MODAL ANALYSIS OF SERPENTINE BELT DRIVE SYSTEMS

1999 ◽  
Vol 222 (2) ◽  
pp. 259-279 ◽  
Author(s):  
L. Zhang ◽  
J.W. Zu
Keyword(s):  
Modal Analysis ◽  
Belt Drive ◽  
Serpentine Belt ◽  
Drive Systems

Complex Modal Analysis of Non-Self-Adjoint Hybrid Serpentine Belt Drive Systems

2000 ◽  
Vol 123 (2) ◽  
pp. 150-156 ◽  
Author(s):  
Lixin Zhang ◽  
Jean W. Zu ◽  
Zhichao Hou
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mode Shapes ◽  
Belt Drive ◽  
Serpentine Belt ◽  
Complex Modal Analysis ◽  
Drive Systems ◽  
Complex Modal

A linear damped hybrid (continuous/discrete components) model is developed in this paper to characterize the dynamic behavior of serpentine belt drive systems. Both internal material damping and external tensioner arm damping are considered. The complex modal analysis method is developed to perform dynamic analysis of linear non-self-adjoint hybrid serpentine belt-drive systems. The adjoint eigenfunctions are acquired in terms of the mode shapes of an auxiliary hybrid system. The closed-form characteristic equation of eigenvalues and the exact closed-form solution for dynamic response of the non-self-adjoint hybrid model are obtained. Numerical simulations are performed to demonstrate the method of analysis. It is shown that there exists an optimum damping value for each vibration mode at which vibration decays the fastest.

Modal Analysis in Coupled Vibration of Serpentine Belt Drive System

2000 ◽  
Author(s):  
Jean W. Zu ◽  
Lixin Zhang
Keyword(s):  
Exact Solution ◽  
Modal Analysis ◽  
Eigenfunction Expansion ◽  
Linear Analysis ◽  
The Other ◽  
Belt Drive ◽  
Entire System ◽  
Coupled Vibration ◽  
Serpentine Belt ◽  
Drive Systems

Abstract The modal analysis of linear prototypical serpentine belt drive systems is performed in this study. The entire system is divided into two subsystems: one with a single belt and its motion is not coupled to the rest of the system in the linear analysis; the other with the remaining components. The explicit exact characteristic equation for eigenvalues is derived, which does not use the iteration approach. The response of serpentine belt drive systems to arbitrary excitations is obtained as a superposition of orthogonal eigenfunctions. The exact solution without using eigenfunction expansion is derived when the excitations are non-resonance harmonic.

Dynamic Modeling of Belt Drive Systems: Effects of the Shear Deformations

2006 ◽  
Vol 128 (5) ◽  
pp. 555-567 ◽  
Author(s):  
Andrea Tonoli ◽  
Nicola Amati ◽  
Enrico Zenerino
Keyword(s):  
Belt Drive ◽  
Automotive Applications ◽  
Axial Deformation ◽  
Shear Deformations ◽  
Viscous Term ◽  
Rubber Layer ◽  
Belt Drives ◽  
Serpentine Belt ◽  
In Series ◽  
Drive Systems

Multiribbed serpentine belt drive systems are widely adopted in accessory drive automotive applications due to the better performances relative to the flat or V-belt drives. Nevertheless, they can generate unwanted noise and vibration which may affect the correct functionality and the fatigue life of the belt and of the other components of the transmission. The aim of the paper is to analyze the effect of the shear deflection in the rubber layer between the pulley and the belt fibers on the rotational dynamic behavior of the transmission. To this end the Firbank’s model has been extended to cover the case of small amplitude vibrations about mean rotational speeds. The model evidences that the shear deflection can be accounted for by an elastic term reacting to the torsional oscillations in series with a viscous term that dominates at constant speed. In addition, the axial deformation of the belt spans are taken into account. The numerical model has been validated by the comparison with the experimental results obtained on an accessory drive transmission including two pulleys and an automatic tensioner. The results show that the first rotational modes of the system are dominated by the shear deflection of the belt.

Design and Analysis of Automotive Serpentine Belt Drive Systems for Steady State Performance

1997 ◽  
Vol 119 (2) ◽  
pp. 162-168 ◽  
Author(s):  
R. S. Beikmann ◽  
N. C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Belt Drive ◽  
Automotive Engine ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems

Serpentine belt drive systems with spring-loaded tensioners are now widely used in automotive engine accessory drive design. The steady state tension in each belt span is a major factor affecting belt slip and vibration. These tensions are determined by the accessory loads, the accessory drive geometry, and the tensioner properties. This paper focuses on the design parameters that determine how effectively the tensioner maintains a constant tractive belt tension, despite belt stretch due to accessory loads and belt speed. A nonlinear model predicting the operating state of the belt/tensioner system is derived, and solved using (1) numerical, and (2) approximate, closed-form methods. Inspection of the closed-form solution reveals a single design parameter, referred to as the “tensioner constant,” that measures the effectiveness of the tensioner. Tension measurements on an experimental drive system confirm the theoretical predictions.

Predictive Fatigue Model for Serpentine Belt Drive Systems

2006 ◽  
Author(s):  
S. Saikrishna ◽  
G. Liang ◽  
K. Chandrashekhara ◽  
L. R. Oliver ◽  
S. G. Holmes
Keyword(s):  
Belt Drive ◽  
Fatigue Model ◽  
Serpentine Belt ◽  
Drive Systems

Nonlinear Coupled Response of Serpentine Belt Drive Systems

1993 ◽  
Author(s):  
R. S. Beikmann ◽  
Noel C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Internal Resonance ◽  
Belt Drive ◽  
Coupling Mechanism ◽  
Nonlinear Coupling ◽  
Pulley System ◽  
Strongly Coupled ◽  
Nonlinear Mechanism ◽  
Serpentine Belt ◽  
Coupled Response ◽  
Drive Systems

Abstract This theoretical and experimental study identifies a key nonlinear mechanism that promotes strongly coupled dynamics of serpentine belt drive systems. Attention is focused on a prototype three-pulley system that contains the essential features of automotive serpentine drives having automatic (spring-loaded) tensioners. A theoretical model is presented that describes pulley and tensioner arm rotations, and longitudinal and transverse belt response. A recent investigation demonstrates that infinitesimal belt stretching creates a linear mechanism that couples transverse belt response to tensioner arm rotation. Here, it is further demonstrated that finite belt stretching creates a nonlinear mechanism that may lead to strongly coupled response in the presence of an internal resonance. Theoretical and experimental results confirm the existence of this nonlinear coupling mechanism. In particular, it is shown that very large transverse belt vibrations can result from small resonant torque pulses applied to the crankshaft or accessory pulleys.

Free Vibration of Serpentine Belt Drive Systems

1996 ◽  
Vol 118 (3) ◽  
pp. 406-413 ◽  
Author(s):  
R. S. Beikmann ◽  
N. C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Drive System ◽  
Belt Drive ◽  
Free Response ◽  
Coupled Equations ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems ◽  
Excessive Noise

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.

Rotational Response and Slip Prediction of Serpentine Belt Drive Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 71-78 ◽  
Author(s):  
S.-J. Hwang ◽  
N. C. Perkins ◽  
A. G. Ulsoy ◽  
R. J. Meckstroth
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Equilibrium Analysis ◽  
Belt Drive ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems ◽  
Nonlinear Equations Of Motion ◽  
Rotational Response

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.

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