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Technical Briefs

Determination of the Most Dangerous Meshing Point for Modified-Hourglass Worm Drives

[+] Author and Article Information
Yimin Zhang

College of Mechanical Engineering and Automation,
Northeastern University,
Shenyang 110089, China

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received April 30, 2012; final manuscript received December 7, 2012; published online January 17, 2013. Assoc. Editor: Qi Fan.

J. Mech. Des 135(3), 034503 (Jan 17, 2013) (5 pages) Paper No: MD-12-1227; doi: 10.1115/1.4023281 History: Received April 30, 2012; Revised December 07, 2012

A type of modified-hourglass worm gear drive, frequently called type-II worm gearing for short, has various favorable meshing features. Its sole shortcoming is the undercutting of the worm wheel. By adopting a slight modification, this problem can be overcome due to the removal of a part of one subconjugate area containing the curvature interference limit line. To measure how effectively the undercutting is avoided, a strategy to determine the meshing point in the most severe condition is proposed for a type-II worm drive. The strategy presented consists of two steps. The first step is to establish a system of nonlinear equations in five variables in accordance with the theory of gearing. The second step is to solve the system of nonlinear equations by a numerical iteration method to ascertain the meshing point required. A numerical example is presented to verify the validity and feasibility of the proposed scheme.

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References

Figures

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Fig. 4

Contact zone and contact lines of the worm pair. (a) Contact zone and contact lines on the worm surface. (b) Contact zone and contact lines on the worm gear tooth surface.

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Fig. 3

Coordinate systems

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Fig. 2

Position relation between σa and σd

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Fig. 1

Axial section of the grinding wheel in σa

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Fig. 5

Circle and sphere vector functions

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