Hypoid gears are one of the most general form of gearing, and a theoretical solution for them has been studied by many researchers. Many hypotheses and theorems about these gears have been proposed—some of them correct and many of them wrong. The tooth surfaces are parts of general curved surfaces and they must have principal directions and principal curvatures on every contact point. However, there has been no detailed research on the fundamental elements of the surface. This study develops necessary conditions for determining these curvatures and principal directions for conjugate gearing with a contact line by introducing the concept of geodesic torsions. [S1050-0472(00)00503-1]
Issue Section:
Technical Papers
1.
Gosselin
, C.
, Nonaka
, T.
, Shiono
, Y.
, Kubo
, A.
, and Tatsuno
, T.
, 1998
, “Identification of the Machine Settings of Real Hypoid Gear Tooth Surfaces
,” ASME J. Mech. Des.
, 120
, pp. 429
–440
.2.
Litvin
, F. L.
, Wang
, A. G.
, and Handscuh
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, 1998
, “Computerized Generation and Simulation of Meshing and Contact of Spiral Bevel Gears with Improved Geometry
,” Comput. Methods Appl. Mech. Eng.
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.3.
Litvin
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, Wang
, A. G.
, and Handschuh
, R. F.
, 1996
, “Computerized Design and Analysis of Face-Milled, Uniform Tooth Height Spiral Bevel Gear Drives
,” ASME J. Mech. Des.
, 118
, pp. 573
–579
.4.
Simon, V., 1996, “Tooth Contact Analysis of Mismatched Hypoid Gears,” Power Transmission and Gearing Conference ASME, DE-Vol. 88, pp. 789–798.
5.
Lin
, C. Y.
, Tsay
, C. B.
, and Fong
, Z. H.
, 1996
, “Contact Pattern Development of Spiral Bevel and Hypoid Gears by Applying Optimization Techniques
,” J. CSME
, 17
, No. 5
, pp. 413
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.6.
Wang
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, and Chosh
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, 1994
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.7.
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8.
Chen
, N.
, “Curvatures and Sliding Ratios of Conjugate Surfaces
,” 1998
, ASME J. Mech. Des.
, 120
, pp. 126
–132
.9.
Handschuh, R. F., and Litvin, F. L., 1991, “How to Determine Spiral Bevel Gear Tooth Geometry for Finite Element Analysis,” JSME International Conference on Motion and Power Transmissions, pp. 704–710.
10.
Kubo
, A.
, Tarutani
, I.
, Gosselin
, C.
, Nonaka
, T.
, Aoyama
, N.
, and Wang
, Z.
, 1997
, “A Computer Based Approach for Evaluation of Operating Performances of Bevel and Hypoid Gears
,” JSME Int. J. Ser. C.
, 40
, No. 4
, pp. 749
–758
.11.
Fong
, Z. H.
, and Tsay
, C. B.
, 1991
, “A Mathematical Model for the Tooth Geometry of Circular-Cut Spiral Bevel Gears
,” ASME J. Mech. Des.
, 113
, pp. 174
–181
.12.
Simon
, V.
, 1998
, “The Influence of Misalignments on Mesh Performances of Hypoid Gears
,” Mech. Mach. Theory
, 33
, pp. 1277
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.13.
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