A Numerical Model for Solving Three-Dimensional Rolling Contact Problems with Elastic Coating Layers

In this work, a numerical model is proposed for three-dimensional rolling contact problems with one or two elastic layers, and the tangential contact solution is emphasized. Previous works on this topic have mostly been two-dimensional, in which only longitudinal creepage has been considered. With the three-dimensional model presented in this work, all possible creepages, such as the longitudinal, lateral and spin creepages are taken into account. In order to improve the calculation efficiency, the conjugate gradient method and the FFT technique are employed. The influence coefficients for displacement and stress are obtained from the corresponding frequency response functions. The numerical results are validated against existing results and good agreement can be found. The effects of the different layers’ thicknesses and elastic moduli under different creepage combinations on the traction distribution and stick/slip results are investigated. It can be seen that by adjusting the layer parameters the traction and stick/slip results can be modified significantly, and it may, therefore, be very useful information for improving the rolling contact fatigue and mitigating wear problems in various mechanical systems. Graphical Abstract

Some Exploration of the Path-Dependence in the Contact Analysis

One of the most frustrating features of joint mechanics is that all the important processes take place precisely where they cannot be seen or measured directly — the interface between contacting bodies. In order to achieve some insight into the mechanisms that give rise to the nonlinearities of joints one naturally turns to analytic or numerical models of interface mechanics. With such models, one can explore the significance of different assumptions of kinematics or surface mechanics and compare those with laboratory experiments on the integrated joints. Among the limitations of such modeling strategies are the twin problems of 1) employing suitable models for friction and 2) solving the resulting equations. There is evidence that the commonly used Coulomb friction model is inconsistent with the experimentally observed behavior of lap joints; it is necessary to explore the use of more complex models. Additionally, even when computing contact and sliding with the relatively simple Coulomb friction model, capturing the evolution of traction fields from one load set to the next in a physically plausible manner has been a continuing challenge. Obtaining fidelity to such path dependence for more complex models would be consequently more difficult. This issue has motivated the research reported here on the source of the difficulty in modeling path-dependent contact and possible solutions. A two-parameter Coulomb friction model is used to test a conventional contact algorithm and a newer one devised specifically to capture path dependence correctly. The evolution of lateral traction during cyclic loading is used to illustrate how the shear traction distribution at each load step evolves from that of the previous.

Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions.

Torque Vectoring Control for Handling Improvement of 4WD EV

Exploiting the structural merit that electric motors can be controlled precisely in speed und torque, this paper investigates the use of Torque Vectoring Control (TVC) for improving handling of electric vehicles. The strategy consists of two control levels. The upper level controller layer achieves reference yaw rate tracking, by using the 2-DOF planar bicycle model with a linear tire model to calculate the desired yaw rate. Then with sliding mode control law the desired yaw moment is determined. The lower control level determines control inputs for four driving motors by means of optimum traction distribution. Simulations are carried out by using the co-simulation of vehicle dynamics software CarSim and Simulink to verify the effectiveness of this control system and the effects of parameter variations (friction coefficient and throttle).