Contact-Time and Relaxation Effects on the Normal Response of Polymer-Coated Internal Cylindrical Surfaces with Deterministic Microtexture: A Layered Viscoelastic Contact Model

Deterministic microtexture and viscoelastic coating deformation affect the normal response of polymer-coated internal cylindrical surfaces. An additive model separates statistical land roughness, deterministic Fourier displacement, and the coated-minus-bare periodic-cell increment. Half-space (HS) and finite-thickness (FT) single-asperity laws describe the same prescribed summit population for isolated imprints (class A) and a connected helical groove (class B). At 1 MPa, the relaxed texture factor exceeds the instantaneous factor for both classes, and class A exceeds class B. Across the sampled open-contact states, secant and tangent stiffness increase sublinearly with pressure; tangent stiffness exceeds secant stiffness, and relaxation reduces both. Substrate confinement lowers the class A instantaneous total normal approach from 1.626 μm in HS to 1.139 μm in FT and its instantaneous-to-relaxed increase from 3.23% to 1.27%. For both texture classes in the FT branch, the total normal approach remains below the residual texture depth at all evaluated states and nominal pressures in the range 0.1–5 MPa. Prescribed azimuthal pressure patterns retain their stiffness-spread ranking across classes and elastic endpoints. For a relaxation time of 250 μs, a fixed-location hold of 0.509 ms develops approximately 84% of the endpoint change in the hereditary FT base approach and increases the total approach by 1.07% relative to its instantaneous value. Local hereditary histories also resolve surface recovery during unloading. With component-level verification, the framework supports comparisons of texture, confinement and loading duration while identifying intercomponent coupling as a question for a fully coupled reference solution.