An Accurate Calculation Method of Natural Frequencies of the Radial-Flux Slotted Motors Considering End Covers

Accurately calculating and reasonably adjusting the natural frequencies of the motor are the key technologies to predict and weaken the electromagnetic vibration of the motor. In this article, we first give the general equivalent models of the stator, including the stator core, windings, and casing. After that, the characteristic equation of natural frequencies of the stator is established based on the energy method, and the complex structures of the stator teeth, windings, and casing are accurately considered. Taking into account the orthotropic characteristics of laminated core and windings, the calculation methods of the equivalent material parameters of stator core and windings are introduced, and the accuracy is verified by the finite-element method and the modal test method. In order to accurately replicate the actual constraints of the end covers to the casing, the accurate calculation method combining the energy method and the artificial springs equivalent method is proposed. By modifying the stiffness coefficients of the artificial springs, any boundary condition, including classical boundary conditions, can be simulated. Based on this, the natural frequencies of the radial-flux slotted motor, including the stator core, windings, casing, and end covers, are calculated accurately by the accurate calculation method. Finally, a general formula for determining the stiffness coefficients of artificial springs corresponding to casings with different thicknesses, lengths, and average diameters is summarized, which facilitates the prediction of natural frequencies of the radial-flux slotted motors considering the influence of the end covers.