Dynamic Analysis of a Brushless D.C. Motor Using a Modified Harmonic Balance Method

Analysis of brushless D.C. motor (BDCM) torque pulsations is an essential step in the diagnosis and control of vibration and noise generated by many electro-mechanical devices. The broad band spectral content of the torque pulsations, as predicted by a mathematical model which accounts for various complex effects, can often be obtained only by numerical integration which is time consuming while permitting little understanding of the dynamic interactions. Prior analytical approaches, such as the Fourier series technique or the d-q axis theory, are limited by the simplifying assumptions needed to compute the torque spectrum. This paper develops a new semi-analytical formulation for the analysis of nonlinear, time-varying BDCM’s which involve both spatial and temporal domains. A modified multi-term harmonic balance method, based on a transformation of the dual-domain problem to a spatial domain formulation, is developed here specifically to compute the magnitude of several harmonics of the pulsating torque. The interacting effects of key parameters, like dynamic eccentricity, magnetic saturation and open stator slots, on the time-varying inductances and rotor flux density distribution are included explicitly in the formulation. The predicted spectra compare very well with those obtained by direct time domain numerical integration. Yet, the proposed method is computationally efficient especially when the model dimension is reduced. It also provides better insight into the high frequency dynamics of the sample case.