Based On Negative Stiffness And Air Spring In Parallel Vehicle Suspension Dynamics Analysis

With the continuous improvement of human social and economic level and the rapid development of science and technology,people have higher and higher requirements for vehicle performance and ride comfort.Air spring is a kind of non-metallic spring,which has excellent elastic properties.Air spring has both stiffness and damping characteristics.It is widely used in vehicle suspension system.In addition,in practice,people found that the system with negative stiffness has the advantages of low natural frequency and large bearing capacity.In order to take advantage of the advantages of negative stiffness in reducing the natural frequency of the mechanism,in practice,most of the parallel positive stiffness mechanisms are used to achieve the purpose of reducing the natural frequency of the original system.Therefore,the dynamic characteristics of vehicle suspension based on the parallel connection of negative stiffness and air spring are studied in this paper.Based on the 1/4 non-linear suspension model with single degree of freedom,the dynamic response of suspension system with negative stiffness and air spring in parallel under external excitation is studied.Considering the stiffness and damping of air spring,the approximate analytical solution of suspension system is solved by means of average method,and the correctness of the approximate analytical solution is verified by Runge-Kutta numerical solution in MATLAB software.The main resonance amplitude-frequency influence curves of air spring and negative stiffness parallel suspension system are obtained.The influence of negative stiffness and non-linear stiffness on the main resonance response of suspension system is analyzed in detail.It is found that 1/3 subharmonic resonance exists in the suspension system by numerical solution,so the 1/3 subharmonic resonance of the suspension system is studied analytically,and the existence condition of steady-state solution is obtained.The influence of negative stiffness,non-linear stiffness and damping on subharmonic resonance response of suspension system is analyzed by using approximate analytical solution.Based on the relevant knowledge of non-linear dynamics theory,the dynamic response of a two-degree-of-freedom non-linear vehicle suspension with negative stiffness in parallel with air spring is studied.A non-linear model of 1/4 vehicle suspension system is established.The stiffness and damping of air spring and the stiffness of negative stiffness spring are considered.Based on the average method theory,the approximate analytical solution of two-degree-of-freedom vehicle suspension model is obtained and compared with the numerical solution.The correctness of the calculation results is verified by comparison.The effects of negative stiffness,air spring and tire stiffness on suspension deformation and body displacement are analyzed.Based on the feedback of suspension velocity difference,fractional order PID control is carried out to study the non-linear dynamic response of vehicle suspension system with two degrees of freedom as control object.The fractional order PID control term is added to the dynamic model,and the approximate analytical solution of the system is obtained by averaging method,which is verified by power series method.By comparing the control performance of fractional-order PID controller with that of integer-order PID controller,it is found that the control performance of fractional-order PID controller is better than that of integer-order PID controller under the same coefficients.The effects of parameters of fractional order PID controller,negative stiffness and air spring parameters on suspension system response are analyzed.