Modeling and Simulation of the Fretting Hysteresis Loop

This work deals with the modeling and simulation of the fretting hysteresis loop. Fretting represents a relative cyclic motion between two surfaces, having a non-uniform distribution of local relative displacement at their contact. Fretting damage is a complex contact phenomenon leading to crack initiation and/or material removal. The shape of the fretting hysteresis loop (loop-like variation of the frictional force versus the relative displacement) is related to the main fretting regimes and transitions between them: stick (no hysteresis), partial slip fretting (elliptical hysteresis), gross slip fretting (parallelogram-like hysteresis), and reciprocating sliding (rectangular hysteresis). Crack initiation and propagation is related to the partial slip fretting, while surface transformation and material removal is related to the gross slip fretting. In this work, based on the models of rotated ellipse and super-ellipse the fretting hysteresis is modeled and simulated. Relationship between the ellipticity, angle of rotation as well the power parameter of the super-ellipse and the fretting regime is illustrated and discussed. Such results are useful for the optimal design of the surfaces with tribological applications and for estimation of the life of machine elements.