On the contact mechanics of a rolling cylinder on a graded coating. Part 1: Analytical formulation

•Fully coupled rolling contact problem for FGMs is investigated.•Analytical formulation for all possible stick/slip regimes are derived.•Singular integral equation approach is used.•Gauss–Chebyshev numerical integration method is applied.•A new numerical algorithm is proposed to solve the problem.

In this paper, the fully coupled rolling contact problem of a graded coating/substrate system under the action of a rigid cylinder is investigated. Using the singular integral equation approach, the governing equations of the rolling contact problem are constructed for all possible stick/slip regimes. Applying the Gauss–Chebyshev numerical integration method, the governing equations are converted to systems of algebraic equations. A new numerical algorithm is proposed to solve these systems of equations. Both the coupled and the uncoupled solutions to the problem are found through an implemented iterative procedure. In Part I of this paper, the analytical formulation of the rolling contact problem and the discretization of the governing equations are introduced for all assumed stick/slip regimes. A detailed discussion of the proposed numerical algorithm, the iteration procedure and the numerical results, obtained using the analytical formulation, are given in Part II.