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TECHNICAL PAPERS

3D Mesh Generation for Static Stress Determination in Spiral Noncircular Gears Used for Torque Balancing

[+] Author and Article Information
D. Barkah, B. Shafiq, D. Dooner

Department of Mechanical Engineering, University of Puerto Rico, Mayagüez, PR 00681-9045

J. Mech. Des 124(2), 313-319 (May 16, 2002) (7 pages) doi:10.1115/1.1470492 History: Received November 01, 2000; Online May 16, 2002
Copyright © 2002 by ASME
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References

Wilcox,  L., and Coleman,  W., 1973, “Application of Finite Elements to the Analysis of Gear Tooth Stresses,” ASME J. Eng. Ind., 95, pp. 1139–1148.
Chabert,  G., Dang Tran,  T., and Mathis,  R., 1974, “An Evaluation of Stresses and Deflection of Spur Gear Teeth Under Strain,” ASME J. Eng. Ind., 96, pp. 85–93.
Tobe,  T., Kato,  M., and Inoue,  K., 1978, “Bending of Stub Cantilever Plate and Some Applications to Strength of Gear Teeth,” ASME J. Mech. Des., 100, pp. 374–381.
Wellauer,  E. J., and Seireg,  A., 1960, “Bending Strength of Gear Teeth by Cantilever-Plate Theory,” ASME J. Eng. Ind., 82, pp. 213–222.
Andrews,  J. D., 1991, “A Finite Element Analysis of Bending Stresses Induced in External and Internal Involute Spur Gears,” J. Strain Anal., 26(3), pp. 154–163.
Reinhart,  W. R., Ferguson,  R. J., and Kerr,  J. H., 1980, “Noncircular Gear Tooth Bending Strength by Finite Element Analysis,” Trans. Can. Soc. Mech. Eng., 6(2), pp. 71–77.
Huseyin,  I. F., and Eyercioglu,  O., 1995, “Evaluation of Gear Tooth Stresses by Finite Element Method,” ASME J. Eng. Ind., 117, pp. 232–239.
Sandeep, M. V., Biplab, S., and Houser, R. D., 1987, “Gear Tooth Profile Determination from Arbitrary Rack Geometry,” AGMA Technical Paper, AGMA 1987, 13pp.
Gengdong,  C., and Hua,  L., 1996, “New Method for Graded Mesh Generation of Quadrilateral Finite Elements,” Computers and Structures,59(5), 823–829.
Cook,  W. A., 1974, “Body Oriented (Natural) Coordinates for Generating Three Dimensional Meshes,” International Journal for Numerical Methods in Engineering,8, pp. 27–43.
Herrmann,  L. R., 1976, “Laplacian-Isoparametric Grid Generation Scheme,” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 102, pp. 749–756.
Shigley, J. E., and Mischke, C. R., 1996, Standard Handbook of Machine Design, Second Edition, McGraw Hill Companies.
Dooner,  D. B., 1997, “Use of Non-Circular Gears to Reduce Torque and Speed Fluctuations in Rotating Shafts,” ASME J. Mech. Des., 119, pp. 299–306.
Dooner, D. B., and Seireg, A., 1995, The Kinematic Geometry of Gearing, John Wiley and Sons, Inc., New York.

Figures

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ABCD Tooth domain boundary of zero displacement
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Delimitation of tooth domain from noncircular gear structure
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Selection of turning points of tooth profile
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Subdivision of tooth domain into sectors
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Patterns for generating mesh
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Mapping of pattern and sectors into unit square
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Mapping unit square mesh into tooth domain sector
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Exploded circular tooth domain showing patterns mapped into sector
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2D and 3D noncircular tooth domain of smoothed mesh
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3D finite element analysis of approximated gear tooth
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Stress distribution along tooth profile in the tensile and compressed fillets
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Noncircular gear pair for sinusoidal torque and speed balancing
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Maximum Von-Mises stress distribution in noncircular gears

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