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Research Papers

Vibrations of Elliptically Shaped Bearings in Strain Wave Gearings

[+] Author and Article Information
Christian Adams

System Reliability and Machine Acoustics SzM,
Department of Mechanical Engineering,
Technische Universität Darmstadt,
Darmstadt 64289, Germany
e-mail: adams@szm.tu-darmstadt.de

Adam Skowronek

System Reliability and Machine Acoustics SzM,
Department of Mechanical Engineering,
Technische Universität Darmstadt,
Darmstadt 64289, Germany
e-mail: adam.skowronek1@gmail.com

Joachim Bös

System Reliability and Machine Acoustics SzM,
Department of Mechanical Engineering,
Technische Universität Darmstadt,
Darmstadt 64289, Germany
e-mail: boes@szm.tu-darmstadt.de

Tobias Melz

Professor
System Reliability and Machine Acoustics SzM,
Department of Mechanical Engineering,
Technische Universität Darmstadt,
Darmstadt 64289, Germany
e-mail: melz@szm.tu-darmstadt.de

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 20, 2015; final manuscript received November 17, 2015; published online January 20, 2016. Assoc. Editor: Patrick S. Keogh.

J. Vib. Acoust 138(2), 021004 (Jan 20, 2016) (6 pages) Paper No: VIB-15-1095; doi: 10.1115/1.4032038 History: Received March 20, 2015; Revised November 17, 2015

The bearing of a strain wave gearing and the covering thin-walled cup, i.e., the so-called flexspline, are elliptically deformed. This leads to a characteristic excitation of vibration. In this paper, a model for describing the vibration of elliptically deformed bearings is presented. First, the flexspline stiffness is calculated using an a priori finite element (FE) analysis that is validated with measured data. Second, the deformation of the bearing and the flexspline is calculated by superimposing single loads. A numerical study shows that vibrations are mainly caused by the rotation of the ellipse. Furthermore, two types of impulses, i.e., negative impulses and positive impulses, lead to vibration excitation. The negative impulses are caused by the balls passing the angular position of the contact force maxima, while the positive impulses are caused by the balls impacting the surfaces of the races due to the radial tolerance of the bearing. Both negative and positive impulses coincide with characteristic frequencies of the nondeformed bearing. If the surfaces of the bearing are considered to be rough, the characteristic frequencies are not affected. Therefore, characteristic frequencies of nondeformed bearings can be utilized to describe vibrations of elliptically shaped bearings as well.

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References

Figures

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Fig. 1

Components of a strain wave gearing, components of the bearing, and ellipse position at 0 deg, 90 deg, and 180 deg (schematically, not to scale)

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Fig. 2

Flexspline and the outer bearing race (schematically, not to scale): left—not deformed and right—elliptically deformed

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Fig. 3

Depiction of the variables used in Eq. (5) for calculating deformation ures,j

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Fig. 4

Flow chart of the calculation scheme

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Fig. 5

Setup for validation by means of an experimental modal analysis

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Fig. 6

Shapes of the first three calculated and measured modes

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Fig. 7

Contact forces of one ball depending on angular position with respect to the large elliptical axis (i.e., φ=0 deg and 180 deg)

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Fig. 14

Spectrum of the acceleration level depending on the radial tolerance, frequency axis corresponds to fn=33.3 s−1

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Fig. 13

Spectrum of the acceleration level at the flexspline surface depending on crough, frequency axis corresponds to fn=33.3 s−1

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Fig. 12

Spectrum of the force level for various radial tolerances, frequency axis corresponds to fn=33.3 s−1

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Fig. 11

Load distribution depending on the angular position with respect to the large elliptical axis (i.e., φ=0 deg)

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Fig. 10

Acceleration versus number of driving shaft rotations depending on the radial tolerance

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Fig. 9

Spectrum of the acceleration level at the flexspline surface, frequency axis corresponds to fn=33.3 s−1

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Fig. 8

Acceleration on the flexspline surface at φ=0 deg: negative impulses are labeled with “–” and positive impulses are labeled with “+”

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