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

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 closedform 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.

Rotational response and slip prediction of serpentine belt drive systems

The vibration of an automotive serpentine belt drive system greatly affects the perceived quality and the reliability of the system. Accessory drives with unfavorable vibration characteristics transmit excessive noise and vibration to other vehicle structures, to the vehicle occupants, and may also promote the fatigue and failure of system components. Moreover, these characteristics are a consequence of decisions made early on in the design and arrangement of the accessory drive system. The present paper focuses on fundamental modeling issues that are central to predicting accessory drive vibration. To this end, a prototypical drive is evaluated, which is composed of a driven pulley, a driving pulley, and a dynamic tensioner. The coupled equations of free response governing the discrete and continuous elements are presented herein. A closed-form solution method is used to evaluate the natural frequencies and modeshapes. Attention focuses on a key linear mechanism that couples tensioner arm rotation and transverse vibration of the adjacent belt spans. Modal tests on an experimental drive confirm the theoretical predictions.

Free Vibration of Serpentine Belt Drive Systems

In this study, a dynamic finite element model is developed for pulley belt-drive systems and is employed to determine the transient and steady-state response of a prototypical belt-drive. The belt is modeled using standard truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulley's angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. One-way clutch elements are modeled using a proportional torque law supporting torque transmission in a single direction. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity and the belt span tensions. Excellent agreement is found. Transient response results for a second belt-drive example involving a one-way clutch are used to demonstrate the utility and flexibility of the finite element solution approach.

Transient and Steady-State Dynamic Finite Element Modeling of Belt-Drives

Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning

Dynamic Analysis of Belt Drive Tension Forces During Rapid Engine Acceleration

Rubber hyperelasticity is characterized by a strain energy function. The strain energy functions fall primarily into two categories: one based on statistical thermodynamics, the other based on the phenomenological approach of treating the material as a continuum. This work is focused on the phenomenological approach. To determine the constants in the strain energy function by this method, curve fitting of rubber test data is required. A review of the available strain energy functions based on the phenomenological approach shows that it requires much effort to obtain a curve fitting with good accuracy. To overcome this problem, a novel method of defining rubber strain energy function by Feedforward Backpropagation Neural Network is presented. The calculation of strain energy and its derivatives by neural network is explained in detail. The preparation of the neural network training data from rubber test data is described. Curve fitting results are given to show the effectiveness and accuracy of th...

Neural Network Based Constitutive Model for Rubber Material

A tensioner (14, 114) for an endless power transmission belt, the belt (12) being driven about a sheave. The tensioner may comprise a base (22, 122), a resilient device (46, 146), and first and second arms (24, 26; 124, 126) pivotally coupled for movement in an opened and a closed direction. The tensioner (14, 114) may also comprise first and second pulleys (25, 27; 125, 127) rotably coupled to the and second arms (24, 26; 124, 126), the resilient device (46, 146) biasing the arms in the closed direction in which the first and second pulleys (25, 27; 125, 127) apply tension to the belt (12). The tensioner (14, 114) may also comprise first and second stops (28, 30; 128, 130) positioned outside the arms on the base (22, 122) to limit the movement of the arms in the open direction in response to an increase in tension in the belt.

Adaptive belt tensioner system for control of reversible torque load pulley

A tensioner for generating tension in a power-transmitting belt (12, 12A, 112, 112A) is provided. The tensioner includes a base (22, 22A, 122, 122A), which may be secured to an engine (10, 10A, 110, 11 OA), and an arm (24, 24A, 124, 125, 124A, 125A) that is movably attached to the base. A pulley (26, 26A, 126, 127, 126A, 127A) is rotatably attached to the arm for engaging the belt. A spring (28, 28A, 128, 128A) is operatively connected to the arm (24, 24A, 124, 125, 124A, 125A) and the base (22, 22A, 122, 122A) for urging the arm to move relative to the base in a first direction. When the arm is moved in the first direction, the pulley (26, 26A, 126, 127, 126A, 127A) is moved into engagement with the belt (12, 12A, 112, 112A) with a force to tension the belt. The tensioner (114, 14A, 114, 114A) further includes a stop (30, 30A, 130, 131, 130A, 131A) that is adjustably positioned on the base (22, 22A, 122, 122A) to limit the movement of the arm (24, 24A, 124, 125, 124A, 125) in a second direction. The position of the stop (30, 30A, 130, 131, 130A, 131A) on the base may be automatically adjusted by the spring (28, 28A, 128, 128A) during installation of the tensioner.

Belt tensioner having an automatically adjustable travel stop

As a part of developing automotive fuel vapor emission control, a two dimensional, time-accurate simulation capability for adsorption/desorption in a carbon canister has been developed. Dubinin-Polanyi adsorption potential model has been used for n-butane (a surrogate for gasoline vapor) adsorption at ambient pressure on activated carbon adsorbent of Westvaco product BAX 950, and nitrogen was chosen as the carrier gas. Linear driving force model is used for heat and mass transfer rates. The impacts of different n-butane concentration on the adsorption phenomena and different initial carbon bed equilibrium adsorption states on desorption phenomena are studied. Results such as adsorption breakthrough curve, desorption curve, adsorption amount, n-butane mole fraction and temperature profiles are provided. Comparisons with results from previous work are made to verify the current model.

Larry R. Oliver

Papers

Dynamic Analysis of Belt Drive Tension Forces During Rapid Engine Acceleration

Neural Network Based Constitutive Model for Rubber Material

Adaptive belt tensioner system for control of reversible torque load pulley

Belt tensioner having an automatically adjustable travel stop

Modeling and Simulation of N-Butane Adsorption/Desorption in a Carbon Canister