Transverse nonlinear vibration modeling and response of eccentric rotor in a switched reluctance motor

摘要

In order to investigate the transverse vibration of eccentric rotor in a 12/8 switched reluctance motor (SRM), a whole nonlinear coupled vibration equation of eccentric rotor is built with finite element method (FEM). Based on single tooth radial force and the key parameters variation with rotor position, an analytical formula of magnetic resultant taking into account of the rotor's vibration displacement is deduced in detail, which is applied onto the intermediate node of eccentric rotor in form of concentrated force. Once the windings currents obtained either by experiments or numerical simulations is input, the vibration response can be solved numerically by Newmark-beta method. Six phase windings currents under angle position control (APC) strategy are chosen as an example and the vibration response are discussed to reflect intrinsic vibration characteristics. From radical resultant vector and its amplitude spectrum, it is proved that the magnetic resultant vector presents multi-petals star shape. The frequency components in magnetic resultant are X, 5X, and 24kX +/- X, 24kX +/- 5X, related to rotational speed, current waveform and minimum common multiple of stator and rotor teeth. However, from displacement locus and its amplitude spectrum, the frequency component of the rotor vibration displacement is also related to the critical whirl speed of the rotor. Transverse superharmonic resonance of eccentric rotor appears at some particular rotational speed and result in a larger rotor vibration. If the rotor runs at the superharmonic speed of 1/19 of first-order critical whirl speed, the maximum vibration displacement radius of the eccentric rotor reaches almost four times that of the rated speed. The vibration locus at these particular speed show rich diversity.