Interactive Modelling Strategy for Predicting the Torsional Dynamic Response of a Damper Pulley

Abstract

Damper pulleys are critical mechanical subsystems in internal combustion engines that attenuate torsional vibrations arising from cyclic combustion pressures and crankshaft torque fluctuations. Existing modelling approaches range from simple empirical or linear models to advanced numerical formulations; however, few studies systematically incorporate the combined frequency and temperature dependence of elastomer viscoelasticity with a robust experimental identification framework. The strong thermo-mechanical coupling and material nonlinearity therefore still challenge accurate prediction of torsional behaviour under realistic conditions. This study proposes an interactive and novel methodology that couples analytical modelling with experimental identification to characterise the torsional dynamic response of a damper pulley in a thermos-viscoelastic context. Key contributions are: (i) identification of the elastomer complex shear modulus by dynamic mechanical analysis across an extended temperature range; (ii) implementation of these temperature-dependent constitutive parameters in a lumped-parameter torsional vibration model incorporating inertia, stiffness, and viscoelastic damping; and (iii) an iterative calibration procedure correlating analytical predictions with modal parameters extracted from instruments impact tests performed at multiple temperatures. The closed-loop identification updates model parameters systematically until the numerical predictions and experimental measurements converge. Parametric studied quantify the influence of temperature and elastomer thickness: increasing temperature or elastomer thickness reduces the first torsional natural frequency, primarily due to a drop in storage modulus and effective torsional stiffness, whereas decreasing thickness raises the resonance frequency. Predicted and measured natural frequencies differ by less than 5% across the investigated thermal domain, demonstrating the robustness formulation. The developed framework provides a validated and original basis for thermo-viscoelastic modelling, sensitivity analysis, and structural optimisation of torsional vibration dampers under varying operating conditions.