A model was used, where the total gear mesh stiffness was approximated by two constant stiffness levels, in order to analyze the influence of the contact ratio on the dynamic response of spur gears. Due to the stiffness variation there is parametric excitation of the transmission error, which generally causes tooth separation at certain critical rotational speeds. The present paper discloses a method to analytically calculate which contact ratio to use in order to avoid tooth separation near a specific critical rotational speed. [S1050-0472(00)02604-0]
Issue Section:
Technical Papers
1.
Den Hartog, J. P., 1956, Mechanical Vibrations, 4th ed., McGraw-Hill, New York, pp. 343–351.
2.
Bollinger
, J. G.
, and Harker
, R. J.
, 1967
, “Instability Potential of High Speed Gearing
,” J. Ind. Math. Soc.
, 17
, pp. 39
–55
.3.
Benton
, M.
, and Seireg
, A.
, 1978
, “Simulation of Resonances and Instability Conditions in Pinion-Gear Systems
,” ASME J. Mech. Des.
, 100
, pp. 26
–32
.4.
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
.5.
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
.6.
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
.7.
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
.8.
Benton
, M.
, and Seireg
, A.
, 1981
, “Factors Influencing Instability and Resonances in Geared Systems
,” ASME J. Mech. Des.
, 103
, pp. 372
–378
.9.
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.
10.
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
.11.
Kahraman
, A.
, and Blankenship
, G. W.
, 1999
, “Effect of Involute Contact Ratio on Spur Gear Dynamics
,” ASME J. Mech. Des.
, 121
, pp. 112
–118
.12.
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
.13.
Cullen, C. G., 1966, Matrices and Linear Transformations, Addison-Wesley, Chap. 8.
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