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Research Papers: Design of Direct Contact Systems

Influence of Installation Tension on Transmission Error Due to Resonance in a Synchronous Belt

[+] Author and Article Information
Masanori Kagotani

Professor
Department of Mechanical Engineering
for Transportation,
Osaka Sangyo University,
3-1-1, Nakagaito, Daito-shi,
Osaka 574-8530, Japan
e-mail: kagotani@tm.osaka-sandai.ac.jp

Hiroyuki Ueda

Associate Professor
Department of Mechanical Engineering
for Transportation,
Osaka Sangyo University,
3-1-1, Nakagaito, Daito-shi,
Osaka 574-8530, Japan
e-mail: ueda@tm.osaka-sandai.ac.jp

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 6, 2014; final manuscript received March 24, 2015; published online June 8, 2015. Assoc. Editor: Zhang-Hua Fong.

J. Mech. Des 137(8), 083301 (Aug 01, 2015) (9 pages) Paper No: MD-14-1400; doi: 10.1115/1.4030204 History: Received July 06, 2014; Revised March 24, 2015; Online June 08, 2015

In synchronous belt drives, a transmission error is generated due to resonance of the belt spanning the driving and driven pulleys when the transverse natural frequency of the belt approaches the meshing frequency of the belt and the pulley teeth. The behavior of this transmission error has been assumed to be dependent on the installation tension. In the present study, the influence of the installation tension on the transmission error in a synchronous belt drive under no transmitted load was experimentally investigated for the case in which first mode vibration due to resonance was induced in both the upper and lower spans. In addition, an analysis of the transmission error based on the experimental results was carried out. A method for reducing the error was also investigated. The transmission error contains two components: one with a period equal to the pitch of the pulley, and the other with a period of half the pulley pitch. Good agreement was found between the calculation and experimental results, thus confirming the validity of the analysis method. For a fixed pulley speed, the transmission error was largest when the installation tension was applied at a position where the displacement of the upper span was equal to that of the lower span. It was found that the transmission error could be reduced by pushing an idler lightly against the center of the span of the belt that was undergoing the largest displacement.

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References

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Makita, K., Kagotani, M., Ueda, H., and Koyama, T., 2004, “Transmission Error in Synchronous Belt Drives With Idler (Influence of Thickness Error of Belt Back Face Under No Load Conditions),” ASME J. Mech. Des., 126(1), pp. 148–155. [CrossRef]
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Figures

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Fig. 1

Experimental results for Δθ, and yU and yL when np = 3.64 s−1. (a) Ti = 303 N, (b) Ti = 314 N, and (c) Ti = 319 N.

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Fig. 2

Complete meshing state, and yU and yL

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Fig. 3

IFT of the experimental transmission error

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Fig. 4

Experimental and calculated results for Δθt/2

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Fig. 5

Experimental and calculated results for Δθt

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Fig. 6

Pulley teeth positions at the beginning and end of meshing over one belt rotation, and −Δxp when ydif > 0

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Fig. 7

Experimental and calculated results for Δθ comprising Δθt/2 and Δθt when np = 3.64 s−1. (a) Ti = 303 N, (b) Ti = 314 N, and (c) Ti = 319 N.

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Fig. 8

Influence of Ti on yUa and yLa

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Fig. 9

Influence of Ti on xbU and xbL, and φ. (a) Starting position of resonance and (b) phase difference between yU and yL.

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Fig. 10

Influence of Ti on ydifa

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Fig. 11

Influence of Ti on Δθt/2A and ΔθtA for a fixed np

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Fig. 12

Experimental results for Δθ due to the change in np with Ti

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Fig. 13

Influence of Ti on fz and behavior of the upper and lower spans. (a) Meshing frequency, (b) amplitudes of yU, yL, and the difference between yU and yL, (c) starting position of resonance, and (d) phase difference between yU and yL.

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Fig. 14

Relationship between ra and Ti

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Fig. 15

Experimental and calculated results for Δθ due to the change in np with Ti. (a) Ti = 236 N and np = 3.13 s−1, (b) Ti = 267 N and np = 3.34 s−1, and (c) Ti = 354 N and np = 3.87 s−1.

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Fig. 16

Influence of Ti on Δθt/2A and ΔθtA due to the change in np with Ti

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Fig. 17

Installation positions for the idler and the laser displacement sensors

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Fig. 18

Experimental results for the displacement of the belt with an idler on the upper or lower span when np = 3.64 s−1. (a) Ti = 302 N and (b) Ti = 317 N.

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Fig. 19

Experimental results for ΔθU and ΔθL with an idler on the upper or lower span when np = 3.64 s−1. (a) Ti = 302 N and (b) Ti = 317 N.

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Fig. 20

Experimental results for ΔθUL with idlers on the upper and lower spans under resonance, and Δθ without any idler under nonresonance conditions

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