Simulation and Experimental Measurement of the Transmission Error of Real Hypoid Gears Under Load

[+] Author and Article Information
Claude Gosselin

Department of Mechanical Engineering, Laval University, Quebec, Canada G1K-7P4

Thierry Guertin, Yves Jean

Department of Mechanical Engineering, Laval University, Quebec, Canada G1K-7P4

Didier Remond

Laboratoire de Conception et Analyse de Systèmes Mécaniques, INSA de Lyon, 20 Avenue A. Elnstein 69621 Villeurbanne, France

J. Mech. Des 122(1), 109-122 (Jan 01, 2000) (14 pages) doi:10.1115/1.533555 History: Received February 01, 1999; Revised January 01, 2000
Copyright © 2000 by ASME
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Krenzer, J. T., “Tooth Contact Analysis of Spiral Bevel and Hypoid Gears Under Load,” Gleason Publication SD3458, April 1981.
Wilcox, L., “An Exact Analytical Method for Calculating Stresses in Bevel and Hypoid Gear Teeth,” Intl. Symposium on Gearing and Power Transmission, Tokyo, 1981.
Wilcox, L., “Analyzing Gear Tooth Stress as a Function of Tooth Contact Pattern Shape and Position,” Gear Technology, January/February 1985.
Gosselin,  C., Cloutier,  L., Nguyen,  Q. D., “A General Formulation for the Calculation of the Load Sharing and Transmission Error Under Load of Spiral Bevel and Hypoid Gears,” IFTOMM, 30, No. 3, pp. 433–450, 1995.
Litvin, F. L., Flong-Tao, L., “Generation and Tooth Contact Analysis of Spiral Bevel Gears with Predesigned Parabolic Functions of Transmissions Errors,” NASA Report 4259, 1989.
Smith, J. D., Gears and their Vibration, Marcel Dekker Inc., MacMillan Press Ltd., New York, 1983.
Houser, D. R., Blankenship, G. W., “Methods for Measuring Transmission Error Under Load and at Operating Speeds,” Transaction of the SAE 98, 1367–1374.
Remond,  D., “Practical Performances of High-Speed Measurement of Gear Transmission Error or Torsional Vibrations with Optical Encoders,” Meas. Sci. Technol., 9, pp. 347–353, 1998.
Gosselin,  C., Nonaka,  T., Shiono,  Y., Kubo,  A., Tatsuno,  T., 1998, “Identification of the Machine Settings of Real Hypold Gear Tooth Surfaces,” ASME J. Mech. Des., 120, pp. 1–12.
Gosselin,  C., Gagnon,  P., Cloutier,  L., 1998, “Accurate Spiral Bevel Gear Tooth Stiffness by the Finite Strip Method,” ASME J. Mech. Des., 120, pp. 599–605.
Attia, A. Y., “Deflection of Spur Gear Teeth Cut in Thin Rims,” Transactions of the ASME, November 1964.


Grahic Jump Location
Gear tooth flank measurement grid (9×5 points)
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CMM measurement data relative to the original summary
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CMM measurement data after Surface Match
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Analog encoder output signal
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Phase difference encoder
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Unfiltered transmission error—optical and analog encoders—[N–m]
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Filtered transmission error—optical and analog encoders—0[N–m]
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Bearing pattern on pinion tooth and measurement grid
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Simulation reference frames
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Meshing pinion gear teeth
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Tooth flank measurement
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Tooth error surface interpretation (a) 1st order spiral and pressure angle errors (b) 2nd order crowning profile curvature and bias errors (c) measurement grid




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