# Analysis and Optimization of Driveline Bushing for Lateral Ride Vibration under Shock Excitation
## 1 Introduction  
It is the two main functions of the bushings in automobiles to isolate vibration transmission between structures and reduce noise transmitted to cabin. Stiffness and damping of bushing have a great influence on the static and dynamic performance of vehicles. As a highly coupled dynamic system, changes of subsystem of vehicle may have considerable impacts on the global responses [1].  
Suspensions (of vehicle/seat) and mounts (of engine/suspension) have the most direct effect on ride comfort and have been well studied [2; 3; 4; 5; 6]. It was justified that the well-designed mechanical properties of the jounce bumper is able to reduce the vertical acceleration at the vehicle centroid at most speeds [7]. The bushing joints of the front suspension have great influence on the vertical displacements and roll accelerations of the vehicle chassis [8]. [PERSON] et al. [9] discussed different sorts of optimization approaches for improving ride comfort and road holding at the same time. [PERSON] [10] proposed a dynamic air spring model and its benefit to ride comfort was examined through a 2-DOF analytical model. A hydropneumatic suspension model with a semiactive suspension control is developed to improve the ride comfort of an agriculture tractor [11]. Powertrain mounting system has also been widely investigated. Researches including the dynamic simulation of the rubber or hydraulic mounts [12; 13; 14; 15], the development of vibration isolation method from engine to chassis [16; 17; 18; 19], and optimization of the mount characteristics [20; 21; 22] were carried out. In addition to suspensions and powertrain mounts,-drivenine components also have considerable influence on the vehicle ride [23], where bushings play a significant role in connecting the front/rear drive units and their subframes and between the subframes and chassis. Effect of the driveline bushings on the dynamic responses at both local system (e.g., differential/subframe vibration) and global system (e.g., the seat rail vibration) is of great importance for vehicle design [24].  
Ride comfort is related to the objective responses of human body to vibration and the subjective sensation and feeling of occupants caused by the vibration accordingly [25]. Both of the objective and subjective response of human depend on the vibration direction [26]. It has been proved that a low-amplitude rotational movement of the upper body can cause same discomfort as high-amplitude vertical movement [27]. Among all six directions, comparing to the vertical vibration the passenger is more sensitive to lateral and roll movements, which are less concerned. In terms of the kind of ride vibration, at low speed the pulse excitation or shock (hump or pit) is the main contributor to the discomfort compared to the random vibration with little magnitude due to the inconspicuous response of the human body to it. Pulse excitation and shock deserve more concern to improve the performance of ride comfort of vehicles while most of the previous studies focused on the other one.  
The objective of the study is to investigate the influence of driveline bushing on ride vibration of a vehicle and to improve the comfort by optimizing the bushing parameters. To this end, a multibody dynamics (MBD) model of a vehicle including a detailed differential-subframe subsystem is developed and validated by the experiment. A sensitivity analysis is carried out to identify significant factors among the bushing parameters affecting the seat rail vibration. Based on the sensitivity result, the relationship between the vibration of seat rail and the bushing parameters is established with the response surface method (RSM). Finally, the optimization of the bushing parameters is carried out with the particle swarm optimization (PSO) method while the fitted response functions is applied to minimize the overall vibration at the driver seat rail.