Analysis of Belt-Driven Mechanics Using a Creep-Rate-Dependent Friction Law

An analysis of the frictional mechanics of a steadily rotating belt drive is carried out using a physically appropriate creep-rate-dependent friction law. Unlike in belt-drive mechanics analyzed using a Coulomb friction law, the current analysis predicts no adhesion zones in the belt-pulley contact region. Regardless of this finding, for the limiting case of a creep-rate law approaching a Coulomb law, all predicted response quantities (including the extent of belt creep on each pulley) approach those predicted by the Coulomb law analysis. Depending on a slope parameter governing the creep-rate profile, one or two sliding zones exist on each pulley, which together span the belt-pulley contact region. Closed-form expressions are obtained for the tension distribution, the sliding-zone arc magnitudes, and the frictional and normal forces per unit length exerted on the belt. A sample two-pulley belt drive is analyzed further to determine its pulley angular velocity ratio and belt-span tensions. Results from this analysis are compared to a dynamic finite element solution of the same belt drive. Excellent agreement in predicted results is found. Due to the presence of arbitrarily large system rotations and a numerically friendly friction law, the analytical solution presented herein is recommended as a convenient comparison test case for validating friction-enabled dynamic finite element schemes.

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Analysis of Belt-Drive Mechanics Using a Creep-Rate Dependent Friction Law

Volume 6B: 18th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc2001/vib-21558 ◽

2001 ◽

Author(s):

Michael J. Leamy ◽

Tamer M. Wasfy

Keyword(s):

Finite Element ◽

Creep Rate ◽

Contact Region ◽

Velocity Ratio ◽

Test Case ◽

Belt Drive ◽

Friction Law ◽

Tension Distribution ◽

Dynamic Finite Element ◽

Rate Dependent

Abstract An analysis of the frictional mechanics of a steadily rotating belt-drive is carried out using a physically-appropriate creep-rate dependent friction law. Unlike in belt-drive mechanics analyzed using a Coulomb friction law, the current analysis predicts no adhesion zones in the belt-pulley contact region, although all response quantities (including the belt creep) approach those of the Coulomb law for a steep enough creep-rate law. Depending on the slope of the profile, one or two sliding zones exist on each pulley, which together, span the belt-pulley contact region. Closed-form expressions are obtained for the tension distribution, the sliding-zone are magnitudes, and the frictional and normal forces exerted on the belt. A sample two-pulley belt-drive is analyzed further to determine its pulley angular velocity ratio and belt-span tensions. Results from this analysis are compared to a dynamic finite element solution of the same belt-drive. Excellent agreement in predicted results is found. Due to the presence of arbitrarily large system rotations and a numerically-friendly friction law, the analytical solution presented herein is recommended as a convenient comparison test case for validating friction-enabled dynamic finite element schemes.

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Transient and Steady-State Dynamic Finite Element Modeling of Belt-Drives

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1513793 ◽

2002 ◽

Vol 124 (4) ◽

pp. 575-581 ◽

Cited By ~ 46

Author(s):

Michael J. Leamy ◽

Tamer M. Wasfy

Keyword(s):

Finite Element ◽

Steady State ◽

Angular Velocity ◽

Frictional Contact ◽

Finite Element Solution ◽

Belt Drive ◽

Element Solution ◽

Dynamic Finite Element ◽

Time Accuracy ◽

Transient And Steady State

In this study, a dynamic finite element model is developed for pulley belt-drive systems and is employed to determine the transient and steady-state response of a prototypical belt-drive. The belt is modeled using standard truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulley’s angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. One-way clutch elements are modeled using a proportional torque law supporting torque transmission in a single direction. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity, and the belt span tensions. Excellent agreement is found. Transient response results for a second belt-drive example involving a one-way clutch are used to demonstrate the utility and flexibility of the finite element solution approach.

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

Journal of Applied Mechanics ◽

10.1115/1.4048317 ◽

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.

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Dynamic Modeling and Stability Analysis of Flat Belt Drives Using an Elastic/Perfectly Plastic Friction Law

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4003796 ◽

2011 ◽

Vol 133 (4) ◽

Cited By ~ 7

Author(s):

Dooroo Kim ◽

Michael J. Leamy ◽

Aldo A. Ferri

Keyword(s):

Finite Element ◽

Stability Analysis ◽

Piecewise Linear ◽

Equations Of Motion ◽

Belt Drive ◽

Equilibrium Solutions ◽

Friction Law ◽

Solution Approach ◽

Perfectly Plastic ◽

Elastic Perfectly Plastic

This paper presents an analysis of a nonlinear (piecewise linear) dynamical model governing steady operation of a flat belt drive using a physically motivated elastic/perfectly plastic (EPP) friction law. The EPP law models frictional contact as an elastic spring in series with an ideal Coulomb damper. As such, the friction magnitude depends on the stretch of the elastic belt and is integral to the solution approach. Application of the extended Hamilton’s principle, accounting for nonconservative work due to friction and mass transport at the boundaries, yields a set of piecewise linear equations of motion and accompanying boundary conditions. Equilibrium solutions to the gyroscopic boundary value problem are determined in closed form together with an expression for the minimum value of the EPP spring constant needed to transmit a given torque. Unlike equilibrium solutions obtained from a strict Coulomb law, these solutions omit adhesion zones. This finding may be important for interpreting belt drive test-stand results and the experimentally determined friction coefficients obtained from them. A local stability analysis demonstrates that the nonlinear equilibrium solutions found are stable to local perturbations. The steady dynamical operation of the drive is also studied using an in-house corotational finite element code. Comparisons of the finite-element solutions with those obtained analytically show excellent agreement.

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