A Continuous Analysis Method for Planar Multibody Systems with Joint Clearance

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Abstract

Clearance from manufacturing tolerances or wear is likely to degrade the dynamic performance of connected machine parts. When joint clearance is introduced, the dynamic response of the mechanical system is substantially changed, seen as high acceleration and force peaks and dissipation of energy. Looking at contact models, the simpler ones, such as the linear Kelvin–Voigt or the nonlinear Hertz model, are characterized by a set of parameters. These include material parameters, coefficient of restitution and possibly a coefficient of friction. The analysis models can be divided into two groups – continuous and dis-continuous, related to whether integration is carried out through the period of contact, or stopped and restarted after the impact.

Based on the equations of motion for a multibody system of rigid bodies, it is suggested that the continuous analysis approach is combined with a contact force model to describe joint clearance in rotational joints. Performing simulations with this methodology allows not only to quantify the overall mechanism behaviour, but also in-depth analysis of the impact mechanics in the clearance joint. Experimental data from a double pendulum impacting a rigid plate is used to verify the suggested continuous analysis method.

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