The electric and thermal fields within a metal graphite brush in sliding electrical contact with a fast moving rotor are simulated. The composite nature of the brush, a carbon graphite matrix with randomly distributed metal (silver) particles, is treated via finite elements in an inner zone about the brush-rotor contact, and composite mixture theory in an outer zone away from the contact. In the inner zone, individual elements are randomly assigned metal or carbon properties in a manner consistent with the volume fraction. Computations are three dimensional. Electrical and frictional heatings are considered. Simulations of thermal and electric fields are performed over ten different specific distributions of metal particles; averages are then taken over this ten-member ensemble. Simulation results indicate and verify the existence of a critical volume fraction of silver for good brush performance. At this critical volume fraction, individual silver particles link into networks and encourage efficient transfer of electrically and frictionally generated heat away from the contact region. Temperatures remain moderate with this critical volume fraction (even at extreme heatings), and a hot zone does not form.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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