PSI - Issue 17

Eduardo A. Lima et al. / Procedia Structural Integrity 17 (2019) 246–253 Eduardo A. Lima/ Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Rolling Models

The rolling models were developed using two sequential procedures, named wheel-rail and just wheel . Wheel-Rail Model – The first rolling contact model between the wheel and the rail was developed in ABAQUS/Standard with linear hexahedral elements of type C3D8R. The size of mesh around the region of the wheel rail contact was 1 mm x 1 mm in both bodies (Zhao and Li, 2011). Moreover, the wheel was modeled with the same mesh size along the longitudinal axis in an arc of 108 mm. A fine mesh was adopted for the head of the rail (1 mm x 1 mm) along with the 300 mm of the rail, as showed in Fig. (3a). The tied contact constraints are used for coarsening the mesh of the remaining part of the rail. In this work, the surface-to-surface algorithm was used to calculate the interaction between wheel-rail contact; a coefficient of friction 0.32 was used and the spin and creepage effects were disregard. The wheel surface was defined as the master surface and rail surface as the slave in the Lagrange multiplier method of the contact solution (Wiest et al. 2008). As already mentioned, the linear kinematic hardening model was adopted to describe the plastic behavior of the material in both components (wheel and rail). This behavior was characterized by a bi-linear curve in room temperature (25ºC), as showed in Fig. (2).

Fig. 3. Boundary conditions of rolling models: a) wheel-rail model b) wheel model.

For the numerical simulation of rolling, a center node was used to transfer the movement to all nodes of the hub. In this central node, the wheel can move in the vertical axis (X) and rotate around the lateral axis (Y), defining the degrees of movement. A sequence of static steps was modelled, defined from the wheel rotation of 1° from the previous position. A vertical load of the 191295 N is applied on the wheel center in all steps (Santos, 2008). With the interaction between the wheel surface and rail surface and the friction, the rolling movement results in advances of the wheel on the rail of about 9 mm by step. Ten angular motions were performed for rolling contact simulation (10 static steps). With these parameters, two conditions were considered: with and without the residual stresses from thermal treatment. The thermal stress distribution obtained in the last step of the thermal treatment process was transferred to the mesh of the wheel-rail model by using the command MAP SOLUTION. Wheel Model – The fatigue life of the railway wheel is calculated after the plastic accumulation and stabilization (elastic shakedown). Using the command CNORMF, the nodal loads were extracted during the complete contact simulation with the wheel-rail model. The loads were then applied as CLOAD on the same wheel mesh in the wheel model, as showed Fig. (3b). The rolling process was repeat eight times on the tread to check if the elastic shakedown phenomenon happens. The process resulted in 80 static steps or simulations, using a routine program created in MATLAB  software. The boundary conditions, material properties, and hardening model in the wheel model were the same employed with wheel-rail model. This modelling technique is expected to reduce the computational cost during the simulation without causing loss of accuracy of the results.