From Rotary Burnishing Parameters to Joint Stiffness: A Two-Level Model for Surfaces with Regular Dimples

Normal contact stiffness is a key property of mechanical surface joints because it governs load transfer, local approach, vibration response, and positioning stability. Rotary burnishing can generate regular dimple patterns without superimposed tool vibration; however, existing process models mainly describe texture geometry and surface-layer modification rather than the mapping from burnishing parameters to normal joint stiffness. This paper develops a two-level semi-analytical model that couples deterministic dimple geometry and load redistribution with a Greenwood–Williamson-type response of the load-bearing land. The main geometrical and contact contributions are expressed explicitly, whereas the spectral summation, micro-roughness quadrature, and nonlinear closure are evaluated numerically. The process parameters define the nominal unit-cell geometry, whereas the residual dimple dimensions and measured post-burnishing descriptors are post-burnishing inputs. Published data for related regular microreliefs are used to benchmark the predicted trends and order of magnitude. For the reference regime, the explicit spectral displacement remains below 1% of the micro-roughness contribution. Periodic BEM predicts an additional approach 14–15% lower than the analytical term, while pressure heterogeneity changes the averaged micro-roughness approach by less than 1.7%. The model is also used for sensitivity analysis and inverse design of rotary-burnishing parameters to generate design maps for preliminary process selection. Within the stated validity domain, the model serves as a fast screening tool for the stabilized repeated-loading stiffness of dimpled joints.