Research On Ground Vibration Induced By P₂ Force Of Wheel-rail In Metro Vehicles

The development of urban rail transit has effectively boosted the process of urbanization in China,and profoundly affected the social change and people ’s way of life.However,the problem of environmental vibration is becoming more and more prominent.Many scholars have conducted a large number of field tests on different metro lines in China,By summarizing the results,it can be found that the vertical vibration of ground caused by subway mainly concentrates in the frequency band of 40～80Hz.This paper focuses on the vertical vibration band,based on the wheel-rail P2 force theory,the vibration mechanism and transmission characteristics are studied from the vibration source,and then effective vibration reduction measures are proposed.The main research contents and conclusions are as follows:(1)Based on Jenkins ’ empirical formula,Winkler foundation model and double-layer composite beam model,vehicle track coupling dynamics models of three different tracks were established to compare and analyse the influence of the main parameters on the impact P1 force and P2 force.The simulation results are in good agreement with the theoretical analysis results.The results show that the P1 force is mainly affected by the impact,and is linearly related to dipped rail joints.It increases gradually with the increase of the stiffness of fastener and speed,and the change range is large.In addition,the effects of parameters not taken into account in Jenkins ’ empirical formula,such as the damping of the fastener,unsprung mass of bogie and the vertical stiffness of bogie primary suspension were also studied,it is found that there is an"optimal interval" for all three.P2 force has a large number of influencing parameters,which are linearly related to dipped rail joints,and increases gradually with the increase of speed,unsprung mass and the stiffness of fastener.In addition,increasing the damping of fastener and the vertical stiffness of bogie primary suspension can inhibit P2 force to some extent.In terms of P2 force frequency,the bearing stiffness and unsprung mass play a decisive role,and the difference of order of magnitude between the vertical stiffness of bogie primary suspension and that of the fastener has little effect on P2 force frequency.(2)The experimental data of four subway lines measured by the research group were analyzed by using the short-time Fourier transform and time-domain comparison method,and based on the test results of falling wheel impact bench,the dominant vertical vibration frequency band of 40～80Hz in subway lines is caused by wheel-rail P2 force.Moreover,when the vibration is transmitted downward to the track system,it is concentrated in the range of 30～100Hz.The acceleration transfer ratio indicates slab has an insufficient attenuation effect on the vibration of this frequency band,and even amplification effect of vibration of some frequency bands occurs.Passing up to the bogie often results in modal resonance of the bogie,and once such resonance is formed,it will greatly affect the fatigue strength of the bogie.In addition,when polygonal abrasion exists in the wheel,resonance may be generated in the P2 force region,resulting in multiple amplification of vibration energy.(3)The model of monolithic track-bed and floating slab ballast bed is established to study the vibration transfer characteristics induced by the impact excitation of dipped rail joints are studied at the cross-end and mid-span locations respectively.The results show that the longitudinal transfer range of vibration is approximately within the distance between the front and rear 5 sleeper,and the transfer rate at the 5th sleeper is less than 10%,the vibration exceeds the normal passing level of the vehicle within the range of the front and rear two pillow spans.The lateral transmission path of vibration is mainly the under-rail system,which shows that the impact vibration is first transmitted vertically to the fastener system,and then transversely to the other side through the sleeper or floating slab.Vibration in the vertical has a strong transmission,the main component of P2 force,the amplitude can reach two to three times the normal value,and not easy to attenuate.When the amplitude of P1 force is large,it can also be transmitted to the fastener force,but it will not continue to be transmitted downward.(4)Based on the analysis results of the influence of the parameters of the wheel-rail impact,the vibration reduction measures are verified by the simulation of the running condition of the line under short-wave excitation.The results show that the shear damper with small stiffness can effectively reduce the P2 force amplitude and P2 force frequency But at the same time,it will weaken the restraint effect of the fastener system on the rail,which will easily cause the high frequency elastic vibration of the rail,and then cause the rail corrugation Therefore,it is necessary to select a reasonable range of parameters.When the values in the model in this paper are 10～20MN/m,both requirements can be well considered.Vibration reduction measures with low unsprung mass can effectively reduce the amplitude of P2 force without adversely affecting the vibration of other sections.Therefore,the unsprung mass should be reduced as far as possible under other conditions.Although the floating slab ballast bed has certain advantages in vibration reduction for P2 force,it may stimulate the vertical bending mode of the floating slab,causing the expansion of P2 force frequency range and greatly affecting the service performance and fatigue life of its concrete structure.Therefore,in the track parameter matching design,it is particularly necessary to reasonably refer to the modal characteristics of the floating slab,so that the P2 force frequency can avoid the vertical bending mode of the floating slab.