This paper presents a simulation method for the power consumption of servo motors, focusing on the influence of vibrations on the motor efficiency. An apparatus consisting of two servo motors connected through a coupling was specifically designed for this study. The efficiency of the servo motor was experimentally investigated for several torque vibration levels imposed through the selection of the control parameters, and the torque vibration level was quantified through the standard deviation of the torque signal. The efficiency map characteristics for each torque oscillating level were determined. A numerical model of the apparatus clarifying the dependency of the coupling characteristics on the oscillating torque was developed, and the torque oscillation of the system was simulated. A model based on the measured motor efficiency maps and the torque oscillation level was developed to simulate the motor efficiency under several torque vibrating conditions. Finally, the power consumption of the motor was simulated based on the simulated efficiency and mechanical power. A balance of input, output, and loss powers was presented, and the experimental measurements were compared with the simulation results. The power consumption of the motor increased when the torque oscillated owing to vibrations, and the loss of power due to both oscillations and the loss of motor efficiency was quantified.

1. [1] “World Energy Balances,” 2020 Edition, Int. Energy Agency, 2020.
2. [2] A. de Almeida, P. Bertoldi, and W. Leonhard, “Energy efficiency improvements in electric motors and drives,” Springer, 1997.
3. [3] D.-J. Sim, D.-H. Cho, J.-S. Chun, H.-K. Jung, and T.-K. Chung, “Efficiency optimization of interior permanent magnet synchronous motor using genetic algorithms,” IEEE Trans. on Magnetics, Vol.33, No.2, pp. 1880-1883, 1997.
4. [4] L. Yu, Y. Zhang, and W. Huang, “Accurate and efficient torque control of an interior permanent magnet synchronous motor in electric vehicles based on hall-effect sensors,” Energies, Vol.10, No.3, doi: 10.3390/en10030410, 2017.
5. [5] P. K. Patel, R. Nagarsheth, and S. Parnerkar, “Performance comparison of permanent magnet synchronous motor and induction motor for cooling tower application,” Int. J. of Emerging Technology and Advanced Engineering, Vol.2, No.8, pp. 167-171, 2012.
6. [6] K. Kurihara and M. A. Rahman, “High-efficiency line-start interior permanent magnet synchronous motors,” IEEE Trans. on Industry Applications, Vol.40, No.3, pp. 789-796, 2004.
7. [7] C. Cavallaro, A. O. Di Tommaso, R. Miceli, A. Raciti, G. R. Galluzzo, and M. Trapanese, “Efficiency enhancement of permanent-magnet synchronous motor drives by online loss minimization approaches,” IEEE Trans. on Industrial Electronics, Vol.52, No.4, pp. 1153-1160, 2005.
8. [8] S. Morimoto, Y. Tong, Y. Takeda, and T. Hirasa, “Loss minimization control of permanent magnet synchronous motor drives,” IEEE Trans. on Industrial Electronics, Vol.41, No.5, pp. 511-517, 1994.
9. [9] S. Vaez, V. I. John, and M. A. Rahman, “Adaptive loss minimization control of inverter-fed IPM motor drives,” Record 28th Annual IEEE Power Electronics Specialists Conf. (PESC97), Vol.2, pp. 861-868, 1997.
10. [10] C. M. Burt, X. Piao, F. Gaudi, B. Busch, and N. F. Taufik, “Electric motor efficiency under variable frequencies and loads,” J. of Irrigation and Drainage Engineering, Vol.134, No.2, pp. 129-136, 2008.
11. [11] H. Xie, X. Wei, Y. Liu, Y. Feng, Y. Zhang, X. Yang, and K. Yang, “Research of asymmetrical bidirectional magnet skewing technique in modular multi-stage axial flux permanent magnet synchronous motor,” IEEE Trans. on Magnetics, Vol.51, No.3, Article Sequence No.8102705, 2015.
12. [12] W.-H. Kim, K.-C. Kim, S.-J. Kim, D.-W. Kang, S.-C. Go, H.-W. Lee, Y.-D. Chun, and J. Lee, “A study on the optimal rotor design of LSPM considering the starting torque and efficiency,” IEEE Trans. on Magnetics, Vol.45, No.3, pp. 1808-1811, 2009.
13. [13] M. Rigacci, R. Sato, and K. Shirase, “Experimental evaluation of mechanical and electrical power consumption of feed drive systems driven by a ball-screw,” Precision Engineering, Vol.64, pp. 280-287, 2020.
14. [14] A. Hayashi, R. Sato, R. Iwase, M. Hashimoto, and K. Shirase, “Measurement and simulation of electric power consumption of feed drive systems,” Proc. of the ASME 2013 Int. Mechanical Engineering Congress and Exposition, Vol.2A, 2013.
15. [15] A. S. Phani and J. Woodhouse, “Viscous damping identification in linear vibration,” J. of Sound and Vibration, Vol.303, No.3-5, pp. 475-500, 2007.
16. [16] S. Adhikari and J. Woodhouse, “Identification of damping: Part 1, Viscous damping,” J. of Sound and Vibration, Vol.243, No.1, pp. 43-61, 2001.
17. [17] S. Adhikari and J. Woodhouse, “Identification of damping: Part 2, Non-viscous damping,” J. of Sound and Vibration, Vol.243, No.1, pp. 63-88, 2001.
18. [18] C. Minas and D. J. Inman, “Identification of a non-proportional damping matrix from incomplete model information,” ASME J. of Vibration and Acoustics, Vol.113, No.2, pp. 219-224, 1991.
19. [19] C.-P. Fritzen, “Identification of mass, damping and stiffness matrices of mechanical systems,” J. of Vibration, Acoustics, Stress, and Reliability in Design, Vol.108, No.1, pp. 9-16, 1986.
20. [20] Y. Pan and Y. Wang, “Iterative method for exponential damping identification,” Computer-Aided Civil and Infrastructure Engineering, Vol.30, No.3, pp. 229-243, 2015.
21. [21] C. Du and L. Xie, “Modeling and control of vibration in mechanical systems,” CRC Press Taylor & Francis Group, 2018.
22. [22] L. Aarniovuori, “Induction motor drive energy efficiency – Simulation and analysis,” Ph.D. Thesis, Lappeenranta University of Technology, 2010.
23. [23] A. Sorniotti, T. Holdstock, G. L. Pilone et al., “Analysis and simulation of the gearshift methodology for a novel two-speed transmission system for electric powertrains with a central motor,” Proc. of the Institution of Mechanical Engineers, Part D: J. of Automobile Engineering, Vol.226, No.7, pp. 915-929, 2012.
24. [24] M. Rigacci, R. Sato, K. Shirase, and T. Sasaki, “Evaluation of torque-dependent coupling characteristics and their influence on the system vibration characteristics,” J. of Advanced Mechanical Design, Systems, and Manufacturing, Vol.15, No.5, JAMDSM0060, 2021.
25. [25] A. Mahmoudi, W. L. Soong, G. Pellegrino, and E. Armando, “Efficiency maps of electric machines,” 2015 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 2791-2799, 2015.
26. [26] M. Rigacci, R. Sato, and K. Shirase, “Evaluating the influence of mechanical system vibration characteristics on servo motor efficiency,” Precision Engineering, Vol.72, pp. 680-689, 2021.