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Research Papers: Other (Seals, Manufacturing)

Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings

[+] Author and Article Information
Shengye Lin

School of Mechanical Engineering,
Southeast University,
2 Southeast Road, Jiangning District,
Nanjing 211189, China

Shuyun Jiang

Professor
School of Mechanical Engineering,
Southeast University,
2 Southeast Road, Jiangning District,
Nanjing 211189, China
e-mail: jiangshy@seu.edu.cn

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 27, 2018; final manuscript received October 24, 2018; published online November 29, 2018. Assoc. Editor: Carl Hager.

J. Tribol 141(3), 032204 (Nov 29, 2018) (13 pages) Paper No: TRIB-18-1211; doi: 10.1115/1.4041895 History: Received May 27, 2018; Revised October 24, 2018

This paper studies the stiffness characteristics of preloaded duplex angular contact ball bearings. First, a five degrees-of-freedom (5DOF) quasi-static model of the preloaded duplex angular contact ball bearing is established based on the Jones bearing model. Three bearing configurations (face-to-face, back-to-back, and tandem arrangements) and two preload mechanisms (constant pressure preload and fixed position preload) are included in the proposed model. Subsequently, the five-dimensional stiffness matrix of the preloaded duplex angular contact ball bearing is derived analytically. Then, an experimental setup is developed to measure the radial stiffness and the angular stiffness of duplex angular contact ball bearings. The simulated results match well with those from experiments, which prove the validity of the proposed model. Finally, the effects of bearing configuration, preload mechanism, and unloaded contact angle on the angular stiffness and the cross-coupling are studied systematically.

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Figures

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Fig. 1

The schematic of duplex angular contact ball bearings with three configurations

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Fig. 2

(a) Coordinate systems for the modeling of duplex angular contact ball bearings: face-to-face, (b) coordinate systems for the modeling of duplex angular contact ball bearings: back-to-back, and (c) coordinate systems for the modeling of duplex angular contact ball bearings: tandem

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Fig. 3

Axial displacements of the inner and outer rings under constant pressure preload

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Fig. 4

Positions of the ball center and raceway groove curvature centers at angular position ψqj

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Fig. 5

The schematic of forces applying on the jth ball of bearing q

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Fig. 6

The calculation flowchart of the stiffness matrix for the preloaded duplex angular contact ball bearing

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Fig. 7

(a) The test rig for measuring the stiffness of duplex angular contact ball bearings: schematic view of the test rig, (b) the test rig for measuring the stiffness of duplex angular contact ball bearings: preload methods for the bearings with three configurations, (c) the test rig for measuring the stiffness of duplex angular contact ball bearings: real scene image of test rig, and (d) the test rig for measuring the stiffness of duplex angular contact ball bearings: the auxiliary equipment and the vibration signal detecting system

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Fig. 8

(a) The measuring method of the bearings' stiffness: radial stiffness. (b) The measuring method of the bearings' stiffness: angular stiffness.

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Fig. 9

(a) The vibration signals of xF0, xR0, xF, xR under the rotary speed of 6000 rpm: radial stiffness. (b) The vibration signals of xF0, xR0, xF, xR under the rotary speed of 6000 rpm: angular stiffness.

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Fig. 10

(a) The stiffness coefficients of duplex bearings with back-to-back and tandem arrangements: radial stiffness. (b) The stiffness coefficients of duplex bearings with back-to-back and tandem arrangements: angular stiffness.

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Fig. 11

(a) Stiffness coefficients of duplex angular contact ball bearings with three configurations: angular stiffness. (b) Stiffness coefficients of duplex angular contact ball bearings with three configurations: cross-coupling stiffness.

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Fig. 12

(a) Force analysis of duplex angular contact ball bearings with three configurations: face-to-face, (b) force analysis of duplex angular contact ball bearings with three configurations: back-to-back, and (c) force analysis of duplex angular contact ball bearings with three configurations: tandem

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Fig. 13

(a) Stiffness coefficients of duplex angular contact ball bearings with respect to the unloaded contact angle: angular stiffness. (b) Stiffness coefficients of duplex angular contact ball bearings with respect to the unloaded contact angle: cross-coupling stiffness.

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Fig. 14

(a) Variations of Le and S with respect to contact angle: Le versus α0. (b) Variations of Le and S with respect to contact angle: S versus α0.

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Fig. 15

(a) Stiffness coefficients of the tandem duplex angular contact ball bearing under two preload mechanisms: angular stiffness. (b) Stiffness coefficients of the tandem duplex angular contact ball bearing under two preload mechanisms: cross-coupling stiffness.

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Fig. 16

(a) Axial displacement of the inner rings under two preload mechanisms: schematic view. (b) Axial displacement of the inner rings under two preload mechanisms: axial displacement.

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Fig. 17

(a) Inner contact angles and inner contact forces under two preload mechanisms: inner contact force. (b) Inner contact angles and inner contact forces under two preload mechanisms: inner contact angle.

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