Quantification of clearance-induced impulsive sources in a torsional system

The impulse response problem in a multi-degree-of-freedom torsional system with multiple clearances is examined with focus on the quantification of the source. This system is related to a vehicle driveline and a map of external transient torque excitations is defined within the operating range of an internal combustion engine. Nonlinear transient solutions are found numerically for the entire excitation map. Proposed metrics include a global metric that indicates the number and nature of impacts, metrics measured just before impact, the relative kinetic energy and relative acceleration of impacting bodies and metrics measured just after impact, initial torque rise, initial velocity rise, peak to peak acceleration and time-windowed mean-square acceleration. Phase plane analysis is applied to explain the differences between the magnitudes of impulses for impact types, illustrating that the relative acceleration between impacting bodies and the relative kinetic energy determine the impact severity. Analysis shows that the metrics measured after impact correlate well. Nonetheless, using numerical or experimental data sets for systems with multiple clearances, it is demonstrated that the windowed mean-square acceleration metric permits an 'energy' calculation with multiple impact events that could be either isolated or combined. Chief contributions of this research include better quantification and an understanding of impulsive sources that arise during rapid changes in external torque excitations. (C) 2007 Elsevier Ltd. All rights reserved.