Skip to main content
SpringerLink
Log in

Mathematical model of a helical gear with asymmetric involute teeth and its analysis

  • Original Article
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This paper describes a simple approach based on the gear theory for deriving a helical gear with asymmetric involute teeth. A helical gear with asymmetric involute teeth can be easily obtained through the envelope theory for the one-parameter family of surfaces. The mathematical models for asymmetric helical gears can be provided by the application of two imaginary rack cutters. The investigation on the undercutting analysis of the asymmetric helical gear is studied based on the developed mathematical model and the method of tooth-profile shifting. Here we provide geometric modeling of the designed asymmetric helical gear meshing when assembly errors are present. Stress analysis for the helical and the cylindrical forms are constructed. To illustrate the effectiveness of the approach, an analytical expression of helical gear with asymmetric involute teeth is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tsay CB, Fong ZH (1991) Computer simulation and stress analysis of helical gears with pinion circular arc teeth and gear involute teeth. Mech Mach Theory 26(2):145–154

    Article  Google Scholar 

  2. Feng PH, Litvin FL, Townsend DP, Handschuh RF (1999) Determination of principal curvatures and contact ellipse for profile crowned helical gears. ASME J Mech Des 121:107–111

    Google Scholar 

  3. DiFrancesco G, Marini S (1997) Structural analysis of asymmetrical teeth: reduction of size and weight Gear Technol 14(5):47–51

  4. Kapelevich AL (2000) Geometry and design of involute spur gears with asymmetric teeth. Mech Mach Theory 35:117–130

    Article  Google Scholar 

  5. Litvin FL, Lian Q, Kapelevich AL (2000) Asymmetric modified spur gear drives: reduction of noise, localization of contact, simulation of meshing and stress analysis. Computer methods in applied mechanics and engineering. 188:363–290

    Google Scholar 

  6. Litvin FL (1994) Gear geometry and applied theory. Prentice-Hall, New Jersey

  7. Swanson Analysis Systems Inc. (1992) ANSYS User’s Manual for Revision 5.0. DN-R300:50.1. Swanson Analysis Systems, Houston, PA

  8. Litvin FL (1989) Theory of gearing. NASA Publication RP-1212, Washington DC

  9. Wilcox LE (1982) AGMA Paper P229.25

  10. Gleason Works (1978) Understanding tooth contact analysis. Gleason Works publication SD319A

  11. Thomas W (2000) Sherlock enhanced version 4.1 Mathematica for Windows. 2000. Wolfram Research, Champaign, IL

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Education and Technology, National Changhua University of Education, Bao-Shan Campus: Number 2, Shi-Da Road, Changhua, 500, Taiwan

    Shyue-Cheng Yang

Authors
  1. Shyue-Cheng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, SC. Mathematical model of a helical gear with asymmetric involute teeth and its analysis. Int J Adv Manuf Technol 26, 448–456 (2005). https://doi.org/10.1007/s00170-003-2033-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-003-2033-z

Keywords

Search

Navigation