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

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.

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.

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.

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.