Coupled Magnetic-Mechanic Analysis Of The Electromagnetic Vibration Of A Permanent Magnet Machine

The acoustic noise and vibration are important parts of researches on PM machines, which consist of electromagnetic vibration and noise, mechanical vibration and noise, and aerodynamic vibration and noise. The electromagnetic vibration and noise, stimulated by electromagnetic forces, are main sources. A model for the prediction of open-circuit magnetic field and coupled magnetic-mechanic vibration characteristics in surface mounted permanent magnet machines is developed in this paper, which considers the effect of stator slots and rotor eccentricity.First, an analytical model for the prediction of open-circuit magnetic field in surface mounted permanent magnet machines is developed, in which the effects of stator slots and rotor eccentricity are considered. The magnetic field domain in PM machines is divided into three simple and regular subdomains, viz. magnet, air-gap and stator slots. The analytical solution is derived by solving the magnetic field governing equations in each subdomain and applying the boundary conditions to the interfaces between these subdomains. A perturbation method is utilized to consider the effect of rotor eccentricity.Second, the analytical subdomain model is used to analyze the electromagnetic forces in three different types of PM machines, viz. a machine with8poles and12slots, a machine with10poles and12slots, and a machine with4poles and48slots. The distribution of the electromagnetic forces in the time and space are derived. By harmonic analysis of the electromagnetic forces, the time-and space distribution of the harmonic components is derived.Then, two types of the coupled magnetic-mechanic vibration analysis method are introduced. In the first method, the analytical subdomain model is used to predict the magnetic field, which is programmed in MATLAB. The FEM method is used to predict the vibration characteristics of the PM machine, which is programmed by AN SYS Parametric Design Language. Then, by creating the data interface between MATLAB and ANSYS, the combined simulation environment is built. In the second method, the analytical subdomain model is also used to predict the magnetic field. However, the rotor is simplified to a spring mass system. The kinematical equation of the spring mass system is built. The Four order Runge Kutta method is used to solve the kinematical equation. The magnetic field and kinematical equation is solved by MATLAB. Then, the vibration responses of the stator are analyzed by transient analysis in ANSYS. Finally, a machine with10poles and12slots and a machine with4poles and48slots are taken for examples to illustrate these two methods. Similar harmonic components’frequencies of the unbalanced magnetic pull can be found in these two methods.Finally, a vibration experiment on a PM machine with4poles and48slots is taken to validate the coupled magnetic-mechanic vibration method. The PM machine is fixed on the platform and runs in no load condition.