Janus Blocks: A Binary System Wear Instability

Abstract

In this manuscript, a simple binary model is devised that describes the wear behavior of two blocks coupled under a constant, dynamically partitioned normal load. In this simple system, the frictional force is reacted by two independent springs and the blocks are allowed to move and wear independently based on system dynamics and kinematics. The only coupling between the blocks occurs through the partitioning of the applied normal load, which uses a pair of springs in parallel to model elasticity. This system is found to preferentially wear one of the blocks until two disparately unique conditions of steady wear are reached in the system: (1) a condition in which the partitioning of the load between the blocks yields equal wear and thus steady partitioning of the load and (2) a condition in which the pair of blocks go to zero wear by having one block not sliding but carrying all of the load and the other block completely slipping but carrying none of the load. These “Janus blocks,” the simplest of binary spring–block systems, begin life in a nominally identical state and then their behavior bifurcates, producing runaway or irregular wear. The onset of this instability can initiate from any differences in load partitioning, spring constants, friction coefficient, or wear rates (no matter how small).