Effect of Eccentricity on a Clutch System Under a Harmonically Varying Normal Load
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Effect of Eccentricity on a Clutch System Under a Harmonically Varying Normal Load Yassine Driss Æ Tahar Fakhfakh Æ Mohamed Haddar
Received: 21 November 2006 / Accepted: 21 February 2007 / Published online: 8 May 2007 ASM International 2007
Abstract This paper describes a clutch model having eleven degrees of freedom and three types of nonlinearity introduced by dry friction, double-stage stiffness, and spline clearances. The Coulomb friction formulations and spline clearance functions are smoothed before they are applied to the nonlinear system. The calculation of the dynamic response of the clutch is done by the Runge Kutta method. The dynamic behavior of both a healthy clutch system and clutch system containing an eccentricity defect is compared in the time and frequency domains. The effects of a harmonically varying load on the dynamic response of the defective clutch system with nonlinear dry friction and under sinusoidal torque excitation are also reported. Keywords splines
dry friction clearance nonlinearity
Introduction Visible clearances and/or multi-valued springs lead to piecewise linear or nonlinear restoring forces (torque) that are characteristic of many machine elements or assemblies such as automotive clutches, splines, gears, and bearings. Most of these systems are generally excited by external periodic forces while under the influence of a mean force or torque. The modeling and analysis of such systems has been the subject of numerous investigations [1]. Gaillard et al. [2] propose five models of an automotive clutch with Y. Driss T. Fakhfakh M. Haddar (&) Unit Research of Mechanical Systems Dynamics, National School of Engineers, Sfax, Tunisia e-mail: [email protected]
dry friction path and study the energy dissipation per cycle for each model. However, they neglect the effect of clearance nonlinearities on the dynamic behaviour of these models. Many other investigations model clutches [2–4] and neglect the effect of the clearance nonlinearity, while some investigations [1, 5–10] have treated this type of nonlinearity. For example, Dubowsky and Freudenstrein [9, 10] modeled a single-degree-of-freedom torsional system with clearance and obtained analytical solutions by using a piecewise linear technique. Padmanabhan et al. [1] have treated the dynamics of a three-degree-of-freedom system that contain splines with nonlinear clearances, and Kim et al. [6] treated the dynamics of a torsional system containing a clearance nonlinearity and multi-stage stiffness variations using the Harmonic Balance Method (HBM). Padmanabhan et al. [11] have also treated a fourdegree-of-freedom torsional system that contains splines, backlash, and multi-stage stiffness nonlinearities. Kim et al. [12] studied the effect of smoothening the nonlinear functions on the frequency response of an oscillator with a clearance nonlinearity. They treated four types of smoothening functions and show the advantages and limitations of each. However
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