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Research Papers: Elastohydrodynamic Lubrication

# Influence of Lubricant Traction Coefficient on Cage's Nonlinear Dynamic Behavior in High-Speed Cylindrical Roller Bearing

[+] Author and Article Information
Wenhu Zhang

School of Mechatronics Engineering,
Northwestern Polytechnical University,
Xi'an 710071, China
e-mail: 526916105@qq.com

Sier Deng

Professor
School of Mechatronics Engineering,
Henan University of Science and Technology,
Luoyang 471003, China
e-mail: dse@haust.edu.cn

Guoding Chen

Professor
School of Mechatronics Engineering,
Northwestern Polytechnical University,
Xi'an 710071, China
e-mail: gdchen@nwpu.edu.cn

Yongcun Cui

School of Mechatronics Engineering,
Northwestern Polytechnical University,
Xi'an 710071, China
e-mail: 372865368@qq.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 12, 2016; final manuscript received March 1, 2017; published online June 30, 2017. Assoc. Editor: Xiaolan Ai.

J. Tribol 139(6), 061502 (Jun 30, 2017) (11 pages) Paper No: TRIB-16-1216; doi: 10.1115/1.4036274 History: Received July 12, 2016; Revised March 01, 2017

## Abstract

In this paper, the formulas of elastohydrodynamic traction coefficients of four Chinese aviation lubricating oils, namely, 4109, 4106, 4050, and 4010, were obtained by a great number of elastohydrodynamic traction tests. The nonlinear dynamics differential equations of high-speed cylindrical roller bearing were built on the basis of dynamic theory of rolling bearings and solved by Hilber–Hughes–Taylor (HHT) integer algorithm with variable step. The influence of lubricant traction coefficient on cage's nonlinear dynamic behavior was investigated, and Poincaré map was used to analyze the influence of four types of aviation lubricating oils on the nonlinear dynamic response of cage's mass center. The period of nonlinear dynamic response of cage's mass center was used to assess cage's stability. The results of this paper provide the theoretical basis for selection of aviation lubricating oil.

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## References

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## Figures

Fig. 1

Construction of the test rig

Fig. 2

Traction coefficient μ under different slide to roll ratio: (a) W = 20 N, U = 15 m/s, T = 80 °C and (b) W = 135 N, U = 15 m/s, T = 27 °C

Fig. 3

Coordinate systems of cylindrical roller bearing

Fig. 4

Schematic diagram of cylindrical roller bearing: (a) unloaded bearing and (b) loaded bearing

Fig. 5

Schematic diagram of roller forces

Fig. 6

Schematic diagram of cage forces

Fig. 7

Solution procedure of dynamics differential equations

Fig. 8

Trajectory and Poincaré map under different bearing speeds (4109): (a) ω = 20,000 r/min, (b) ω = 30,000 r/min, and (c) ω = 40,000 r/min

Fig. 10

Trajectory and Poincaré map under different bearing speeds (4050 and 4010): (a) 4050, ω = 20,000–40,000 r/min and (b) 4010, ω = 20,000–40,000 r/min

Fig. 9

Trajectory and Poincaré map under different speeds (4106): (a) ω = 20,000 r/min, (b) ω = 30,000 r/min, and (c) ω = 40,000 r/min

Fig. 11

Trajectory and Poincaré map under different radial forces (4109 and 4106): (a) 4109, Fr = 1000–8000 N and (b) 4106, Fr = 1000–8000 N

Fig. 12

Trajectory and Poincaré map under different radial forces (4050): (a) Fr = 1000 N, (b) Fr = 4000 N, and (c) Fr = 8000 N

Fig. 13

Trajectory and Poincaré map under different radial forces (4010): (a) Fr = 1000 N, (b) Fr = 4000 N, and (c) Fr = 8000 N

Fig. 14

Trajectory and Poincaré map under different lubricant temperatures (4109): (a) T = 80 °C, Fr = 1000 N, (b) T = 130 °C, Fr = 1000 N, (c) T = 180 °C, Fr = 1000 N, and (d) T = 80–180 °C, Fr = 8000 N

Fig. 15

Trajectory and Poincaré map under different lubricant temperatures (4106): (a) T = 80 °C, Fr = 1000 N, (b) T = 130 °C, Fr = 1000 N, (c) T = 180 °C, Fr = 1000 N, (d) T = 80 °C, Fr = 8000 N, (e) T = 130 °C, Fr = 8000 N, and (f) T = 180 °C, Fr = 8000 N

Fig. 16

Trajectory and Poincaré map under different lubricant temperatures (4050): (a) T = 80–180 °C, Fr = 1000 N, (b) T = 80 °C, Fr = 8000 N, (c) T = 130 °C, Fr = 8000 N, and (d) T = 180 °C, Fr = 8000 N

Fig. 17

Trajectory and Poincaré map under different lubricant temperatures (4010): (a) T = 80 °C, Fr = 1000 N, (b) T = 130–180 °C, Fr = 1000 N, and (c) T = 80–180 °C, Fr = 8000 N

Fig. 18

Cage dynamic performance test rig for aerobearing

Fig. 19

Whirl orbit of cage detected by test rig: (a) 4109, (b) 4106, (c) 4050, and (d) 4010

Fig. 20

Whirl orbit of cage detected by test rig: (a) 4109, (b) 4106, (c) 4050, and (d) 4010

## Errata

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