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Research Papers: Applications

Dynamic Analysis of Cage Stress in Tapered Roller Bearings Using Component-Mode-Synthesis Method

[+] Author and Article Information
Tomoya Sakaguchi, Kazuyoshi Harada

Elemental Technological R&D Center, NTN Corporation, 3066, Higashikata, Kuwana, Mie 511-8678, Japan

J. Tribol 131(1), 011102 (Dec 04, 2008) (9 pages) doi:10.1115/1.3002326 History: Received February 27, 2008; Revised September 09, 2008; Published December 04, 2008

In order to investigate cage stress in tapered roller bearings, a dynamic analysis tool considering both the six degrees of freedom of motion of the rollers and cage and the elastic deformation of the cage was developed. Cage elastic deformation is equipped using a component-mode-synthesis (CMS) method. Contact forces on the elastically deforming surfaces of the cage pocket are calculated at all node points of finite-elements on it. The location and pattern of the boundary points required for the component-mode-synthesis method were examined by comparing cage stresses in a static condition of pocket forces and constraints calculated by using the finite-element and the CMS methods. These results indicated that one boundary point lying at the center on each bar is appropriate for the effective dynamic analysis model focusing on the cage stress, especially at the pocket corners of the cages, which are actually broken. A behavior measurement of a polyamide cage in a tapered roller bearing was conducted for validating the analysis model. It was confirmed in both the experiment and analysis that the cage whirled under a large axial load condition and the cage center oscillated in a small amplitude under a small axial load condition. In the analysis, the authors discussed the four models including elastic bodies having a normal eigenmode of 0, 8 or 22, and rigid-body. There were small differences among the cage center loci of the four models. These two cages having normal eigenmodes of 0 and rigid-body whirled with imperceptible fluctuations. At least approximately 8 normal eigenmodes of cages should be introduced to conduct a more accurate dynamic analysis although the effect of the number of normal eigenmodes on the stresses at the pocket corners was insignificant. From the above, it was concluded to be appropriate to introduce one boundary point lying at the center on each pocket bar of cages and approximately 8 normal eigenmodes to effectively introduce the cage elastic deformations into a dynamic analysis model.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Interaction elements considered in this analysis (2)

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Figure 2

Boundary condition to compare cage stresses using component-mode-synthesis and finite-element methods

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Figure 3

Maximum von-Mises stress on cage due to point load on pocket surface. (a) von-Mises stress and (b) pattern of the boundary points with respect to a pocket bar.

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Figure 4

Example of pocket force locations on cage due to roller contacts

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Figure 5

Experimental appratus

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Figure 6

Schematic of the bearing and the sensors

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Figure 7

Measured cage center loci (gravity is downward)

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Figure 8

Numerical simulated cage center loci (Normal eigenmode No.: 8, friction coefficient on cage pocket: 0.06, and boundary point: 1 / bar)

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Figure 9

History of numerical simulated cage center (Normal eigenmode No.: 8, friction coefficient on cage pocket: 0.06, and boundary point: 1 / bar)

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Figure 10

Numerical simulated cage center loci in various cases of cage body assumptions. (a) Rigid, (b) normal eigenmode No.: 0, (c) normal eigenmode No.: 8, and (d) normal eigenmode No.: 22. (Friction coefficient on cage pocket: 0.06, and boundary point: 1 / bar.)

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Figure 11

von-Mises stress distributions and roller interactions on cages under axial load conditions. (a) Fa/Cr=0.5%, and (b) Fa/Cr=8%. (Rollers and races are invisible, and gravity is downward, friction coefficient on cage pocket: 0.06, and boundary point: 1 / bar.)

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Figure 12

Maximum von-Mises stress on cage in pocket corners with various number of its eigenmodes and friction coefficient fc on pockets. (a) Fa/Cr=0.5%, and (b) Fa/Cr=8%. (Normal eigenmode No.: 8, friction coefficient on cage pocket: 0.06, and boundary point: 1 / bar.)

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