Numerical Modeling of the Coupled Electromagnetic and Mechanical Phenomena of Linear Stepping Motors

Mustapha Zaouia, Nacereddine Benamrouche, M'hemed Rachek

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DOI: 10.4236/jemaa.2012.41001                

Abstract

In this paper, we propose an electromagnetic-mechanical model based on the finite element and Macro-Element (ME) technique to analyse and study the dynamic characteristics of a Tubular Linear Switched Reluctance Stepping Motor (LSRSM). After the resolution of the non-linear electromagnetic equation governing the behaviour of the different materials of the motor using the nodal-based finite element method, this equation is then coupled to the mechanical equation firstly through the magnetic force computed by Maxwell stress tensor, and secondly by the modified flux distribution due to the moving part. Because of the precision required in the mobile part displacement and the very small air gap of stepping motors, the simulation of the movement is assured by the Macro-Element (ME) technique compared to other movement techniques that present many disadvantages. The validity of the developed model is verified through the comparison of the computed displacement of the LSRSM moving part with those given experimentally [2]. The Results shows satisfactory agreement. The obtained dynamic characteristics, particularly the starting magnetic force, are obtained by considering two values of the supplying currents.

Keywords

Numerical Modeling; Electromagnetic-Mechanical Phenomena; Finite Element; Movement; Stepping Motors

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	W. Missaoui, L. EL Amraoui, F. Gillon, M. Benrejeb and P. Brochet, “Performance Comparison of Three and Four- Phase Linear Tubular Stepping Motor,” Proceeding of the ICEM06, Paper No. 467, Greece, 2006.
[2]	L. EL Amraoui, “Conception Electromécanique d’une Gamme d’Actionneurs Linéaires Tubulaires à Réluctance Variable,” PH.D. Thesis, University of Sciences and Technology of Lille, Lille, 2002.
[3]	L. EL Amraoui, F. Gillon, S. Vivier, P. Brochet and M. Benrejeb, “Optimal Design Approach for Tubular Linear Machine,” IEEE 2002 IEEE International Conference on Systems, Man and Cybernetics, Hammamet, 6-9 October 2002.
[4]	L. EL Amraoui, F. Gillon, S. Vivier, P. Brochet and M. Benrejeb, “Robust Electromagnetic Optimization of Linear Tubular Actuators,” IEEE Transactions on Magnetics, Vol. 40, No. 2, 2004, pp. 1192-1195. doi:10.1109/TMAG.2004.825304
[5]	L. EL Amraoui Ouni, F. Gillon, P. Brochet and M. Benrejeb, “Use of Inverse Models Built for Accurate Micro Stepping of Linear Switched Reluctance Step Actuator,” IMACS Multiconference on Computational Engineering in Systems Applications (CESA), Beijing, 4-6 October 2006, pp. 424-430.
[6]	A. K. Daud and R. Hanitsch, “Linear Stepping Motor (LSM) with Reduced Force Ripple,” Symposium on Power Electronics, Industrial Drives, Power Quality, Traction Systems, Capri, 16-18 June 2004, pp. 870-874.
[7]	D. Casadei, C. Rossi, G. Serra and A. Tani, “Optimal Design of a Tubular Hybrid Stepping Motor under Volumetric Constraints,” Symposium on Power Electronics, Industrial Drives, Power Quality, Traction Systems, Capri, 16-18 June 2004, pp. 857-853.
[8]	J.-K. Seok, T.-S. Hwang and D.-H. Kim, “Initial Position Estimation for Closed-Loop Linear Hybrid Stepping Motor Drives Using DC Excitation,” IEEE Transactions on Magnetics, Vol. 42, No. 8, 2006, pp. 2071-2076. doi:10.1109/TMAG.2006.875838
[9]	T.-S. Hwang and J.-K. Seok, “Observer-Based Ripple Force Compensation for Linear Hybrid Stepping Motor Drives,” IEEE Transactions on Industrial Electronics, Vol. 54, No. 5, 2007, pp. 2417-2424. doi:10.1109/TIE.2007.900344
[10]	A. Marroco, “Analyse Numérique des Problèmes d’éle- ctrotechniques,” Annale des Sciences Mathematiques du Quèbec, Vol. 1, No. 2, 1977, pp. 217-296.
[11]	H. Mohellebi, M. E. Latrèche and M. Féliachi, “Coupled Axisymmetric Analytical and Finite Element Analysis of Induction Devices Having Moving Part,” IEEE Transactions on Magnetics, Vol. 34, No. 5, 1998, pp. 3308-3310. doi:10.1109/20.717777
[12]	F. Azzouz, B. Bendjima and M. Féliachi, “Application of Macro-Element and Finite Element Coupling for the Behaviors Analysis of Magnetoforming System,” IEEE Tr- ansactions on Magnetics, Vol. 35, No. 3, 1999, pp. 1845- 1848. doi:10.1109/20.767392
[13]	M. Zaouia, H. Mohellebi and M. Abdellah, “Electric- Magnetic-Mechanical Coupled Model for Analysing Dynamic Characteristics with Feeding Effects of Linear Induction Launcher,” IASME Transactions, Vol. 1, No. 2, 2004, pp. 235-240.
[14]	M. Rachek, M. Zaouia, H. Denoun and C. Birouche, “Finite Element Computational Model for Defect Simulation and Detection by Eddy Currents Non Destructive Testing,” CD-ROM Proceedings of the 9th WSEAS International Conference on Circuit and Systems, Athens, 11-13 July 2005, Paper No. 497-304.
[15]	M. Rachek, M. Zaouia, H. Denoun and C. Birouche, “Two-Dimensional Finite Element Numerical Modelling of Eddy Current Non Destructive Testing for Defect Sim- ulation and Detection and Sensor Movement Simulating by Geometrical Band technique,” WSEAS Transactions on Circuits and Systems, Vol. 4, No. 6, 2005, pp. 574- 582.
[16]	M. Rachek, M. Feliachi and M. Zaouia, “Three Dimensional Finite Element Modelling for Sensor Movement Simulation by Geometrical Band and Nodal Interpolation Techniques in Eddy Current Non Destructive Testing,” WSEAS Transactions on Circuits and Systems, Vol. 4, No. 6, 2005, pp. 535-542.