Robust kinematics design of MacPherson suspension based on a double-loop multi-objective particle swarm optimization algorithm

Abstract

In the traditional design of a vehicle suspension system, mechanical parameters, such as spring stiffness and tire radial stiffness, are determined before optimizing the coordinates of suspension hard-points based on handling and stability. However, the mechanical parameters of vehicle suspension systems vary with repeated changes in ambient temperature and loading conditions. Consequently, the original hard-point coordinates cannot guarantee satisfactory handling and stability after long-term vehicle use. To address this issue, an A0 class vehicle with a MacPherson suspension was modeled in ADAMS/Car and was validated against the results of field tests. The relationships between the maximum absolute values of front wheel alignment parameters during parallel wheel travel analysis and the coordinates of suspension hard-points, spring stiffness, and tire radial stiffness were determined using support vector regression. Next, a multi-objective optimization function was formulated based on the interval analysis method. Finally, a novel double-loop multi-objective particle swarm optimization algorithm was designed for global optimization of hard-point coordinates. The ADAMS simulation results indicated that, compared with the vehicle with the original hard-point coordinates, the double-loop multi-objective particle swarm optimization algorithm, the traditional multi-objective particle swarm optimization algorithm, and the genetic algorithm can effectively reduce the variation ranges of front wheel alignment parameters, regardless of the values of the mechanical parameters. It also showed that the double-loop multi-objective particle swarm optimization algorithm performs better than the traditional multi-objective particle swarm optimization and the genetic algorithm with both the original and changed mechanical parameters. Except for an increase in the variation range of the caster angle by 9.24–10.69%, the variation ranges of the toe angle, camber angle, and kingpin inclination angle under various mechanical parameters using the double-loop multi-objective particle swarm optimization algorithm were observed to be reduced by 50.45–79.39%, 1.84–4.24%, and 2.11–2.96%, respectively. Last but not least, the proposed double-loop multi-objective particle swarm optimization algorithm provided better handling, stability, and ride comfort values than the traditional multi-objective particle swarm optimization algorithm and the genetic algorithm.