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Research Papers

Natural Frequency Clusters in Planetary Gear Vibration

[+] Author and Article Information
Tristan M. Ericson

Visiting Assistant Professor
Department of Mechanical Engineering,
Bucknell University,
Lewisburg, PA 17837
e-mail: tme006@bucknell.edu

Robert G. Parker

L. S. Randolph Professor and Department Head
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: r.parker@vt.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received July 24, 2012; final manuscript received March 4, 2013; published online June 19, 2013. Assoc. Editor: Philippe Velex.

J. Vib. Acoust 135(6), 061002 (Jun 19, 2013) (13 pages) Paper No: VIB-12-1211; doi: 10.1115/1.4023993 History: Received July 24, 2012; Revised March 04, 2013

This paper investigates how the natural frequencies of planetary gears tend to gather into clusters (or groups). This behavior is observed experimentally and analyzed in further detail by numerical analysis. There are three natural frequency clusters at relatively high frequencies. The modes at these natural frequencies are marked by planet gear motion and contain strain energy in the tooth meshes and planet bearings. Each cluster contains one rotational, one translational, and one planet mode type discussed in previous research. The clustering phenomenon is robust, continuing through parameter variations of several orders of magnitude. The natural frequency clusters move together as a group when planet parameters change. They never intersect, but when the natural frequencies clusters approach each other, they exchange modal properties and veer away. When central member parameters are varied, the clusters remain nearly constant except for regions in which natural frequencies simultaneously shift to different cluster groups. There are two conditions that disrupt the clustering effect or diminish its prominence. One is when the planet parameters are similar to those of the other components, and the other is when there are large differences in mass, moment of inertia, bearing stiffness, or mesh stiffness among the planet gears. The clusters remain grouped together with arbitrary planet spacing.

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References

Figures

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Fig. 1

Analytical lumped-parameter planetary gear model

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Fig. 2

Expanded planetary gear system model with additional components of the experimental fixtures

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Fig. 3

Planetary gear modal testing setup (a) photograph and (b) schematic diagram showing the sun gear shaft connected to the bedplate through a load cell on an extension arm and the carrier shaft connected to a torque actuator through the compliant coupling

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Fig. 4

Comparison of strain energy distribution between a low-frequency fixture mode (black bar) and a high-frequency gear mode (gray bar) in (a) two rotational modes, and (b) two translational modes from the analytical model

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Fig. 5

Experimentally measured planet gear rotational acceleration in the gear mode range of the (top) three-planet, (middle) four-planet, and (bottom) five-planet gear systems with the modal shaker tangentially exciting the planet gear body. The applied torque is 68 N m at the sun gear in all three configurations.

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Fig. 6

Natural frequencies from the analytical model of a five-planet gear system showing three clusters of gear modes, each with one () rotational, one () translational, and one () planet mode

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Fig. 7

Analytical model mode shapes of the five-planet test gear in Table 1 in the high-frequency gear mode range grouped into three clusters

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Fig. 8

Natural frequency sensitivity from the analytical model of () rotational, () translational, and (— —) planet gear modes in the five-planet gear system to (a) sun-planet mesh stiffness and (b) both sun-planet and ring-planet mesh stiffnesses with the nominal values indicated in the center of both plots

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Fig. 9

Natural frequency sensitivity from the analytical model of () rotational, () translational, and (— —) planet gear modes in the five-planet gear system to planet bearing stiffness with the nominal planet bearing stiffnesses indicated in the center of (a), and (b) a zoomed view of cluster 1 passing through the fixture mode range with mode shapes showing veering

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Fig. 10

Natural frequency sensitivity from the analytical model of () rotational, () translational, and (— —) planet gear modes in the five-planet gear system to planet moment of inertia with the nominal planet moment of inertia indicated in the center of (a), and (b) a zoomed view of veering between cluster 2 and cluster 3 with the nominal value indicated at 1:606 × 10−3 kg m2

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Fig. 11

Natural frequency sensitivity from the analytical model of () rotational, () translational, and (— —) planet gear modes in the five-planet gear system to planet (a) mass, and (b) both mass and moment of inertia with the nominal values indicated in the center of both plots

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Fig. 12

Natural frequency sensitivity from the analytical model of () rotational, () translational, and (— —) planet gear modes in the five-planet gear system to (a) sun gear moment of inertia with the nominal value indicated at 64.04 × 10−3 kg m2 and (a) carrier bearing stiffness with the nominal stiffness value of 10.1 × 106 N/m on the left-hand side of the plot

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Fig. 13

Natural frequencies from the analytical model of () rotational, () translational, and (— —) planet gear modes in the five-planet experimental gear system as planet parameters are changed to sun gear parameters. The nominal planet parameters are used on the left-hand side of the plot. Moving right, planet mass and moment of inertia are decreased and planet bearing stiffness is increased on a log scale. The planet parameters equal the sun gear parameters on the right-hand side.

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Fig. 15

Natural frequencies from the analytical model of the three-planet gear system with variation in ring-planet mesh stiffness of (a) −10% in planet 1, +10% in planet 3; (b) −25% in planet 1, +25% in planet 3; and (c) −50% in planet 1, +50% in planet 3. Planet 2 ring-planet mesh stiffness has the nominal value in all cases. The same planet bearing stiffness (315 × 106 N m) is used in the tangential and radial directions.

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Fig. 16

Natural frequencies from the analytical model of the three-planet gear system with variation in planet bearing stiffness of (a) −10% in planet 1, +10% in planet 3; (b) −25% in planet 1, +25% in planet 3; and (c) −50% in planet 1, +50% in planet 3. Planet 2 bearing stiffness has the nominal value in all cases. The same planet bearing stiffness (315 × 106 N m) is used in the tangential and radial directions.

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Fig. 17

Natural frequencies from the analytical model of the three-planet gear system with simultaneous variation in planet mass and moment of: inertia of (a) −1% in planet 1, +1% in planet 3; (b) −5% in planet 1, +5% in planet 3; and (c) −10% in planet 1, +10% in planet 3. Planet 2 mass and moment of inertia have the nominal values in all cases. The same planet bearing stiffness (315 × 106 N m) is used in the tangential and radial directions.

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Fig. 18

Natural frequencies from the analytical model of the three-planet gear system with planets arbitrarily spaces at 0 deg, 77 deg, and 192 deg. The same planet bearing stiffness (315 × 106 N m) is used in the tangential and radial directions.

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Fig. 19

Natural frequencies from the analytical model of the three-planet gear system with planet 1 fixed at 0 deg, planet 2 at 77 deg, and the location of planet 3 varied from 120 deg to 340 deg. The same planet bearing stiffness (315 × 106 N m) is used in the tangential and radial directions.

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Fig. 14

Natural frequencies from the analytical model of the three-planet gear system showing three clusters of gear modes from the analytical model with () rotational and () translational modes. Mass and stiffness parameters are the same in each planet. The same planet bearing stiffness (315 × 106 N m) is used in the tangential and radial directions.

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