc.Izy 0 1 Spatial identity matrix, zy component Domains 1, 15
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domains 1, 15
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domains 1, 15
mfnc.Izz 1 1 Spatial identity matrix, zz component Domains 1, 15
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domains 1, 15
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domains 1, 15
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domains 1, 15
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domains 1, 15
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domains 1, 15
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domains 1, 15
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domains 1, 15
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domains 1, 15
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domains 1, 15
mfnc.Brx 0 T Remanent flux density, x component Domains 1, 15
mfnc.Bry 0 T Remanent flux density, y component Domains 1, 15
mfnc.Brz 0 T Remanent flux density, z component Domains 1, 15
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domains 1, 15
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 1–5, 312
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 1–5, 312
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 1–5, 312
mfnc.unTx mfnc.unTmx Pa Maxwell upward surface stress tensor, x component Boundaries 136–139, 168–169
mfnc.unTy mfnc.unTmy Pa Maxwell upward surface stress tensor, y component Boundaries 136–139, 168–169
mfnc.unTz mfnc.unTmz Pa Maxwell upward surface stress tensor, z component Boundaries 136–139, 168–169
mfnc.unTx mfnc.unTmx Pa Maxwell upward surface stress tensor, x component Boundaries 6–135, 140–167, 170–311
mfnc.unTy mfnc.unTmy Pa Maxwell upward surface stress tensor, y component Boundaries 6–135, 140–167, 170–311
mfnc.unTz mfnc.unTmz Pa Maxwell upward surface stress tensor, z component Boundaries 6–135, 140–167, 170–311
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 1–5, 312
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 1–5, 312
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 1–5, 312
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 136–139, 168–169
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 136–139, 168–169
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 136–139, 168–169
mfnc.dnTx 0 Pa Maxwell downward surface stress tensor, x component Boundaries 6–135, 140–167, 170–311
mfnc.dnTy 0 Pa Maxwell downward surface stress tensor, y component Boundaries 6–135, 140–167, 170–311
mfnc.dnTz 0 Pa Maxwell downward surface stress tensor, z component Boundaries 6–135, 140–167, 170–311
mfnc.unx unx Normal vector up direction, x component Boundaries 1–312
mfnc.uny uny Normal vector up direction, y component Boundaries 1–312
mfnc.unz unz Normal vector up direction, z component Boundaries 1–312
mfnc.dnx dnx Normal vector down direction, x component Boundaries 1–312
mfnc.dny dny Normal vector down direction, y component Boundaries 1–312
mfnc.dnz dnz Normal vector down direction, z component Boundaries 1–312
mfnc.W mfnc.Wm J/m^3 Energy density Domains 1, 15
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domains 1, 15
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domains 1, 15
mfnc.mfc1.minput_temperature model.input.minput_temperature K Temperature Domains 1, 15
mfnc.mfc1.minput_pressure model.input.minput_pressure Pa Absolute pressure Domains 1, 15
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domains 1, 15
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domains 1, 15

2.4.2. Magnetic Insulation 1

physics_mfnc_mi1.png

Magnetic Insulation 1

Selection
Geometric entity level Boundary
Selection Boundaries 1–5, 312
Equations

equ_mfnc_mi1.png

Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Boundaries 6–311

2.4.3. Initial Values 1

physics_mfnc_init1.png

Initial Values 1

Selection
Geometric entity level Domain
Selection Domains 1–32
Settings
Description Value
Magnetic scalar potential 0

2.4.4. ArrayBMagnet1

physics_mfnc_mfc2.png

ArrayBMagnet1

Selection
Geometric entity level Domain
Selection Domain 29
Equations

equ_mfnc_mfc2_1.png

equ_mfnc_mfc2_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi*(0*60 + corr_b)/360)
Remanent flux density, y component BB*sin(2*pi*(0*60 + corr_b)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 272–281
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 272–281
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 272–281
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 29
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 29
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 29
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 272–281
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 272–281
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 272–281
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 29
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 29
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 29
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 29
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 29
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 29
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 29
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 29
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 29
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 29
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 29
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 29
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 29
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 29
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 29
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 29
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 29
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 29
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 29
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 29
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 29
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 29
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 29
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 29
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 29
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 29
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 29
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 29
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 29
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 29
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 29
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 29
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 29
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 29
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 29
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 29
mfnc.Brx BB*cos(pi*corr_b/180) T Remanent flux density, x component Domain 29
mfnc.Bry BB*sin(pi*corr_b/180) T Remanent flux density, y component Domain 29
mfnc.Brz 0 T Remanent flux density, z component Domain 29
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 29
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 272–281
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 272–281
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 272–281
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 272–281
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 272–281
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 272–281
mfnc.unx unx Normal vector up direction, x component Boundaries 272–281
mfnc.uny uny Normal vector up direction, y component Boundaries 272–281
mfnc.unz unz Normal vector up direction, z component Boundaries 272–281
mfnc.dnx dnx Normal vector down direction, x component Boundaries 272–281
mfnc.dny dny Normal vector down direction, y component Boundaries 272–281
mfnc.dnz dnz Normal vector down direction, z component Boundaries 272–281
mfnc.W mfnc.Wm J/m^3 Energy density Domain 29
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 29
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 29
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 29
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 29

2.4.5. ArrayBMagnet2

physics_mfnc_mfc3.png

ArrayBMagnet2

Selection
Geometric entity level Domain
Selection Domain 28
Equations

equ_mfnc_mfc3_1.png

equ_mfnc_mfc3_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(1*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(1*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 28
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 28
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 28
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 28
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 28
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 28
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 28
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 28
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 28
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 28
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 28
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 28
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 28
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 28
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 28
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 28
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 28
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 28
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 28
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 28
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 28
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 28
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 28
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 28
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 28
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 28
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 28
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 28
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 28
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 28
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 28
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 28
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 28
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 28
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 28
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 28
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 28
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 28
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 28
mfnc.Brx BB*cos(pi*(60+corr_b)/180) T Remanent flux density, x component Domain 28
mfnc.Bry BB*sin(pi*(60+corr_b)/180) T Remanent flux density, y component Domain 28
mfnc.Brz 0 T Remanent flux density, z component Domain 28
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 28
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.unx unx Normal vector up direction, x component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.uny uny Normal vector up direction, y component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.unz unz Normal vector up direction, z component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dnx dnx Normal vector down direction, x component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dny dny Normal vector down direction, y component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.dnz dnz Normal vector down direction, z component Boundaries 254–257, 259, 261, 263, 267, 269, 271
mfnc.W mfnc.Wm J/m^3 Energy density Domain 28
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 28
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 28
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 28
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 28

2.4.6. ArrayBMagnet3

physics_mfnc_mfc4.png

ArrayBMagnet3

Selection
Geometric entity level Domain
Selection Domain 23
Equations

equ_mfnc_mfc4_1.png

equ_mfnc_mfc4_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(2*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(2*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 23
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 23
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 23
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 23
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 23
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 23
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 23
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 23
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 23
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 23
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 23
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 23
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 23
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 23
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 23
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 23
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 23
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 23
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 23
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 23
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 23
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 23
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 23
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 23
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 23
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 23
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 23
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 23
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 23
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 23
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 23
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 23
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 23
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 23
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 23
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 23
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 23
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 23
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 23
mfnc.Brx BB*cos(pi*(120+corr_b)/180) T Remanent flux density, x component Domain 23
mfnc.Bry BB*sin(pi*(120+corr_b)/180) T Remanent flux density, y component Domain 23
mfnc.Brz 0 T Remanent flux density, z component Domain 23
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 23
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.unx unx Normal vector up direction, x component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.uny uny Normal vector up direction, y component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.unz unz Normal vector up direction, z component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dnx dnx Normal vector down direction, x component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dny dny Normal vector down direction, y component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.dnz dnz Normal vector down direction, z component Boundaries 206–209, 211, 213, 215, 217, 219, 231
mfnc.W mfnc.Wm J/m^3 Energy density Domain 23
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 23
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 23
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 23
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 23

2.4.7. ArrayBMagnet4

physics_mfnc_mfc5.png

ArrayBMagnet4

Selection
Geometric entity level Domain
Selection Domain 19
Equations

equ_mfnc_mfc5_1.png

equ_mfnc_mfc5_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(3*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(3*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 159–163, 166–167, 172–173, 175
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 19
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 19
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 19
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 159–163, 166–167, 172–173, 175
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 159–163, 166–167, 172–173, 175
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 159–163, 166–167, 172–173, 175
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 19
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 19
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 19
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 19
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 19
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 19
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 19
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 19
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 19
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 19
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 19
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 19
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 19
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 19
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 19
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 19
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 19
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 19
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 19
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 19
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 19
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 19
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 19
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 19
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 19
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 19
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 19
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 19
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 19
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 19
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 19
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 19
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 19
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 19
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 19
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 19
mfnc.Brx BB*cos(pi*(180+corr_b)/180) T Remanent flux density, x component Domain 19
mfnc.Bry BB*sin(pi*(180+corr_b)/180) T Remanent flux density, y component Domain 19
mfnc.Brz 0 T Remanent flux density, z component Domain 19
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 19
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 159–163, 166–167, 172–173, 175
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 159–163, 166–167, 172–173, 175
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 159–163, 166–167, 172–173, 175
mfnc.unx unx Normal vector up direction, x component Boundaries 159–163, 166–167, 172–173, 175
mfnc.uny uny Normal vector up direction, y component Boundaries 159–163, 166–167, 172–173, 175
mfnc.unz unz Normal vector up direction, z component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dnx dnx Normal vector down direction, x component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dny dny Normal vector down direction, y component Boundaries 159–163, 166–167, 172–173, 175
mfnc.dnz dnz Normal vector down direction, z component Boundaries 159–163, 166–167, 172–173, 175
mfnc.W mfnc.Wm J/m^3 Energy density Domain 19
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 19
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 19
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 19
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 19

2.4.8. ArrayBMagnet5

physics_mfnc_mfc6.png

ArrayBMagnet5

Selection
Geometric entity level Domain
Selection Domain 12
Equations

equ_mfnc_mfc6_1.png

equ_mfnc_mfc6_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(4*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(4*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 12
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 12
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 12
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 12
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 12
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 12
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 12
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 12
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 12
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 12
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 12
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 12
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 12
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 12
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 12
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 12
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 12
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 12
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 12
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 12
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 12
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 12
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 12
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 12
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 12
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 12
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 12
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 12
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 12
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 12
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 12
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 12
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 12
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 12
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 12
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 12
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 12
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 12
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 12
mfnc.Brx BB*cos(pi*(240+corr_b)/180) T Remanent flux density, x component Domain 12
mfnc.Bry BB*sin(pi*(240+corr_b)/180) T Remanent flux density, y component Domain 12
mfnc.Brz 0 T Remanent flux density, z component Domain 12
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 12
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.unx unx Normal vector up direction, x component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.uny uny Normal vector up direction, y component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.unz unz Normal vector up direction, z component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dnx dnx Normal vector down direction, x component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dny dny Normal vector down direction, y component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.dnz dnz Normal vector down direction, z component Boundaries 98–101, 103, 107, 109, 111, 113, 115
mfnc.W mfnc.Wm J/m^3 Energy density Domain 12
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 12
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 12
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 12
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 12

2.4.9. ArrayBMagnet6

physics_mfnc_mfc7.png

ArrayBMagnet6

Selection
Geometric entity level Domain
Selection Domain 7
Equations

equ_mfnc_mfc7_1.png

equ_mfnc_mfc7_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(5*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(5*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 7
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 7
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 7
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 7
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 7
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 7
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 7
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 7
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 7
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 7
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 7
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 7
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 7
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 7
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 7
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 7
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 7
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 7
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 7
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 7
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 7
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 7
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 7
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 7
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 7
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 7
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 7
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 7
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 7
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 7
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 7
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 7
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 7
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 7
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 7
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 7
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 7
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 7
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 7
mfnc.Brx BB*cos(pi*(300+corr_b)/180) T Remanent flux density, x component Domain 7
mfnc.Bry BB*sin(pi*(300+corr_b)/180) T Remanent flux density, y component Domain 7
mfnc.Brz 0 T Remanent flux density, z component Domain 7
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 7
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.unx unx Normal vector up direction, x component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.uny uny Normal vector up direction, y component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.unz unz Normal vector up direction, z component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dnx dnx Normal vector down direction, x component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dny dny Normal vector down direction, y component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.dnz dnz Normal vector down direction, z component Boundaries 50–53, 55, 57, 59, 71, 73, 75
mfnc.W mfnc.Wm J/m^3 Energy density Domain 7
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 7
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 7
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 7
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 7

2.4.10. ArrayBMagnet7

physics_mfnc_mfc8.png

ArrayBMagnet7

Selection
Geometric entity level Domain
Selection Domain 5
Equations

equ_mfnc_mfc8_1.png

equ_mfnc_mfc8_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(6*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(6*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 36–45
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 36–45
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 36–45
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 5
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 5
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 5
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 36–45
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 36–45
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 36–45
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 5
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 5
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 5
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 5
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 5
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 5
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 5
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 5
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 5
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 5
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 5
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 5
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 5
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 5
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 5
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 5
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 5
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 5
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 5
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 5
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 5
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 5
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 5
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 5
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 5
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 5
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 5
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 5
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 5
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 5
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 5
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 5
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 5
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 5
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 5
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 5
mfnc.Brx BB*cos(pi*(360+corr_b)/180) T Remanent flux density, x component Domain 5
mfnc.Bry BB*sin(pi*(360+corr_b)/180) T Remanent flux density, y component Domain 5
mfnc.Brz 0 T Remanent flux density, z component Domain 5
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 5
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 36–45
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 36–45
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 36–45
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 36–45
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 36–45
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 36–45
mfnc.unx unx Normal vector up direction, x component Boundaries 36–45
mfnc.uny uny Normal vector up direction, y component Boundaries 36–45
mfnc.unz unz Normal vector up direction, z component Boundaries 36–45
mfnc.dnx dnx Normal vector down direction, x component Boundaries 36–45
mfnc.dny dny Normal vector down direction, y component Boundaries 36–45
mfnc.dnz dnz Normal vector down direction, z component Boundaries 36–45
mfnc.W mfnc.Wm J/m^3 Energy density Domain 5
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 5
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 5
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 5
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 5

2.4.11. ArrayBMagnet8

physics_mfnc_mfc9.png

ArrayBMagnet8

Selection
Geometric entity level Domain
Selection Domain 6
Equations

equ_mfnc_mfc9_1.png

equ_mfnc_mfc9_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(7*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(7*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 6
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 6
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 6
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 6
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 6
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 6
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 6
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 6
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 6
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 6
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 6
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 6
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 6
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 6
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 6
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 6
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 6
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 6
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 6
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 6
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 6
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 6
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 6
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 6
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 6
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 6
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 6
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 6
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 6
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 6
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 6
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 6
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 6
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 6
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 6
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 6
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 6
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 6
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 6
mfnc.Brx BB*cos(pi*(420+corr_b)/180) T Remanent flux density, x component Domain 6
mfnc.Bry BB*sin(pi*(420+corr_b)/180) T Remanent flux density, y component Domain 6
mfnc.Brz 0 T Remanent flux density, z component Domain 6
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 6
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.unx unx Normal vector up direction, x component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.uny uny Normal vector up direction, y component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.unz unz Normal vector up direction, z component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dnx dnx Normal vector down direction, x component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dny dny Normal vector down direction, y component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.dnz dnz Normal vector down direction, z component Boundaries 46–49, 54, 56, 58, 70, 72, 74
mfnc.W mfnc.Wm J/m^3 Energy density Domain 6
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 6
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 6
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 6
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 6

2.4.12. ArrayBMagnet9

physics_mfnc_mfc13.png

ArrayBMagnet9

Selection
Geometric entity level Domain
Selection Domain 11
Equations

equ_mfnc_mfc13_1.png

equ_mfnc_mfc13_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(8*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(8*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 11
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 11
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 11
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 11
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 11
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 11
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 11
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 11
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 11
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 11
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 11
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 11
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 11
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 11
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 11
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 11
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 11
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 11
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 11
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 11
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 11
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 11
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 11
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 11
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 11
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 11
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 11
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 11
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 11
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 11
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 11
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 11
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 11
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 11
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 11
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 11
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 11
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 11
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 11
mfnc.Brx BB*cos(pi*(480+corr_b)/180) T Remanent flux density, x component Domain 11
mfnc.Bry BB*sin(pi*(480+corr_b)/180) T Remanent flux density, y component Domain 11
mfnc.Brz 0 T Remanent flux density, z component Domain 11
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 11
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.unx unx Normal vector up direction, x component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.uny uny Normal vector up direction, y component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.unz unz Normal vector up direction, z component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dnx dnx Normal vector down direction, x component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dny dny Normal vector down direction, y component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.dnz dnz Normal vector down direction, z component Boundaries 94–97, 102, 106, 108, 110, 112, 114
mfnc.W mfnc.Wm J/m^3 Energy density Domain 11
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 11
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 11
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 11
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 11

2.4.13. ArrayBMagnet10

physics_mfnc_mfc15.png

ArrayBMagnet10

Selection
Geometric entity level Domain
Selection Domain 18
Equations

equ_mfnc_mfc15_1.png

equ_mfnc_mfc15_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(9*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(9*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 154–158, 164–165, 170–171, 174
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 18
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 18
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 18
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 154–158, 164–165, 170–171, 174
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 154–158, 164–165, 170–171, 174
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 154–158, 164–165, 170–171, 174
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 18
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 18
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 18
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 18
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 18
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 18
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 18
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 18
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 18
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 18
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 18
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 18
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 18
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 18
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 18
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 18
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 18
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 18
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 18
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 18
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 18
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 18
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 18
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 18
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 18
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 18
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 18
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 18
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 18
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 18
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 18
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 18
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 18
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 18
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 18
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 18
mfnc.Brx BB*cos(pi*(540+corr_b)/180) T Remanent flux density, x component Domain 18
mfnc.Bry BB*sin(pi*(540+corr_b)/180) T Remanent flux density, y component Domain 18
mfnc.Brz 0 T Remanent flux density, z component Domain 18
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 18
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 154–158, 164–165, 170–171, 174
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 154–158, 164–165, 170–171, 174
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 154–158, 164–165, 170–171, 174
mfnc.unx unx Normal vector up direction, x component Boundaries 154–158, 164–165, 170–171, 174
mfnc.uny uny Normal vector up direction, y component Boundaries 154–158, 164–165, 170–171, 174
mfnc.unz unz Normal vector up direction, z component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dnx dnx Normal vector down direction, x component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dny dny Normal vector down direction, y component Boundaries 154–158, 164–165, 170–171, 174
mfnc.dnz dnz Normal vector down direction, z component Boundaries 154–158, 164–165, 170–171, 174
mfnc.W mfnc.Wm J/m^3 Energy density Domain 18
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 18
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 18
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 18
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 18

2.4.14. ArrayBMagnet11

physics_mfnc_mfc14.png

ArrayBMagnet11

Selection
Geometric entity level Domain
Selection Domain 22
Equations

equ_mfnc_mfc14_1.png

equ_mfnc_mfc14_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(10*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(10*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 22
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 22
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 22
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 22
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 22
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 22
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 22
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 22
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 22
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 22
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 22
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 22
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 22
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 22
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 22
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 22
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 22
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 22
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 22
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 22
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 22
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 22
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 22
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 22
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 22
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 22
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 22
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 22
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 22
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 22
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 22
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 22
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 22
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 22
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 22
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 22
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 22
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 22
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 22
mfnc.Brx BB*cos(pi*(600+corr_b)/180) T Remanent flux density, x component Domain 22
mfnc.Bry BB*sin(pi*(600+corr_b)/180) T Remanent flux density, y component Domain 22
mfnc.Brz 0 T Remanent flux density, z component Domain 22
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 22
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.unx unx Normal vector up direction, x component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.uny uny Normal vector up direction, y component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.unz unz Normal vector up direction, z component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dnx dnx Normal vector down direction, x component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dny dny Normal vector down direction, y component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.dnz dnz Normal vector down direction, z component Boundaries 202–205, 210, 212, 214, 216, 218, 230
mfnc.W mfnc.Wm J/m^3 Energy density Domain 22
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 22
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 22
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 22
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 22

2.4.15. ArrayBMagnet12

physics_mfnc_mfc12.png

ArrayBMagnet12

Selection
Geometric entity level Domain
Selection Domain 27
Equations

equ_mfnc_mfc12_1.png

equ_mfnc_mfc12_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BB*cos(2*pi/360*(11*60 + corr_b))
Remanent flux density, y component BB*sin(2*pi/360*(11*60 + corr_b))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 27
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 27
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 27
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 27
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 27
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 27
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 27
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 27
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 27
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 27
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 27
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 27
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 27
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 27
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 27
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 27
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 27
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 27
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 27
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 27
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 27
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 27
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 27
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 27
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 27
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 27
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 27
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 27
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 27
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 27
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 27
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 27
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 27
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 27
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 27
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 27
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 27
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 27
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 27
mfnc.Brx BB*cos(pi*(660+corr_b)/180) T Remanent flux density, x component Domain 27
mfnc.Bry BB*sin(pi*(660+corr_b)/180) T Remanent flux density, y component Domain 27
mfnc.Brz 0 T Remanent flux density, z component Domain 27
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 27
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.unx unx Normal vector up direction, x component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.uny uny Normal vector up direction, y component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.unz unz Normal vector up direction, z component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dnx dnx Normal vector down direction, x component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dny dny Normal vector down direction, y component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.dnz dnz Normal vector down direction, z component Boundaries 250–253, 258, 260, 262, 266, 268, 270
mfnc.W mfnc.Wm J/m^3 Energy density Domain 27
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 27
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 27
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 27
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 27

2.4.16. ArrayCMagnet1

physics_mfnc_mfc16.png

ArrayCMagnet1

Selection
Geometric entity level Domain
Selection Domain 26
Equations

equ_mfnc_mfc16_1.png

equ_mfnc_mfc16_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BC*cos(2*pi/360*(0*60 + corr_c))
Remanent flux density, y component BC*sin(2*pi/360*(0*60 + corr_c))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 236–245
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 236–245
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 236–245
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 26
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 26
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 26
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 236–245
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 236–245
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 236–245
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 26
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 26
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 26
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 26
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 26
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 26
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 26
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 26
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 26
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 26
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 26
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 26
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 26
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 26
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 26
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 26
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 26
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 26
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 26
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 26
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 26
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 26
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 26
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 26
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 26
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 26
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 26
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 26
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 26
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 26
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 26
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 26
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 26
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 26
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 26
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 26
mfnc.Brx BC*cos(pi*corr_c/180) T Remanent flux density, x component Domain 26
mfnc.Bry BC*sin(pi*corr_c/180) T Remanent flux density, y component Domain 26
mfnc.Brz 0 T Remanent flux density, z component Domain 26
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 26
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 236–245
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 236–245
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 236–245
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 236–245
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 236–245
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 236–245
mfnc.unx unx Normal vector up direction, x component Boundaries 236–245
mfnc.uny uny Normal vector up direction, y component Boundaries 236–245
mfnc.unz unz Normal vector up direction, z component Boundaries 236–245
mfnc.dnx dnx Normal vector down direction, x component Boundaries 236–245
mfnc.dny dny Normal vector down direction, y component Boundaries 236–245
mfnc.dnz dnz Normal vector down direction, z component Boundaries 236–245
mfnc.W mfnc.Wm J/m^3 Energy density Domain 26
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 26
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 26
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 26
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 26

2.4.17. ArrayCMagnet3

physics_mfnc_mfc18.png

ArrayCMagnet3

Selection
Geometric entity level Domain
Selection Domain 21
Equations

equ_mfnc_mfc18_1.png

equ_mfnc_mfc18_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BC*cos(2*pi/360*(2*60 + corr_c))
Remanent flux density, y component BC*sin(2*pi/360*(2*60 + corr_c))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 21
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 21
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 21
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 21
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 21
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 21
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 21
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 21
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 21
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 21
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 21
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 21
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 21
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 21
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 21
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 21
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 21
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 21
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 21
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 21
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 21
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 21
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 21
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 21
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 21
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 21
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 21
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 21
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 21
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 21
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 21
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 21
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 21
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 21
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 21
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 21
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 21
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 21
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 21
mfnc.Brx BC*cos(pi*(120+corr_c)/180) T Remanent flux density, x component Domain 21
mfnc.Bry BC*sin(pi*(120+corr_c)/180) T Remanent flux density, y component Domain 21
mfnc.Brz 0 T Remanent flux density, z component Domain 21
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 21
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.unx unx Normal vector up direction, x component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.uny uny Normal vector up direction, y component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.unz unz Normal vector up direction, z component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dnx dnx Normal vector down direction, x component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dny dny Normal vector down direction, y component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.dnz dnz Normal vector down direction, z component Boundaries 186–189, 191, 193, 195, 197, 199, 201
mfnc.W mfnc.Wm J/m^3 Energy density Domain 21
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 21
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 21
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 21
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 21

2.4.18. ArrayCMagnet5

physics_mfnc_mfc20.png

ArrayCMagnet5

Selection
Geometric entity level Domain
Selection Domain 14
Equations

equ_mfnc_mfc20_1.png

equ_mfnc_mfc20_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BC*cos(2*pi/360*(4*60 + corr_c))
Remanent flux density, y component BC*sin(2*pi/360*(4*60 + corr_c))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 14
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 14
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 14
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 14
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 14
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 14
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 14
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 14
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 14
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 14
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 14
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 14
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 14
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 14
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 14
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 14
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 14
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 14
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 14
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 14
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 14
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 14
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 14
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 14
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 14
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 14
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 14
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 14
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 14
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 14
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 14
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 14
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 14
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 14
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 14
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 14
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 14
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 14
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 14
mfnc.Brx BC*cos(pi*(240+corr_c)/180) T Remanent flux density, x component Domain 14
mfnc.Bry BC*sin(pi*(240+corr_c)/180) T Remanent flux density, y component Domain 14
mfnc.Brz 0 T Remanent flux density, z component Domain 14
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 14
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.unx unx Normal vector up direction, x component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.uny uny Normal vector up direction, y component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.unz unz Normal vector up direction, z component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dnx dnx Normal vector down direction, x component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dny dny Normal vector down direction, y component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.dnz dnz Normal vector down direction, z component Boundaries 120–123, 125, 127, 129, 131, 133, 135
mfnc.W mfnc.Wm J/m^3 Energy density Domain 14
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 14
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 14
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 14
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 14

2.4.19. ArrayCMagnet7

physics_mfnc_mfc22.png

ArrayCMagnet7

Selection
Geometric entity level Domain
Selection Domain 10
Equations

equ_mfnc_mfc22_1.png

equ_mfnc_mfc22_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BC*cos(2*pi/360*(6*60 + corr_c))
Remanent flux density, y component BC*sin(2*pi/360*(6*60 + corr_c))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 80–89
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 80–89
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 80–89
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 10
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 10
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 10
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 80–89
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 80–89
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 80–89
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 10
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 10
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 10
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 10
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 10
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 10
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 10
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 10
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 10
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 10
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 10
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 10
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 10
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 10
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 10
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 10
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 10
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 10
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 10
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 10
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 10
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 10
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 10
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 10
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 10
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 10
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 10
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 10
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 10
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 10
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 10
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 10
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 10
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 10
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 10
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 10
mfnc.Brx BC*cos(pi*(360+corr_c)/180) T Remanent flux density, x component Domain 10
mfnc.Bry BC*sin(pi*(360+corr_c)/180) T Remanent flux density, y component Domain 10
mfnc.Brz 0 T Remanent flux density, z component Domain 10
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 10
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 80–89
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 80–89
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 80–89
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 80–89
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 80–89
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 80–89
mfnc.unx unx Normal vector up direction, x component Boundaries 80–89
mfnc.uny uny Normal vector up direction, y component Boundaries 80–89
mfnc.unz unz Normal vector up direction, z component Boundaries 80–89
mfnc.dnx dnx Normal vector down direction, x component Boundaries 80–89
mfnc.dny dny Normal vector down direction, y component Boundaries 80–89
mfnc.dnz dnz Normal vector down direction, z component Boundaries 80–89
mfnc.W mfnc.Wm J/m^3 Energy density Domain 10
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 10
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 10
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 10
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 10

2.4.20. ArrayCMagnet9

physics_mfnc_mfc24.png

ArrayCMagnet9

Selection
Geometric entity level Domain
Selection Domain 13
Equations

equ_mfnc_mfc24_1.png

equ_mfnc_mfc24_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BC*cos(2*pi/360*(8*60 + corr_c))
Remanent flux density, y component BC*sin(2*pi/360*(8*60 + corr_c))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 13
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 13
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 13
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 13
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 13
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 13
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 13
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 13
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 13
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 13
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 13
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 13
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 13
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 13
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 13
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 13
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 13
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 13
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 13
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 13
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 13
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 13
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 13
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 13
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 13
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 13
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 13
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 13
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 13
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 13
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 13
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 13
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 13
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 13
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 13
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 13
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 13
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 13
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 13
mfnc.Brx BC*cos(pi*(480+corr_c)/180) T Remanent flux density, x component Domain 13
mfnc.Bry BC*sin(pi*(480+corr_c)/180) T Remanent flux density, y component Domain 13
mfnc.Brz 0 T Remanent flux density, z component Domain 13
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 13
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.unx unx Normal vector up direction, x component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.uny uny Normal vector up direction, y component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.unz unz Normal vector up direction, z component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dnx dnx Normal vector down direction, x component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dny dny Normal vector down direction, y component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.dnz dnz Normal vector down direction, z component Boundaries 116–119, 124, 126, 128, 130, 132, 134
mfnc.W mfnc.Wm J/m^3 Energy density Domain 13
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 13
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 13
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 13
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 13

2.4.21. ArrayCMagnet11

physics_mfnc_mfc26.png

ArrayCMagnet11

Selection
Geometric entity level Domain
Selection Domain 20
Equations

equ_mfnc_mfc26_1.png

equ_mfnc_mfc26_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BC*cos(2*pi/360*(10*60 + corr_c))
Remanent flux density, y component BC*sin(2*pi/360*(10*60 + corr_c))
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 20
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 20
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 20
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 20
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 20
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 20
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 20
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 20
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 20
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 20
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 20
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 20
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 20
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 20
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 20
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 20
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 20
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 20
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 20
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 20
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 20
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 20
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 20
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 20
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 20
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 20
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 20
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 20
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 20
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 20
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 20
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 20
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 20
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 20
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 20
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 20
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 20
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 20
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 20
mfnc.Brx BC*cos(pi*(600+corr_c)/180) T Remanent flux density, x component Domain 20
mfnc.Bry BC*sin(pi*(600+corr_c)/180) T Remanent flux density, y component Domain 20
mfnc.Brz 0 T Remanent flux density, z component Domain 20
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 20
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.unx unx Normal vector up direction, x component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.uny uny Normal vector up direction, y component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.unz unz Normal vector up direction, z component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dnx dnx Normal vector down direction, x component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dny dny Normal vector down direction, y component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.dnz dnz Normal vector down direction, z component Boundaries 182–185, 190, 192, 194, 196, 198, 200
mfnc.W mfnc.Wm J/m^3 Energy density Domain 20
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 20
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 20
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 20
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 20

2.4.22. ArrayAMagnet1

physics_mfnc_mfc28.png

ArrayAMagnet1

Selection
Geometric entity level Domain
Selection Domain 32
Equations

equ_mfnc_mfc28_1.png

equ_mfnc_mfc28_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(0*60)/360)
Remanent flux density, y component BA*sin(2*pi*(0*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 300–306, 309–311
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 300–306, 309–311
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 300–306, 309–311
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 32
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 32
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 32
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 300–306, 309–311
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 300–306, 309–311
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 300–306, 309–311
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 32
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 32
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 32
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 32
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 32
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 32
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 32
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 32
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 32
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 32
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 32
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 32
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 32
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 32
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 32
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 32
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 32
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 32
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 32
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 32
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 32
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 32
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 32
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 32
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 32
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 32
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 32
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 32
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 32
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 32
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 32
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 32
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 32
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 32
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 32
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 32
mfnc.Brx BA T Remanent flux density, x component Domain 32
mfnc.Bry 0 T Remanent flux density, y component Domain 32
mfnc.Brz 0 T Remanent flux density, z component Domain 32
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 32
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 300–306, 309–311
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 300–306, 309–311
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 300–306, 309–311
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 300–306, 309–311
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 300–306, 309–311
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 300–306, 309–311
mfnc.unx unx Normal vector up direction, x component Boundaries 300–306, 309–311
mfnc.uny uny Normal vector up direction, y component Boundaries 300–306, 309–311
mfnc.unz unz Normal vector up direction, z component Boundaries 300–306, 309–311
mfnc.dnx dnx Normal vector down direction, x component Boundaries 300–306, 309–311
mfnc.dny dny Normal vector down direction, y component Boundaries 300–306, 309–311
mfnc.dnz dnz Normal vector down direction, z component Boundaries 300–306, 309–311
mfnc.W mfnc.Wm J/m^3 Energy density Domain 32
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 32
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 32
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 32
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 32

2.4.23. ArrayAMagnet2

physics_mfnc_mfc29.png

ArrayAMagnet2

Selection
Geometric entity level Domain
Selection Domain 31
Equations

equ_mfnc_mfc29_1.png

equ_mfnc_mfc29_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(1*60)/360)
Remanent flux density, y component BA*sin(2*pi*(1*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 31
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 31
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 31
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 31
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 31
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 31
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 31
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 31
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 31
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 31
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 31
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 31
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 31
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 31
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 31
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 31
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 31
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 31
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 31
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 31
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 31
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 31
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 31
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 31
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 31
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 31
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 31
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 31
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 31
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 31
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 31
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 31
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 31
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 31
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 31
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 31
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 31
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 31
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 31
mfnc.Brx BA*cos(pi/3) T Remanent flux density, x component Domain 31
mfnc.Bry BA*sin(pi/3) T Remanent flux density, y component Domain 31
mfnc.Brz 0 T Remanent flux density, z component Domain 31
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 31
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.unx unx Normal vector up direction, x component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.uny uny Normal vector up direction, y component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.unz unz Normal vector up direction, z component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dnx dnx Normal vector down direction, x component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dny dny Normal vector down direction, y component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.dnz dnz Normal vector down direction, z component Boundaries 286–289, 291, 293, 295, 297, 299, 308
mfnc.W mfnc.Wm J/m^3 Energy density Domain 31
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 31
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 31
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 31
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 31

2.4.24. ArrayAMagnet3

physics_mfnc_mfc30.png

ArrayAMagnet3

Selection
Geometric entity level Domain
Selection Domain 25
Equations

equ_mfnc_mfc30_1.png

equ_mfnc_mfc30_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(2*60)/360)
Remanent flux density, y component BA*sin(2*pi*(2*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 25
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 25
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 25
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 25
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 25
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 25
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 25
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 25
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 25
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 25
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 25
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 25
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 25
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 25
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 25
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 25
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 25
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 25
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 25
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 25
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 25
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 25
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 25
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 25
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 25
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 25
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 25
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 25
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 25
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 25
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 25
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 25
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 25
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 25
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 25
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 25
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 25
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 25
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 25
mfnc.Brx BA*cos(2*pi/3) T Remanent flux density, x component Domain 25
mfnc.Bry BA*sin(2*pi/3) T Remanent flux density, y component Domain 25
mfnc.Brz 0 T Remanent flux density, z component Domain 25
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 25
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.unx unx Normal vector up direction, x component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.uny uny Normal vector up direction, y component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.unz unz Normal vector up direction, z component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dnx dnx Normal vector down direction, x component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dny dny Normal vector down direction, y component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.dnz dnz Normal vector down direction, z component Boundaries 224–227, 229, 233, 235, 247, 249, 265
mfnc.W mfnc.Wm J/m^3 Energy density Domain 25
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 25
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 25
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 25
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 25

2.4.25. ArrayAMagnet4

physics_mfnc_mfc31.png

ArrayAMagnet4

Selection
Geometric entity level Domain
Selection Domain 17
Equations

equ_mfnc_mfc31_1.png

equ_mfnc_mfc31_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(3*60)/360)
Remanent flux density, y component BA*sin(2*pi*(3*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 145–151, 178–180
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 145–151, 178–180
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 145–151, 178–180
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 17
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 17
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 17
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 145–151, 178–180
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 145–151, 178–180
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 145–151, 178–180
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 17
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 17
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 17
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 17
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 17
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 17
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 17
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 17
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 17
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 17
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 17
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 17
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 17
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 17
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 17
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 17
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 17
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 17
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 17
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 17
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 17
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 17
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 17
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 17
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 17
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 17
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 17
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 17
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 17
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 17
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 17
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 17
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 17
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 17
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 17
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 17
mfnc.Brx BA*cos(pi) T Remanent flux density, x component Domain 17
mfnc.Bry BA*sin(pi) T Remanent flux density, y component Domain 17
mfnc.Brz 0 T Remanent flux density, z component Domain 17
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 17
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 145–151, 178–180
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 145–151, 178–180
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 145–151, 178–180
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 145–151, 178–180
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 145–151, 178–180
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 145–151, 178–180
mfnc.unx unx Normal vector up direction, x component Boundaries 145–151, 178–180
mfnc.uny uny Normal vector up direction, y component Boundaries 145–151, 178–180
mfnc.unz unz Normal vector up direction, z component Boundaries 145–151, 178–180
mfnc.dnx dnx Normal vector down direction, x component Boundaries 145–151, 178–180
mfnc.dny dny Normal vector down direction, y component Boundaries 145–151, 178–180
mfnc.dnz dnz Normal vector down direction, z component Boundaries 145–151, 178–180
mfnc.W mfnc.Wm J/m^3 Energy density Domain 17
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 17
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 17
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 17
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 17

2.4.26. ArrayAMagnet5

physics_mfnc_mfc32.png

ArrayAMagnet5

Selection
Geometric entity level Domain
Selection Domain 9
Equations

equ_mfnc_mfc32_1.png

equ_mfnc_mfc32_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(4*60)/360)
Remanent flux density, y component BA*sin(2*pi*(4*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 9
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 9
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 9
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 9
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 9
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 9
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 9
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 9
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 9
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 9
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 9
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 9
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 9
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 9
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 9
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 9
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 9
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 9
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 9
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 9
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 9
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 9
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 9
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 9
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 9
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 9
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 9
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 9
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 9
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 9
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 9
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 9
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 9
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 9
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 9
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 9
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 9
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 9
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 9
mfnc.Brx BA*cos(4*pi/3) T Remanent flux density, x component Domain 9
mfnc.Bry BA*sin(4*pi/3) T Remanent flux density, y component Domain 9
mfnc.Brz 0 T Remanent flux density, z component Domain 9
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 9
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.unx unx Normal vector up direction, x component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.uny uny Normal vector up direction, y component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.unz unz Normal vector up direction, z component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dnx dnx Normal vector down direction, x component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dny dny Normal vector down direction, y component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.dnz dnz Normal vector down direction, z component Boundaries 64–67, 69, 77, 79, 91, 93, 105
mfnc.W mfnc.Wm J/m^3 Energy density Domain 9
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 9
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 9
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 9
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 9

2.4.27. ArrayAMagnet6

physics_mfnc_mfc33.png

ArrayAMagnet6

Selection
Geometric entity level Domain
Selection Domain 4
Equations

equ_mfnc_mfc33_1.png

equ_mfnc_mfc33_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(5*60)/360)
Remanent flux density, y component BA*sin(2*pi*(5*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 4
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 4
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 4
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 4
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 4
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 4
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 4
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 4
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 4
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 4
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 4
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 4
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 4
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 4
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 4
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 4
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 4
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 4
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 4
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 4
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 4
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 4
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 4
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 4
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 4
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 4
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 4
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 4
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 4
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 4
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 4
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 4
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 4
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 4
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 4
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 4
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 4
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 4
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 4
mfnc.Brx BA*cos(5*pi/3) T Remanent flux density, x component Domain 4
mfnc.Bry BA*sin(5*pi/3) T Remanent flux density, y component Domain 4
mfnc.Brz 0 T Remanent flux density, z component Domain 4
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 4
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.unx unx Normal vector up direction, x component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.uny uny Normal vector up direction, y component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.unz unz Normal vector up direction, z component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dnx dnx Normal vector down direction, x component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dny dny Normal vector down direction, y component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.dnz dnz Normal vector down direction, z component Boundaries 17–20, 22, 27, 29, 31, 33, 35
mfnc.W mfnc.Wm J/m^3 Energy density Domain 4
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 4
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 4
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 4
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 4

2.4.28. ArrayAMagnet7

physics_mfnc_mfc34.png

ArrayAMagnet7

Selection
Geometric entity level Domain
Selection Domain 2
Equations

equ_mfnc_mfc34_1.png

equ_mfnc_mfc34_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(6*60)/360)
Remanent flux density, y component BA*sin(2*pi*(6*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 6–12, 23–25
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 6–12, 23–25
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 6–12, 23–25
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 2
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 2
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 2
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 6–12, 23–25
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 6–12, 23–25
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 6–12, 23–25
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 2
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 2
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 2
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 2
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 2
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 2
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 2
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 2
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 2
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 2
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 2
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 2
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 2
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 2
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 2
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 2
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 2
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 2
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 2
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 2
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 2
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 2
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 2
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 2
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 2
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 2
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 2
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 2
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 2
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 2
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 2
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 2
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 2
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 2
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 2
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 2
mfnc.Brx BA*cos(2*pi) T Remanent flux density, x component Domain 2
mfnc.Bry BA*sin(2*pi) T Remanent flux density, y component Domain 2
mfnc.Brz 0 T Remanent flux density, z component Domain 2
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 2
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 6–12, 23–25
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 6–12, 23–25
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 6–12, 23–25
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 6–12, 23–25
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 6–12, 23–25
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 6–12, 23–25
mfnc.unx unx Normal vector up direction, x component Boundaries 6–12, 23–25
mfnc.uny uny Normal vector up direction, y component Boundaries 6–12, 23–25
mfnc.unz unz Normal vector up direction, z component Boundaries 6–12, 23–25
mfnc.dnx dnx Normal vector down direction, x component Boundaries 6–12, 23–25
mfnc.dny dny Normal vector down direction, y component Boundaries 6–12, 23–25
mfnc.dnz dnz Normal vector down direction, z component Boundaries 6–12, 23–25
mfnc.W mfnc.Wm J/m^3 Energy density Domain 2
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 2
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 2
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 2
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 2

2.4.29. ArrayAMagnet8

physics_mfnc_mfc35.png

ArrayAMagnet8

Selection
Geometric entity level Domain
Selection Domain 3
Equations

equ_mfnc_mfc35_1.png

equ_mfnc_mfc35_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(7*60)/360)
Remanent flux density, y component BA*sin(2*pi*(7*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 3
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 3
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 3
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 3
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 3
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 3
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 3
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 3
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 3
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 3
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 3
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 3
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 3
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 3
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 3
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 3
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 3
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 3
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 3
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 3
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 3
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 3
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 3
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 3
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 3
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 3
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 3
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 3
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 3
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 3
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 3
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 3
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 3
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 3
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 3
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 3
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 3
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 3
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 3
mfnc.Brx BA*cos(7*pi/3) T Remanent flux density, x component Domain 3
mfnc.Bry BA*sin(7*pi/3) T Remanent flux density, y component Domain 3
mfnc.Brz 0 T Remanent flux density, z component Domain 3
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 3
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.unx unx Normal vector up direction, x component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.uny uny Normal vector up direction, y component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.unz unz Normal vector up direction, z component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dnx dnx Normal vector down direction, x component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dny dny Normal vector down direction, y component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.dnz dnz Normal vector down direction, z component Boundaries 13–16, 21, 26, 28, 30, 32, 34
mfnc.W mfnc.Wm J/m^3 Energy density Domain 3
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 3
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 3
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 3
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 3

2.4.30. ArrayAMagnet9

physics_mfnc_mfc36.png

ArrayAMagnet9

Selection
Geometric entity level Domain
Selection Domain 8
Equations

equ_mfnc_mfc36_1.png

equ_mfnc_mfc36_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(8*60)/360)
Remanent flux density, y component BA*sin(2*pi*(8*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 8
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 8
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 8
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 8
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 8
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 8
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 8
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 8
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 8
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 8
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 8
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 8
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 8
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 8
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 8
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 8
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 8
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 8
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 8
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 8
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 8
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 8
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 8
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 8
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 8
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 8
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 8
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 8
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 8
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 8
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 8
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 8
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 8
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 8
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 8
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 8
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 8
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 8
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 8
mfnc.Brx BA*cos(8*pi/3) T Remanent flux density, x component Domain 8
mfnc.Bry BA*sin(8*pi/3) T Remanent flux density, y component Domain 8
mfnc.Brz 0 T Remanent flux density, z component Domain 8
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 8
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.unx unx Normal vector up direction, x component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.uny uny Normal vector up direction, y component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.unz unz Normal vector up direction, z component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dnx dnx Normal vector down direction, x component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dny dny Normal vector down direction, y component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.dnz dnz Normal vector down direction, z component Boundaries 60–63, 68, 76, 78, 90, 92, 104
mfnc.W mfnc.Wm J/m^3 Energy density Domain 8
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 8
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 8
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 8
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 8

2.4.31. ArrayAMagnet10

physics_mfnc_mfc37.png

ArrayAMagnet10

Selection
Geometric entity level Domain
Selection Domain 16
Equations

equ_mfnc_mfc37_1.png

equ_mfnc_mfc37_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(9*60)/360)
Remanent flux density, y component BA*sin(2*pi*(9*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 140–144, 152–153, 176–177, 181
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 16
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 16
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 16
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 140–144, 152–153, 176–177, 181
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 140–144, 152–153, 176–177, 181
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 140–144, 152–153, 176–177, 181
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 16
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 16
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 16
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 16
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 16
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 16
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 16
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 16
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 16
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 16
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 16
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 16
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 16
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 16
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 16
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 16
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 16
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 16
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 16
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 16
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 16
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 16
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 16
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 16
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 16
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 16
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 16
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 16
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 16
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 16
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 16
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 16
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 16
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 16
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 16
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 16
mfnc.Brx BA*cos(3*pi) T Remanent flux density, x component Domain 16
mfnc.Bry BA*sin(3*pi) T Remanent flux density, y component Domain 16
mfnc.Brz 0 T Remanent flux density, z component Domain 16
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 16
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 140–144, 152–153, 176–177, 181
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 140–144, 152–153, 176–177, 181
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 140–144, 152–153, 176–177, 181
mfnc.unx unx Normal vector up direction, x component Boundaries 140–144, 152–153, 176–177, 181
mfnc.uny uny Normal vector up direction, y component Boundaries 140–144, 152–153, 176–177, 181
mfnc.unz unz Normal vector up direction, z component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dnx dnx Normal vector down direction, x component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dny dny Normal vector down direction, y component Boundaries 140–144, 152–153, 176–177, 181
mfnc.dnz dnz Normal vector down direction, z component Boundaries 140–144, 152–153, 176–177, 181
mfnc.W mfnc.Wm J/m^3 Energy density Domain 16
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 16
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 16
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 16
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 16

2.4.32. ArrayAMagnet11

physics_mfnc_mfc38.png

ArrayAMagnet11

Selection
Geometric entity level Domain
Selection Domain 24
Equations

equ_mfnc_mfc38_1.png

equ_mfnc_mfc38_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(10*60)/360)
Remanent flux density, y component BA*sin(2*pi*(10*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 24
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 24
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 24
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 24
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 24
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 24
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 24
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 24
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 24
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 24
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 24
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 24
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 24
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 24
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 24
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 24
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 24
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 24
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 24
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 24
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 24
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 24
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 24
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 24
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 24
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 24
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 24
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 24
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 24
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 24
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 24
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 24
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 24
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 24
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 24
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 24
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 24
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 24
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 24
mfnc.Brx BA*cos(10*pi/3) T Remanent flux density, x component Domain 24
mfnc.Bry BA*sin(10*pi/3) T Remanent flux density, y component Domain 24
mfnc.Brz 0 T Remanent flux density, z component Domain 24
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 24
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.unx unx Normal vector up direction, x component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.uny uny Normal vector up direction, y component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.unz unz Normal vector up direction, z component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dnx dnx Normal vector down direction, x component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dny dny Normal vector down direction, y component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.dnz dnz Normal vector down direction, z component Boundaries 220–223, 228, 232, 234, 246, 248, 264
mfnc.W mfnc.Wm J/m^3 Energy density Domain 24
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 24
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 24
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 24
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 24

2.4.33. ArrayAMagnet12

physics_mfnc_mfc39.png

ArrayAMagnet12

Selection
Geometric entity level Domain
Selection Domain 30
Equations

equ_mfnc_mfc39_1.png

equ_mfnc_mfc39_2.png

Settings
Description Value
Constitutive relation Remanent flux density
Remanent flux density, x component BA*cos(2*pi*(11*60)/360)
Remanent flux density, y component BA*sin(2*pi*(11*60)/360)
Remanent flux density, z component 0
Relative permeability From material
Relative permeability {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Properties from material
Property Material Property group
Relative permeability Soft Iron (without losses) Basic
Variables
Name Expression Unit Description Selection
mfnc.dnTmx -0.5*mfnc.unx*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bx))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, x component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dnTmy -0.5*mfnc.uny*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.By))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, y component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dnTmz -0.5*mfnc.unz*(real(down(mfnc.Bx))*real(down(mfnc.Hx))+real(down(mfnc.By))*real(down(mfnc.Hy))+real(down(mfnc.Bz))*real(down(mfnc.Hz)))+real(down(mfnc.Bz))*(real(down(mfnc.Hx))*mfnc.unx+real(down(mfnc.Hy))*mfnc.uny+real(down(mfnc.Hz))*mfnc.unz) Pa Maxwell downward magnetic surface stress tensor, z component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.Hx -Vmx A/m Magnetic field, x component Domain 30
mfnc.Hy -Vmy A/m Magnetic field, y component Domain 30
mfnc.Hz -Vmz A/m Magnetic field, z component Domain 30
mfnc.tHx -VmTx A/m Tangential magnetic field, x component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.tHy -VmTy A/m Tangential magnetic field, y component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.tHz -VmTz A/m Tangential magnetic field, z component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.normH sqrt(realdot(mfnc.Hx,mfnc.Hx)+realdot(mfnc.Hy,mfnc.Hy)+realdot(mfnc.Hz,mfnc.Hz)) A/m Magnetic field norm Domain 30
mfnc.murxx model.input.mur11 1 Relative permeability, xx component Domain 30
mfnc.muryx model.input.mur21 1 Relative permeability, yx component Domain 30
mfnc.murzx model.input.mur31 1 Relative permeability, zx component Domain 30
mfnc.murxy model.input.mur12 1 Relative permeability, xy component Domain 30
mfnc.muryy model.input.mur22 1 Relative permeability, yy component Domain 30
mfnc.murzy model.input.mur32 1 Relative permeability, zy component Domain 30
mfnc.murxz model.input.mur13 1 Relative permeability, xz component Domain 30
mfnc.muryz model.input.mur23 1 Relative permeability, yz component Domain 30
mfnc.murzz model.input.mur33 1 Relative permeability, zz component Domain 30
mfnc.Bx mu0_const*mfnc.Ixx*mfnc.Hx+mu0_const*mfnc.Ixy*mfnc.Hy+mu0_const*mfnc.Ixz*mfnc.Hz+mu0_const*mfnc.chimxx*mfnc.Hx+mu0_const*mfnc.chimxy*mfnc.Hy+mu0_const*mfnc.chimxz*mfnc.Hz+mfnc.Brx T Magnetic flux density, x component Domain 30
mfnc.By mu0_const*mfnc.Iyx*mfnc.Hx+mu0_const*mfnc.Iyy*mfnc.Hy+mu0_const*mfnc.Iyz*mfnc.Hz+mu0_const*mfnc.chimyx*mfnc.Hx+mu0_const*mfnc.chimyy*mfnc.Hy+mu0_const*mfnc.chimyz*mfnc.Hz+mfnc.Bry T Magnetic flux density, y component Domain 30
mfnc.Bz mu0_const*mfnc.Izx*mfnc.Hx+mu0_const*mfnc.Izy*mfnc.Hy+mu0_const*mfnc.Izz*mfnc.Hz+mu0_const*mfnc.chimzx*mfnc.Hx+mu0_const*mfnc.chimzy*mfnc.Hy+mu0_const*mfnc.chimzz*mfnc.Hz+mfnc.Brz T Magnetic flux density, z component Domain 30
mfnc.normB sqrt(realdot(mfnc.Bx,mfnc.Bx)+realdot(mfnc.By,mfnc.By)+realdot(mfnc.Bz,mfnc.Bz)) T Magnetic flux density norm Domain 30
mfnc.Mx mfnc.Bx/mu0_const-mfnc.Ixx*mfnc.Hx-mfnc.Ixy*mfnc.Hy-mfnc.Ixz*mfnc.Hz A/m Magnetization, x component Domain 30
mfnc.My mfnc.By/mu0_const-mfnc.Iyx*mfnc.Hx-mfnc.Iyy*mfnc.Hy-mfnc.Iyz*mfnc.Hz A/m Magnetization, y component Domain 30
mfnc.Mz mfnc.Bz/mu0_const-mfnc.Izx*mfnc.Hx-mfnc.Izy*mfnc.Hy-mfnc.Izz*mfnc.Hz A/m Magnetization, z component Domain 30
mfnc.normM sqrt(realdot(mfnc.Mx,mfnc.Mx)+realdot(mfnc.My,mfnc.My)+realdot(mfnc.Mz,mfnc.Mz)) A/m Magnetization norm Domain 30
mfnc.Ixx 1 1 Spatial identity matrix, xx component Domain 30
mfnc.Iyx 0 1 Spatial identity matrix, yx component Domain 30
mfnc.Izx 0 1 Spatial identity matrix, zx component Domain 30
mfnc.Ixy 0 1 Spatial identity matrix, xy component Domain 30
mfnc.Iyy 1 1 Spatial identity matrix, yy component Domain 30
mfnc.Izy 0 1 Spatial identity matrix, zy component Domain 30
mfnc.Ixz 0 1 Spatial identity matrix, xz component Domain 30
mfnc.Iyz 0 1 Spatial identity matrix, yz component Domain 30
mfnc.Izz 1 1 Spatial identity matrix, zz component Domain 30
mfnc.chimxx -1+mfnc.murxx 1 Magnetic susceptibility, xx component Domain 30
mfnc.chimyx mfnc.muryx 1 Magnetic susceptibility, yx component Domain 30
mfnc.chimzx mfnc.murzx 1 Magnetic susceptibility, zx component Domain 30
mfnc.chimxy mfnc.murxy 1 Magnetic susceptibility, xy component Domain 30
mfnc.chimyy -1+mfnc.muryy 1 Magnetic susceptibility, yy component Domain 30
mfnc.chimzy mfnc.murzy 1 Magnetic susceptibility, zy component Domain 30
mfnc.chimxz mfnc.murxz 1 Magnetic susceptibility, xz component Domain 30
mfnc.chimyz mfnc.muryz 1 Magnetic susceptibility, yz component Domain 30
mfnc.chimzz -1+mfnc.murzz 1 Magnetic susceptibility, zz component Domain 30
mfnc.Brx BA*cos(11*pi/3) T Remanent flux density, x component Domain 30
mfnc.Bry BA*sin(11*pi/3) T Remanent flux density, y component Domain 30
mfnc.Brz 0 T Remanent flux density, z component Domain 30
mfnc.normBr sqrt(realdot(mfnc.Brx,mfnc.Brx)+realdot(mfnc.Bry,mfnc.Bry)+realdot(mfnc.Brz,mfnc.Brz)) T Remanent flux density norm Domain 30
mfnc.unTx 0 Pa Maxwell upward surface stress tensor, x component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.unTy 0 Pa Maxwell upward surface stress tensor, y component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.unTz 0 Pa Maxwell upward surface stress tensor, z component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dnTx mfnc.dnTmx Pa Maxwell downward surface stress tensor, x component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dnTy mfnc.dnTmy Pa Maxwell downward surface stress tensor, y component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dnTz mfnc.dnTmz Pa Maxwell downward surface stress tensor, z component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.unx unx Normal vector up direction, x component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.uny uny Normal vector up direction, y component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.unz unz Normal vector up direction, z component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dnx dnx Normal vector down direction, x component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dny dny Normal vector down direction, y component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.dnz dnz Normal vector down direction, z component Boundaries 282–285, 290, 292, 294, 296, 298, 307
mfnc.W mfnc.Wm J/m^3 Energy density Domain 30
mfnc.dWm mfnc.Wm J/m^3 Integrand for total magnetic energy Domain 30
mfnc.Wm 0.5*mu0_const*((mfnc.murxx*mfnc.Hx+mfnc.murxy*mfnc.Hy+mfnc.murxz*mfnc.Hz)*mfnc.Hx+(mfnc.muryx*mfnc.Hx+mfnc.muryy*mfnc.Hy+mfnc.muryz*mfnc.Hz)*mfnc.Hy+(mfnc.murzx*mfnc.Hx+mfnc.murzy*mfnc.Hy+mfnc.murzz*mfnc.Hz)*mfnc.Hz) J/m^3 Magnetic energy density Domain 30
Shape Functions
Name Shape function Unit Description Shape frame Selection
Vm Lagrange (Quadratic) A Magnetic scalar potential Material Domain 30
Weak Expressions
Weak expression Integration frame Selection
mfnc.d*(-mfnc.Bx*test(Vmx)-mfnc.By*test(Vmy)-mfnc.Bz*test(Vmz)) Material Domain 30

2.5. Mesh 1

Mesh statistics
Property Value
Minimum element quality 0.008909
Average element quality 0.7156
Tetrahedral elements 6739177
Triangular elements 335544
Edge elements 44176
Vertex elements 496

mesh_mesh1.png

Mesh 1

2.5.1. Size (Size)

Settings
Name Value
Maximum element size 0.021
Minimum element size 9.0E-4
Curvature factor 0.3
Resolution of narrow regions 0.85
Maximum element growth rate 1.35
Predefined size Extra fine

2.5.2. Free Tetrahedral 2 (Ftet2)

Selection
Geometric entity level Domain
Selection No domains

mesh_mesh1_ftet2.png

Free Tetrahedral 2

Size 1 (Size1)
Selection
Geometric entity level Domain
Selection Domain 15

mesh_mesh1_ftet2_size1.png

Size 1

Settings
Name Value
Maximum element size 0.0005
Minimum element size 1.0E-4
Curvature factor 0.3
Curvature factor Off
Resolution of narrow regions 0.85
Resolution of narrow regions Off
Maximum element growth rate 1.35
Maximum element growth rate Off
Predefined size Extra fine
Custom element size Custom

2.5.3. Free Tetrahedral 3 (Ftet3)

Selection
Geometric entity level Remaining
Size 1 (Size1)
Selection
Geometric entity level Domain
Selection Domains 2–14, 16–32

mesh_mesh1_ftet3_size1.png

Size 1

Settings
Name Value
Maximum element size 0.05
Minimum element size 0.006
Curvature factor 0.5
Curvature factor Off
Resolution of narrow regions 0.6
Resolution of narrow regions Off
Maximum element growth rate 1.45
Maximum element growth rate Off
Predefined size Fine
Custom element size Custom

2.5.4. Free Tetrahedral 4 (Ftet4)

Selection
Geometric entity level Remaining
Size 1 (Size1)
Selection
Geometric entity level Domain
Selection Geometry geom1

mesh_mesh1_ftet4_size1.png

Size 1

Settings
Name Value
Maximum element size 0.06
Minimum element size 0.0108
Curvature factor 0.6
Resolution of narrow regions 0.5
Maximum element growth rate 1.5

3. Study 1

3.1. Stationary

Study settings
Property Value
Include geometric nonlinearity Off
Physics and variables selection
Physics interface Discretization
Magnetic Fields, No Currents (mfnc) physics
Mesh selection
Geometry Mesh
Geometry 1 (geom1) mesh1

3.2. Solver Configurations

3.2.1. Solution 1

Compile Equations: Stationary (St1)
Study and step
Name Value
Use study Study 1
Use study step Stationary
Dependent Variables 1 (V1)
General
Name Value
Defined by study step Stationary
Initial values of variables solved for
Name Value
Solution Zero
Values of variables not solved for
Name Value
Solution Zero
Magnetic Scalar Potential (Comp1.Vm) (Comp1_Vm)
General
Name Value
Field components comp1.Vm
Stationary Solver 1 (S1)
General
Name Value
Defined by study step Stationary
Log
Stationary Solver 1 in Solution 1 started at 2-Mar-2016 11:33:03.
Linear solver
Number of degrees of freedom solved for: 8989380.
Symmetric matrices found.
Scales for dependent variables:
Magnetic scalar potential (comp1.Vm): 1
Orthonormal null-space function used.
Iter      SolEst     Damping    Stepsize #Res #Jac #Sol LinIt   LinErr   LinRes
   1        0.96   1.0000000        0.96    1    1    1    28  0.00064 1.8e-006
Stationary Solver 1 in Solution 1: Solution time: 260 s (4 minutes, 20 seconds)
                                   Physical memory: 13.79 GB
                                   Virtual memory: 14.29 GB
Fully Coupled 1 (Fc1)
General
Name Value
Linear solver Iterative 1
Iterative 1 (I1)
General
Name Value
Solver Conjugate gradients
Multigrid 1 (Mg1)
General
Name Value
Solver Algebraic multigrid

4. Results

4.1. Data Sets

4.1.1. Study 1/Solution 1

Solution
Name Value
Solution Solution 1
Component Save Point Geometry 1

dataset_dset1.png

Data set: Study 1/Solution 1

4.1.2. Cut Plane XY

Data
Name Value
Data set Study 1/Solution 1
Plane data
Name Value
Plane type Quick
Plane xy - planes
z-coordinate 0.075
Advanced
Name Value
Space variables {cpl1x, cpl1y}

dataset_cpl1.png

Data set: Cut Plane XY

4.1.3. AlongXAxis

Data
Name Value
Data set Cut Plane XY
Line data
Name Value
Line entry method Two points
Points {{-0.15, 0}, {0.15, 0}}
Advanced
Name Value
Space variable cln1x

dataset_cln1.png

Data set: AlongXAxis

4.1.4. AlongYAxis

Data
Name Value
Data set Cut Plane XY
Line data
Name Value
Line entry method Two points
Points {{0, -0.15}, {0, 0.15}}
Advanced
Name Value
Space variable cln2x

dataset_cln2.png

Data set: AlongYAxis

4.1.5. Cut Plane YZ

Data
Name Value
Data set Study 1/Solution 1
Plane data
Name Value
Plane type Quick
x-coordinate 0
Advanced
Name Value
Space variables {cpl2x, cpl2y}

dataset_cpl2.png

Data set: Cut Plane YZ

4.1.6. AlongZAxis

Data
Name Value
Data set Study 1/Solution 1
Line data
Name Value
Line entry method Two points
Points {{0, 0, -0.15}, {0, 0, 0.15}}
Advanced
Name Value
Space variable cln3x

dataset_cln3.png

Data set: AlongZAxis

4.1.7. Cut Point 2D 1

Data
Name Value
Data set Cut Plane XY
Point data
Name Value
Entry method Grid
Settings
Name Value
x {-0.02, -0.01, 0, 0.009999999999999998, 0.02}
y {-0.02, -0.01, 0, 0.009999999999999998, 0.02}

dataset_cpt1.png

Data set: Cut Point 2D 1

4.2. Tables

4.2.1. Table 1

Point Evaluation 1 (mfnc.normB)

Table 1
Magnetic flux density norm (T), Point: (-0.02, -0.02) Magnetic flux density norm (T), Point: (-0.01, -0.01) Magnetic flux density norm (T), Point: (0, 0) Magnetic flux density norm (T), Point: (0.01, 0.01) Magnetic flux density norm (T), Point: (0.02, 0.02) Magnetic flux density norm (T), Point: (-0.02, -0.02) Magnetic flux density norm (T), Point: (-0.01, -0.02) Magnetic flux density norm (T), Point: (0, -0.02) Magnetic flux density norm (T), Point: (0.01, -0.02) Magnetic flux density norm (T), Point: (0.02, -0.02) Magnetic flux density norm (T), Point: (-0.02, -0.01) Magnetic flux density norm (T), Point: (-0.01, -0.01) Magnetic flux density norm (T), Point: (0, -0.01) Magnetic flux density norm (T), Point: (0.01, -0.01) Magnetic flux density norm (T), Point: (0.02, -0.01) Magnetic flux density norm (T), Point: (-0.02, 0) Magnetic flux density norm (T), Point: (-0.01, 0) Magnetic flux density norm (T), Point: (0, 0) Magnetic flux density norm (T), Point: (0.01, 0) Magnetic flux density norm (T), Point: (0.02, 0) Magnetic flux density norm (T), Point: (-0.02, 0.01) Magnetic flux density norm (T), Point: (-0.01, 0.01) Magnetic flux density norm (T), Point: (0, 0.01) Magnetic flux density norm (T), Point: (0.01, 0.01) Magnetic flux density norm (T), Point: (0.02, 0.01) Magnetic flux density norm (T), Point: (-0.02, 0.02) Magnetic flux density norm (T), Point: (-0.01, 0.02) Magnetic flux density norm (T), Point: (0, 0.02) Magnetic flux density norm (T), Point: (0.01, 0.02) Magnetic flux density norm (T), Point: (0.02, 0.02) Magnetic flux density norm (T), Point: (-0.02, -0.02) Magnetic flux density norm (T), Point: (-0.01, -0.02) Magnetic flux density norm (T), Point: (0, -0.02) Magnetic flux density norm (T), Point: (0.01, -0.02) Magnetic flux density norm (T), Point: (0.02, -0.02) Magnetic flux density norm (T), Point: (-0.02, -0.01) Magnetic flux density norm (T), Point: (-0.01, -0.01) Magnetic flux density norm (T), Point: (0, -0.01) Magnetic flux density norm (T), Point: (0.01, -0.01) Magnetic flux density norm (T), Point: (0.02, -0.01) Magnetic flux density norm (T), Point: (-0.02, 0) Magnetic flux density norm (T), Point: (-0.01, 0) Magnetic flux density norm (T), Point: (0, 0) Magnetic flux density norm (T), Point: (0.01, 0) Magnetic flux density norm (T), Point: (0.02, 0) Magnetic flux density norm (T), Point: (-0.02, 0.01) Magnetic flux density norm (T), Point: (-0.01, 0.01) Magnetic flux density norm (T), Point: (0, 0.01) Magnetic flux density norm (T), Point: (0.01, 0.01) Magnetic flux density norm (T), Point: (0.02, 0.01) Magnetic flux density norm (T), Point: (-0.02, 0.02) Magnetic flux density norm (T), Point: (-0.01, 0.02) Magnetic flux density norm (T), Point: (0, 0.02) Magnetic flux density norm (T), Point: (0.01, 0.02) Magnetic flux density norm (T), Point: (0.02, 0.02) Magnetic flux density norm (T), Point: (-0.02, -0.02) Magnetic flux density norm (T), Point: (-0.01, -0.02) Magnetic flux density norm (T), Point: (0, -0.02) Magnetic flux density norm (T), Point: (0.01, -0.02) Magnetic flux density norm (T), Point: (0.02, -0.02) Magnetic flux density norm (T), Point: (-0.02, -0.01) Magnetic flux density norm (T), Point: (-0.01, -0.01) Magnetic flux density norm (T), Point: (0, -0.01) Magnetic flux density norm (T), Point: (0.01, -0.01) Magnetic flux density norm (T), Point: (0.02, -0.01) Magnetic flux density norm (T), Point: (-0.02, 0) Magnetic flux density norm (T), Point: (-0.01, 0) Magnetic flux density norm (T), Point: (0, 0) Magnetic flux density norm (T), Point: (0.01, 0) Magnetic flux density norm (T), Point: (0.02, 0) Magnetic flux density norm (T), Point: (-0.02, 0.01) Magnetic flux density norm (T), Point: (-0.01, 0.01) Magnetic flux density norm (T), Point: (0, 0.01) Magnetic flux density norm (T), Point: (0.01, 0.01) Magnetic flux density norm (T), Point: (0.02, 0.01) Magnetic flux density norm (T), Point: (-0.02, 0.02) Magnetic flux density norm (T), Point: (-0.01, 0.02) Magnetic flux density norm (T), Point: (0, 0.02) Magnetic flux density norm (T), Point: (0.01, 0.02) Magnetic flux density norm (T), Point: (0.02, 0.02)
0.012518 0.012282 0.012188 0.012279 0.012506 0.012518 0.012304 0.012282 0.012306 0.012475 0.012467 0.012282 0.012221 0.012273 0.012477 0.012421 0.012265 0.012188 0.012270 0.012413 0.012488 0.012277 0.012186 0.012279 0.012483 0.012515 0.012306 0.012275 0.012319 0.012506 0.013655 0.013496 0.013430 0.013518 0.013639 0.013536 0.013425 0.013368 0.013419 0.013543 0.013554 0.013406 0.013334 0.013410 0.013574 0.013558 0.013417 0.013342 0.013422 0.013575 0.013647 0.013488 0.013428 0.013499 0.013644 0.013655 0.013496 0.013430 0.013518 0.013639 0.013536 0.013425 0.013368 0.013419 0.013543 0.013554 0.013406 0.013334 0.013410 0.013574 0.013558 0.013417 0.013342 0.013422 0.013575 0.013647 0.013488 0.013428 0.013499 0.013644

4.3. Plot Groups

4.3.1. 1D Plot Group 1

plotgroup_pg1.png

Line Graph: Magnetic flux density, x component (T)

4.3.2. 2D Plot Group 2

plotgroup_pg2.png

Arrow Surface: Magnetic flux density