Rotational Response and Slip Prediction of Serpentine Belt Drive

A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single {long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closed-form procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip. 1 Introduction The trend in automotive accessory drives has been to replace multiple V-belt drives with a single flat belt drive to power all the accessories. Such systems are termed "serpentine" belt drives and include a spring loaded tensioner, as well as multiple accessory pulleys (see Fig. 1). These systems can exhibit com­plex dynamic behavior, including rotational vibrations of the pulleys with the belt spans serving as coupling springs, and transverse belt vibrations in the various spans. The transverse vibrations of translating belts [1, 2] belongs to the broad cat­egory of systems referred to as axially moving materials. Other examples of axially moving materials include chain drives [3, 4], band saws [5, 6, 7], V-belts [8], moving threadlines [9], translating cables [10], etc. The recent literature on axially moving materials is reviewed in [11]. Several recent studies have focused on serpentine belt drive systems (see Fig. 1). Gasper etal. [12] and Hawker [13] consider longitudinal deflection of the belt and rotational vibrations of the pulleys in the analysis of free and forced response. These studies, however, do not consider the effect of the tensioner on either the equilibrium state (steady-state tensions) or the dynamic response. The influence of the tensioner on longi­tudinal belt deflection is examined by Barker et al. [14] who focus on transient response due to drive pulley acceleration. Beikmann et al. [15] develop a prototypical model (two pulleys with a tensioner) to calculate the steady-state tensions and the tensioner position as functions of steady operating conditions. Ulsoy et al. [16] consider the coupling between the transverse