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Research Papers: Applications

A Dynamic Analysis of Cage Instability in Ball Bearings

[+] Author and Article Information
Takashi Nogi

Japan Aerospace Exploration Agency,
7-44-1 Jindaiji-higashimachi,
Chofu, Tokyo 182-8522, Japan
e-mail: nogitak@gmail.com

Kazuaki Maniwa

Japan Aerospace Exploration Agency,
2-1-1 Sengen,
Tsukuba, Ibaraki 305-8505, Japan
e-mail: maniwa.kazuaki@jaxa.jp

Noriko Matsuoka

Japan Aerospace Exploration Agency,
7-44-1 Jindaiji-higashimachi,
Chofu, Tokyo 182-8522, Japan
e-mail: matsuoka.noriko@jaxa.jp

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 22, 2017; final manuscript received March 24, 2017; published online July 10, 2017. Assoc. Editor: Xiaolan Ai.

J. Tribol 140(1), 011101 (Jul 10, 2017) (12 pages) Paper No: TRIB-17-1030; doi: 10.1115/1.4036451 History: Received January 22, 2017; Revised March 24, 2017

Cage motions in ball bearings are investigated using a dynamic analysis program. Increases in the cage friction coefficient induce unstable motions of the cage. The instability is more likely to occur under high load and low‐speed conditions due to less ball-race sliding. A simple theory of cage instability is developed, and a critical cage friction coefficient formula is proposed, which is a function of the cage mass, ball-race traction, ball-cage contact stiffness, cage rotational speed, and number of balls. The prediction of this formula agrees with the results of the dynamic analysis. With a nonuniform separation between the balls, a high-speed whirl is superimposed on the normal whirl with the ball group speed. The direction of the high-speed whirl is the same as the cage rotational direction in inner race rotation (IR), but they are opposite in outer race rotation (OR). These results agree with some experimental results in the literature and validate the dynamic analysis.

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Figures

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Fig. 1

Coordinate frames for ball-inner race contact

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Fig. 2

Contact ellipse divided into strips to calculate EHL traction

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Fig. 3

Coordinate frames for ball-cage contact

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Fig. 5

Position of the center of the cage in the 7003 bearing (IR): axial load of 10 N, rotational speed of 1500 rpm, and friction coefficient of 0.1

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Fig. 6

Position of the center of the cage in the 7003 bearing (IR): axial load of 10 N, rotational speed of 6000 rpm, and friction coefficient of 0.1

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Fig. 7

Position of the center of the cage in the 7003 bearing (IR): axial load of 44 N, rotational speed of 1500 rpm, and friction coefficient of 0.1

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Fig. 9

Relation between the whirl velocity ratio and the friction coefficient

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Fig. 10

Ball-cage relative velocity in the 7003 bearing (IR): axial load of 44 N, rotational speed of 6000 rpm, and friction coefficient of 0.1

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Fig. 11

Ball-cage contact load in the 7003 bearing (IR): axial load of 44 N, rotational speed of 6000 rpm, and friction coefficient of 0.1

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Fig. 12

Cage angular velocity in the 7003 bearing (IR): axial load of 44 N, rotational speed of 1500 rpm, and friction coefficient of 0.1

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Fig. 13

Ball-cage contact load in the 7003 bearing (IR): axial load of 44 N, rotational speed of 1500 rpm, and friction coefficient of 0.1

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Fig. 14

Relation between the whirl velocity ratio and the friction coefficient ratio

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Fig. 15

Azimuth angle between two adjacent balls in the 7003 bearing (IR): axial load of 10 N, rotational speed of 6000 rpm, and friction coefficient of 0.1

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Fig. 16

Stable motion of the cage in the 7003 bearing (OR): axial load of 10 N, rotational speed of 6000 rpm, and friction coefficient of 0.1

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Fig. 17

Unstable motion of the cage in the 7003 bearing (OR): axial load of 44 N, rotational speed of 1850 rpm, and friction coefficient of 0.1

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Fig. 18

Stable motion of the cage in the 7003 bearing (IR): axial load of 10 N, rotational speed of 1500 rpm, and friction coefficient of 0.1

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Fig. 19

Unstable motion of the cage in the 7003 bearing (IR): axial load of 44 N, rotational speed of 1500 rpm, and friction coefficient of 0.1

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Fig. 20

Position of the center of the cage in the 7003 bearing (IR): axial load of 44 N, rotational speed of 6000 rpm, and friction coefficient of 0.15. Gravity is in the −z direction.

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Fig. 21

Position of the center of the cage in the 7003 bearing (IR): axial load of 44 N, rotational speed of 12,000 rpm, and friction coefficient of 0.30. Gravity is in the −z direction.

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