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]

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.

Steady Motion of a Slack Belt Drive: Dynamics of a Beam in Frictional Contact With Rotating Pulleys

2020 ◽  
Vol 87 (12) ◽  
Author(s):  
Jakob Scheidl ◽  
Yury Vetyukov
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Boundary Value Problem ◽  
Contact Region ◽  
Boundary Value ◽  
Steady Motion ◽  
Steady State Solution ◽  
Belt Drive ◽  
Creep Theory ◽  
Lagrangian Finite Element

Abstract We seek the steady-state motion of a slack two-pulley belt drive with the belt modeled as an elastic, shear-deformable rod. Dynamic effects and gravity induce significant transverse deflections due to the low pre-tension. In analogy to the belt-creep theory, it is assumed that each contact region between the belt and one of the pulleys consists of a single sticking and a single sliding zone. Based on the governing equations of the rod theory, we for the first time derive the corresponding boundary value problem and integrate it numerically. Furthermore, a novel mixed Eulerian–Lagrangian finite element scheme is developed that iteratively seeks the steady-state solution. Finite element solutions are validated against semi-analytic results obtained by numerical integration of the boundary value problem. Parameter studies are conducted to examine solution dependence on the stiffness coefficients and the belt pre-tension.

Nonlinear Coupled Vibration Response of Serpentine Belt Drive Systems

1996 ◽  
Vol 118 (4) ◽  
pp. 567-574 ◽  
Author(s):  
R. S. Beikmann ◽  
N. C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Vibration Response ◽  
Belt Drive ◽  
Coupling Mechanism ◽  
Rotational Mode ◽  
Pulley System ◽  
Strongly Coupled ◽  
Nonlinear Mechanism ◽  
Serpentine Belt ◽  
Mode Characteristics ◽  
Drive Systems

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 prototypical 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 vibration response. A recent investigation demonstrates that infinitesimal belt stretching creates a linear mechanism that couples transverse belt vibration to tensioner arm rotation. Here, it is further demonstrated that finite belt stretching creates a nonlinear mechanism that may lead to strong coupling between pulley/tensioner arm rotation and transverse belt vibration, 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. These large amplitude transverse vibrations are particularly sensitive to seemingly small changes in the rotational mode characteristics.

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.

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.

Asperity Spring Friction Model With Application to Belt-Drives

2003 ◽  
Author(s):  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Coulomb Friction ◽  
Friction Model ◽  
Belt Drive ◽  
Finite Element Code ◽  
Time Step ◽  
Stick Slip ◽  
Normal Contact ◽  
Belt Drives ◽  
Coulomb Friction Model

An asperity spring friction model that uses a variable anchor point spring along with a velocity dependent force is presented. The model is incorporated in an explicit timeintegration finite element code. The friction model is used along with a penalty-based normal contact model to simulate the dynamic response of a two-pulley belt-drive system. It is shown that the present friction model accurately captures the stick-slip behavior between the belt and the pulleys using a much larger time-step than a pure velocity-dependent approximate Coulomb friction model.

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