Nonlinearity Characterization of Flexible Hinge Piezoelectric Stages Under Dynamic Preload via a Force-Dependent Prandtl–Ishlinskii Model with a Force-Analyzed Finite Element Method

The operational performance of Flexible Hinge Piezoelectric Stages (FHPSs), essential components in precision engineering, is fundamentally constrained by the inherent hysteresis of the piezoelectric actuator (PEA). A significant deficiency in prevailing characterization methods is their failure to consider the dynamic nature of the mechanical preload exerted by the flexible hinge. This position-dependent preload induces substantial deviations in the PEA’s response characteristics, thereby compromising the predictive accuracy of conventional design frameworks. To address this limitation, this paper proposes a Force-Dependent Prandtl–Ishlinskii (FPI) model that explicitly formulates the PEA’s hysteretic behavior as a function of variable preload conditions. The FPI model is subsequently integrated into a comprehensive FPI-FFEM characterization framework. Within this framework, a Force-analyzed Finite Element Method (FFEM) is utilized to compute the dynamic preload throughout the actuator’s operational stroke. This information, notably neglected in conventional FEM analysis, is essential to the fidelity of the proposed FPI model. Experimental validation demonstrates the superior fidelity of the FPI model in comparison to the traditional PI model for tracking preload-induced nonlinearities. Furthermore, the complete FPI-FFEM framework exhibits substantially enhanced prediction accuracy relative to both conventional PI-FEM and advanced LDPI-FEM methodologies, as demonstrated by a significant reduction in the Mean Absolute Error (MAE).