Analysis of vibration amplification in a multi-staged clutch damper during engine start-up

Transient vibration amplifications of torsional systems passing through critical speeds have been of interest for a considerable amount of time. However, previous investigations on the piecewise linear system have focused mostly on numerical methods, and thus a reliable analytical method is not available for predicting transient amplification events. This article overcomes this void by developing and utilizing the closed-form solution of a linear single-degree-of-freedom torsional system, given a motion input under a constant acceleration rate, to approximate the transient responses of a piecewise linear system. This system represents a simplified vehicle powertrain system with a multi-staged clutch damper during the engine start-up process under an instantaneous motion input from the flywheel. First, the utility of a single-degree-of-freedom system and the motion input for the start-up process are experimentally and numerically illustrated by vehicle start-up measurements. Second, a closed-form solution of a linear damped torsional oscillator, given instantaneous-frequency excitation, is successfully developed and numerically verified. Finally, the proposed analytical solution of a linear system is utilized to predict the approximate peak-to-peak value of the displacement of a piecewise linear system during transient amplification for a rapid variation in speed.