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.

Mechanics and Sliding Friction in Belt Drives With Pulley Grooves

2005 ◽  
Vol 128 (2) ◽  
pp. 494-502 ◽  
Author(s):  
Lingyuan Kong ◽  
Robert G. Parker
Keyword(s):  
System Analysis ◽  
Sliding Friction ◽  
General Purpose ◽  
Computational Technique ◽  
Belt Drive ◽  
Friction Forces ◽  
Belt Drives ◽  
Contact Points ◽  
Torque Loss ◽  
Axially Moving

The steady mechanics of a two-pulley belt drive system are examined where the pulley grooves, belt extension and wedging in the grooves, and the associated friction are considered. The belt is modeled as an axially moving string with the tangential and normal accelerations incorporated. The pulley grooves generate two-dimensional radial and tangential friction forces whose undetermined direction depends on the relative speed between belt and pulley along the contact arc. Different from single-pulley analyses, the entry and exit points between the belt spans and pulleys must be determined in the analysis due to the belt radial penetration into the pulley grooves and the coupling of the driver and driven pulley solutions. A new computational technique is developed to find the steady mechanics of a V-belt drive. This allows system analysis, such as speed/torque loss and maximum tension ratio. The governing boundary value problem (BVP) with undetermined boundaries is converted to a fixed boundary form solvable by a general-purpose BVP solver. Compared to flat belt drives or models that neglect radial friction, significant differences in the steady belt-pulley mechanics arise in terms of belt radial penetration, free span contact points, tension, friction, and speed variations.

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.

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.

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.

Steady-State Responses of Pulley-Belt Systems With a One-Way Clutch and Belt Bending Stiffness

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Hu Ding ◽  
Jean W. Zu
Keyword(s):  
Time Series ◽  
Steady State ◽  
Differential Equations ◽  
Dynamic Model ◽  
Time Discretization ◽  
Bending Stiffness ◽  
Response Curves ◽  
Axially Moving ◽  
The One ◽  
Belt System

A nonlinear hybrid discrete-continuous dynamic model is established to analyze the steady-state response of a pulley-belt system with a one-way clutch and belt bending stiffness. For the first time, the translating belt spans in pulley-belt systems coupled with one-way clutches are modeled as axially moving viscoelastic beams. Moreover, the model considers the rotations of the driving pulley, the driven pulley, and the accessory. The differential quadrature and integral quadrature methods are developed for space discretization of the nonlinear integropartial-differential equations in the dynamic model. Furthermore, the four-stage Runge–Kutta algorithm is employed for time discretization of the nonlinear piecewise ordinary differential equations. The time series are numerically calculated for the driven pulley, the accessory, and the translating belt spans. Based on the time series, the fast Fourier transform is used for obtaining the natural frequencies of the nonlinear vibration. The torque-transmitting directional behavior of the one-way clutch is revealed by the steady-state of the clutch torque in the primary resonances. The frequency-response curves of the translating belt, the driven pulley, and the accessory show that the one-way clutch reduces the resonance of the pulley-belt system. Furthermore, the belt cross section's aspect ratio significantly affects the dynamic response.

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.

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

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.

Elastic creep in serpentine belt drives and adopting a suitable strain measure

2004 ◽  
Vol 218 (12) ◽  
pp. 1421-1433 ◽  
Author(s):  
M Schulz
Keyword(s):  
Mass Conservation ◽  
Logarithmic Strain ◽  
Linear Strain ◽  
Strain Measure ◽  
Creep Theory ◽  
Hooke’S Law ◽  
Belt Drives ◽  
Serpentine Belt ◽  
Hooke's Law ◽  
System Equations

The paper deals with the transient dynamics of serpentine belt drives. A model for the rotational motion that has been proposed in the literature is extended to elastic belt creep. However, unlike previous articles, this paper adopts a logarithmic strain measure to describe elastic creep. A condition for the existence of steady state motions with constant belt tensions, as a solution of the mass conservation law, is derived. This condition is violated for the linear strain measure together with Hooke's law, whereas it holds for the logarithmic strain measure. As a consequence, only the logarithmic strain measure, together with Hooke's law, leads to system equations that cover steady operating states. In the case of linear strain, belt tensions and tensioner position do not converge towards constant values when choosing a set of external torques that balance each other out. This is illustrated by two numerical examples. Furthermore, the considerations are reinforced and anchored in the automotive field by analysing the transient belt drive behaviour during a ‘revving-up’ manoeuvre of a common rail diesel engine. The considerations are generally applicable, not only to the classical elastic creep theory but also to any other, more sophisticated theory.

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