Alternative Equation of Meshing for Worm-Gear Drives and Its Application to Determining Undercutting and Reverse Engineering

[+] Author and Article Information
Xiaogen Su, Donald R. Houser

Department of Mechanical Engineering, The Ohio State University, 206 W. 18th Ave., Columbus, OH 43210

J. Mech. Des 122(2), 207-212 (Mar 01, 2000) (6 pages) doi:10.1115/1.533561 History: Received April 01, 1998; Revised March 01, 2000
Copyright © 2000 by ASME
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Litvin, F. L., 1994, Gear Geometry and Applied Theory, PTR Prentice Hall.
Su, X., and Houser, D. R., 1997, Coordinate Measurement and Reverse Engineering of ZK Type Worm Gearing, AGMA 97FTMS1.
Kin, V., 1988, Limitations of Worm and Worm-Gear Surfaces in Order to Avoid Undercutting and Appearance of Envelope of Lines in Contact, AGMA 88FTMS1.
Litvin, F. L., and Wang, A. G., 1996, “Local Synthesis and Tooth Contact Analysis of Face-Milled, Uniform Tooth Height Spiral Bevel Gears,” NASA Contractor Report 4757.
Colbourne, J. R., 1994, Undercutting in Worms and Worm Gears, AGMA 94FTM1.
Colbourne, J. R., 1987, The Geometry of Involute Gears, Springer-Verlag.
Buckingham, E., and Ryffel, H. H., 1960, Design of Worm and Spiral Gears, The Industrial Press.


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Two equivalent meshing motions of worm-gear drives
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u and θ lines on worm surface and generated gear tooth, respectively
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Lines of Δ1=0,Δ2=0 and Δ3=0 of a ZK worm (end view)
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Lines of Δ1=0,Δ2=0 and Δ3=0 of a ZA worm (end view)
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Alternative limiting line and the corresponding limiting line
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u and θ lines on worm surface and generated gear tooth with undercutting
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Area of meshing of a ZK type of worm-gear drive
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Lines of constant u, θ and ϕ1 on gear tooth calculated with ordinary meshing equation
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Deviations of the measured gear surface from the fit surface




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