Research on low-frequency longitudinal–torsional coupled vibration of in-wheel motor driving vehicles

Peibao WU, Rongkang LUO, Hui MA, Zhichao HOU

Journal of Tsinghua University(Science and Technology) ›› 2026, Vol. 66 ›› Issue (10) : 2035-2044.

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Journal of Tsinghua University(Science and Technology) ›› 2026, Vol. 66 ›› Issue (10) : 2035-2044. DOI: 10.16511/j.cnki.qhdxxb.2026.28.012
Vehicle and Traffic

Research on low-frequency longitudinal–torsional coupled vibration of in-wheel motor driving vehicles

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Abstract

Objective: Drivability is one of the key performance indices of electric vehicles and is closely related to the dynamic characteristics of the drivetrain. In-wheel motor drives differ from centralized motor drives in that the mechanical half-shaft is shorter or even eliminated, while the motor mass and corresponding rotational inertia are added directly to the wheel. These changes, together with the mass and stiffness distribution of the drivetrain system, give rise to new longitudinal–torsional coupled vibration characteristics in the low-frequency range. This study aims to investigate the underlying mechanisms and characteristics of longitudinal and torsional vibrations in the low-frequency range of vehicles driven by in-wheel motors and to clarify the differences between in-wheel motor configurations and their centralized counterparts. Methods: A dynamics model was established to describe the longitudinal–torsional coupled vibration of the in-wheel motor drive system in the low-frequency range. For torsional vibration, the motor and wheel were represented as equivalent rotational degrees of freedom, while the unsprung mass and vehicle body were modeled as translational degrees of freedom for longitudinal vibration. To capture the coupling between rotational and longitudinal motions, the longitudinal tire force was linearized under the assumption of small slip and combined with a first-order relaxation model. Based on the established models, dynamic analyses were conducted for three representative drivetrain configurations: centralized motor drive, in-wheel motor drive with inner rotors, and in-wheel motor drive with outer rotors. The configurations were compared by evaluating their natural frequencies, mode shapes, frequency responses, and transient responses under tip-in conditions. For the in-wheel motor drive with outer rotors, the effects of motor mass, rotor inertia, suspension bushing stiffness, suspension bushing damping, initial wheel speed, and motor time constant were also evaluated. Results: The dominant low-frequency vibration of the centralized motor drive system was a torsional mode caused by half-shaft flexibility, with a frequency of approximately 7.5 Hz. In contrast, in the in-wheel motor drive systems, longitudinal vibration of the unsprung mass, with a frequency of about 10 Hz, dominated due to the removal of the half-shaft and the increased unsprung mass. For the configuration with inner rotors, a rotor torsional mode appeared near 20 Hz. For the configuration with outer rotors, a rotor–wheel coupled torsional mode was observed at 26.6 Hz. Under tip-in excitation, all three configurations exhibited noticeable transient vibrations. The centralized motor drive system showed a single low-frequency torsional oscillation, whereas the in-wheel motor systems exhibited higher-frequency coupled oscillations. Parametric sensitivity analysis of the in-wheel motor drive configurations indicated that increasing suspension bushing damping effectively suppressed the first longitudinal mode vibration. Increasing the motor time constant reduced the amplitude of both longitudinal and torsional vibrations, although at the expense of a slower torque response. Conclusions: The vibration characteristics of in-wheel motor driving vehicles in the low-frequency range differ fundamentally from those of centralized motor driving vehicles. In the latter, the dominant vibration is a torsional mode governed by half-shaft flexibility, whereas in the former, the dominant motion is a longitudinal mode associated with the unsprung mass. The proposed model effectively captured the vibration characteristics of all three drivetrain configurations and provides a theoretical basis for structural design, parameter matching, and motor control in in-wheel motor drive systems.

Key words

drivability / in-wheel motor drive / longitudinal–torsional coupled vibration / dynamics modeling / parametric sensitivity analysis

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Peibao WU , Rongkang LUO , Hui MA , et al. Research on low-frequency longitudinal–torsional coupled vibration of in-wheel motor driving vehicles[J]. Journal of Tsinghua University(Science and Technology). 2026, 66(10): 2035-2044 https://doi.org/10.16511/j.cnki.qhdxxb.2026.28.012

References

1
高炳钊, 洪金龙, 陈虹. 汽车传动系统平顺性驾驶品质控制[J]. 控制理论与应用, 2017, 34(7): 849- 866.
GAO B Z , HONG J L , CHEN H . Drivability control of automotive drivetrain[J]. Control Theory & Applications, 2017, 34(7): 849- 866.
2
SCAMARCIO A , GRUBER P , DE PINTO S , et al. Anti-jerk controllers for automotive applications: A review[J]. Annual Reviews in Control, 2020, 50, 174- 189.
3
KOCH A , SCHULZ L , JAKSTAS G , et al. Drivability optimization by reducing oscillation of electric vehicle drivetrains[J]. World Electric Vehicle Journal, 2020, 11(4): 68.
4
SCAMARCIO A , METZLER M , GRUBER P , et al. Comparison of anti-jerk controllers for electric vehicles with on-board motors[J]. IEEE Transactions on Vehicular Technology, 2020, 69(10): 10681- 10699.
5
范仲杰. 电动汽车动力传动系统的扭振特性与控制研究[D]. 济南: 山东大学, 2024.
FAN Z J. Research on torsional vibration characteristics and control strategy of electric vehicle drivetrains[D]. Jinan: Shandong University, 2024. (in Chinese)
6
许健富, 章桐, 于蓬, 等. 针对电动车喘振问题的控制方法研究[J]. 机电一体化, 2014, 20(8): 23- 28.
XU J F , ZHANG T , YU P , et al. Study of the control method aimed at surge problem of electric vehicle[J]. Mechatronics, 2014, 20(8): 23- 28.
7
于蓬, 章桐, 王晓华, 等. 集中驱动式纯电动车抖动分析及主被动控制研究[J]. 振动与冲击, 2015, 34(13): 53–59, 65.
YU P , ZHANG T , WANG X H , et al. Surge analysis and active- passive control for a central driven pure electric vehicle[J]. Journal of Vibration and Shock, 2015, 34(13): 53–59, 65.
8
王亚丽, 姚立纲, 蔡永武, 等. 电动轮驱动电动汽车用减速器的发展与挑战[J]. 机械传动, 2019, 43(11): 161- 171.
WANG Y L , YAO L G , CAI Y W , et al. Development and challenge of reducer for electric wheel drive electric vehicle[J]. Journal of Mechanical Transmission, 2019, 43(11): 161- 171.
9
CHEN L, ZHANG S, BIAN M, et al. An explanation of the in-wheel motor drive system's vibration at low velocity using motor-wheel frequency characteristics: 2016-01-1673[R]. Warrendale: SAE International, 2016.
10
LI J Q , SONG Z Y , WEI Y T , et al. Influence of tire dynamics on slip ratio estimation of independent driving wheel system[J]. Chinese Journal of Mechanical Engineering, 2014, 27(6): 1203- 1210.
11
YAMADA S , BEAUDUIN T , FUJIMOTO H , et al. Active model-based suppression of secondary ride for electric vehicles with in-wheel motors[J]. IEEE/ASME Transactions on Mechatronics, 2022, 27(6): 5637- 5646.
12
ZUO S G , HU X R , LI D Q , et al. Analysis and suppression of longitudinal vibration of electric wheel system considering rotor position error[J]. IEEE Transactions on Transportation Electrification, 2021, 7(2): 671- 682.
13
TUONONEN A J , LAJUNEN A . Modal analysis of different drivetrain configurations in electric vehicles[J]. Journal of Vibration and Control, 2018, 24(1): 126- 136.
14
ZHAO Z , TAGHAVIFAR H , DU H P , et al. In-wheel motor vibration control for distributed-driven electric vehicles: A review[J]. IEEE Transactions on Transportation Electrification, 2021, 7(4): 2864- 2880.
15
ZUO S G , LI D Q , MAO Y , et al. Longitudinal vibration analysis and suppression of electric wheel system driven by in-wheel motor considering unbalanced magnetic pull[J]. Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering, 2019, 233(11): 2729- 2745.
16
左曙光, 李多强, 毛钰, 等. 考虑机电耦合的电动轮系统纵向振动特性建模及验证[J]. 农业工程学报, 2017, 33(22): 61- 68.
ZUO S G , LI D Q , MAO Y , et al. Modeling and validation on longitudinal vibration characteristics of electric wheel system considering electromechanical coupling[J]. Transactions of the Chinese Society of Agricultural Engineering, 2017, 33(22): 61- 68.
17
TUONONEN A J, HARTIKAINEN L, PETRY F et al. Parameterization of in-plane rigid ring tire model from instrumented vehicle measurements[C]//Proceedings of the 11th International Symposium on Advanced Vehicle Control. Seoul, South Korea: AVEC, 2012: 1–6.

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