Magnetostatic Analysis of Solenoid

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Magnetostatic Analysis of Solenoid 1. Introduction 2. Model View 3. Materials 4. Load & Restraint Information 5. Coils Information 6. Force and Torque Information 7. Study Properties 8. Results Table 9. Magnetic Flux Density Results 10. Magnetic Field Intensity Results 11. Applied Current Density Results 12. Force Density Results 13. Temperature Results 14. Temperature Gradient Results 15. Heat Flux Results 16. Appendix Author: EMWorks Company: ElectroMagnetic Works Inc Date: January 25, 2012 1. Introduction This is a Magnetostatic analysis of a solenoid. The study was coupled with motion to investigate the effect of the current induced electromagnetic force on the motion of the plunger. It was also coupled with thermal analysis to study the effect of Joule heating

2. Model View SOLENOID Current View (Mesh)

SOLENOID Isometric View

3. Materials Note: R.P. stands for Relative Permeability Nbr. Part Name Material Name Permeability Type 1 air1^solenoid-1-body 1 (Cavity1) Air Isotropic 2 Band^SOLENOID-1-Body 1 (Cavity1) Air Isotropic 3 coil-1-body 1 (Split1[1]) Copper Isotropic 4 coil-1-body 2 (Split1[2]) Copper Isotropic 5 Outer Air^SOLENOID-1-Body 1 (Cavity1) Air Isotropic 6 plunger-1-body 1 (Boss-Extrude1) Mild Steel Isotropic 7 stator-1-body 1 (Cut-Extrude1) Mild Steel Isotropic 4. Load & Restraint Information Nbr. Name Selected Faces Selected Components Nb r. Name 1 Convectio n - 1 Convection Coefficient (W/(m^2.K)) Thermal Loads Ambient Temperature (Kelvin) Selec ted Faces 1.000e+001 3.000e+002 0 Selected Components Outer Air^SOLENOID -1

5. Coils Information Nb r. Name Coil Type 1 Wound Coil - 1 Current driven coil Nbr.Of Turns 50 Coils Magnitu de 8.000000e- 001 Components & Bodies coil-1 6. Force and Torque Information Nbr. Name Torque Center Components & Bodies 1 Virtual Work - 1 At origin plunger-1 7. Study Properties Motion Time Step Nbr.Of Nodes Mesh Information Nbr.Of Elements Element Size (mm) Tolerance (mm) 1 21260 124216 6 0.000006 2 21250 124143 6 0.000006 3 21200 123865 6 0.000006 4 21105 123302 6 0.000006 5 21036 122914 6 0.000006 6 21046 122970 6 0.000006 7 22117 128828 6 0.000006 8 22191 129321 6 0.000006 9 22368 130249 6 0.000006 10 22437 130739 6 0.000006 11 22502 131103 6 0.000006

Solver Type Solver information Direct Solver Nbr. Current Increments 1 Compute circuit parameters Yes Thermal Analysis Yes Motion Analysis Yes 8. Results Table Results for Motion Time Value: 0.000000000 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-6.793357e-005 1.457917e-002-1.815544e-004 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-6.691595e-007-1.066488e-007 1.740798e-006 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 5.250530e-004 Coil Name Wound Coil - 1 Flux Linkage Results Flux Linkage (Wb) 4.200424e-004 Coil Name BACK EMF Results BACK EMF (V) Wound Coil - 1 0.000000e+000

Energy Results Energy (J) Co-Energy (J) 1.680170e-004 1.680170e-004 Results for Motion Time Value: 0.100000001 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-2.343442e-005 1.494142e-002-1.517773e-004 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-2.288155e-006 4.556477e-007 3.972127e-006 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 5.441097e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 4.352878e-004 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1 3.049063e-004 Energy Results Energy (J) Co-Energy (J) 1.741151e-004 1.741151e-004

Results for Motion Time Value: 0.200000003 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1 8.897812e-005 2.175359e-002-8.345780e-005 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1 1.899288e-006-1.127149e-006 3.966033e-007 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 6.158430e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 4.926744e-004 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1 7.683624e-004 Energy Results Energy (J) Co-Energy (J) 1.970698e-004 1.970698e-004

Results for Motion Time Value: 0.300000012 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-2.500379e-004 6.297097e-002 6.138717e-005 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1 2.121146e-005-2.000940e-006 9.059513e-006 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 8.611835e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 6.889468e-004 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1 2.492732e-003 Energy Results Energy (J) Co-Energy (J) 2.755787e-004 2.755787e-004

Results for Motion Time Value: 0.400000006 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1 7.594768e-004 5.597393e-002-1.948300e-003 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-6.706260e-005-7.012031e-006 1.032527e-005 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 1.974572e-003 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 1.579658e-003 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1 1.235032e-002 Energy Results Energy (J) Co-Energy (J) 6.318631e-004 6.318631e-004

Results for Motion Time Value: 0.500000000 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1 5.883708e-003-5.660642e-002 7.774945e-004 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-8.511491e-005-1.791517e-006-1.755431e-005 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 2.096822e-003 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 1.677457e-003 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1 1.173716e-003 Energy Results Energy (J) Co-Energy (J) 6.709830e-004 6.709830e-004

Results for Motion Time Value: 0.600000024 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-1.274547e-004-1.661855e-002-1.156982e-004 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-8.302575e-006-3.096911e-007-1.535899e-006 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 5.653326e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 4.522661e-004 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1-9.925817e-003 Energy Results Energy (J) Co-Energy (J) 1.809064e-004 1.809064e-004

Results for Motion Time Value: 0.699999988 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-6.624250e-006-8.270898e-003-5.411318e-006 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-2.143395e-006-1.215897e-007-1.195198e-006 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 3.493696e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 2.794957e-004 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1-1.588907e-003 Energy Results Energy (J) Co-Energy (J) 1.117983e-004 1.117983e-004

Results for Motion Time Value: 0.800000012 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-5.107905e-005-5.488443e-003 4.372090e-005 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1 8.569302e-008-1.951790e-007 1.001087e-006 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 2.357989e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 1.886391e-004 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1-8.680159e-004 Energy Results Energy (J) Co-Energy (J) 7.545566e-005 7.545566e-005

Results for Motion Time Value: 0.899999976 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-3.082236e-005-3.890470e-003-7.618725e-005 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-2.745116e-006 6.983304e-008 1.046635e-006 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 1.636523e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 1.309219e-004 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1-5.588295e-004 Energy Results Energy (J) Co-Energy (J) 5.236874e-005 5.236874e-005

Results for Motion Time Value: 1.000000000 sec Force Results Fx-axis (N) Fy-axis (N) Fz-axis (N) Virtual Work - 1-1.298306e-005-2.578605e-003-1.289843e-005 Torque Results Tx-axis (N.m) Ty-axis (N.m) Tz-axis (N.m) Virtual Work - 1-1.658983e-007 1.694995e-008 4.948084e-007 Coil Name Wound Coil - 1 Resistance Results Resistance(Ohms) 1.477570e-001 Inductance Results (H) Coil Name Wound Coil - 1 Wound Coil - 1 1.172929e-004 Flux Linkage Results Coil Name Flux Linkage (Wb) Wound Coil - 1 9.383434e-005 BACK EMF Results Coil Name BACK EMF (V) Wound Coil - 1-3.620471e-004 Energy Results Energy (J) Co-Energy (J) 3.753374e-005 3.753374e-005

9. Magnetic Flux Density Results Magnetic Flux Density - 1

Magnetic Flux Density - 2

Magnetic Flux Density - 3

Magnetic Flux Density - 4

10. Magnetic Field Intensity Results Magnetic Field Intensity - 1

Magnetic Field Intensity - 2

Magnetic Field Intensity - 3

Magnetic Field Intensity - 4

11. Applied Current Density Results Applied Current Density - 1

12. Force Density Results Force Density - 1

13. Temperature Results Temperature - 1

14. Temperature Gradient Results Temperature Gradient - 1

15. Heat Flux Results Heat Flux - 1

16. Appendix Material Name: Air Permeability Type: Isotropic Note: R.P. stands for Relative Permeability R.P. Permanent Magnet Thermal Conductivity (W/m.K) 1.000e+000 No 2.400e-002 Material Name: Copper Permeability Type: Isotropic Note: R.P. stands for Relative Permeability R.P. Permanent Magnet Thermal Conductivity (W/m.K) 1.000e+000 No 4.010e+002 Material Name: Mild Steel Permeability Type: Isotropic Note: R.P. stands for Relative Permeability R.P. Permanent Magnet Thermal Conductivity (W/m.K) 2.000e+003 No 4.000e+001

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