Physics-Driven Parameter Identification for High-Fidelity Extraction of Spindle Static Nonlinear Axial Stiffness

The nonlinear operational stiffness characteristics of machine tool spindles directly influence machining precision and bearing service life. Traditional static stiffness tests rely on direct differential operations on raw experimental load–displacement data, which are highly susceptible to measurement noise and fundamentally fail to capture accurate nonlinear features. To address this limitation, this study proposes a physics-driven parameter identification methodology to accurately extract the static nonlinear axial stiffness characteristics of spindles under static non-rotating conditions. Specifically, the smoothness priors approach (SPA) is introduced as a robust preprocessing technique to mitigate high-frequency noise while preserving the underlying low-frequency displacement trends, thereby ensuring high-fidelity feature extraction. Subsequently, a physics-dependent spindle mechanics model is directly integrated with a two-stage hybrid optimization algorithm—combining Global Search and Pattern Search—to inversely reconstruct the actual nonlinear load–displacement relationships. Numerical simulation results demonstrate that the hybrid optimization algorithm exhibits high computational accuracy, with an identification error of only 0.67% under ideal conditions and bounded parameter identification errors within 4.68% under synthetic noise levels up to 5%. Furthermore, experimental validation conducted on a position-preloaded spindle setup under initial preloads of 507 N and 862 N yields corresponding verification errors of 12.3% and 11.6%, respectively, confirming that the proposed method can effectively extract the static nonlinear stiffness features of the spindle from noisy measurements. The results demonstrate that this approach successfully overcomes the bottlenecks of conventional techniques, providing a robust and practical tool for the precise characterization of the spindle’s static nonlinear baseline stiffness. While currently validated under static non-rotating conditions, the established framework provides a fundamental baseline for extending parameter identification to dynamic operational environments in future studies.