Modeling and analytical calculation of road damage coefficient considering tire pressure and damping of vehicles

The road damage coefficientβis a significant indicator to estimate the degree of the road damage caused by vehicles.The existing calculation method ofβis not convenient for the engineering application.To effectively evaluate the damage degree and facilitate the engineering application,this paper studied the simple and reliable analytical calculation method ofβ.Firstly,a dynamic model of the vehicle–road system was created.The tire pressure and the tire damping were considered in the model.Moreover,the relationship between the tire vertical stiffness and the tire pressure is approximated as a linear function.Secondly,based on the dynamic model,according to the definition ofβ,a concise analytical formula ofβwas derived and verified by numerical simulations.The relative errors of the analytical calculation results are all less than 0.1%.Thirdly,the influences of the tire pressure p,the damping ratioξs of the suspension system,and the damping ratioξt of the wheel system onβwere analyzed.Moreover,based on the analytical formula ofβ,a mathematical model of the optimal damping matching for the suspension system was established and a case study was also given.The research results show that the larger the tire pressure p,the larger the value ofβis.For each p,there is an optimal damping ratioξs.If the tire damping is ignored,it will lead to the design error forξs.Finally,some important conclusions were drawn.The analytical formula ofβand the conclusions can provide valuable references for the analysis of the road damage and the initial design of vehicle suspensions.