Wheel-rail Non-hertzian Contact Method And Its Application In The Study Of Wheel-rail Dynamic Interaction On High-speed Railway

Relative to the traditional railway,wheel-rail dynamic interaction of the high-speed railway is more sensitive to the change of wheel-rail relationship.Change of the wheel-rail contact geometry induced by wheel-rail wear have a significant influence on the wheel-rail coupled dynamics under high-speed driving conditions,which will even threaten the running safety,stability and ride comfort of the vehicle.Meanwhile,high-speed railway present a huge challenge to wheel-rail materials.The deterioration and damage of the wheel-rail materials are gradually exposed with the increase of the operation time of the high-speed railway.Therefore,it is necessary to study the high-speed wheel-rail interaction mechanism and explore the characteristics of wheel-rail wear and damage evolution.Wheel-rail contact theory is the basis for studying wheel-rail dynamic interaction.Wheel-rail non-Hertzian contact theory can better explain the principle of wheel-rail dynamic interaction.In view of this,this paper considers the drawback of the existing wheel-rail non-Hertzian contact method in dynamics calculation,and proposes a new non-Hertzian contact method suitable for wheel-rail dynamics calculation.Based on the non-Hertzian contact theory,the basic characteristics of high-speed wheel-rail dynamic interaction and wheel-rail material wear and damage are studied.Primarily,the common wheel-rail normal contact theory that can be applied for wheel-rail dynamic interaction and wheel-rail wear calculation are introduced systematically,the system studies,including Hertz contact theory,three non-Hertzian contact methods based on virtual interpenetration,and Kalker's complete theory.Based on Kalker's complete theory and NORM algorithm,the normal contact module of S-CONTACT software is compiled.The correctness of S-CONTACT software is verified by compared with the results of Hertz contact theory and the calculation results of CONTACT software.Taking the calculation results of S-CONTACT software as references,the disadvantages in the vehicle dynamic calculation of the Hertz contact and simplified non-Hertzian contact methods based on virtual interpenetration are discussed.A more robust wheel-rail non-Hertzian contact method named MKP contact method is proposed based on the idea of Kik-Piotrowski method.Taking the results estimated by S-CONTACT and Kik–Piotrowski method as references,MKP contact method is validated by three contact cases,including the typical non-Hertzian contact and the typical two-point contact,contact between standard wheel and rail as well as worn wheel and rail.The simulation results indicate that,compared with Kik–Piotrowski method,the proposed MKP method achieves better computational accuracy and computational stability,whereas lower computational efficiency.The MKP method is more suitable for online calculation of wheel-rail dynamic non-Hertzian contact.Next,the common used wheel-rail tangential contact method,including Kalker's linear theory,Kalker's simplified theory,FaStrip method,and Kalker's complete theory are described.The tangential contact module of S-CONTACT software is developed based on Kalker's TANG algorithm and ConvexGS algorithm.The correctness of the tangential contact module of S-CONTACT software is verified by Kalker's linear theory and the calculation results of CONTACT software.Taking the calculation results of S-CONTACT as references,the influence of four equivalent elliptical modes of non-Hertzian contact patch on the non-Hertzian linear creep coefficient is analyzed,and the computational accuracy of FASTSIM and FaStrip in non-Hertzian tangential contact calculation is assessed.The simulation results indicate that,using the MKP method to calculate the wheel-rail normal contact,using the equivalent ellipse modes adopted in Kik-Piotrowski method to calculate the coefficient C_ij and the flexibility coefficient L_i,and applying FaStrip method to calculate the wheel-rail tangential contact,the calculation result is relatively close to the S-CONACT software and is suitable for vehicle-track coupled dynamics simulation.Based on the vehicle-track coupling dynamics theory,a high-speed vehicle-slab track coupling dynamics model considering wheel-rail non-Hertzian contact is established.The MKP wheel-rail non-Hertzian contact model taking into account the effect of angle of the wheelset is proposed to meet the requirements of the wheel-rail contact analysis in dynamics calculation.In order to simulate the vehicle move on the infinite length track efficiently,a step-moving window method is developed.Based on the proposd dynamic model and wheel-rail non-Hertzian dynamic contact method,the simulation softwear TTAP?dynamic module?is compiled.The accuracy and reliability of the TTAP software are verified by comparison of the multi-body dynamics software SIMPACK and related literature results.Then,the roots of the hollow wear?the most common wear?of the high-speed EMU wheel is discussed,and the static and dynamic interaction characteristics between hollow-worn wheel and rail are analyzed.By comparing with the standard wheel,the influence of wheel hollow wear on the wheel-rail vertical and lateral forces excited by the track random irregularity and the weld irregularity are analyzed.Furthermore,the influence of hollow wear on the wheel rolling contact fatigue is studied based on the Shakedown theory and the damage function.Results show that,hollow wear of the wheel tread will significantly change the wheel-rail contact relationship,slight hollow depth lead to wheel-rail conformal contact,while large hollow depth result in two-point contact at the boundary of the wear center.Compared with the dynamic response of the vehicle without worn-wheel,the wheel-rail contact forces are slightly affected by the tread hollow-worn wheel under the excitation of track random irregularity,however,due to the increase of wheel rail normal contact stiffness induced by hollow wear,the wheel rail force will be greatly affected in certain conditions under the excitation of track weld irregularity.Hollow wear has a direct impact on rolling contact fatigue,especially for seriously hollow-worn wheels,which may cause fatigue oblique cracks on the outside of the wear center.Finnaly,a rail non-uniform wear evolution prediction model for calculating the three dimensional distribution along the longitudinal and transverse directions of the rail is proposed.In the simulation model,the vehicle-track coupled dynamics model considering the wheel-rail non-Hertzian contact is adopted to calculate the wheel-rail dynamic interaction,Kalker's variational method is applied for the wheel-rail local contact analysis,and the material wear model developed by University of Sheffield is used to calculate the material wear.Taking the service characteristics of the rail into consideration,a novel sampling and accumulation strategy is applied to obtain the wear distribution of special cross-sections.Based on the proposed model,the non-uniform wear characteristics of high-speed railway rails and their effects on vehicle dynamics are discussed.Results indicate that,the wear band is almost parallel to the rolling direction and shows an extended trend with the increase of the number of vehicle passages,and the average wear area increases almost linearly with the increasing number of passages.The distribution of rail wear area along the track is highly correlated with the wear number of vehicles passing through the corresponding locations.Rail wear has a great impact on the wheel-rail contact geometry,which enlarges the wheel rail contact range.In the initial operation phase of the track,the rail non-uniform wear has little effect on the wheel-rail vertical dynamic interaction and car body acceleration,while it has significant influence on the wheel-rail lateral interaction.