Multi-objective optimization of a sports car suspension system using simplified quarter-car models

In this paper, first, the vibrational governing equations for the suspension system of a selected sports car were derived using Lagrange's Equations. Then, numerical solutions of the equations were obtained to find the characteristic roots of the oscillating system, and the natural frequencies, mode shapes, and mass and stiffness matrices were obtained and verified. Next, the responses to unit step and unit impulse inputs were obtained. The paper compares the effects of various values of the damping coefficient and spring stiffness in order to identify which combination causes better suspension system performance. In this regard, we obtained and compared the time histories and the overshoot values of vehicle unsprung and sprung mass velocities, unsprung mass displacement, and suspension travel for various values of suspension stiffness (KS ) and damping (CS ) in a quarter-car model. Results indicate that the impulse imparted to the wheel is not affected by the values of CS and KS . Increasing KS will increase the maximum values of unsprung and sprung mass velocities and displacements, and increasing the value of CS slightly reduces the maximum values. By increasing both KS and CS we will have a smaller maximum suspension travel value. Although lower values of CS provide better ride quality, very low values are not effective. On the other hand, high values of CS and KS result in a stiffer suspension and the suspension will provide better handling and agility; the suspension should be designed with the best combination of design variables and operation parameters to provide optimum vibration performance. Finally, multi-objective optimization has been performed with the approach of choosing the best value for CS and KS and decreasing the maximum accelerations and displacements of unsprung and sprung masses, according to the TOPSIS method. Based on optimization results, the optimum range of KS is between 130 000–170 000, and the most favorable is 150, and 500 is the optimal mode for CS