The solution of frictional wheel–rail rolling contact with a 3D transient finite element model: Validation and error analysis

▶ A 3D transient FE model is developed to treat the friction rolling contact. ▶ The normal and the tangential problems are both obtained for arbitrary geometry. ▶ Validation is performed for the case of wheel tread–rail top contact. ▶ Influence of element size on solution accuracy is examined. Wheel–rail frictional rolling contact has been solved for linear elasticity and statics and with the half-space assumption in three dimensions. In recent years, the normal contact problem has also been treated in elasticity and elasto-plasticity with the finite element (FE) method; the half-space assumption is dropped. In this paper, a 3D transient FE model is presented to solve both the normal and the tangential contact problems simultaneously for arbitrary geometry. The explicit time integration scheme employed renders it intrinsically suitable for transient analysis of high frequency dynamic processes. The model is first validated with Hertz theory and Kalker's computer program CONTACT for the normal solution and with CONTACT for the tangential solution, for the case of wheel tread–rail top contact. Subsequently, the influence of element size on solution accuracy is examined by comparing the results of different element sizes. The analyses show that the presented model is valid for the solution of frictional rolling.