Dynamic analysis for mechanical system with clearance joint considering dependent interval parameters

Uncertainties caused by measuring errors or incomplete knowledge affect the dynamic response and functional reliability of the mechanical system, particularly for the mechanisms with clearance joints. Considering that dependency between the interval parameters in the uncertain quantification of mechanical systems with clearance joints is prone to be ignored, in this article, a dynamic analysis procedure considering the correlation between interval parameters is presented. Firstly, the continuous contact force model and modified friction force model are embedded into the deterministic dynamic governing equations of the mechanical system with clearance joints derived by the Lagrangian method. To characterize the correlation between interval uncertainties, the convex ellipsoid model is employed, and a Chebyshev-based convex scanning method is developed to obtain the bounds of dynamic response. Finally, a robot manipulator with clearance joint considering dependent uncertainties is illustrated as an example to investigate the clearance effect and correlations between uncertainties on the dynamic behavior. In the numerical simulation, the geometrical parameters of the manipulator arm are regarded as dependent interval parameters. The results show that the dependence between interval uncertainties induces relatively conservative bounds and should be considered carefully in the case of a large clearance size existing in the mechanical system.