A Coupled Rigid-Flexible Dynamics and Stochastic Process Model for Wear Prediction in Multi-bar Linkages

Accurately predicting wear in multi-bar linkages is essential for their long-term performance and high reliability. The progressive wear of joints often leads to a loss of kinematic precision and even catastrophic failure. However, conventional methods, which rely on deterministic models, neglect the stochastic nature of wear that arises under dynamic contact conditions. Consequently, these models may fail to accurately predict the wear process under the dynamics of rigid-flexible coupling framework. Moreover, they overlook the non-linearity of the wear degradation process. To overcome these limitations mentioned above, this paper presents an integrated wear prediction method to capture randomness and nonlinear behavior under the influence of rigid-flexible coupling dynamics. Firstly, a rigid-flexible coupling dynamic model is developed by combining screw theory with the Floating Frame of Reference Formulation. Screw theory describes the rigid-body motion and joint constraints, while the Floating Frame of Reference Formulation characterizes the elastic deformations of flexible links. Secondly, the wear model is established based on Archard's theory. The Gamma process, taking into account multiple uncertainties, is used to describe the wear degradation process under dynamic contact conditions. Thirdly, an integrated framework combining dynamic model and multiple wear degradation processes is established. Within this framework, the geometric clearance and contact characteristics of all joints are progressively updated to update the wear rate in a step-by-step manner. Finally, the effectiveness of the proposed method is demonstrated through a case study involving a spatial Revolute-Spherical-Spherical-Revolute four-bar linkage. Results demonstrate a significant improvement in wear prediction accuracy over conventional deterministic models. By capturing both the random and non-linear characteristics of degradation, the proposed method provides a reliable tool for the wear prediction of rigid-flexible coupling mechanisms.

Keywords: Rigid-flexible coupling dynamics, Joint wear prediction, Archard wear model, Gamma process, Multibar linkages.