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Research Papers

Transmission Error in Synchronous Belt With Resonance Under Installation Tension

[+] Author and Article Information
Masanori Kagotani

Department of Mechanical Engineering for Transportation,  Osaka Sangyo University, 3-1-1, Nakagaito, Daito-shi, Osaka, 574-8530, Japankagotani@tm.osaka-sandai.ac.jp

Hiroyuki Ueda

Department of Mechanical Engineering for Transportation,  Osaka Sangyo University, 3-1-1, Nakagaito, Daito-shi, Osaka, 574-8530, Japanueda@tm.osaka-sandai.ac.jp

J. Mech. Des 134(6), 061003 (Apr 24, 2012) (12 pages) doi:10.1115/1.4006524 History: Received December 27, 2011; Revised March 22, 2012; Published April 23, 2012; Online April 24, 2012

Synchronous belt drives generate resonance on the belt spans between the driving and driven pulleys when the transverse natural frequency of the belt, matches the meshing frequency of the belt tooth and the pulley tooth. The resonance of the belt spans affects the accuracy of rotation transmission. In the present study, the mechanisms generating the transmission error in synchronous belt drives under installation tension and a pulley speed ratio of 1:1 are investigated theoretically and experimentally for the case in which the belt spans generate first mode vibration due to resonance. In addition, the change in the shaft load caused by resonance is examined. The calculated and experimental transmission errors show good agreement, and so the validity of our analysis is confirmed. Transmission error is generated by the difference in displacement between the upper and lower belt spans due to the convex or concave shape, the difference in the amount of belt climbing at the beginning and end of meshing, and the generation of torque due to the moment of inertia on the driven side. The transmission error has a period of 1/2 of one pitch of the pulley, and the generated change in the shaft load, which is the sum of the displacement due to the convex or concave shape of the upper and lower spans and the sum of the belt climbing at the beginning and end of meshing, has a period of one pitch of the pulley.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Dimensions of the test belt and pulley

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Figure 2

Experimental apparatus for measuring the transmission error

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Figure 3

Photograph of the experimental apparatus

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Figure 4

Installation positions of laser displacement and eddy current type sensors

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Figure 5

Experimental results under the first mode vibration due to resonance (Ti  = 300 N) and nonresonance (Ti  = 240 N) conditions

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Figure 6

Power spectrum of the transmission error under the first mode vibration due to resonance

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Figure 7

Influence of the flanges on the displacement of the belt span and the transmission error under the first mode vibration due to resonance

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Figure 8

Relationship between the transmission error and the displacement of the belt spans under the first mode vibration due to resonance

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Figure 9

Relationship between the transmission error and the displacement of the belt spans under the second mode vibration due to resonance

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Figure 10

Measurement positions of the displacement of the belt spans under the second mode vibration due to resonance

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Figure 11

Relationship between the transmission error and the displacement of the belt span under the third mode vibration due to resonance

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Figure 12

Relationship between the change in shaft load and the displacement of the belt spans under the first mode vibration due to resonance

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Figure 13

Relationship between the displacement of the upper span and the meshing position at the beginning of meshing due to resonance

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Figure 14

Measurement position of the pulley signal at the beginning of meshing

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Figure 15

Relationship between the movement of the upper span and the complete meshing part

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Figure 16

Incomplete meshing state between the belt and pulley teeth at the horizontal position on the upper span

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Figure 17

Calculated result of the load distribution at the beginning of meshing

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Figure 18

Belt climbing at the beginning of meshing due to resonance (Ti  = 300 N) and nonresonance (Ti  = 280 N) conditions

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Figure 19

Displacement conditions of the belt spans due to resonance

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Figure 20

Displacement of the upper and lower spans due to resonance

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Figure 21

Belt climbing model at the beginning of meshing due to resonance

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Figure 22

Calculated results of the transmission errors due to ΔθS , ΔθC , and ΔθT

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Figure 23

Experimental and calculated results of the transmission error

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Figure 24

Calculated results of the change in shaft load due to WS and WC

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Figure 25

Experimental and calculated results of the change in shaft load

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