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.

Research on Key Issues of Consistency Analysis of Vehicle Steering Characteristics

“…(21) exist and are unique: (22) x = A (1) b + I n − A (1) A y. (23) x = A (1,4) b, (24) x = A (1,3) b. (25) x = A + b, A (1,3) ∈ A{1, 3}.…”

“…It is relatively easy to ensure the performance of a car; however, ensuring that all cars are simultaneously near the ideal target value is difficult, and there are no particularly stringent requirements for part manufacturing, which is a major challenge for automotive design and performance engineers. At present, multi-objective optimization software [2][3][4][5][6], such as Isight, is used in the industry. The performance of the target vehicle is satisfied by optimizing the sensitive parameters.…”

Influence of the Load Distribution and Sizes on the Wheel Geometry in Passenger Cars

“…The suspension system of a modern vehicle largely reduces the forces, reaction forces and vibrations transmitted to the car body from the road [24][25]. The issue of changes in the wheel geometry, depending on the load, was discussed in [26][27]. It was found that in the suspension systems with a simpler and less complex design (e.g.…”

Influence of the Size and Distribution of Load on the Damping Coefficient of Shock Absorbers in Passenger Vehicles

“…A decrease in the load value influencing the vehicle body and improvement in the vehicle steering properties stems from the structure of the suspension system and the steering system. In [15] it was noted that the driveability and stability of a vehicle may change depending on the stiffness and resilience of the suspension system. On the other hand, the parameters of the suspension system while travelling are influenced by ambient temperature, type of tyres, tyre pressure and vehicle load conditions.…”

“…On the other hand, the parameters of the suspension system while travelling are influenced by ambient temperature, type of tyres, tyre pressure and vehicle load conditions. Thus, the initial parameters of the shock absorbers operation do not guarantee proper driveability of a vehicle when used under varied load conditions and varied environmental conditions [5,15]. Keeping all components in the right technical condition may provide the user with improved safety [8].…”