An approximate model of surface ploughing by a rotating disc and other indenters

The version of the upper bound method developed by the authors earlier to find the configuration of a stress-free surface, is extended here for a more complicated kinematic field and geometry of indenter. The purpose of this generalization is twofold. Firstly, this gives more flexibility in using the results of the present friction study for a wider set of problems, including the case of interfering asperities. As an example, we present some numerical results for a row of asperities with different degrees of penetration up to full embedment. Secondly, the algorithm was used to model the indentation of a rigid wheel pressed into softer rigid-perfectly plastic material, and then dragged through it, leaving a groove behind. The wheel may be prevented from rotation or may be torque free. Key issues to be determined from the analysis include an evaluation of local pressures, sliding speeds, development of plastic deformation and exposure of nascent material. Surprisingly, the numerical results have shown that for a certain range of parameters, the ratio of ploughing force to vertical force may decrease as the local adhesion increases.