Research Papers: Friction and Wear

Recursive Characteristics of a Running-in Attractor in a Ring-on-Disk Tribosystem

[+] Author and Article Information
Cong Ding

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: dingcong@cumt.edu.cn

Hua Zhu

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: zhuhua83591917@163.com

Yu Jiang

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: Jiangyu@cumt.edu.cn

Guodong Sun

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: guodongsun@cumt.edu.cn

Chunling Wei

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: clweilove@126.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 22, 2018; final manuscript received July 21, 2018; published online August 24, 2018. Assoc. Editor: Daejong Kim.

J. Tribol 141(1), 011604 (Aug 24, 2018) (10 pages) Paper No: TRIB-18-1087; doi: 10.1115/1.4041018 History: Received February 22, 2018; Revised July 21, 2018

To explore the recursive characteristics of a running-in attractor, recurrence plot (RP) and recursive parameters are used to investigate the dynamic features of the structure. The running-in attractor is constructed based on friction noise signals generated from the ring-on-disk wear experiments. The RPs of the running-in attractor are then reproduced in a two-dimensional space. Recursive parameters, recurrence rate (RR), entropy (ENTR), and trend of recurrence (RT) are calculated. Results show that the RP evolves from a disrupted pattern to a homogeneous pattern and then returns to a disrupted pattern in the entire wear process, corresponding to the “formation–stabilization–disappearance” stage of the running-in attractor. The RR and ENTR of the running-in attractor sharply increase at first, remain steady, and then sharply decrease. Moreover, the inclination of RT in the normal wear process is smaller than those in the other two processes. This observation reveals that the running-in attractor exhibits high stability and complexity. This finding may contribute to the running-in state identification, process prediction, and control.

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Fig. 1

Schematic of tribometer

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Fig. 2

Time series of friction noise and coefficient signals: (a) test 1 (P = 1.49 MPa, v = 0.911 m/s), (b) test 2 (P = 1.05 MPa, v = 0.911 m/s), (c) test 3 (P = 1.05 MPa, v = 0.835 m/s), and (d) test 4 (P = 1.05 MPa, v = 0.835 m/s)

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Fig. 3

Photographs of worn specimens: (a) worn ring and (b) worn disk

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Fig. 4

Schematic of principle of RP

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Fig. 5

Typical patterns of RP: (a) disrupted and (b) homogeneous (logistic system)

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Fig. 6

Delaying time τ and embedding dimension m chosen for three tests: (a) delaying time τ and (b) embedding dimension m

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Fig. 7

Recurrence plots based on different ε in different stages of test 1: (a1) ε = σ/8, (a2) ε = σ/4, (a3) ε = σ/2 in the running-in stage and (b1) ε = σ/2, (b2) ε = σ, (b3) ε = 1.5σ in the normal wear stage

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Fig. 8

Evolutions of phase trajectory and RP in test 1: (a1)–(i1) phase trajectories, (a2)–(i2) RPs, (a1), (a2): 0–19 min, (b1), (b2): 38–57 min, (c1), (c2): 76–95 min, (d1), (d2): 95–114 min, (e1), (e2): 209–228 min, (f1), (f2): 323–342 min, (g1), (g2): 437–456 min, (h1), (h2): 475–494 min, and (i1), (i2): 494–516 min

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Fig. 9

Fractal features of RP

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Fig. 10

Recurrence rate and ENTR evolutions of running-in attractor: (a) test 1 (P = 1.49 MPa, v = 0.911 m/s), (b) test 2 (P = 1.05 MPa, v = 0.911 m/s), (c) test 3 (P = 1.05 MPa, v = 0.835 m/s), and (d) test 4 (P = 1.05 MPa, v = 0.835 m/s)

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Fig. 11

Trend of recurrence of running-in attractor in the wear stage

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Fig. 12

Time series of variation z in Lorenz equation

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Fig. 13

Selection of no-scale interval

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Fig. 14

Recurrence plots of logistics system with different lengths: (a) n = 500 and (b) n = 2000



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