Sensitivity Analysis for Optimal Design of Multibody Systems with Clearance Joint

This paper deals with the sensitivity analysis and optimization of system parameters for a classical slider-crank mechanism as a multibody system which includes a clearance between the joints of coupler and slider. Due to the nonlinearity involved in the dynamics of clearance joints, the base reaction force, exerted on the base from the crank, changes roughly and does not vary as smooth as the case of the mechanism with ideal joint. Variation of the base reaction force can be a measure of the undesired vibrations induced due to the effect of clearance joint. After deriving the equations of motion and modeling the clearance, the direct differentiation method is used to conduct a local sensitivity analysis to assess the sensitivity measure of the base reaction force on some kinematic and contact parameters. The results show that the reaction force is more sensitive to the variation of link lengths and link masses compared to the variation of contact surface characteristics such as Young’s modulus, restitution coefficient and contact generalized stiffness in most parts of the motion cycle. On the other hand, the sensitivity of the base reaction force to the clearance size is very higher than its sensitivity to the above-mentioned kinematic and contact properties. Finally, based on the results of the sensitivity analysis, an optimization procedure is used to reduce the amount of the maximum base reaction force by choosing the optimized link lengths.