# Dynamic Characteristic Analysis of Permanent Magnet Brushless DC Motor System with Rolling Rotor
###### Abstract  
With the wide application of permanent magnet brushless DC motors (BLDCMs) in home appliances and electric vehicles, there is increasing demand for BLDCMs with low vibration and noise. This paper aims to study the dynamic characteristics of a type of BLDCM with a rolling rotor. Firstly, a dynamic model of a BLDCM with eighteen degrees of freedom (18 DOFs) is built, for which the electromagnetic force and the oil-film force of the sliding bearing are considered. Then, the system responses are solved by Runge-Kutta numerical method, and the effects of the rotational speed, bearing backlash and eccentric distance of the rolling rotor on the dynamic response are analyzed in detail. The time history, frequency plot, axis trajectory diagram and phase portrait are introduced to discuss the dynamic behavior of the motor system. Analysis results show that eccentric force increases obviously with increasing rotational speed or eccentric distance, which can change the dynamic response through suppressing the electromagnetic force. The effect of bearing clearance on the rotor and stator is negatively correlated. Therefore, system parameters should be determined properly to improve the running performance of the motor system. Numerical results can provide a useful guide for the design and vibration control of such motor systems. premanent magnet brushless DC motor; dynamic characteristic; bearing clearance; rolling rotor; eccentric distance +
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artificially pulsating torque and thus reduce the radial vibration of the permanent magnet motor. This method focuses on the study of new algorithms or prediction models to better control the motor. The second group investigates the electromagnetic field of the motor and further analyzes the effect of electric magnetization on system dynamics. For example, [PERSON] et al. [17] evaluated the exciting force of a permanent magnet motor to optimize the motor parameters, including stator winding, rotor permanent magnet shape and skew angle. Considering the dynamic and static eccentricity, [PERSON] et al. [18] calculated the unbalanced magnetic pull (UMP) to investigate its effect on the vibration response of the motor. [PERSON] et al. [19] analyzed the radial vibration force by finite element method and studied the influence of stator slotting and air gap on the vibration force. By alternating the distribution of the radial flux density, [PERSON] et al. [20] carried out harmonic elimination of vibration and noise of a permanent magnet motor. [PERSON] et al. [21] presented a new method to calculate electromagnetic torque in a permanent magnet synchronous motor and studied the effect of sixth-order torque ripple on the vibration and noise of electric vehicles. From the structural dynamics point of view, another method emphatically analyzes the dynamic characteristics of the motor system to optimize structural parameters, achieving the reduction of the vibration and noise. [PERSON] et al. [22] presented a state-space technique to analyze the dynamic performance of permanent magnet BLDCMs. Considering the air gap variation between the rotor and the stator, [PERSON] et al. [23] built a dynamic model of a BLDCM in which the displacements and currents were coupled, and researched the dynamic behavior of the system. Based on the built dynamic model [23], [PERSON] et al. [24] further designed a new BLDCM with higher torque, higher speed and lower vibration. Considering the effect of unbalanced magnetic pull, [PERSON] et al. [25] established the dynamic model of an offset rotor-bearing system for a permanent magnet synchronous motor and investigated the dynamic characteristics under varying parameters, including rotor offsets, radial clearances and static displacement eccentricities. Based on a mathematical model of a permanent magnet BLDC in-wheel motor system, [PERSON] et al. [26] investigated the electromechanical coupling vibration of the system caused by the distortion of the air gap magnetic field.