Analytical Calculation Method of Motor Natural Frequencies Based on Equivalent Model of Three-Layer Cylindrical Shell

Accurate calculation of natural frequencies is significant for accurate prediction and suppression of motor vibration and noise. In order to reduce the errors caused by simplified structure in the analytical method, a new analytical calculation method (ACM) of the natural frequencies of the motor is proposed in this article. The motor enclosure, stator yoke, and stator teeth and windings are equivalent to a three-layer cylindrical shell model. The motor feet are equivalent to the axial ribs on the cylindrical shell. The artificial springs are used to simulate arbitrarily complex boundary conditions between the end covers and the enclosure. The combination of zig-zag theory and first-order shear deformation theory (FSDT) is used to calculate the natural frequencies of the equivalent model of the motor proposed in this article. According to the zig-zag theory model, the respective displacement function and energy equation are established for each cylindrical shell. The different structural dimensions and material properties between the motor enclosure, stator core and windings are considered. The FSDT is adopted in the displacement model of each layer of cylindrical shell, which considers transverse shear deformation, rotational inertia, and orthotropy of materials. Finally, the accuracy of the ACM proposed in this article is verified by finite element simulation and hammering method modal test.