In this paper, research on transverse vibrations of axially moving strings and their control is thoroughly reviewed. In the last few decades, there have been extensive studies on analysis and control of transverse vibrations of axially moving strings because of the wide applications of many engineering devices that axially moving strings represent. In the investigations adopting linear models of moving strings, the paper summarizes recent studies on modal analysis, complicatedly constrained strings, coupled vibrations, and parametric vibration, as well as some early results. In the investigations adopting nonlinear models of moving strings, the paper presents the governing equations with large amplitude, and reviews progress on discretized or direct approximate analytical analyses and numerical approaches based on the Galerkin method or the finite difference method. Furthermore, investigations are reported on modeling of damping mechanisms as viscoelastic materials, coupled vibration of power transmission systems, and bifurcation and chaos. The state of the art of active control of moving strings is surveyed on controllability and observability, the Laplace transform domain analysis and the energy analysis, nonlinear vibration control and adaptive vibration control. Finally, future research directions are suggested such as nonlinear vibration of moving strings under complex constraints and couplings, energetics of nonlinear and time-varying strings, bifurcation and chaos in transverse motion of moving strings, control of hybrid systems containing moving strings, robust and adaptive controls of nonlinear moving strings, and experimental investigations. In this review article there are 242 references cited. @DOI: 10.1115/1.1849169#

Analysis and Control of Transverse Vibrations of Axially Moving Strings

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

Belt drives have long been utilized in engine applications to power accessories such as alternators, pumps, compressors and fans. Drives employing a single, flat, serpentine belt tensioned by an automatic tensioner are now common in automotive engine applications. The automatic tensioner helps maintain constant belt tension and to dissipate unwanted belt drive vibration through dry friction. The objective of this study is to predict the periodic rotational response of the entire drive to harmonic excitation from the crankshaft. To this end, a multi-degree of freedom incremental harmonic balance method (IHB) is utilized to compute periodic solutions to the nonlinear equations of motion over a wide range of engine speeds. Computed results illustrate primary and secondary resonances of the accessory drive and tensioner stick-slip motions.

Nonlinear Periodic Response of Engine Accessory Drives With Dry Friction Tensioners

Dynamics of a belt-drive system using a linear complementarity problem for the belt–pulley contact description

Pasteurization is an important, if not the most important, process step in the packaging of milk. It is subject to alterations stemming from the variation in the temperature, pH and raw milk quality. The variability may manifest itself in changes in the formation of the deposit (fouling) in the pasteurization unit, such that there is a need for tools, both instrumentation and computational, to help in monitoring the process and keeping it on the desired course. In this paper we describe a practical procedure based on artificial neural networks (ANN) that allows prediction of the deposit thickness, the overall heat transfer coefficient and the critical time (the time that the unit has to be stopped for cleaning) for reducing the impact of fouling on such processes. The procedure determines when the cleaning operation is required once the system is under critical conditions of operations. A combination of fundamental studies and plant measurements were used for study of the operating conditions and thus evaluation of the trades-offs between operating conditions and longer operating life span. The results are encouraging, enough to validate current operating industrial techniques. Copyright © 2005 Society of Chemical Industry

Estimation of fouling in a plate heat exchanger through the application of neural networks

The effects of damping on rotational vibratory solutions of a multiple pulley-flat viscoelastomeric belt system with rotary arm tensioner is developed. A complex model procedure is developed to solve both underdamped and overdamped cases. This complex modal procedure allows for future extension to include nonsymmetric rotational models, such as transverse belt vibration coupling. The modal solution enables rapid analysis over a spectrum of frequencies. Seven pulley system experimental results reported in the literature support the analytical development. Belt damping has significant vibration and belt tension amplitude effects. Tensioner spring rate and coulomb damping has minor effects.

G. W. Fan

Papers

Complex Modal Analysis of a Flat Belt Pulley System With Belt Damping and Coulomb-Damped Tensioner