Computational Issues Associated with Gear Rattle Analysis

Abstract

This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. It also outlines appropriate evaluation criteria for direct time domain integration algorithms used to solve such problems. The procedure is necessary due to the non-analytical nature of the mathematical formulation describing vibro-impacts, which can lead to numerical “stiffness” problems. The method is essentially an “intelligent” pre-processing stage and is based on our experience in simulating such systems. Important concepts such as model order reduction, gear or clutch stiffness contact ratio, appropriate choice of non-dimensionalization parameters are illustrated through examples. Several case studies of increasing complexity are solved using various well known numerical algorithms; solutions are compared qualitatively and quantitatively using the proposed evaluation criteria, and specific numerical problems are identified. Some of the simulation models have also been validated by comparing predictions with experimental data.