Trajectory-sweep inversion of normal force in precision belt grinding with load-dependent contact patch evolution

Precision abrasive belt grinding requires reliable inverse planning of path-varying normal force for deterministic material removal. The problem becomes challenging when force varies within the swept contact support, because force simultaneously changes the normal contact-stress field and the Hertzian contact-patch size. Conventional pointwise or centerline inversion relies on a local-constant assumption and may become structurally inconsistent under rapid force variation. This study proposes a trajectory-sweep forward operator (TSFO) that maps a one-dimensional normal-force trajectory to the material-removal field through a force-dependent Hertz–Preston swept contact patch. Based on TSFO, a trajectory-sweep inversion (TSI) method is developed to recover a continuous force trajectory by minimizing the full-field removal residual under the nonlinear sweep operator, while centerline explicit inversion (CEI) is constructed as a local baseline and evaluated using the same TSFO. Under ideal single-pass matched-model conditions, TSI maintains removal-map errors close to the numerical residual level. For two multi-scale targets, CEI produces map NRMSE values of 5.138% and 5.308%, whereas TSI reduces them to 0.015% and 0.012%, respectively. A sweep-scale force-gradient descriptor explains CEI residual migration into the path interior as force variation over the contact-support scale increases. The framework provides a physically consistent basis for inverse force-trajectory planning with force-dependent contact patches in abrasive belt grinding.