Analysis Of Electromagnetic Vibration-and-Noise Of Permanent-Magnet Direct Current Commutator Motors

With the social development and the increased awareness of theenvironment protection, peoples are paying more attention to thevibration-and-noise pollution in the living and working environments. In theindustrial and domestic products, the permanent-magnet direct current (PMDC)commutator motors are widely used for their advantages of simplicity, low cost,and high efficiency. When these widely used permanent-magnet motors supplythe power, the motors also introduces extensive and notable vibration andnoise into the environment. Therefore, the researches of the vibration andnoise of the PMDC commutator motor would help to improve comfort andreduce the pollution of the environment. Furthermore, Low-noise motors couldadvance the competition of the company and improve the profits of theproducts.For small and middle sized PMDC commutator motors, the vibration andnoise of motors are mainly excited by the electromagnetic forces. Theelectromagnetic vibration and noise of the motor can be classified into aproblem of the multiphysics field, which includes the magnetic field, themodal parameters of the motor structure, the forced vibration of the motor, andthe radiated acoustic field. In the multiphysics field, the magnetic field of themotor has a weak-coupled relationship with the forced vibration of the motorstructure. And the vibration of the motor structure directly controls the radiatedacoustic field of the motor.In order to thoroughly investigate the above mentioned multiphysics field,this paper develops an analytical model to predict readily the magnetic field and the magnetic forces of the PMDC commutator motor. An analytical modelwhich is used to predict the electromagnetic vibration of the motor is extendedfrom a two-dimensional model to a three-dimensional model. Furthermore,numerical models are built up to calculate the magnetic field, the magneticforces, the modal parameters, the electromagnetic vibration, and the radiatedsound pressures of the motor.Based on the two-dimensional field theory, formulas are derived for theradial flux density in the air-gap region of the motor in polar coordinates.Based on the derived radial flux density, the Maxwell Stress Tensor method isused to calculate the radial magnetic force. As to the tangential magnetic force,an analytical model is indirectly derived with the cogging torque.In order to validate the analytical model of the magnetic field andmagnetic forces, and to consider the nonlinear effects of the magneticsaturation and the current commutation, a two-dimensional finite-elementmodel (FEM) is built up to calculate the magnetic field of the PMDCcommutator motor. The finite-element model can accurately predict themagnetic field and the magnetic forces in the both time and frequency domains.Besides deriving the analytical model and building up the finite-element model,the cogging torque of the PMDC commutator motor is also measured. Themeasured cogging torque agrees well with those modeled and calculated by theanalytical model and the numerical model, respectively. Our researchconcluded that the frequencies of the magnetic forces are the integral multiplesof the product of the slot number and the rotation frequency, and the magneticforces mostly act on the inner surfaces of the permanent-magnets.The structure of the PM motor is excited to vibrate by the time-varyingmagnetic forces. Therefore, the mechanical structure of the PMDCcommutator motor also controls the vibration and noise behaviors of the motor.Based on the theory of shells (simply supported shell) and the Reissnerequation, both the free vibration and the forced vibration of the stator structureare formulated. These formulas can easily estimate the natural frequencies, the mode shapes, and the transient responses of the motor-stator. The formulas canalso explain the relationship between the modes of the magnetic force and themode shapes of the stator.In order to accurately calculate the modal parameters and theelectromagnetic vibration of the PMDC commutator motor, athree-dimensional finite-element model of the present motor is constructed.The natural frequencies and the mode shapes calculated by the finite-elementmodel agree with those measured in the laboratory. By applying the magneticforces on the nodes of the permanent-magnets and the rotor of the structuralfinite-element model, the transient accelerations of the PMDC motor iscalculated by using the mode-superposition method. After comparing themeasured accelerations with those calculated from the numerical model, weconclude that the calculated electromagnetic vibration can be used in practice.In order to accurately predict the electromagnetic noise of the PMDCcommutator motor and to present the effects of the electromagnetic vibrationon the distribution of the noise, a three-dimensional boundary-element model(BEM) is constructed to calculate the radiated acoustic noise of the motor.After applying the velocity-boundary condition on the outer surfaces of themodel and constructing the field-points according to the ISO standard, theboundary-element mode accurately calculates the radiated sound pressures ofthe studied motor. The sound pressures calculated by the model agree wellwith those measured in a hemi-anechoic room. Our research concluded that,when the frequencies of the noise are lower than the natural frequencies of themotor, the electromagnetic vibration and noise of the motor are mainlycontrolled by the magnetic forces of the motor. Whereas, when thenoise-frequencies distribute among the range of the natural frequencies, theelectromagnetic vibration and noise are controlled by the resonance.By using the validated finite-element model and the boundary-elementmodel of the PMDC commutator motor, the electromagnetic vibration andnoise of the present motor with the rotor eccentricity are further investigated. Our research concluded that static rotor eccentricity exaggerates theelectromagnetic vibration and noise of the PMDC commutator motor. Thefrequencies of the increased sound pressures due to the eccentricity mostlyconcentrate on the range of the natural frequencies. Besides the rotoreccentricity, the epoxide-resin glue is also found to cause the unevendistribution of the electromagnetic noise of the PMDC commutator motor.This paper builds up the analytical model and the numerical model tothoroughly research the magnetic forces, the motor structure, and the radiatedacoustic field. By combining the theories of the magnetic field and thestructural vibration with the numerical method (FEM and BEM), this papercan explain the mechanism of the electromagnetic vibration and noise of thepresent motor completely, can analyze the effects of the design parameters onthe vibration and noise behaviors of the motor, can precisely predict theelectromagnetic vibration and noise of the PMDC commutator motor, and canhelp the motor manufacturing enterprise to resolve some vibration and noiseproblem in practice.