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Research Papers

Development and Validation of a Model for Flat Belt Tracking in Pulley Drive Systems

[+] Author and Article Information
Dilip Prasad

Aero Thermal Fluids Analysis, Pratt & Whitney Rocketdyne, Canoga Park, CA 91309

Brice N. Cassenti

Department of Mechanical Engineering,  University of Connecticut, Storrs, CN 02629

J. Dyn. Sys., Meas., Control 134(1), 011006 (Dec 02, 2011) (8 pages) doi:10.1115/1.4005280 History: Received March 29, 2010; Revised September 12, 2011; Published December 02, 2011; Online December 02, 2011

This investigation examines the problem of lateral belt motion (“tracking”) in belt drive systems using a mechanics-based approach. It is shown that the motion of a belt over a pulley of arbitrary shape with angular misalignment between the belt and pulley axes can be decomposed into two simpler problems: belt transport over a locally conforming cone and that over a cylindrical pulley at the specified angle of misalignment. The physical models are based on the assumptions that lateral deformations of the belt may be treated as those of a slender beam and that no slip occurs between the belt and the pulley surface. In the case of the conical pulley, a similarity parameter that incorporates the nominal pulley radius, mean normal stress in the belt and its stiffness and width is identified as the primary controlling influence on the tracking behavior. For the problem of tracking on a cylindrical pulley at a steering angle, a kinematic model is found to correctly predict the scaling of the tracking speed. In both models, it is necessary to introduce empirical constants to account for physical effects that have not been included. The tracking speed predicted by these models is nevertheless found to compare well with numerical simulations and experiments. The models are then used to determine the equilibrium position of a belt on a circular-arc crowned pulley. The predicted position was found to be in good agreement with experimental data, indicating that the present approach can be used as the basis for a systematic design procedure.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Tracking on an arbitrary pulley: geometry and nomenclature

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Figure 2

Belt tracking on a conical pulley

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Figure 3

Velocity triangle for the conical pulley

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Figure 4

Tracking rate on a 1 deg conical pulley as a function of (a) the Λ-parameter and (b) wrap angle

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Figure 5

Comparison of numerical tracking rate with model prediction: 1 deg cone (○) and 2 deg cone (); the solid line of unit slope represents perfect agreement between the model and simulations

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Figure 6

Schematic of the test rig employed for measurement of belt tracking, illustrating the configuration for 180 deg-wrap angle on the moveable pulley (top). The addition of an idler pulley permits wrap angles of 90 deg and 110 deg to be examined (bottom).

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Figure 7

Comparison of predicted tracking rate with experimental data for E/σ = 1346.8 (○,——) and E/σ = 676.1 (◊,– – –): (a) 1 deg cone and (b) 2 deg cone

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Figure 8

Belt tracking on a cylindrical pulley

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Figure 9

(a) Experimental data (symbols) for conical pulleys as a function of steering angle; the broken lines are provided as a visual guide. (b) Collapsed data, illustrating the universal steering angle dependence; the line represents the fit to the data, given by τcyl  = .

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Figure 10

Belt equilibrium position on a crowned pulley at steering angle α

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Figure 11

Belt equilibrium position on circular-arc crowned pulleys: (a) dependence on α, and (b) dependence on Rcr . The symbols represent experimentally determined values, while the lines illustrate the theoretical prediction given by Eq. 25.

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