This study develops a crowned elliptical gear drive that prevents edge contact when an elliptical gear drive has axial misalignment. According to the theory of gearing and a gear-generation mechanism with longitudinal crowing, the mathematical model of a crowned elliptical gear is derived using a rack cutter. Pointed teeth typically appear on the tips of the teeth of elliptical gears at major axis. Additionally, a three-dimensional geometric relation is applied to prevent pointed teeth from developing on elliptical gears. Moreover, a computer simulation program is employed to generate the tooth profiles of crowned elliptical gears without pointed teeth and locate the contact position for longitudinal middle tooth profiles. Two numerical examples demonstrate the design process and the tooth profile graphs.
Issue Section:
Technical Briefs
Topics:
Gears
1.
Freudenstein
, F.
, and Chen
, C. K.
, 1991, “Variable-Ratio Chain Drives With Noncircular Sprockets and Minimum Slack-Theory and Application
,” ASME J. Mech. Des.
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, pp. 253
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.2.
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, T.
, and Arakawa
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, D. B.
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,” ASME J. Mech. Des.
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), pp. 299
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.6.
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, G.
, and Angeles
, J.
, 2003, “The Synthesis of Elliptical Gears Generated by Shaper-Cutters
,” ASME J. Mech. Des.
0161-8458, 125
, pp. 793
–801
.7.
Bair
, B. W.
, 2002, “Computer Aided Design of Elliptical Gears
,” ASME J. Mech. Des.
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), pp. 787
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.8.
Bair
, B. W.
, 2004, “Computer Aided Design of Elliptical Gears With Circular-Arc Teeth
,” Mech. Mach. Theory
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, pp. 153
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Bair
, B. W.
, Chen
, C. F.
, Chen
, S. F.
, and Chou
, C. Y.
, 2007, “Mathematical Model and Characteristic Analysis of Elliptical Gears Manufactured by Circular-Arc Shaper Cutters
,” ASME J. Mech. Des.
0161-8458, 129
(2
), pp. 210
–217
.10.
Bair
, B. W.
, Sung
, M. H.
, Wang
, J. S.
, and Chen
, C. F.
, 2009, “Tooth Profile Generation and Analysis of Oval Gears With Circular-arc Teeth
,” Mech. Mach. Theory
0094-114X, 44
(6
), pp. 1306
–1317
.11.
Litvin
, F. L.
, Gonzalez-Perez
, I.
, Yukishima
, K.
, Fuents
, A.
, and Hayasaka
, K.
, 2007, “Generation of Planar and Helical Elliptical Gears by Application of Rack-Cutter, Hob, and Shaper
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 196
, pp. 4321
–4336
.12.
Yan
, J.
, Yang
, D. C. H.
, and Tong
, S. H.
, 2008, “On the Generation of Analytical Noncircular Multilobe Internal Pitch Curves
,” ASME J. Mech. Des.
0161-8458, 130
, p. 092601
.13.
Xia
, J.
, Liu
, Y.
, Geng
, C.
, and Song
, J
, 2008, “Noncircular Bevel Gear Transmission With Intersecting Axes
,” ASME J. Mech. Des.
0161-8458, 130
, p. 054502
.14.
Kahraman
, A.
, Bajpai
, P.
, and Anderson
, N. E.
, 2005, “Influence of Tooth Profile Deviations on Helical Gear Wear
,” ASME J. Mech. Des.
0161-8458, 127
, pp. 656
–663
.15.
Hotait
, M
, and Kahraman
, A.
, 2008, “Experiments on Root Stresses of Helical Gears With Lead Crown and Misalignments
,” ASME J. Mech. Des.
0161-8458, 130
, p. 074502
.16.
Chang
, S. L.
, Tsay
, C. B.
, and Tseng
, C. H.
, 1997, “Kinematic Optimization of a Modified Helical Gear Train
,” ASME J. Mech. Des.
0161-8458, 119
, pp. 307
–314
.17.
Litvin
, F. L.
, Gonzalez-Perez
, I.
, Fuentes
, A.
, Hayasaka
, K.
, and Yukishima
, K.
, 2005, “Topology of Modified Surfaces of Involute Helical Gears With Line Contact Developed for Improvement of Bearing Contact, Reduction of Transmission Errors, and Stress Analysis
,” Math. Comput. Modell.
0895-7177, 42
, pp. 1063
–1078
.18.
Litvin
, F. L.
, 1994, Gear Geometry and Applied Theory
, Prentice-Hall
, Englewood Cliffs, NJ
.Copyright © 2009
by American Society of Mechanical Engineers
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