Functionally graded coatings are used in tribology due to their ability to reduce wear and extend fatigue life. This paper models the dry/lubricated contact problem of cylindrical bodies with graded coatings as a three-dimensional axially semi-periodic problem. The frequency response functions (FRFs) are used to obtain the pressure-displacement and pressure-stress influence coefficients (ICs) for the graded layered materials. The effect of pressure from neighboring regions is considered, and the deformation and stress distributions under surface pressure are calculated using a DC-FFT algorithm modified with the summation of ICs. The Reynolds equation and Conjugate Gradient Method (CGM) are combined to establish a lubricated contact model and a dry contact model for the graded coating-substrate system. The bisection method is employed to evaluate the effects of coating stiffness, interface stiffness, and gradient index on the elastic limit load () and the initial yielding location under both elastohydrodynamic lubrication (EHL) and dry contact conditions. The findings offer practical guidelines for optimizing graded coatings to enhance tribological performance.
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