Mathematical Modelling of the Rear Drive Unit of a Lightweight Vehicle for Sensitivity Analysis of Vibration

Abstract

Lightweight technology is applied in the automobile industry because mass reduction is beneficial in improving fuel efficiency and reducing CO2 emissions. Apart from the car body and the power unit (the two heaviest parts of a vehicle), the driveline also has potential for a reduction in weight. The driveline transfers power to the wheels and plays an important role in the vehicle system. Vibration is induced by the road input and by unbalanced forces transmitted through the driveline to the car body. Mass reduction in the driveline could influence the dynamic behaviour of a vehicle but it is not yet clear how mass reduction affects vibration of the driveline, the vehicle ride and NVH performance — important considerations when designing a lightweight driveline. In the prototype design stage, a mathematical model provides a more flexible and less costly method of optimising the system dynamics. In this paper, a 14 degree-of-freedom mathematical model is developed to study the dynamics of a rear drive unit (RDU). The system consists of a rear differential gearbox, left and right constant velocity joints and driveshafts, a rear sub-frame, and bushings between the RDU and the sub-frame and between the sub-frame and the car body. Excitations from the rear wheels, rear suspensions, and input shaft were considered. The vertical acceleration at the rear sub-frame was calculated and correlated with a calibrated multi-body dynamic model of the vehicle developed in a parallel study. Using a fractional factorial design with the vehicle travelling on a smooth road at various speeds, a sensitivity analysis was carried out with the developed mathematical model to identify the contributions of the mass properties of the RDU and the bushing parameters to the vibration at the centre of gravity (COG) of the rear sub-frame. Results indicate that the effects of design parameters on the rear sub-frame vibration vary according to the vehicle speed. For vibration at the rear sub-frame, the most influential factors are the masses of the rear differential gearbox and the driveshaft, and the stiffness of the front right bushings between the RDU and the sub-frame. The stiffness of the front left bushing between the RDU and the sub-frame also has considerable effect on the subsystem response but only at higher speeds. Reducing the mass of the CV joint is beneficial in decreasing the vertical vibration at the COG of the rear sub-frame, while reductions in masses of the gearbox and the driveshafts tend to slightly increase the vertical vibration at the same location. However, the adverse effect brought by lightweight differential gearbox and driveshafts on vibration is relatively small that may be hardly detected by passengers. The adverse effect (if any) can be compromised by adjusting the stiffness of the front bushings between the gearbox and the sub-frame.