The problem of a ball bearing in normal contact between two transversely isotropic coated substrates is investigated using the finite element method (FEM). A three-dimensional finite element model is developed that accurately determines the steady friction force in low-speed bearing systems containing soft layered solid lubricant films. Extensive numerical results, which are verified using Hertzian contact theory and laboratory experiments, are obtained at 540 operating conditions by varying coating material, coating thickness, normal load, ball material, and ball radius. Friction force results generated from the FEM are normalized by introducing the dimensionless transversely isotropic coating parameter, ξ. A numerical expression for the normalized friction force in coated ball bearings is determined by curvefitting the results of the 540 simulations performed. The relevance of such an expression, as related to the durability of low-speed bearings, is subsequently ascertained and discussed.

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