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Mathematical model and geometrical model of double pitch ZN-type worm gear set based on generation mechanism

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Abstract

The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set (e.g., ZN, ZA, or ZK). The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6´10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400030, China

    Linsen Shu, Huajun Cao, Chenglong Zhang & Yuxia Li

Authors
  1. Linsen Shu
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  2. Huajun Cao
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  3. Xianchong Li
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  4. Chenglong Zhang
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  5. Yuxia Li
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Corresponding author

Correspondence to Huajun Cao.

Additional information

Supported by Major National Basic Research Program of China (973 Program, Grant No. 2011CB013400-05), and PhD Programs Foundation of Ministry of Education of China (Grant No. 20110191110005)

SHU Linsen, born in 1982, is currently a PhD candidate at Chongqing University, China. His research interests include the remanufacturing of mechanized equipment.

CAO Huajun, born in 1978, is currently a professor and a PhD advisor at Chongqing University, China. He received his PhD degree from Chongqing University, China. His research interests include manufacturing systems engineering, green manufacturing and remanufacturing.

LI Xianchong, born in 1989, is currently a master candidate at Chongqing University, China. His research interests include the remanufacturing of mechanized equipment.

ZHANG Chenglong, born in 1988, is currently a master candidate at State Key Laboratory of Mechanical Transmission, Chongqing University, China.

LI Yuxia, born in 1989, is currently a master candidate at State Key Laboratory of Mechanical Transmission, Chongqing University, China.

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Shu, L., Cao, H., Li, X. et al. Mathematical model and geometrical model of double pitch ZN-type worm gear set based on generation mechanism. Chin. J. Mech. Eng. 28, 549–555 (2015). https://doi.org/10.3901/CJME.2015.0409.039

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  • DOI: https://doi.org/10.3901/CJME.2015.0409.039

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