Wear Modeling of a Collection of Current Carrying Cantilevered Fibers Sliding against a Plane Moving Surface in a Three Dimensional Magnetic Field

This paper builds on a previously developed model which describes the electromechanical behavior of a collection of cantilevered current carrying fibers subject to sliding on a moving planar surface in a three component arbitrary magnetic field. The collection of fibers carries a transport current and an external mechanical force is applied to the sum of the fibers to keep their free ends in electrical contact with the moving surface. The fibers themselves change shape as the applied electric potential necessary to drive the current varies with conditions such as slider speed and differing magnetic field conditions. We discovered a bifurcation in the solution space of such fibers which leads to a history dependant equilibrium condition. Because the slider cuts flux, a potential gradient exists across the slider face and therefore between the fibers of the collection and circulating currents result. These currents cause individual fibers to move with, against or perpendicular to the direction of slider motion and depend on the direction of the transport current and magnetic field. Hysteresis is seen in both the Joulean heating and the contact potential necessary to drive the transport current. The present study incorporates the effects of wear into the model of the behavior of this collection of fibers. Following the results of Kuhlmann-Wilsdorf, the mechanical wear of the individual fibers varies non-linearly with their individually varying contact force. Furthermore, the anode/cathode effect (the difference in wear rate between anode and cathode fibers) was incorporated into the simulation from results of Boyer, Noel and Chaberie. The combination of these two contributions to wear results in individual fibers having different wear rates, different lengths, different contact forces and carrying different currents that all change from fiber to fiber as the collection of fibers wears over time while the sum of the transport currents and total mechanical load remains c- - onstant. Two sample cases are presented. Sample cases with negative transport current(electromagnetic body forces in the same direction as rotation) showed fibers converging smoothly to a constant wear rate over time. In sample cases with positive transport currents, (electromagnetic body forces in the opposite direction as rotation) wear rates for individual fibers exhibited unstable behavior in which wear rates of individual fibers could instantaneously increase or decrease sharply, and wear rates were higher for these cases.