Semi-Analytical 3D Force Calculation of an Ironless Cylindrical Permanent Magnet Actuator for Magnetic Levitation Systems

Authors

  • Mousa Lahdo 1 Department of Informatics, Electrical Engineering and Mechatronics University of Applied Sciences Mittelhessen, Friedberg, 61169, Germany,2 Department of Mechatronics Ilmenau University of Technology, Ilmenau, 98693, Germany
  • Tom Ströhla Department of Mechatronics Ilmenau University of Technology, Ilmenau, 98693, Germany
  • Sergej Kovalev Department of Informatics, Electrical Engineering and Mechatronics University of Applied Sciences Mittelhessen, Friedberg, 61169, Germany

Keywords:

Cylindrical permanent magnet actuator, electromagnetic analysis, Lorentz force, magnetic levitation

Abstract

The semi-analytical calculation of magnetic forces is currently an interesting alternative to the timeconsuming three-dimensional finite-element modeling (3D-FEM) due to its high accuracy and low computational cost. This paper presents novel equations for determining the magnetic forces of a cylindrical permanent magnet actuator used in high precision magnetic levitation positioning systems. Compared to the already available equations in literature, these equations consider the magnetic forces as a function of the current magnet position. Moreover, these equations are also suitable for designing and analyzing the cylindrical permanent magnet actuator. The results of our force equations and the verification by 3D-FEM and measurements are presented in this paper.

Downloads

Download data is not yet available.

References

S. Verma, H. Shakir and W.-J. Kim, “Novel electromagnetic actuation scheme for multiaxis nanopositioning,” IEEE Trans. Magn., vol. 42, no. 8, pp. 2052-2062, May 2006.

X. Lu and I. Usman, “6D direct-drive technology for planar motion stages,” CIRP Ann.-Manuf. Technol., vol. 61, no. 1, pp. 359-362, 2012.

W.-J. Kim and D. L. Trumper, “High-precision magnetic levitation stage for photolithography,” Precis. Eng., vol. 22, no. 2, 1998, pp. 66-77, Apr. 1998.

J. W. Jansen, C. M. M. van Lierop, E.A. Lomonova and A. J. A. Vandanput, “Magnetically levitated planar actuator with moving magnets,” IEEE Trans. Ind. Appl., vol. 44, no. 4, pp. 1108-1115, July 2008.

L. Guo, H. Zhang, M. Galea, J. Li, W. Lu, and C. Gerada, “Analysis and design of a magnetically levitated planar motor with novel multilayer windings,” IEEE Trans. Magn., vol. 51, no. 8, art. no. 8106909, Aug. 2015.

A. C. P. de Klerk, G. Z. Angelis, and J. van Eijk, “Design of a next generation 6 Dof stage for scanning application in vacuum with nanometer accuracy and mGauss magnetic stray field,” Proc. Annu. Meeting-Amer. Soc. Precis. Eng., pp. 60-63, 2004.

T. J. Teo, I.-M. Chen, G. Yang, and W. Lin, “Magnetic field modeling of a dual-magnet configuration,” J. Appl. Phys., vol. 102, art. no. 074924, 2007.

M. Lahdo, T. Ströhla, and S. Kovalev, “Magnetic propulsion force calculation of a 2-DoF large stroke actuator for high-precision magnetic levitation system,” ACES Journal, vol. 32, no. 8, Aug. 2017.

A. Shiri and A. Shoulaie, “Calculation of the magnetic forces between planar spiral coils using concentric rings,” ACES Journal, vol. 25, no. 5, May 2010.

R. Muscia, “Magneto-mechanical model of passive magnetic axial bearings versus the eccentricity error - Part 1: physical mathematical model,” ACES Journal, vol. 32, no. 8, Aug. 2017.

J. L. G. Janssen, J. J. H. Paulides, and E. A. Lomonova, “3-D analytical calculation of the torque between perpendicular magnetized magnets in magnetic suspensions,” IEEE Trans. Magn., vol. 47, no. 10, pp. 4286-4289, Oct. 2011.

S. Wu, S. Zuo, X. Wu, F. Lin, and J. Shen, “Magnet modification to reduce pulsating torque for axial flux permanent magnet synchronous machines,” ACES Journal, vol. 31, no. 3, Mar. 2016.

R. Bjork, A. Smith, and C. R. H. Bahl, “Analysis of the magnetic field, force and torque for twodimensional Halbach cylinders,” J. Magn. Magn. Mater., vol. 322, no. 1, pp. 131-141, 2010.

T. R. N. Mhiócháin, D. Weaire, S. M. McMurry, and J. M. D. Coey, “Analysis of torque in nested magnetic cylinders,” J. Appl. Phys., vol. 86, no. 11, pp. 3412-3424, 1999.

L. Guo, H. Zhang, M. Galea, J. Li, and C. Gerada, “Multiobjective optimization of a magnetically levitated planar motor with multilayer windings,” IEEE Trans. Ind. Elect., vol. 63, no. 6, pp. 3522- 3532, June 2016.

J. W. Jansen, J. L. G. Janssen, J. M. M. Rovers, J. J. H. Paulides, and E. Lomonova, “(Semi-) analytical models for the design of high precision permanent magnet actuators,” Int. Compumag. Soc. Newslett., vol. 16, no. 02, pp. 4-17, 2009.

J. W. Jansen, J. P. C. Smeets, T. T. Overboom, J. M. M. Rovers, and E. A. Lomonova, “Overview of analytical models for the design of linear and planar motors,” IEEE Trans. Magn., vol. 50, no. 11, art. no. 8206207, Dec. 2014.

H. Zhang, B. Kou, H. Zhang, and Y. Xi, “A threedegree-of-freedom short-stroke Lorentz-force-driven planar motor using a Halbach permanent magnet array with unequal thickness,” IEEE Trans. Ind. Elect., vol. 62, no. 6, pp. 3640-3650, June 2015.

K. S. Jung and Y. S. Baek, “Study on a novel contact-free planar system using direct drive DC coils and permanent magnets,” IEEE/ASME Trans. Mech., vol. 7, no. 2, pp. 35-43, Mar. 2002.

M.-Y. Chen, T.-B. Lin, S.-K. Hung, and L.-C. Fu, “Design and experiment of a macro-micro planar maglev positioning system,” IEEE Trans. Ind. Elect., vol. 59, no. 11, pp. 4128-4139, Nov. 2012.

J. M. M. Rovers, J. W. Jansen, and E. A. Lomonova, “Analytical calculation of the force between a rectangular coil and a cuboidal permanent magnet,” IEEE Trans. Magn., vol. 46, no. 6, pp. 1656-1659, June 2010.

M. Lahdo, T. Ströhla, and S. Kovalev, “Repulsive magnetic levitation force calculation for a high precision 6-DoF magnetic levitation positioning system,” IEEE Trans. Magn., vol. 53, no. 3, Mar. 2017.

J. Peng, Y. Zhou, and G. Liu, “Calculation of a new real-time control model for the magnetically levitated ironless planar motor,” IEEE Trans. Magn., vol. 49, no. 4, pp. 1416-1422, Apr. 2013.

F. Liu, M. Zhang, Y. Zhu, and C. Hu, “A real-time model of ironless planar motors with stationary circular coils,” IEEE Trans. Magn., vol. 51, no. 7, art. no. 8203110, July 2015.

C. M. M. van Lierop, J. W. Jansen, A. A. H. Damen, E. A. Lomonova, P. P. J. van den Bosch, and A. J. A. Vandenput, “Model-based commutation of a long-stroke magnetically levitated linear actuator,” IEEE Trans. Ind. Appl., vol. 45, no. 6, pp. 1982- 1990, Nov./Dec. 2009.

S. Verma, W.-J. Kim, and H. Shakir, “Multi-axis maglev nanopositioner for precision manufacturing and manipulation applications,” IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 1159-1167, Sep./Oct. 2009.

W. Robertson, B. Cazzolato, and A. Zander, “Axial force between a thick coil and a cylindrical permanent magnet: Optimizing the geometry of an electromagnetic actuator,” IEEE Trans. Magn., vol. 48, no. 9, pp. 2479-2487, Sep. 2012.

R. Ravaud, G. Lemarquand, S. Babic, V. Lamarquand, and C. Akyel, “Cylindrical magnets and coils: Fields, forces, and inductances,” IEEE Trans. Magn., vol. 46, no. 9, pp. 3585-3590, Sep. 2010.

H. Zhang, B. Kou, Y. Jin, and H. Zhang, “Modeling and analysis of a new cylindrical magnetic levitation gravity compensator with low stiffness for the 6- DOF fine stage,” IEEE Trans. Ind. Elect., vol. 62, no. 6, pp. 3629-3639, June 2015.

P. Berkelman and M. Dzadovsky, “Magnetic levitation over large translation and rotation ranges in all directions,” IEEE/ASME Trans. Mech., vol. 18, no. 1, pp. 44-52, Feb. 2013.

Y. C. Lai, Y. L. Lee, and J. Y. Yen, “Design and servo control of a single-deck planar maglev stage,” IEEE Trans. Magn., vol. 43, no. 6, pp. 2600-2602, June 2007.

S. Earnshaw, “On the nature of the molecular forces which regulate the constitution of the luminiferous ether,” Trans. Cambridge Philos. Soc., vol. 7, pp. 97-112, Mar. 1839.

E. P. Furlani, Permanent Magnet and Electromechanical Devices: Materials, Analysis and Application. 6th Edition, Academic Press, London, 2001.

W. Braunbek, “Freischwebende Körper im elektrischen und magnetischen Feld,” Z. Physik, vol. 112, pp. 753-763, 1939.

Downloads

Published

2019-04-01

How to Cite

[1]
Mousa Lahdo, Tom Ströhla, and Sergej Kovalev, “Semi-Analytical 3D Force Calculation of an Ironless Cylindrical Permanent Magnet Actuator for Magnetic Levitation Systems”, ACES Journal, vol. 34, no. 04, pp. 520–527, Apr. 2019.

Issue

2019: Vol 34 Iss 4

Section

Articles