Elastohydrodynamic Lubrication

A New Approach for Including Cage Flexibility in Dynamic Bearing Models by Using Combined Explicit Finite and Discrete Element Methods

[+] Author and Article Information
Ankur Ashtekar

 School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907ankur@purdue.edu

Farshid Sadeghi

 School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907sadeghi@ecn.purdue.edu

See online version of this article

J. Tribol 134(4), 041502 (Sep 04, 2012) (12 pages) doi:10.1115/1.4007348 History: Received December 16, 2011; Revised April 07, 2012; Published September 04, 2012; Online September 04, 2012

In this investigation, a new approach was developed to study the influence of cage flexibility on the dynamics of inner and outer races and balls in a bearing. A 3D explicit finite element model (EFEM) of the cage was developed and combined with an existing discrete element dynamic bearing model (DBM) with six degrees of freedom. The EFEM was used to determine the cage dynamics, deformation, and resulting stresses in a ball bearing under various operating conditions. A novel algorithm was developed to determine the contact forces between the rigid balls and the flexible (deformable) cage. In this new flexible cage dynamic bearing model, the discrete and finite element models interact at each time step to determine the position, velocity, acceleration, and forces of all bearing components. The combined model was applied to investigate the influence of cage flexibility on ball-cage interactions and the resulting ball motion, cage whirl, and the effects of shaft misalignment. The model demonstrates that cage flexibility (deflection) has a significant influence on the ball-cage interaction. The results from this investigation demonstrate that the magnitude of ball-cage impacts and the ball sliding reduced in the presence of a flexible cage; however, as expected, the cage overall motion and angular velocity were largely unaffected by the cage flexibility. During high-speed operation, centrifugal forces contribute substantially to the total cage deformation and resulting stresses. When shaft misalignment is considered, stress cycles are experienced in the bridge and rail sections of the cage where fatigue failures have been observed in practice and in experimental studies.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 4

Tetrahedron and sphere (ball). (a) Q and Q′ distinct. (b) Q and Q′ coincident.

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Figure 5

Ball in contact with two elements

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Figure 1

Model flowchart (FEM = finite element model, DEM = discrete element model)

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Figure 2

Soft DEM contacts (superscript I = inertia fram; r = rotating body frame; a = azimuthal frame). (a) Ball-ball conformal contact. (b) Inner race reference frames. (c) Ball-race non-conformal contact.

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Figure 12

Comparison of ball—cage contact force (red: rigid, blue: flexible). See online version of this article.

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Figure 13

Comparison of ball angular velocity (blue: EFEM, red: Weinzapfel and Sadeghi [7]). See online version of this article.

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Figure 14

Ball motion with flexible cage (red) and rigid cage (blue). See online version of this article.

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Figure 15

Cage whirl: (a) rigid cage and (b) flexible cage

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Figure 16

Deformation of machined-cage in bearing #1 and 20,000 rpm. (a) Cage radius. (b) Cage stress and deformation (1000 × deformation).

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Figure 17

Cage operating and high speed: (a) cage expansion and (b) cage stress

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Figure 18

Ball-cage contact force for moment loads: (a) My = 100 Nm, (b) My = 500 Nm, and (c) My = 1000 Nm

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Figure 19

von Mises stress (Pa) of cage finite element

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Figure 6

Ball in contact with multiple elements. (a) Ball in contact with fine mesh. (b) Coarse mesh. (c) Medium mesh. (d) Fine mesh.

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Figure 7

Hertzian and EFEM contact pressure for a contact. (a) Comparison of Hertzian pressure (black) with EFEM pressure (blue). (b) Percent difference in pressures.See online version of this article.

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Figure 8

Experimental model analysis setup and procedure

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Figure 9

Frequency response of cage

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Figure 10

Cage model verification with ABAQUS: (a) cage loading, (b) EFEM, and (c) ABAQUS results

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Figure 11

Comparison of ball—cage contact force (black: rigid, red: EFEM, blue: Weinzapfel and Sadeghi [7]). See online version of this article.



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