Geometric Optimization of Concentrated Contacts for Minimum Microslips

Microslip between concentrated contacts is discussed and design charts are presented for microslips, maximum pressure, closing-in of the contacting bodies, and optimized shapes for minimum microslips. Computer programs for the foregoing are given and they are based on a previous analysis on a generalization of the Hertz problem and that of the Mindlin problem for fourth-order paraboloids in contact. In particular, the microslips and the annulus of slip were sought. To this end an inverse method was devised. Moreover, an optimization procedure was described for finding the geometry for a given loading condition and set of material properties, within the family of paraboloids, which gives minimum slip. It is shown in an example that the annulus of slip may be reduced by 60 percent while the maximum slip may be reduced by 90 percent.