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Torque Modeling

  • Liang YanEmail author
  • I-Ming Chen
  • Chee Kian Lim
  • Guilin Yang
  • Kok-Meng Lee
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 4)

Abstract

By utilizing the analytical magnetic field model, the actuator torque caused by the interaction between current carrying coils and the magnetic field of the PM-pole rotor is formulated based on Lorentz force law. This torque model relates the torque output of the spherical actuator to the current inputs of coils and the rotor orientation, which indicates that the torque output of the PM spherical actuator is orientation dependant. Nonsingularity is one of the important advantages of the PM spherical actuator. Based on the torque model, existence of inverse electromagnetics solution or nonsingularity workspace of the PM spherical actuator is verified through the condition numbers of the torque matrix. In addition, the minimum right-inverse electromagnetics solution is proposed to calculate the required current inputs for desired torque output. This solution can minimize the electric power consumption of the spherical actuator. The linear torque model can facilitate the real-time motion control of the actuator. It can also be used for the spherical actuator design to maximize the actuator torque output.

Keywords

Condition Number Current Input Torque Output Electric Power Consumption Switch Reluctance Motor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Gieras J F, Wing M et al (1998) Permanent Magnet Motor Technology. Marcel Dekker, Inc., New York, USA, 1998. Google Scholar
  2. 2.
    Hamler A, Hribernik B, Likar M, Guid N et al (1995) Torque Calculation by Bernstein Bezier’s Surfaces. IEEE Transactions on Magnetics, vol. 31, no. 3:1885–1887, May 1995. CrossRefGoogle Scholar
  3. 3.
    Im D H, Kim C E et al (1994) Finite Element Force Calculation of a Linear Induction Motor Taking Account of the Movement. IEEE Transactions on Magnetics, vol. 30, no. 5:3495–3498, September 1994. CrossRefGoogle Scholar
  4. 4.
    Yamasawa K, Suzuki S, Biringer P P et al (1990) A Proposal for a Finite-Element Force Approximation an Automotive Magnetic Actuator. IEEE Transactions on Magnetics, vol. 26, no. 4:1270–1273, July 1990. CrossRefGoogle Scholar
  5. 5.
    Davey K, Vachtsevanos G, Powers R et al (1987) The analysis of fields and torques in spherical induction motors. IEEE Transactions on Magnetics, vol. 9, no. 1:273–282, January 1987. CrossRefGoogle Scholar
  6. 6.
    Krause P C, Wasynczuk O et al (1989) Electromechanical Motion Devices. McGraw-Hill, Inc., USA, 1989. Google Scholar
  7. 7.
    Lee K M, Roth R B, Zhou Z et al (1996) Dynamic modeling and control of a ball-joint-like variable-reluctance spherical motor. ASME Journal of Dynamic Systems, Measurement, and Control, vol. 118:29–40, March 1996. zbMATHCrossRefGoogle Scholar
  8. 8.
    Lee K M, Sosseh R A et al (2002) Effects of the Torque Model on the Control of a VR Spherical Motor. Proceedings of the 2nd IFAC Conference on Mechatronic Systems, Berkeley, California, USA, 9–11 December 2002. Google Scholar
  9. 9.
    Roth R B (1992) An Experimental Investigation and Optimization of a Variable Reluctance Spherical Motor. Thesis of Georgia Institute of Technology, GA, USA, 1992. Google Scholar
  10. 10.
    Sahoo S K, Zheng Q, Panda S K, Xu J X et al (2003) Model-based torque estimator for switched reluctance motors. Proceedings of The Fifth International Conference on Power Electronics and Drive Systems, PEDS, vol. 2:959–963, Singapore, 17–20 November 2003. Google Scholar
  11. 11.
    Materu P, Krishnan R et al (1990) Analytical prediction of SRM inductance profile and steady-state average torque. Conference Record of the 1990 IEEE Industry Applications Society Annual Meeting, vol. 1:214–223, Seattle, WA, USA, 7–12 October 1990. Google Scholar
  12. 12.
    Sadiku N O M (2001) Elements of Electromagnetics. Oxford University Press, UK, 2001. Google Scholar
  13. 13.
    Sathuvalli U B, Bayazitoglu Y et al (1996) The lorentz forces on an electrically conducing sphere in an alternating magnetic field. IEEE Transactions on Magnetics, vol. 32, no. 2:386–399, March 1996. CrossRefGoogle Scholar
  14. 14.
    Wang J, Jewell G W, Howe D et al (2003) Analysis of a spherical permanent magnet actuator. Journal of Applied Physics, vol. 81, no. 8:4266–4268, April 1997. CrossRefGoogle Scholar
  15. 15.
    Wang J, Wang W, Jewell G W, Howe D et al (1998) A novel spherical actuator with three degrees-of-freedom. IEEE Transactions on Magnetics, vol. 34, no. 4:2078–2080, July 1998. CrossRefGoogle Scholar
  16. 16.
    Craig J J (1989) Introduction to Robotics: Mechanics and Control. Addison-Wesley Publishing Company, USA, 1989. zbMATHGoogle Scholar
  17. 17.
    Wilde C (1988) Linear Algebra. Addison-Wesley Publishing Company, USA, 1988. zbMATHGoogle Scholar
  18. 18.
    Griffel D H (1989) Linear Algebra and Its Applications. Ellis Horwood Limited, UK, 1989. Google Scholar
  19. 19.
    Nakamura Y (1991) Advanced Robotics: Redundancy and Optimization. Addision-Wesley Publishing Company, USA, 1991. Google Scholar
  20. 20.
    Zhou Z (1995) Real-Time Control and Characterization of a Variable Reluctance Spherical Motor. Thesis of Georgia Institute of Technology, GA, USA, May 1995. Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Liang Yan
    • 1
    Email author
  • I-Ming Chen
    • 2
  • Chee Kian Lim
    • 3
  • Guilin Yang
    • 4
  • Kok-Meng Lee
    • 5
  1. 1.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingPeople’s Republic of China
  2. 2.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.School of Mechanical & Aeronautical EngineeringSingapore PolytechnicSingaporeSingapore
  4. 4.Singapore Institute of Manufacturing TechnologyNanyangSingapore
  5. 5.Georgia Institute of TechnologyAtlantaUSA

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