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Research Papers: Design of Direct Contact Systems

Analysis of a Cycloid Speed Reducer Considering Tooth Profile Modification and Clearance-Fit Output Mechanism

[+] Author and Article Information
Xuan Li

State Key Laboratory of
Mechanical Transmission,
Chongqing University,
174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: xli_china@cqu.edu.cn

Chaoyang Li

State Key Laboratory of
Mechanical Transmission,
Chongqing University,
174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: li_zhaoyang77@cqu.edu.cn

Yawen Wang

College of Engineering and Applied Science,
University of Cincinnati,
2901 Woodside Drive,
Cincinnati, OH 45221
e-mail: wang2y4@mail.uc.edu

Bingkui Chen

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: bkchen@cqu.edu.cn

Teik C. Lim

College of Engineering and Applied Science,
University of Cincinnati,
2901 Woodside Drive,
Cincinnati, OH 45221
e-mail: e-mteik.lim@uc.edu

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 13, 2016; final manuscript received December 13, 2016; published online January 16, 2017. Assoc. Editor: Hai Xu.

J. Mech. Des 139(3), 033303 (Jan 16, 2017) (12 pages) Paper No: MD-16-1639; doi: 10.1115/1.4035541 History: Received September 13, 2016; Revised December 13, 2016

The load distribution analysis plays a significant role in the performance evaluation of cycloid speed reducer. However, current analytical models usually ignore elastic deformation, clearances, or assembly errors. These factors must be considered for realistic performance evaluation of cycloid speed reducer. This paper proposes an analytical model for cycloid speed reducer based on unloaded tooth contact and load distribution analyses. The proposed model can predict the loads on various components of the speed reducer in the presence of clearances and eccentricity errors. The results are compared with those predicted by the cycloid speed reducer model based on theoretical geometry. The effect of radial and pin-hole clearances as well as eccentricity errors, on some key design factors, such as contact stress, transmission error, gear ratio, and load on bearing, is investigated. This study can be used to assist the optimal design of cycloid speed reducers.

Copyright © 2017 by ASME
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References

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Figures

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Fig. 1

Typical structure of a cycloid speed reducer (output rollers neglected)

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Fig. 2

Coordinate system for the generation and modification of cycloid tooth profile

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Fig. 3

Flowchart of overall analysis methodology for cycloid speed reducer

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Fig. 4

Coordinate system for unloaded tooth contact analysis (TCA)

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Fig. 5

Backlash between output pin-hole pairs

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Fig. 6

Hertzian contact stiffness model

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Fig. 7

Deformation compatibility model

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Fig. 8

Load and torque equilibrium mechanics model

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Fig. 9

Load distribution among tooth pairs at (a) 0 deg, (b) 60 deg, and (c) 120 deg crankshaft angles

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Fig. 10

Load distribution among pin-hole pairs at (a) 0 deg, (b) 60 deg, and (c) 120 deg crankshaft angles

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Fig. 11

Number of (a) tooth and (b) pin-hole pairs in contact

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Fig. 12

Variation of (a) load on bearing and (b) eccentric angle

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Fig. 13

Contact stress on (a) tooth and (b) pin profiles

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Fig. 14

Contact stiffness of (a) tooth and (b) pin-hole pairs

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Fig. 17

Effects of radial and pin-hole clearances on the maximum contact stress on tooth and pin profiles ((a) and (b)), maximum load on bearing (c), mean value of STE (d), and peak-to-peak value of GR of the example cycloid speed reducer (e)

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Fig. 15

Static transmission error of the cycloid speed reducer

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Fig. 16

Gear ratio of the cycloid speed reducer

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Fig. 18

Effects of positive and negative eccentricity errors on the maximum contact stress on tooth and pin profiles ((a) and (b)), maximum load on bearing (c), mean value of STE (d), and peak-to-peak value of GR of the example cycloid speed reducer (e)

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