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Research Papers

Analysis on Skew of Flat Belts in Two-Pulley Drives

[+] Author and Article Information
Weiming Zhang

 MKP Structural Design Associate Inc., Dexter, MI 48130david.weiming.zhang@gmail.com

J. Mech. Des 133(11), 111001 (Nov 01, 2011) (11 pages) doi:10.1115/1.4004982 History: Received August 16, 2009; Revised July 15, 2011; Published November 01, 2011; Online November 01, 2011

A troublesome problem in flat belt transmission is a phenomenon known as skew, where the belt moves along the axial direction of the pulleys in operation. Skew usually is caused by angular misalignment of pulleys. Angular misalignment can be classified in two types, in-plane misalignment and out-of-plane misalignment. The former is where the axes of a pulley pair, driving and driven, are in the same plane but not parallel. The latter is where the axes of pulleys are not in the same plane. In this paper, both cases of the belt skew caused by out-of-plane and in-plane misalignment are addressed. Theoretical analyses are provided following discussions of the simulation results by finite element method. It is found: (1) in case of out-of-plane misalignment, the skew ratio, an index describing the degree of skew, is determined by a very simple formula in which only three geometrical parameters are required; (2) in case of in-plane misalignment, the skew is much more complicated than that in case of out-of-plane misalignment, and the skew ratio is determined by a system of nonlinear simultaneous equation. An iteration method for solving the system of nonlinear simultaneous equations is proposed. The theoretical analyses for both cases are verified with the FEM results and factors that influence the skew are discussed.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Model and deployment of belt and pulleys in case of out-of-plane misalignment

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Figure 2

Skew versus rotation angle and traveling distance

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Figure 3

Observation coordinates systems

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Figure 4

Change of shape of the belt centerline from transient state to steady state

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Figure 5

Expansion plan of belt on pulleys

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Figure 6

Motion trajectory of reference point P on the belt

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Figure 7

Illustration of shape and behavior of belt centerline

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Figure 8

Belt centerline expanded along the traveling direction

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Figure 9

Expanded trajectory of reference point P on belt

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Figure 10

Model and deployment of belt and pulleys in case of in-plane misalignment

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Figure 11

Skew versus rotation angle and traveling

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Figure 12

Projection of the belt centerline

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Figure 13

Expansion of belt line on driving pulley

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Figure 14

Shape and expansion of the belt centerline

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Figure 15

Free body diagrams of the belt

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Figure 16

Skew ratio versus belt width

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Figure 17

Skew ratio versus friction coefficient

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Figure 18

Skew ratio versus belt length

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Figure 19

Skew ratio versus pulley diameter

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Figure 20

Skew ratio versus installation force

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Figure 21

Skew ratio versus belt Young’s modulus

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Figure 22

Skew ratio versus misalignment angle and comparison with Yanabe’s FEM results [3]

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Figure 23

Free span and expansion of the belt centerline on pulleys

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