Method for accurate determination of resonant frequencies and vibration behaviour of stators of electrical machines

Accurate determination of values of resonant frequencies and vibration characteristics of stators is essential for the purpose of designing quiet electrical machines. In this paper, an analysis of rigorous and general nature for the determination of resonant frequencies and natural response of stators having encased construction is presented. The analysis is based on the three-dimensional theory of elasticity and it is therefore capable of providing information about not only the radial vibrations of a stator but also about the torsional and axial vibrations. Further, the effects of teeth, windings and frame are incorporated in the analysis. The derived frequency equation is applicable to all modes of vibration including the breathing and the beam-type modes. It delivers values of the lowest as well as the higher-order resonant frequencies. The terms of the frequency equation are given in dimensionless quantities so that the equation can be used for stators of small as well as medium and large size machines. The analysis also provides information on the nature of stator vibrations at the various resonances. This information lays foundation to explain several important phenomena related to the natural response of stators. Among these are the phenomenon of multiple resonances, the phenomenon of coupling between various components of displacement and the phenomenon of dual resonances. Simplified frequency equations are also derived from the general frequency equation for the special modes of uniform vibrations along stator circumference and stator length. The experimental verification of the analysis is reported in a companion paper.