Skip to main content
SpringerLink
Log in

Torque Modelling and Validation for a Spherical Motor with Stepped Permanent Magnets

  • Original Article
  • Published:
Journal of Electrical Engineering & Technology Aims and scope Submit manuscript

Abstract

A spherical motor is an electromagnetic device with multi-degree-of-freedom motion. Three-dimensional (3-D) magnetic field analysis and torque analysis are needed for the design, optimization and control of the motor. Presently, these analyses are carried out by the finite-element method (FEM) with a large amount of calculation and time consumption. An analytical method (AM) can reduced the computational burden of the FEM without sacrifice of the accuracy. A stepped permanent magnet (PM) can obtain a large range of the magnetic field while effectively saving PM materials. However, its special structure causes difficulties in analytical modelling. This paper presents an AM for the 3-D magnetic field and torque of a permanent magnet spherical motor with stepped PMs. The analytical model of the 3-D magnetic field of the stepped PM is derived based on the loop current method, and the electromagnetic force of the stator coil is calculated based on the Lorentz force method. Thus the 3-D magnetic field and torque can be calculated efficiently with reasonable accuracy. The analytical model is verified by the FEM and experimental tests. The test results confirm the high accuracy of the developed model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Yan L, Liu DL, Jiao ZX, Chen CY, Chen IM (2016) Magnetic field modeling based on geometrical equivalence principle for spherical actuator with cylindrical shaped magnet poles. Aerosp Sci Technol 49:17–25. https://doi.org/10.1016/j.ast.2015.11.021

    Article  Google Scholar 

  2. Li Z, Chen Q, Wang Q (2019) Analysis of multi-physics coupling field of multi-degree-of-freedom permanent magnet spherical motor. IEEE Trans Magn 55(6):1–5. https://doi.org/10.1109/TMAG.2019.2899259

    Article  Google Scholar 

  3. Li Z, Wang Q (2016) Levitation mechanism and improvements of 3-DOF deflection type PM actuator. IEEE Trans Appl Supercond 26(7):1–5. https://doi.org/10.1109/TASC.2016.2599853

    Article  Google Scholar 

  4. Li Z (2009) Robust control of PM spherical stepper motor based on neural networks. IEEE Trans Ind Electron 56(8):2945–2954. https://doi.org/10.1109/TIE.2009.2023639

    Article  Google Scholar 

  5. Wen Y, Li G, Wang Q, Guo X (2019) Robust adaptive sliding-mode control for permanent magnet spherical actuator with uncertainty using dynamic surface approach. J Electr Eng Technol 14:2341. https://doi.org/10.1007/s42835-019-00273-z

    Article  Google Scholar 

  6. Yan L, Zhang J, Duan H, Jiao Z (2016) Structure optimization of permanent magnet spherical motor utilizing improved Particle Swarm algorithm. In: 2016 IEEE Chinese guidance, navigation and control conference (CGNCC), 12–14 Aug 2016, pp 2255–2259. https://doi.org/10.1109/cgncc.2016.7829143

  7. Lu Y, Hu CG, Wang QJ, Hong Y, Shen WX, Zhou CQ (2018) A new rotor position measurement method for permanent magnet spherical motors. Appl Sci Basel 8(12):2415. https://doi.org/10.3390/app8122415

    Article  Google Scholar 

  8. Zhao Y, Li S, Zhao L, Guo X, Wang Q, Wen Y (2016) Sliding-mode control of permanent magnetic spherical motor based on co-simulation platform. In: 2016 IEEE 11th conference on industrial electronics and applications (ICIEA), 5–7 June 2016, pp 119–123. https://doi.org/10.1109/iciea.2016.7603562

  9. Hasanzadeh S, Rezaei H, Qiyassi E (2018) Analysis and optimization of permanent magnet dimensions in electrodynamic suspension systems. J Electr Eng Technol 13(1):307–314. https://doi.org/10.5370/jeet.2018.13.1.307

    Article  Google Scholar 

  10. Ju L, Qian Z, Li G, Zhou R (2016) Research on torque optimization of the spherical motor based on SVM. In: 2016 IEEE 11th conference on industrial electronics and applications (ICIEA), 5–7 June 2016, pp 1786–1790. https://doi.org/10.1109/iciea.2016.7603876

  11. Lee HJ, Park HJ, Ryu GH, Oh SY, Lee J (2012) Performance improvement of operating three-degree-of-freedom spherical permanent-magnet motor. IEEE Trans Magn 48(11):4654–4657. https://doi.org/10.1109/TMAG.2012.2200470

    Article  Google Scholar 

  12. Zhou F, Li G, Zhou R, Ju L, Ma G, Cao X (2017) Structural parameters optimization of permanent magnet spherical motor based on BP neural network model. In: 2017 12th IEEE conference on industrial electronics and applications (ICIEA), 18–20 June 2017, pp 1831–1837. https://doi.org/10.1109/iciea.2017.8283136

  13. Yan L, Wu ZW, Jiao ZX, Chen CY, Chen IM (2015) Equivalent energized coil model for magnetic field of permanent-magnet spherical actuators. Sens Actuators A Phys 229:68–76. https://doi.org/10.1016/j.sna.2015.03.016

    Article  Google Scholar 

  14. Yan L, Liang FQ, Jiao ZX, Wang TY (2016) Magnetic field analysis of novel spherical actuators with three-dimensional pole arrays. Rev Sci Instrum 87(6):065006. https://doi.org/10.1063/1.4953920

    Article  Google Scholar 

  15. Liu JM, Li XR, Chen WH, Liu L, Bai SP (2020) Magnetic field modeling and validation for a spherical actuator with cylindrical permanent magnets. Simul Model Pract Theory. https://doi.org/10.1016/j.simpat.2019.101954

    Article  Google Scholar 

  16. Wang Q, Li Z, Ni Y, Xia K (2005) 3D magnetic field analysis and torque calculation of a PM spherical motor. In: 2005 international conference on electrical machines and systems (ICEMS), 27–29 Sept. 2005, vol 3, pp 2116–2120. https://doi.org/10.1109/icems.2005.202938

  17. Yan LA, Chen IM, Lim CK, Yang GL, Lin W, Lee KM (2011) Hybrid torque modeling of spherical actuators with cylindrical-shaped magnet poles. Mechatronics 21(1):85–91. https://doi.org/10.1016/j.mechatronics.2010.08.009

    Article  Google Scholar 

  18. Cheng G, Guo X, Wen Y, Wang Q, Li G, Zhou R (2018) Electromagnetic modeling and analysis of 3-DOF permanent magnet spherical motor using magnetic equivalent circuit method. In: 2018 21st international conference on electrical machines and systems (ICEMS), 7–10 Oct. 2018, pp 2643–2648. https://doi.org/10.23919/icems.2018.8548998

  19. Guo X, Li S, Wang Q, Wen Y, Gong N (2019) Dynamic analysis and current calculation of a permanent magnet spherical motor for point-to-point motion. IET Electr Power Appl 13(4):426–434. https://doi.org/10.1049/iet-epa.2018.5149

    Article  Google Scholar 

  20. He J, Li G, Zhou R, Wang Q (2020) Optimization of permanent-magnet spherical motor based on Taguchi method. IEEE Trans Magn 56(2):1–7. https://doi.org/10.1109/TMAG.2019.2947863

    Article  Google Scholar 

  21. Lee K, Son H (2007) Distributed multipole model for design of permanent-magnet-based actuators. IEEE Trans Magn 43(10):3904–3913. https://doi.org/10.1109/TMAG.2007.904709

    Article  Google Scholar 

  22. Song S, Li B, Qiao W, Hu C, Ren H, Yu H et al (2014) 6-D magnetic localization and orientation method for an annular magnet based on a closed-form analytical model. IEEE Trans Magn 50(9):1–11. https://doi.org/10.1109/TMAG.2014.2315592

    Article  Google Scholar 

  23. Xia C, Li H, Shi T (2008) 3-D magnetic field and torque analysis of a novel Halbach array permanent-magnet spherical motor. IEEE Trans Magn 44(8):2016–2020. https://doi.org/10.1109/TMAG.2008.922782

    Article  Google Scholar 

  24. Xia C, Song P, Li H, Li B, Shi T (2009) Research on torque calculation method of permanent-magnet spherical motor based on the finite-element method. IEEE Trans Magn 45(4):2015–2022. https://doi.org/10.1109/TMAG.2009.2012390

    Article  Google Scholar 

  25. Yan LA, Chen IM, Son H, Lim CK, Yang GL (2010) Analysis of pole configurations of permanent-magnet spherical actuators. IEEE-ASME Trans Mechatron 15(6):985–989. https://doi.org/10.1109/tmech.2010.2051160

    Article  Google Scholar 

  26. Li H, Ma Z, Han B, Li B, Li G (2018) Calculation of magnetic field for cylindrical stator coils in permanent magnet spherical motor. J Electr Eng Technol 13(6):2158–2167. https://doi.org/10.5370/jeet.2018.13.6.2158

    Article  Google Scholar 

  27. Volakis JL, Davidson DB (2004) Calculating directivities with the two-dimensional Simpson’s rule. IEEE Antennas Propag Mag 46(4):106–112. https://doi.org/10.1109/MAP.2004.1374025

    Article  Google Scholar 

  28. Yan L, Chen IM, Lim CK, Yang GL, Lee KM (2012) Modeling and iron-effect analysis on magnetic field and torque output of electromagnetic spherical actuators with iron stator. IEEE-ASME Trans Mechatron 17(6):1080–1087. https://doi.org/10.1109/tmech.2011.2159238

    Article  Google Scholar 

  29. Wen Y, Wang Q, Li G, Guo X (2014) Adaptive fuzzy tracking control based on backstepping for permanent magnet spherical motor. In: 2014 17th international conference on electrical machines and systems (ICEMS), 22–25 Oct. 2014, pp 2176–2181. https://doi.org/10.1109/icems.2014.7013863

  30. Rong Y, Wang Q, Lu S, Li G, Lu Y, Xu J (2019) Improving attitude detection performance for spherical motors using a MEMS inertial measurement sensor. IET Electr Power Appl 13(2):198–205. https://doi.org/10.1049/iet-epa.2018.5195

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Key Project of the China National Natural Science Foundation (51637001) and the Nature Science Research Project of Anhui province (1908085QE236).

Author information

Authors and Affiliations

  1. National Engineering Laboratory of Energy-Saving Motor and Control Technology, Anhui University, Hefei, 230601, China

    Guoli Li

  2. School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Jingxiong He, Rui Zhou & Yuanzhong Qiao

  3. Collaborative Innovation Centre of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, 230601, China

    Qunjing Wang

Authors
  1. Jingxiong He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoli Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qunjing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuanzhong Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guoli Li.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, J., Li, G., Zhou, R. et al. Torque Modelling and Validation for a Spherical Motor with Stepped Permanent Magnets. J. Electr. Eng. Technol. 15, 2661–2673 (2020). https://doi.org/10.1007/s42835-020-00538-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42835-020-00538-y

Keywords

Search

Navigation