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.

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 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

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

Modal Analysis of Mechanical System Containing Nonlinear Joint

2011 ◽  
Vol 105-107 ◽  
pp. 244-249 ◽  
Author(s):  
Zdenek Poruba ◽  
Jan Szweda
Keyword(s):  
Boundary Conditions ◽  
Modal Analysis ◽  
Nonlinear Behavior ◽  
Linear Analysis ◽  
Mode Shapes ◽  
Entire System ◽  
Force Transfer ◽  
Linear Description ◽  
Real Behavior ◽  
Nonlinear Joint

The paper describes modal analysis of lifting platform usually used in theatre technologies. The platform itself consists of several components mutually connected by joints. The behavior of particular joints can be linear or nonlinear. The connection of two main parts - tables and pillars of lifting platform-must be considered as nonlinear because the force transfer between these parts can occur only in one direction. Since standard modal analysis is in principle linear, the method of linear description of nonlinear behavior has to be proposed. The contribution presents such method using application of three different boundary conditions which allow describing the nonlinear behavior of system by tools of linear analysis. Consequently, the modal analysis of the entire system is performed for all three types of boundary conditions. On the base of mode shapes visualization the proper mode shapes are extracted which satisfy the real behavior of the lifting platform.

An Exact Solution for Steady Motion of an Extensible Belt in Multipulley Belt Drive Systems

2000 ◽  
Vol 122 (3) ◽  
pp. 311-316 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Exact Solution ◽  
Compatibility Condition ◽  
Coulomb Friction ◽  
Steady Motion ◽  
Belt Drive ◽  
State Equations ◽  
Creep Theory ◽  
Pulley System ◽  
Present Solution ◽  
Drive Systems

The creep theory of multipulley belt drive systems is reexamined and the belt is modeled as an elastic extensible string. An exact solution of the nonlinear steady state equations of a string is obtained which includes, elastic extension, Coulomb friction, radial and tangential accelerations, and the power loss due to friction between the belt and the pulleys. Most importantly, the present solution uses the correct compatibility condition that ensures that the same belt is considered for all applied moments and speeds. An example of a two pulley system is considered which shows that existing approximations of the compatibility condition cause previous solutions for full slip to: underpredict the maximum transmitted moment; over predict the efficiency η; and underpredict both the low and high values of the tension. [S1050-0472(00)01503-8]

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