Key design parameters optimization and joint control of double throttling pipe air damping spring

The double throttling pipe air damping spring can significantly extend the stiffness and damping adjustable range of air springs. Focusing on the double-throttling air damping spring with length and diameter as key design parameters, this study establishes a dynamic mechanical model that accounts for turbulent effects of airflow passing through the throttling pipe. Subsequently, an eight-degree-of-freedom vehicle model incorporating this spring system is constructed. To enhance vehicle ride comfort and handling stability, a multi-objective grey wolf optimization algorithm is employed to determine the optimal pipe length and diameter for B-Class and C-Class roads. Post-optimization results demonstrate maximum improvements of the body acceleration, roll angle, pitch angle, lateral acceleration, and yaw velocity of the vehicle body on B-Class and C-Class roads are 21.46%, 16.13%, 17.94%, 7.82%, and 26.47%, respectively. Furthermore, a novel joint control strategy is proposed by integrating Sky-Hook reference sliding mode control with switching control, enhancing both adaptability and robustness of the suspension system. The results present that after adopting the joint control strategy, the aforementioned performance metrics are improved by 31.44%, 42.37%, 44.97%, 18.8%, and 55.32%, respectively. This research can provide theoretical guidance for the design, matching, and accurate control of double throttling pipe air damping suspension systems.