Influences Of The Inerter On Regenerative Suspension Dynamics And Its Damping Control

Traditional shock absorbers dissipate suspension vibration energy as heat waste by passing viscous fluid through orifices,so as to guarantee the ride performances of vehicles.Energy harvesting shock absorbers recover this part of energy into electric energy and provide continuously adjustable damping,which can achieve identical or even better performances than traditional shock absorbers.Current energy harvesting shock absorbers can be categorized into three types,the linear energy harvesting shock absorbers,the rotary energy harvesting shock absorbers,and the arm-mechanism-based energy harvesting shock absorbers.Among them,the rotary energy harvesting shock absorbers,especially the mechanical one and the hydraulic one,are most popular due to their large energy density.This paper focused on the analysis of the inerter in the rotary energy harvesting shock absorbers.Influences of the inerter on the characteristics of rotary energy harvesting shock absorbers and the corresponding suspensions were studied first.Then,the inerter and damping were optimized.Based on the optimized energy harvesting shock absorbers,several semi-active controllers were developed.The problems were theoretically and experimentally studied as follows.(1)A mechanical energy harvesting shock absorber was proposed for heavy-duty vehicles,and the mathematical model and bench tests were utilized to study influences of the inerter on its characteristics.The proposed mechanical energy harvesting shock absorber utilized a single-axis structure and a mechanical motion rectifier(MMR),which make the system simple and reliable.There were two one-way clutches in the MMR that makes the mechanical energy harvesting shock absorber a piecewise linear system switching between the engaged and disengaged states.Lagrangian mechanics and Newton mechanics were used to model the system dynamics and the switching condition.The model showed that its inertance and damping communally determine the shock absorber output force and switching condition.The experimental results verified the model,and the damping coefficient of the mechanical energy harvesting shock absorber was 5-35 kNs / m,which can meet the damping requirements for an amount of heavy-duty vehicles.(2)A hydraulic energy harvesting shock absorber was proposed.The model wasbuilt first and then the experiments were conducted.Both the model and experiments were used to analyze the influences of the inerter and other parameters on the characteristics of the hydraulic energy harvesting shock absorber.The dynamic model is built with the consideration of the inerter for the first time.The model shows that there are four parts in the output force model,including the viscous damping force,the electric damping force,the accumulator force,and the inerter force of the rotational parts.The model also shows that the accumulator force can counteract the inerter force.Experimental results verified the inference,and also showed that hydraulic efficiency can reach 30% with a corresponding regenerative power as 220 W.The hydraulic energy harvesting shock absorber can provide a damping range as32-92 kNs / m which can meet the damping requirement of most heavy-duty vehicles.(3)Influences of the regenerative inerter on vehicle performances were comprehensively studied on several vehicles,including car,bus,and three types of trucks.Because of the counteracting effect between the inerter force and the accumulator force in the hydraulic energy harvesting shock absorber,the inerter effect in the hydraulic energy harvesting shock absorber was not studied here and the mechanical one is studied.Two mechanical energy harvesting suspensions were studied.One was with a linear inerter,called the NonMMR regenerative suspension.The other was with a nonlinear inerter,called the MMR regenerative suspension.Results showed that both the linear inerter and the nonlinear inerter can improve the vehicle ride comfort,but only the nonlinear inerter can improve the vehicles road handling performance.Moreover,the improvement increased when the suspension damping ratio or the stiffness ratio(tire stiffness / suspension stiffness)decrease.Especially,when the damping ratio and the stiffness ratio are both smaller than a certain value,the nonlinear inerter can improve the vehicle comfort and handling at the same time through a rational design of the inertance.(4)The nonlinear inerter and damping in the MMR regenerative suspension were optimized first and then three controllers were designed to control the damping.In this part,the MMR regenerative suspension was selected,because of the superiority of the nonlinear inerter over the linear inerter,as well as the difficulty in realizing control about the hydraulic energy harvesting shock absorber due to its valve delay problem.This paper obtained the Pareto front of the vehicle comfort andhandling by using numerical calculation.Based on the Pareto front,one MMR regenerative suspension was selected to be controlled.Three semi-active controllers were designed and compared,including the skyhook-power-driven damper(SH-PDD),model predictive control(MPC),and clipped optimal control(clipped-LQR).Results show that the SH-PDD can greatly enhance the vehicle comfort and achieve comparable performance as the MPC while greatly reducing the calculation effort.However,the SH-PDD deteriorates the vehicle handling.Clipped-LQR can appropriately balance the vehicle ride comfort and handling.Therefore,SH-PDD can be used if high quality of vehicle comfort is required,and Clipped-LQR can be used for more balanced comfort and handling performance.