Equilibrium and Belt-Pulley Vibration Coupling in Serpentine Belt Drives

2003 ◽  
Vol 70 (5) ◽  
pp. 739-750 ◽  
Author(s):  
L. Kong ◽  
R. G. Parker
Keyword(s):  
Linear Span ◽  
Bending Stiffness ◽  
Computational Method ◽  
Equilibrium Equations ◽  
Belt Drives ◽  
Design Variables ◽  
Serpentine Belt ◽  
String Models ◽  
Problem Solvers ◽  
Vibration Coupling

Serpentine belt drives with spring-loaded tensioners are now widely used in the automotive industry. Experimental measurements show that linear system vibration coupling exists between the pulley rotations and the transverse span deflections. Former models that treat the belt as a string and neglect the belt bending stiffness cannot explain this coupling phenomenon. In this paper, a new serpentine belt system model incorporating the belt bending stiffness is established. The finite belt bending stiffness causes nontrivial transverse span equilibria, in contrast to string models with straight span equilibria. Nontrivial span equilibria cause linear span-pulley coupling, and the degree of coupling is determined by the equilibrium curvatures. A computational method based on boundary value problem solvers is developed to obtain the numerically exact solution of the nonlinear equilibrium equations. An approximate analytical solution of closed-form is also obtained for the case of small bending stiffness. Based on these solutions, the effects of design variables on the equilibrium deflections and span-pulley coupling are investigated.

Coupled Belt-Pulley Vibration in Serpentine Drives With Belt Bending Stiffness

2004 ◽  
Vol 71 (1) ◽  
pp. 109-119 ◽  
Author(s):  
Lingyuan Kong ◽  
Robert G. Parker
Keyword(s):  
Eigenvalue Problems ◽  
String Model ◽  
Bending Stiffness ◽  
Vibration Modes ◽  
Discrete Eigenvalue ◽  
Belt Drives ◽  
Design Variables ◽  
Moving Beam ◽  
Serpentine Belt ◽  
String Models

A method is developed to evaluate the natural frequencies and vibration modes of serpentine belt drives where the belt is modeled as a moving beam with bending stiffness. Inclusion of bending stiffness leads to belt-pulley coupling not captured in moving string models. New dynamic characteristics of the system induced by belt bending stiffness are investigated. The belt-pulley coupling is studied through the evolution of the vibration modes. When the belt-pulley coupling is strong, the dynamic behavior of the system is quite different from that of the string model where there is no such coupling. The effects of major design variables on the system are discussed. The spatial discretization can be used to solve other hybrid continuous/discrete eigenvalue problems.

Coupled Belt-Pulley Vibration in Serpentine Drives With Belt Bending Stiffness

2003 ◽  
Author(s):  
Lingyuan Kong ◽  
Robert G. Parker
Keyword(s):  
Eigenvalue Problems ◽  
String Model ◽  
Bending Stiffness ◽  
Vibration Modes ◽  
Discrete Eigenvalue ◽  
Belt Drives ◽  
Design Variables ◽  
Moving Beam ◽  
Serpentine Belt ◽  
String Models

A method is developed to evaluate the natural frequencies and vibration modes of serpentine belt drives where the belt is modeled as a moving beam with bending stiffness. Inclusion of bending stiffness leads to belt-pulley coupling not captured in moving string models. New dynamic characteristics of the system induced by the belt bending stiffness are investigated. The belt-pulley coupling is studied through the evolution of the vibration modes. When the belt-pulley coupling is strong, the dynamic behavior of the system is quite different from that of the string model where there is no such coupling. The effects of major design variables on the system are discussed. The spatial discretization can be used to solve other hybrid continuous/discrete eigenvalue problems.

Mechanics of Serpentine Belt Drives with Tensioner Assemblies and Belt Bending Stiffness

2004 ◽  
Vol 127 (5) ◽  
pp. 957-966 ◽  
Author(s):  
Lingyuan Kong ◽  
Robert G. Parker
Keyword(s):  
Steady State ◽  
A Priori ◽  
Bending Stiffness ◽  
Belt Drive ◽  
Creep Theory ◽  
Factors Affecting ◽  
Belt Drives ◽  
Contact Points ◽  
Serpentine Belt ◽  
Axially Moving

Steady state analysis is conducted on a multipulley serpentine belt drive with a spring-loaded tensioner assembly. Classical creep theory is extended to incorporate belt bending stiffness as well as the belt stretching and centripetal accelerations. The belt is modeled as an axially moving Euler–Bernoulli beam with nonuniform speed due to belt extensibility and variation of belt tension. The geometry of the belt-pulley contact zones and the corresponding belt tension and friction distributions are the main factors affecting belt slip. Bending stiffness introduces nontrivial span deflections, reduces the wrap angles, and makes the belt-pulley contact points unknown a priori. The free span boundary value problems (BVP) with undetermined boundaries are transformed to a fixed boundary form. A two-loop iteration method, necessitated by the tensioner assembly, is developed to find the system steady state. The effects of system parameters on serpentine drive behavior are explored in the context of an actual automotive belt drive.

Optimization of Twin Tensioner Performance in a Belt-Driven Integrated Starter-Generator System for Micro-Hybrids

2009 ◽  
Author(s):  
Adebukola Olatunde ◽  
J. W. Zu
Keyword(s):  
Sequential Quadratic Programming ◽  
Equation Of Motion ◽  
Optimized Design ◽  
Original Design ◽  
Generator System ◽  
Belt Drives ◽  
Design Variables ◽  
Serpentine Belt ◽  
Hybrid Transmission ◽  
Starter Generator

The objective of this paper is to optimize the belt tensioning mechanism, known as the Twin Tensioner. The optimized tensioner achieves the minimum magnitude of belt tension in a Belt-driven Integrated Starter-generator (B-ISG) system. The B-ISG is an emerging hybrid transmission that closely resembles conventional serpentine belt drives. The system contains an integrated starter-generator (ISG) unit that performs a start-stop function on the engine. A derivation of the system’s equation of motion is simulated in this paper. A parametric study evaluates the Twin Tensioner’s parameters with respect to their impact on static tensions. Design variables are selected from these parameters for optimization. The optimization uses the genetic algorithm (GA) and the sequential quadratic programming (SQP) searches. Computations for belt tension based on the optimized design variables indicate the optimal system contains spans with static tensions that are significantly lower in magnitude than in the original design.

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.

A Study on Jumping Characteristics in Synchronous Belt Drives

2000 ◽  
Author(s):  
Tomio Koyama ◽  
Weiming Zhang ◽  
Masanori Kagotani
Keyword(s):  
Empirical Formula ◽  
Bending Stiffness ◽  
Belt Drives ◽  
Tensile Stiffness

Abstract The jumping characteristics at the driven pulley of synchronous belt drives are experimentally discussed. The jumping of synchronous belt occurs when the elongation of free span of the belt is over than a certain value. In this paper, an empirical formula for the jumping torque of L type synchronous belt is presented. The following parameters are considered in the empirical formula: tensile stiffness of belt, height of belt tooth, coefficient of traction, belt installation tension, wrapping angle of belt, diameter of pulley pitch circle, bending stiffness of shaft.

Complex modal analysis of serpentine belt drives based on beam coupling model

2017 ◽  
Vol 116 ◽  
pp. 162-177 ◽  
Author(s):  
Yue Pan ◽  
Xiandong Liu ◽  
Yingchun Shan ◽  
Gang(Sheng) Chen
Keyword(s):  
Modal Analysis ◽  
Coupling Model ◽  
Belt Drives ◽  
Beam Coupling ◽  
Serpentine Belt ◽  
Complex Modal Analysis ◽  
Complex Modal

A Coupled Two Degree of Freedom Model for Nano/Micromirrors Under van der Waals Force

2012 ◽  
Author(s):  
Hamid Moeenfard ◽  
Ali Darvishian ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Coupled Model ◽  
Bending Stiffness ◽  
Degree Of Freedom ◽  
Instability Mode ◽  
Equilibrium Equations ◽  
Bending Mode ◽  
Minimum Potential ◽  
Vdw Force ◽  
Torsion Stiffness ◽  
Two Degree Of Freedom

The current paper presents a two degree of freedom model for the problem of nano/micromirrors under the effect of vdW force. Energy method, the principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the nano/micromirror. Then using the implicit function theorem, a coupled bending-torsion model is presented for the pull-in characteristics of nano/micromirrors under vdW force and the concept of instability mode is introduced. It is observed that with increasing the ratio of the bending stiffness to the torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. It is shown that when the bending stiffness of the system is relatively low, the equilibrium point of a one degree of freedom torsion model considerably deviates from that of coupled model. The presented model in this paper can be used for safe and stable design of nano/micromirrors under vdW force.

Piece-wise linear dynamic analysis of serpentine belt drives with a one-way clutch

2008 ◽  
Vol 222 (7) ◽  
pp. 1165-1176 ◽  
Author(s):  
F Zhu ◽  
R G Parker
Keyword(s):  
Relative Velocity ◽  
Power Transmission ◽  
Design Guidelines ◽  
Computational Time ◽  
System Response ◽  
Dynamic Tension ◽  
Belt Drives ◽  
Serpentine Belt ◽  
The One ◽  
Clutch Torque

A prototypical three-pulley serpentine belt drive with belt bending stiffness is extended to include a one-way clutch in order to understand the non-linear dynamics of the system with the one-way clutch performance. The clutch is modelled based on the relative velocity of the driven pulley and its accessory. The clutch locks (engages) the pulley and accessory for zero relative velocity and produces a positive inner clutch torque. Zero clutch torque initiates clutch disengagement, allowing unequal velocities of the two components. This model leads to a piece-wise linear system. The transition matrix is used to evaluate the system response in discrete time series for the two linear configurations, saving significant computational time. The system dynamics including response and dynamic tension drop are examined for varying excitation frequencies, inertia ratio of the pulley and accessory, and external load. The investigation of vibration reduction because of the single-direction power transmission of the clutch provides design guidelines in practice.

Dynamic behaviour of V-belt drive system in the presence of sheaves’ lateral misalignment

2008 ◽  
Vol 222 (9) ◽  
pp. 1673-1679
Author(s):  
S Fenina ◽  
T Fakhfakh ◽  
M Haddar
Keyword(s):  
Dynamic Behaviour ◽  
Continuous Model ◽  
Operating Conditions ◽  
Drive System ◽  
Transverse Motion ◽  
Belt Drive ◽  
Continuous Variables ◽  
System A ◽  
Design Variables ◽  
Serpentine Belt

This paper presents the effects of lateral misalignment of sheaves, on the transverse span displacements of a serpentine belt drive system that contains a driving sheave, a driven sheave, a belt, and a dynamic tensioner. This defect gives rise to dangerous operating conditions for the system. A hybrid discrete—continuous model is adopted, in which the coupling between the discrete variables describing the rotational motion of the three sheaves and the tensioner arm and the continuous variables describing the transverse motion of the belt spans is taken into account. An analytical method based on the perturbation method is used to determine the explicit expressions of the transverse span displacements and permits the study of the effects of design variables on the dynamic behaviour of the system in the presence of the defect described earlier.

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