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.