Vibration mitigation for in-wheel switched reluctance motor driven electric vehicle with dynamic vibration absorbing structures
Introduction
The development and optimization of electric vehicle (EV) has attracted the attention of both academia and the automobile industry and much research has been done on the topic in recent years [[1], [2], [3]]. On the basis of the propulsion system, EVs can be broadly divided into two categories, namely, centrally driven and in-wheel motor (IWM) driven. Compared to the centrally driven EV, which is similar to the conventional internal combustion engine vehicle, the IWM driven configuration has several advantages and provides vehicle engineers with a new research perspective. The advantages of this propulsion system include weight and space saving, fast and precise dynamic response, high energy efficiency, easier application of X-by-wire chassis control, etc. Aspects such as lateral stability [4], vehicle dynamics control [5,6], and steering control [[7], [8], [9]] of EVs with IWMs have been much studied.
Two types of motors are commonly used as IWM for EVs, i.e. permanent magnet synchronous motor (PMSM) [10,11] and switched reluctance motor (SRM) [12,13], and each type has its advantages and disadvantages. The features of both PMSM and SRM are summarized in Table 1.
A notable demerit of PMSM is that it requires permanent magnets, and the rare earth materials required for their manufacture are limited and expensive. The increase in the price of NdFeB from US $250/kg in 2005 to US $437/kg in 2012 has brought SRM to the fore as a strong candidate for IWM driven vehicles of the future since it dispenses with permanent magnets [14]. This has led to many studies being conducted on SRM design and optimization in IWM driven systems [[15], [16], [17]].
However, the demerits of SRM include torque ripple and vibration/noise problem, hindering its extensive application. One reason is the phase current commutation and many methods have been proposed to improve its performance in EVs from the perspectives of the circuit design and torque control. Chai et al. [18] presented a comparative evaluation from the perspective of electronic switching control while Takiguchi et al. [19] designed the driving current to eliminate the third harmonic component in the sum of the radial force. Xue et al. [12] applied a multi-objective optimization method to improve the average torque, the torque smoothness factor, and the maximum torque per ampere of SRM with adjustment of the turn-on and turn-off angles. Sun et al. [13] designed a modified current chopping controller (MCCC) to improve the performance in both starting and constant speed working conditions.
Unlike conventional vehicle suspensions, suspensions in EVs with IWMs become coupled IWM-suspension systems, and the influence of IWMs on the suspension has been the subject of much research in recent decades. Previous research has shown that the application of IWMs leads to a deterioration in the suspension performance especially the road-handling performance because of the additional unsprung mass [20]. Taking IWM dynamics into consideration, Wang et al. [21,22] investigated the SRM electromagnetic mechanism and pointed out that the eccentricity in the radial direction of the SRM, which is related to road excitations, will generate an unbalanced electromagnetic force (UEMF), and thus would dramatically deteriorate the dynamics response of the vehicle.
For the sake of improving the performance, some researchers attempted to apply active suspension control techniques to deal with the increased unsprung mass [23,24]. Given the complexity of the active suspension system, the concept of dynamic vibration absorbing structure (DVAS) for IWM-suspension system was proposed to improve the performance. In this structure, IWMs are typically suspended by an extra spring and a damper, which connect to either the sprung mass (known as “chassis” type) [25] or the axle (known as “tire” type) [26]. Numerical optimization methods for suspension system parameters were proposed to improve the dynamic response. However, previous literature related to DVAS considered the influence of neither the UEMF nor the coupled longitudinal-vertical dynamic, which was far from reality. To the best knowledge of authors, there are little or no studies that investigate the mitigation of IWM-suspension system with SRM from the perspective of structural design.
To deal with the abovementioned problems and improve the performance of the coupled IWM-suspension system with SRM (called the SRM-suspension system), this paper presents an extensive study on the application of novel DVAS in SRM-suspension system, and the findings of this study can be concluded as follows:
- a)
The coupling effects between the UEMF induced by the SRM and the suspension system are investigated by creating a coupled longitudinal-vertical system model with the consideration of the aerodynamic force and the road unevenness.
- b)
More practical and novel DVAS vertical models including both “chassis” and “tire” types are proposed and their superiority to the conventional SRM-suspension model is demonstrated. In addition, the feasibility of the preferred “tire” type is validated by a multi-body simulation (MBS) software, namely LMS Motion.
This paper is organized as follows: Firstly, an analytical nonlinear SRM model is formulated based on the Fourier series, and the calculation of torque and the UEMF is presented in Section 2. Then, the coupled longitudinal-vertical dynamic models for the traditional suspension, conventional SRM-suspension, and “chassis” and “tire” type DVASs are created with consideration of the aerodynamics drag force and road excitations. For comparison, particle swarm optimization (PSO) is used to optimize parameters in SRM-suspension systems. System response comparisons for different ISO road levels and velocities are presented in Section 4, followed by the MBS validation for the “tire” type DVAS. Section 5 provides the conclusion and future work.
Section snippets
SRM modeling and torque controller
This section describes the development of an analytical, nonlinear model for the SRM, and details the structure and functioning of the torque controller.
SRM-suspension modeling and the novel DVAS
Dynamic responses of road vehicles are affected by many factors, e.g. road profile, road bank angle, road surface, and aerodynamics. To investigate the coupling effects of vehicle suspension and SRM for various input road profiles, a coupled longitudinal-vertical SRM-suspension model is developed. When developing such a model, the steering input, the coefficient of road adhesion, and the road bank angle are not considered. The coupled dynamics of a quarter-vehicle model with SRM is depicted in
Simulation results and discussion
In this section, the negative effects caused by the increased unsprung mass and induced UEMF are firstly presented, and the performance of different SRM-suspension structures are compared for various velocities and road levels. The definition of road excitation and the simulations are subsequently discussed.
Conclusions and future work
This paper presented a vibration mitigation method for EVs with SRMs by a novel DVAS design. An analytical Fourier-series model of the SRM is formulated at first, and then the coupled longitudinal-vertical dynamic models are developed for two novel DVASs. According to the numerical simulation, the influence of the UEMF on the SRM-suspension system is investigated under varying road levels and velocities, and MBS validation is finally performed to prove the feasibility of the novel “tire” type
Acknowledgments
The authors acknowledge the support of the National Natural Science Foundation of China (Grant No. U1564210), Innovative talent support program for Chinese post doctorates (Grant No. BX201600017), and the China Postdoctoral Science Foundation funded project (Grant No. 2016M600934). Authors would also thank Dr. Yanjun Huang of the University of Waterloo for his kind suggestions.
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