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Research Papers

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

[+] Author and Article Information
Dooroo Kim, Aldo A. Ferri

Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Michael J. Leamy1

Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332michael.leamy@me.gatech.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(4), 041009 (Apr 11, 2011) (10 pages) doi:10.1115/1.4003796 History: Received May 14, 2010; Revised January 18, 2011; Published April 11, 2011; Online April 11, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Friction laws employed in flat belt drive studies

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Figure 2

Elastic/perfectly plastic spring and sliding damper representation of friction

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Figure 3

Two pulley belt drive system with system variables

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Figure 4

Friction zones for the flat belt drive: adhesion, elastic creep, and fully developed slip

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Figure 5

Real part of the first three eigenfunctions for a typical drive

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Figure 6

Friction force with Coulomb friction

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Figure 7

Friction force with EPP friction

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Figure 8

Tension with Coulomb friction

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Figure 9

Tension with EPP friction

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Figure 10

Transition and slip angle as a function of high tension TH

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Figure 11

Initial tension To as a function of the EPP spring constant kf

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Figure 12

Initial incremental strain du/ds(0) as a function of the EPP spring constant kf

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Figure 13

Detail of the initial incremental strain du/ds(0) as a function of the EPP spring constant kf

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Figure 14

Analytical and finite element predicted contact forces per unit length, kf=2.8×107 N/m2

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Figure 15

Analytical and finite element predicted contact forces per unit length, kf=2×108 N/m2

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Figure 16

Analytical and finite element predicted contact forces per unit length, kf=8.1×109 N/m2

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