Vertical Nonlinear Vibration Characteristic Of Vehicle Systems

Railway vehicles generally adopt two-stage vibration isolation systems,and a large number of rubber parts are used in the suspension systems.Most of the rubber parts,such as air spring,stop,axle box rubber spring and so on,have non-linear characteristics,which are manifested in the frequency-dependent and amplitude-dependent characteristics of suspension parameters.In traditional vehicle dynamics calculation,most rubber parts are usually simplified as a linear spring-damper element without considering the influence of its non-linear characteristics.In this paper,the nonlinear vibration phenomenon is understood through the analysis of the actual measured acceleration data of a vehicle system.Then,the 1/4 vehicle vertical nonlinear dynamic model with two-degree-of-freedom is established,which includes the non-linear model of air spring fitted by cubic polynomial.Incremental Harmonic Balance Method(IHBM)is used to analyze the effect of secondary suspension vertical damping,excitation amplitude and non-linear stiffness on the main resonance of the system under single-frequency excitation.The results show that the amplitude-frequency curve of the system will tilt to right and encounter the jump phenomenon when the vertical damping of the secondary suspension is small or the cubic nonlinear stiffness of the air spring is large or the excitation amplitude is large.Increasing the quadratic nonlinear stiffness of the air spring can tilt the amplitude-frequency curve of the system to the left.The IHB method can clearly show the contribution of each order harmonic.The sub-harmonic resonance,super-harmonic resonance,internal resonance and combined resonance phenomena of this system are analyzed through multi-scale method.For the sub-harmonic resonance,the calculation results show that increasing the vertical damping of the secondary suspension,reducing the quadratic or cubic nonlinear stiffness,or reducing the excitation amplitude can prevent the generation of 1/2 or 1/3 sub-harmonic resonance.There are no redundant restrictions on the generation of super-harmonic resonance.Increasing the vertical damping,reducing the excitation amplitude and reducing the quadratic or cubic nonlinear stiffness can reduce the amplitude of the 2 or 3 super-harmonic resonance.For internal resonance,the calculation results show that under single-frequency excitation,the system with quadratic and cubic nonlinear stiffness may generate internal resonance when the natural frequency ratio of a system is 2 or 3.For combined resonance,the results show that under multi-frequency excitation,long-term terms still generated even if the excitation frequency is far from the natural frequency of the system.and at the mean time,a vehicle vertical vibration model considering the elastic car body is established.The vibration characteristics of the system under the conditions of float-sink,nodding and combined excitation conditions are analyzed.The Frequency Doubling phenomenon of the main frequency is reproduced in the calculation results of the vertical and pitch conditions,which shows that it is reasonable to use the cubic polynomial to fit the air spring stiffness.The calculation results of combined excitation show that in a nonlinear system,the frequency component of the combined excitation is much more than the frequency component of the linear system,and it is possible to excite some elastic or rigid mode when the excitation frequency is away from the system's elastic or rigid modal frequency.