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Research Papers: Design of Direct Contact Systems

Transmission Error Due to Resonance in Synchronous Belt Drive With Eccentric Pulley

[+] Author and Article Information
Masanori Kagotani

Department of Automobile Maintenance,
Kitakyushu Automobile College,
1-2-24, Ninatawakazono, Kokuraminami-ku,
Kitakyushu-shi 802-0814, Fukuoka, Japan
e-mail: m_kagotani@zenryo-g.com

Hiroyuki Ueda

Department of Mechanical
Engineering for Transportation,
Osaka Sangyo University,
3-1-1, Nakagaito,
Daito-shi 574-8530, Osaka, 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 March 21, 2017; final manuscript received July 18, 2017; published online October 3, 2017. Assoc. Editor: Qi Fan.

J. Mech. Des 139(12), 123301 (Oct 03, 2017) (10 pages) Paper No: MD-17-1224; doi: 10.1115/1.4037761 History: Received March 21, 2017; Revised July 18, 2017

In synchronous belt drives, it is generally difficult to eliminate pulley eccentricity, because the pulley teeth and shaft hole are produced separately and the pulley is installed on an eccentric shaft. This eccentricity affects the accuracy of rotation transmission, so that the belt tension changes during a single rotation of the pulley. This in turn affects the occurrence of resonance in the spans. In the present study, the transmission error in a synchronous belt drive with an eccentric pulley in the absence of a transmitted load was experimentally investigated for the case in which the spans undergo first-mode transverse vibration due to resonance. The transmission error was found to have a component with a period equal to the span displacement, in addition to a component with a period of half the span displacement. During a single rotation of the pulley, the magnitude of the transmission error increased, and its frequency decreased, with decreasing belt tension. The transmission error exhibited the large value when two frequency conditions were satisfied: one was that the meshing frequency was within the range of span frequency variations due to the eccentricity, and the other was that the minimum span frequency was close to an integer multiple of the pulley rotation frequency. Even if both of these conditions occurred, if the range of span frequency variations due to the eccentricity was larger than 13 Hz, the transmission error could be eliminated by adjusting the belt tension, so that the average span frequency corresponded to the meshing frequency.

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References

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Figures

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Fig. 1

Photograph of experimental apparatus for measuring transmission error

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Fig. 2

Schematic diagram of driving and driven pulleys with eccentricity

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Fig. 3

Calculation results for dependence of span length on eccentric phase angle for driven pulley

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Fig. 4

State of contact between belt and pulley teeth at beginning and end of meshing on upper span: (a) θ = 0 rad and (b) θ > 0 rad

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Fig. 5

Relationship between belt tension and degree of contact

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Fig. 6

Experimental and calculation results for change in belt tension during pulley rotation

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Fig. 7

Experimental and calculation results for change in maximum and minimum value of belt tension due to eccentric phase angle for fixed Tθmax

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Fig. 8

Upper-span displacement and power spectrum: (a) yU and (b) fb

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Fig. 9

Relationship between installation tension and first-mode transverse natural frequency of span when Θ = 0 rad

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Fig. 10

Experimental results for displacement of span and transmission error when Θ = 6 × 2π/zp rad: (a) Tθ, (b) yU and yL, (c) ydif, and (d) Δθ

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Fig. 11

Experimental results for belt tension and transmission error when Θ = 0 rad: (a) Tθ and (b) Δθ

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Fig. 12

Power spectra for displacement of upper span and transmission error: (a) yU and (b) Δθ

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Fig. 13

Experimental results for frequency of first-mode transmission error and displacement of upper span, and calculation results for string-like vibration of span

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Fig. 14

Experimental and calculation results for transmission error, and experimental results for displacement of span: (a) Δθ in vicinity of Tθmin and (b) Δθ in vicinity of Tθmax

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Fig. 15

Experimental and calculation results for transmission error when Tθmin ≅ 242 N: (a) yU and yL and (b) Δθ

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Fig. 16

Experimental results for magnitude of displacement of span and transmission error due to change in minimum belt tension for fixed Θ: (a) yU and yL, (b) φ, (c) ydif, and (d) Δθ

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Fig. 17

Experimental and calculation results for maximum and minimum frequencies of span due to change in minimum belt tension for fixed Θ

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Fig. 18

Experimental results for dependence of maximum and minimum value of belt tension on eccentric phase angle

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Fig. 19

Power spectra for displacement of upper span due to change in eccentric phase angle: (a) Θ = 0 rad, (b) Θ = 4 × 2π/zp rad, and (c) Θ = 8 × 2π/zp rad

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Fig. 20

Experimental results for dependence of magnitude of displacement of span and transmission error on eccentric phase angle: (a) yU and yL, and ydif, (b) φ, and (c) Δθ

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Fig. 21

Experimental results for dependence of maximum and minimum value of belt tension, and magnitude of displacement of span and transmission error on eccentric phase angle for fixed Tθav: (a) Tθmax and Tθmin, (b) yU and yL, and ydif, and (c) Δθ

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