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TECHNICAL PAPERS

An Analytical Study of the Effect of the Contact Ratio on the Spur Gear Dynamic Response

[+] Author and Article Information
Anette Andersson

Department of Machine Elements, Lund Institute of Technology, Box 118, SE-221 00 Lund, Swedene-mail: Anette.Andersson@mel.lth.se

J. Mech. Des 122(4), 508-514 (May 01, 1999) (7 pages) doi:10.1115/1.1320819 History: Received May 01, 1999
Copyright © 2000 by ASME
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References

Den Hartog, J. P., 1956, Mechanical Vibrations, 4th ed., McGraw-Hill, New York, pp. 343–351.
Bollinger,  J. G., and Harker,  R. J., 1967, “Instability Potential of High Speed Gearing,” J. Ind. Math. Soc., 17, pp. 39–55.
Benton,  M., and Seireg,  A., 1978, “Simulation of Resonances and Instability Conditions in Pinion-Gear Systems,” ASME J. Mech. Des., 100, pp. 26–32.
Matsuhisa,  H., Miyaji,  Y., and Sato,  S., 1982, “Parametrically Excited Vibration with External Constant Load and Damping,” Memoirs of the Faculty of Engineering, Kyoto University, 44, pp. 158–167.
Tordion,  G. V., and Gauvin,  R., 1977, “Dynamic Stability of a Two-Stage Gear Train under the Influence of Variable Meshing Stiffnesses,” ASME J. Eng. Ind., 99, pp. 785–791.
Sato,  T., Umezawa,  K., and Ishikawa,  J., 1983, “Effects of Contact Ratio and Profile Correction on Gear Rotational Vibration,” Bull. JSME, 26, pp. 2010–2016.
Liou,  C. H., Lin,  H. H., Oswald,  F. B., and Townsend,  D. P., 1996, “Effect of Contact Ratio on Spur Gear Dynamic Load with No Tooth Profile Modifications,” ASME J. Mech. Des., 118, pp. 439–443.
Benton,  M., and Seireg,  A., 1981, “Factors Influencing Instability and Resonances in Geared Systems,” ASME J. Mech. Des., 103, pp. 372–378.
Iwatsubo, T., Arii, S., and Kawai, R., 1984, “The Coupled Lateral Torsional Vibration of a Geared Rotor System,” Proc. ImechE Vibrations in Rotating Machinery Conference, paper C265/84, pp. 59–66.
Amabili,  M., and Rivola,  A., 1997, “Dynamic Analysis of Spur Gear Pairs: Steady-State Response and Stability of the SDOF Model with Time-Varying Meshing Damping,” Mech. Syst. Signal Process., 11, pp. 375–390.
Kahraman,  A., and Blankenship,  G. W., 1999, “Effect of Involute Contact Ratio on Spur Gear Dynamics,” ASME J. Mech. Des., 121, pp. 112–118.
Maatar,  M., and Velex,  P., 1996, “An Analytical Expression for the Time-Varying Contact Length in Perfect Cylindrical Gears: Some Possible Applications in Gear Dynamics,” ASME J. Mech. Des., 118, pp. 586–589.
Cullen, C. G., 1966, Matrices and Linear Transformations, Addison-Wesley, Chap. 8.

Figures

Grahic Jump Location
Variation of the non-dimensional dynamic transmission error in steady-state when k=0.4341,λ2=1.7 and ζ2=0.0001. Tooth contact maintained (solid line) and tooth contact lost (dashed line).
Grahic Jump Location
Variation of the non-dimensional dynamic transmission error in steady-state when k=0.2772,λ2=1.7 and ζ2=0.0001. Tooth contact maintained (solid line) and tooth contact lost (dashed line).
Grahic Jump Location
The value of the parameter k which gives maintained tooth contact, depending on the relationship, λ2, between the two stiffness levels when q=3 (solid line) and q=4 (dashed line). The dashed curve in the middle valid for q=4 is also valid for q=2.
Grahic Jump Location
Gear mesh stiffness variation
Grahic Jump Location
The non-dimensional dynamic transmission error (solid line) and the non-dimensional static transmission error (dashed line)
Grahic Jump Location
Variation of the non-dimensional dynamic transmission error in steady-state when k=0.9,λ2=1.7 and ζ2=0.005. Tooth contact maintained (solid line) and tooth contact lost (dashed line).
Grahic Jump Location
Areas with unstable response. ζ2=0.
Grahic Jump Location
(a) Areas with lost tooth contact. ζ2=0 (solid line) and ζ2=0.06 (dash-dotted line). (b) Areas with lost tooth contact. ζ2=0.01.
Grahic Jump Location
Areas where the tooth contact is maintained and where the tooth contact is lost, respectively. A: tooth contact lost, q=3.0 (solid line). B: tooth contact lost, q=2.5 (dashed line).

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