Brushless DC Motor Electromagnetic Torque Estimation with Single-Phase Current Sensing

  • Cham, Chin-Long (School of Mechanical Engineering, Universiti Sains Malaysia) ;
  • Samad, Zahurin Bin (School of Mechanical Engineering, Universiti Sains Malaysia)
  • Received : 2013.06.07
  • Accepted : 2013.11.28
  • Published : 2014.05.01


The purpose of this paper was to find an effective method for measuring electromagnetic torque produced by a brushless DC motor with single-phase current sensing in real-time. A torque equation is derived from the theory of brushless DC motor. This equation is then validated experimentally with a motor dynamometer. A computer algorithm is also proposed to implement the electromagnetic torque estimation equation in real-time. Electromagnetic torque is a linear function of phase current. Estimating the electromagnetic torque in real-time using single-phase current is not appropriate with existing equations, however, because of the rectangular alternating-pulse nature of the excitation current. With some mathematical manipulation to the existing equations, the equation derived in this paper overcame this limitation. The equation developed is simple and so it is computationally efficient, and it takes only motor torque constant and single-phase current to evaluate the electromagnetic torque; no other parameters such as winding resistances, inductances are needed. The equation derived is limited to the three-phase brushless DC motor. It can, however, easily be extended to the multiphase brushless DC motor with the technique described in this paper.


Brushless DC motor;Electromagnetic torque;Algorithm;Mathematical methods


  1. P. Yedamale, "Brushless DC (BLDC) Motor Fundamentals," Microchip Technology Inc., Arizona, 2003.
  2. M. Ehsani, , Y. Gao, A. Emadi, "Permanent Magnetic BLDC Motor Drives," in Modern Electric, Hybrid Electric, and Fuel Cell Vehicles Fundamentals, Theory, and Design, 2nd ed., New York: CRC Press, 2010, pp. 200-216.
  3. N. Hashemnia, "Comparative study of using different motors in the electric vehicles," in 18th International Conference on Electrical Machines ICEM 2008, 2008, pp. 1-5.
  4. D. C. Hanselman, "Minimum torque ripple, maximum efficiency excitation of brushless permanent magnet motor," IEEE transaction on industrial electronics, vol. 41, pp. 292-300, Jun. 1994.
  5. L. Sun, H. Gao, Q. Song, J. Nei, "Measurement of torque ripple in pm brushless motors," in Industry Applications Conference, 2002. 37th IAS Annual Meeting, 2002, pp. 2567-2571.
  6. C. L. Chu, M. C. Tsai, H. Y. Chen, "Torque control of brushless dc motors applied to electric vehicles," in IEEE International Electric Machines and Drives Conference, 2001, pp. 82-87.
  7. M. Markovic, A. Holder, Y. Perriard, "An analytical determination of the torque speed and efficiency speed characteristics of a bldc motor," in IEEE 2009 Energy Conversion Congress and Exposition, 2009, pp. 168-172.
  8. H. Tan, S. L. Ho, "A novel single current sensor technique suitable for bldcm drives," in proceedings of the IEEE 1999 International Conference on Power Electronics and Drive Systems, 1999, pp. 133-138.
  9. J. C. Fang, X. X. Zhou, G. Liu, "Instantaneous torque control of small inductance brushless DC motor," IEEE Transactions on Power Electronics, Vol. 27, pp. 4952-4964, Dec. 2012.
  10. U. Y. Huh, J. H. Lee, T. G. Lee, "A torque control strategy of brushless DC motor with low resolution encoder," in Proc. International Conference on Power Electronics and Drive Systems, 1995, pp. 496-501.
  11. Y. Liu, Z. Q. Zhu, D. Howe, "Instantaneous torque estimation in sensorless direct-torque-controlled brushless DC motors," IEEE Transactions on Industry Applications, Vol. 42, pp. 1275-1283, Sept. 2006.
  12. P. D. Gipper, "Accurate torque-speed performance prediction for brushless DC motors," in Proc. NAECON, 1988, pp. 1092-1097.

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