Force–Depth–Stiffness Modeling of Rotary Ball-Burnished Dimples on an External Cylinder for Adaptive Guideway Stiffness Mapping

This study develops a theoretical and computational mechanics framework for regular dimples produced by rotary ball burnishing on an external cylindrical surface. The model combines the local quadratic ball–cylinder gap, an effective mean indentation pressure Heff, an unloading factor λ, residual dimple geometry, a Greenwood–Williamson pressure–approach law for the load-bearing lands, and an elastic spectral reference calculation. The dimple area fraction Fn is obtained from the periodic union of loaded-imprint footprints for the nominal stiffness maps, whereas the residual profile determines the specific oil capacity, defined as retained cavity volume per unit nominal area. Numerical checks include algebraic consistency, mesh-converged periodic FFT-BEM calculations, and a separate sinusoidal benchmark. For a representative 3mm ball and 25mm cylinder with Heff=2GPa, the model maps burnishing force and texture pitch to idle- and working-pressure secant stiffness. Within the stated range Fn≤0.20, the low-fidelity index preserves the ordering of all evaluated non-tied design points; the mean and maximum differences from the spectral reference are 6.6% and 15.2%. A discrete force–pitch grid yields three feasible points under illustrative stiffness windows and two candidates after non-dominated sorting and secondary selection by specific oil capacity. The selected textures reduce idle-pressure stiffness slightly more than working-pressure stiffness, increasing the nonlinearity ratio from 5.70 to 5.91. The framework provides a reproducible model-based tool for preliminary force–pitch selection; application to a specific material–process pair requires identification of Heff, λ, and the load-bearing-land response and validation against process-specific measurements.