A Novel Dynamic Modeling Framework for Flexure Mechanism-Based Piezoelectric Stick–Slip Actuators with Integrated Design Parameter Analysis

This paper presents an enhanced pseudo-rigid body model (PRBM) integrated with the LuGre friction law to analyze the dynamic behavior of flexure-hinge-based piezoelectric stick–slip actuators (PSSAs). The PRBM captures flexure compliance through Lagrangian dynamics, while Newtonian mechanics describe the piezoelectric stack and slider motion. Non-linear contact effects, including stick–slip transitions, are modeled using the LuGre formulation. A mass–spring–damper model (MSDM) is also implemented as a baseline for comparison. The models are solved in MATLAB Simulink version R2021a and validated against experimental data from a published prototype. The enhanced PRBM achieves strong agreement with experiments, with a root mean square error of 20.19%, compared to 51.65% for the MSDM. By reformulating the equations into closed-form expressions, it removes symbolic evaluations required in the standard PRBM, resulting in one to two orders of magnitude faster simulation time while preserving accuracy. Stable transient simulations are achieved at fine time steps (Δt=10−8 s). A systematic parametric study highlights preload force, flexure stiffness, friction coefficients, and tangential stiffness as dominant factors in extending the linear frequency–velocity regime. Overall, the PRBM–LuGre framework bridges the gap between computationally intensive finite element analysis and oversimplified lumped models, providing an accurate and efficient tool for design-oriented optimization of compliant piezoelectric actuators.