Optimization design of steering trapezoid mechanism based on an improved particle swarm optimization

Errors exist between actual trajectories and theoretic trajectories of vehicle steering trapezoid mechanisms in the process of steering, which leads to shorter service life of wheels and worse vehicle handling, stability, and safety. Parameter optimization of steering trapezoid mechanisms can efficiently reduce these errors and improve the safety of these vehicles. The principal purpose of this paper is to develop an improved particle swarm optimization for an optimal design of steering trapezoid mechanisms. First, a nonlinear optimization model of the steering trapezoid mechanism is established by investigating how they work and how they influence the stability of vehicle maneuvering characteristics. The sum of the absolute value of difference between actual rotational angle of anterolateral steering wheel and theoretical rotational angle of anterolateral steering wheel is taken as the objective function of the nonlinear optimization model, while the bottom angle and steering arm length of steering trapezoid mechanisms are selected to be design variables. After that, an improved particle swarm optimization algorithm (IPSO) is proposed based on the traditional particle swarm optimization by introducing over-flow dealing functions to deal with complicated nonlinear constraints. The core idea of IPSO can be described as follows: complex nonlinear constraints are regarded as over-flow dealing functions, check whether over-flow dealing functions meet restricting condition at each iteration, if not, initialize design variables in proper ranges and then repeat the check, otherwise, go to next iteration. Finally, codes for IPSO are programmed and parameters of steering trapezoid mechanisms for three different models are optimized. To test the accuracy of the IPSO algorithm as proposed above, the nonlinear optimization problems for three different models (Nissan Duke, Patrol GRX and Patrol GL) are given; numerical results show that errors of the objective function's actual values and objective function's optimization values are less than 0.1%, which means that IPSO possesses high accuracy in solving nonlinear optimization problems, and that IPSO is a promising method for solving complicated constraint optimization problems. To verify effectiveness and efficiency of the IPSO algorithm, performance comparison experiments of three intelligent algorithms were analyzed. The problem of the steering trapezoid mechanism of Patrol GRX was carried out, with the Improved particle swarm optimization algorithm (IPSO), traditional particle swarm optimization (TPSO), and particle swarm algorithms based on simulated annealing (SA-PSO) being used as the optimizing parameters. For Patrol GR with the same initialization parameters and error percentage of objective function's actual values and objective function's optimization values (Percentage of Error), the minimum number of iterations to get the objective function's optimum solution, the minimum number of iterations to obtain the objective function's optimum solution (Min-iterationNum), the average number of iterations to obtain the objective function's optimum solution (Ave-iterationNum), and the total number of times to obtain the objective function's optimum solution (Total-Times) were selected as key performance comparison indicators of three intelligent algorithms of performance comparison experiments. The performance comparison experiment results indicates that the proposed new algorithm is superior to the particle swarm algorithm based on simulated annealing and traditional particle swarm optimization in fast convergence and small calculating quantity, but a little inferior to particle swarm algorithm based on simulated annealing in calculation accuracy in the process of optimization.