| With the continuous speed-up of China’s high-speed railway,the locomotive vibration caused by external factors such as rail vertical deformation and track irregularity excitation is becoming more and more prominent.This phenomenon caused the deterioration of the running state,and the contradiction between the safe operation of the train and the speed increase is becoming more and more serious.As an important part of the locomotive,the air suspension system directly affects the driving stability and ride comfort of the locomotive at high speed.Therefore,it is of great practical significance to explore the dynamic characteristics of the locomotive and study the vibration control to ensure the safe and stable operation of the train.The air spring has obvious nonlinear characteristics,and the air spring is a typical viscoelastic device.The fractional calculus theory can better reflect the viscoelastic characteristics of the device.In this thesis,the fractional calculus theory is introduced to establish the fractional order model of air spring,to explore the dynamic characteristics of air suspension system,and to study its vibration control.The main contents include:(1)The structure composition,classification and characteristics of different kinds of air springs are introduced.The composition of the air suspension system and the working principle of the components of the suspension system are analyzed.The basic theory and main properties of fractional calculus are studied,and the processing method of fractional calculus is determined.(2)Taking air spring as the research object,the experimental research is carried out.By analyzing the test data,the characteristic curves of stiffness and damping characteristics,force and displacement of air spring under different working conditions are obtained.The fractional calculus theory is introduced to establish the fractionalorder nonlinear dynamic model of air spring.The least square method is used to identify the model parameters,fit the test data and verify the accuracy of the model.(3)Based on the fractional-order nonlinear dynamic model of air spring,a twodegree-of-freedom fractional-order nonlinear dynamic model of 1/4 air suspension is established to study the dynamic characteristics of air suspension system.The approximate analytical solution of the system is obtained by the average method.Compared with the numerical solution,the accuracy of the analytical results is verified,and the influence of parameter changes on the vibration characteristics of the air suspension system is analyzed.(4)Considering the universality of time-delay phenomenon,the fractional-order time-delay speed feedback control strategy is introduced into the air suspension system,and the control effect of the air suspension system under the fractional-order time-delay speed feedback control is studied.The approximate analytical solution of the model is obtained,and the accuracy of the analytical solution is verified by comparing with the numerical solution obtained by the power series method.Under the same working conditions,compared with passive control,fractional-order time-delay feedback control can effectively suppress system vibration.The influence of fractional-order time-delay velocity feedback control parameters on the vibration characteristics of air suspension system is analyzed. |