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Research Papers: Design of Direct Contact Systems

Theoretical Method for Calculating the Unit Curve of Gear Integrated Error

[+] Author and Article Information
Zhaoyao Shi

Beijing Engineering Research Center of Precision
Measurement Technology and Instruments,
Beijing University of Technology,
Beijing 100124, China
e-mail: shizhaoyao@bjut.edu.cn

Xiaoyi Wang

Beijing Engineering Research Center of Precision
Measurement Technology and Instruments,
Beijing University of Technology,
Beijing 100124, China;
School of Mechatronics Engineering,
Henan University of Science and Technology,
Luoyang 471023, China
e-mail: wxy2.0@163.com

Zanhui Shu

Beijing Engineering Research Center of Precision
Measurement Technology and Instruments,
Beijing University of Technology,
Beijing 100124, China
e-mail: shuzanhui@emails.bjut.edu.cn

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 21, 2015; final manuscript received December 8, 2015; published online January 13, 2016. Assoc. Editor: Hai Xu.

J. Mech. Des 138(3), 033301 (Jan 13, 2016) (8 pages) Paper No: MD-15-1660; doi: 10.1115/1.4032400 History: Received September 21, 2015; Revised December 08, 2015

A theoretical method is proposed in this paper to calculate the unit curve of gear integrated error (GIE). The calculated GIE unit curve includes the quasi-static transmission error (TE) curves of the approach stage, the involute stage, and the recession stage of the ZI worm and helical gear transmission. The misalignments between the two axes of the worm and gear, as well as the modifications or errors of the tooth flanks of the gear, are considered in the procedure of calculation. Optimization algorithm is introduced to replace the solving of implicit differential equations of the conventional tooth contact analysis (TCA) method. It is proved that the proposed method is clearer and more convenient than the conventional TCA methods in calculating the GIE unit curve. The correctness and merits of the proposed method are verified by two experiments.

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Copyright © 2016 by ASME
Topics: Gears , Errors
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References

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Figures

Grahic Jump Location
Fig. 1

Relative positions of the teeth-skipped worm and the gear

Grahic Jump Location
Fig. 2

The forming of a GIE unit curve (rack method)

Grahic Jump Location
Fig. 3

The coordinate system of the gear

Grahic Jump Location
Fig. 4

The Simulation of tooth flanks of gear tooth surface equations

Grahic Jump Location
Fig. 5

The coordinate system of the worm

Grahic Jump Location
Fig. 6

Simulation of meshing between worm and gear

Grahic Jump Location
Fig. 7

The complete flow scheme of the method

Grahic Jump Location
Fig. 8

A theoretical unit curve of GIE acquired by the proposed method

Grahic Jump Location
Fig. 9

The trace of contact point on the tooth surface in process of meshing

Grahic Jump Location
Fig. 10

The 3D demonstration of the contact point trace in the forming of GIE unit curve

Grahic Jump Location
Fig. 11

Comparison of the measured GIE curves and the theoretical GIE unit curves (of four different center distances)

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