An improved slicing technique for finite line contacts in the modelling of rolling element bearings

Mechanical system often involves the finite line contact of key components such as rolling element bearings and gear pairs. Different contact models have been developed to predict the load-displacement relationship and contact pressure distribution, but there usually exists a trade-off between the accuracy of simulation results and computational cost. An improved slicing technique is presented in this work. According to the half-space theory, a tri-linear fitting model is developed to express the load-displacement relationship and coupling behavior in slices of contact region, which is originally controlled by a spatial convolution. The improved slicing technique is thus formulated based on the tri-linear model. A modified Newton-Raphson algorithm is adopted to solve the free boundary problem of the improved slicing technique. The improved slicing technique is validated to be able to correctly predict the load-displacement relationships and the contact pressure distributions of different contact profiles, especially for contact pressure concentrations which other slicing techniques are unable to predict accurately. The computation speed of the proposed method is much faster than the semi-analytical method and is of the same order of other slicing technique. The high accuracy and low computational cost enable the proposed method to be applied in the on-line calculation of rolling element bearings and other sophisticated mechanical systems.