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TECHNICAL PAPERS

# On a Perturbation Method for the Analysis of Unsteady Belt-Drive Operation

[+] Author and Article Information
Michael J. Leamy

Advanced Science and Automation, Smithfield, VA 23430michael.leamy@ascience.com

This statement would be exactly true if $ωDN$ was constant.

J. Appl. Mech 72(4), 570-580 (Oct 29, 2004) (11 pages) doi:10.1115/1.1940660 History: Received November 04, 2003; Revised October 29, 2004

## Abstract

A perturbation method is presented for use in analyzing unsteady belt-drive operation. The method relies on the important assumption that for operating states close to steady operation, the friction state (i.e., whether the belt is creeping or sticking at any location on the pulley) is similar to that of the well-known steady solution in which a lone stick arc precedes a lone slip arc (Johnson, K. L., 1985, Contact Mechanics, Cambridge U.P., London, Chap. 8; Smith, D. P., 1999, Tribol. Int., 31(8), pp. 465–477). This assumption, however, is not used to determine the friction force distribution, and, in fact, the friction forces in the stick zone are found to be nonzero, in direct contrast to the steady solution. The perturbation analysis is used to derive expressions for the span tensions, the pulley tension distributions, the contact forces between the belt and the pulleys, and the angular velocity of the driven pulleys. Validity criteria are developed which determine bounds on the operation state for which the assumed friction state is upheld. Verification of response quantities from the perturbation solution is accomplished through comparison to quantities predicted by an in-house dynamic finite element model and excellent agreement is found. Additionally, the finite element model is used to verify the key assumption that a lone slip arc precedes a lone stick arc.

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## Figures

Figure 1

Example two-pulley belt drive

Figure 2

Belt element used to develop the belt-drive governing equations

Figure 3

Control volume used for driven pulley conservation of angular momentum

Figure 4

Coordinates used in determining the belt angular velocity

Figure 5

Tension time histories in the low- and high-tension spans for the analytical and finite element solutions

Figure 6

Pulley angular velocity time histories for the analytical and finite element solutions

Figure 7

Tension distribution (predicted by the finite element model) along the driver pulley contact arc for one period of excitation

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