An extended three-dimensional model is used for calculating dynamic tooth loads on a planetary gear set. Time dependent mesh stiffnesses are determined and an original Ritz method aimed at solving large parametrically excited differential systems is proposed. Results from the Ritz method compare favorably with those given by direct integrations for highly reduced computation times. The difference between local critical speeds (for one individual mesh) and global critical speeds (for sun or ring gear-planet meshes) on a sequential spur gear train is pointed out. Finally, it is shown that, for linear behaviors, mesh stiffnesses are largely controlling dynamic tooth loads while the influence of a floating sun or ring gear is less important.
Issue Section:
Research Papers
1.
Antony, G., 1988, “Gear Vibration-Investigation of the Dynamic Behaviour of One Stage Epicyclic Gears,” AGMA Technical Paper 88-FTM-12, 9 p.
2.
August
R.
Kasuba
R.
1986
, “Torsional Vibrations and Dynamic Loads in a Basic Planetary Gear System
,” ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design
, Vol. 108
, pp. 348
–353
.3.
Badgley, R. H., and Hartman, R. M., 1974, “Gearbox Noise Reduction: Prediction and Measurement of Mesh-Frequency Vibrations within an Operating Helicopter Rotor-Drive Gearbox,” ASME Journal of Engineering for Industry, pp. 567–577.
4.
Botman, M., 1976, “Epicyclic Gear Vibrations,” ASME Journal of Engineering for Industry, pp. 811–815.
5.
Boyd, L. S., and Pike, J., 1987, “Expansion of Epicyclic Gear Dynamic Analysis Program,” Hamilton Standard, NASA CR 179563, 76 p.
6.
Chiang, T., and Badgley, R. H., 1973, “Reduction of Vibration and Noise Generated by Planetary Ring Gears in Helicopter Aircraft Transmissions,” ASME Journal of Engineering for Industry, pp. 1149–1158.
7.
Cunliffe, F., Smith, J. D., and Welbourn, D. B., 1974, “Dynamic Tooth Loads in Epicyclic Gears,” ASME Journal of Engineering for Industry, pp. 578–584.
8.
Hayashi
T.
Xie
L. Y.
Hayashi
I.
Endou
K.
Watanabe
W.
1986
, “Measurement and Some Discussions on Dynamic Load Sharing in Planetary Gears
,” Bull. JSME
, Vol. 29
, No. 253
, pp. 2290
–2297
.9.
Hidaka
T.
Terauchi
Y.
1976
a, “Dynamic Behaviour of Planetary Gear (1st Report: Load Distribution in Planetary Gear)
, Bull. JSME
, Vol. 19
, No. 132
, pp. 690
–698
.10.
Hidaka
T.
Terauchi
Y.
Ishioka
K.
1976
b, “Dynamic Behavior of Planetary Gear (2nd Report: Displacement of Sun Gear and Ring Gear)
, Bull. JSME
, Vol. 19
, No. 138
, pp. 1563
–1570
.11.
Hidaka
T.
Terauchi
Y.
Nohara
M.
Oshita
J.
1977
, “Dynamic Behavior of Planetary Gear (3rd Report: Displacement of Ring Gear in Direction of Line of Action)
, Bull. JSME
, Vol. 20
, No. 150
, pp. 1663
–1672
.12.
Hidaka
T.
Terauchi
Y.
Fujii
M.
1980
, “Analysis of Dynamic Tooth Load on Planetary Gear
,” Bull. JSME
, Vol. 23
, No. 176
, pp. 315
–323
.13.
Kahraman
A.
1994
, “Planetary Gear Train Dynamics
,” ASME JOURNAL OF MECHANICAL DESIGN
, Vol. 116
, pp. 713
–720
.14.
Kahraman, A., and Blankenship, G. W., 1994, “Planet Mesh Phasing in Epicyclic Gear Sets,” Proc. of Int. Gearing Conf., Newcastle, pp. 99–104.
15.
Kasuba, R., and August, R., 1984, “Gear Mesh Stiffness and Load Sharing in Planetary Gearing,” ASME Paper 84-DET-229, 6 p.
16.
Lalanne, M., and Ferraris, G., 1990, “Rotordynamics-Prediction in Engineering,” J. Wiley, 206 p.
17.
Maatar, M., Velex, P., and Flamand, L., 1994, “Numerical Simulations of the Non-Linear Dynamic Behaviour of Misaligned Gears,” Proc. Int. Gearing Conf., Newcastle, pp. 111–116.
18.
Maatar, M., 1995, “Contribution a` l’analyse du comportement dynamique de re´ducteurs a` engrenages avec e´carts de forme et de´fauts de montage,” The`se de Doctorat. INSA Lyon, 192 p.
19.
Saada, A., Velex, P., and Flamand, L., 1992a, “Un mode`le torsionnel pour l’analyse du chargement dynamique sur les dentures de trains plane´taires,” Proc. 3rd World Congress on Gearing and Power Trans., Paris, Vol. 1, pp. 865–875.
20.
Saada, A., and Velex, P., 1992b, “An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains,” Proc. 6th ASME Int. Power Trans. Gearing Conf., Phoenix, Vol. 2, pp. 513–520 (also in the ASME JOURNAL OF MECHANICAL DESIGN, 1995, Vol. 117, pp. 241–247).
21.
Stockton, R. J., 1985, “Sun Gear Traveling Wave Vibration in a Sequential Planetary Gear Box,” ASME Paper 85-DET-167, 8 p.
22.
Velex, P., and Berthe, D., 1989, “Dynamic Tooth Loads on Geared Trains,” Proc. 5th ASME Int. Power Trans, and Gearing Conf., Chicago, Vol. 1, pp. 447–454.
23.
Velex, P., and Berthe, D., 1990, “A Survey of Dynamic Loading Conditions on Gear Tooth Contacts,” Vibration and Wear in High Speed Rotating Machinery, NATO ASI Series E, Kluwer Academic Publishers, pp. 631–652.
24.
Velex, P., and Saada, A., 1991a, “A Model for the Dynamic Behaviour of Multistage Geared Systems,” Proc. 8th IFToMM World Congress, Prague, Vol. 2, pp. 621–624.
25.
Velex, P., and Saada, A., 1991b, “Modal Analysis for the Prediction of Dynamic Tooth Loads in Geared Trains,” Proc. 3rd JSME MPT Int. Conf., Hiroshima, pp. 117–122.
26.
Velex, P., Pichon, V., Randrianarivo, L., and Wittman, R., 1994, “Dynamic Behaviour of Epicyclic Trains. Experimental and Numerical Analyses,” Proc. Int. Gearing Conf., Newcastle, pp. 265–269.
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