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Research Papers: Applications

Multivariate Graph-Based Analysis on Coefficient of Friction Signal During the Friction Process

[+] Author and Article Information
Guodong Sun, Cong Ding

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China

Hua Zhu

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

Shihui Lang

School of Mechatronic Engineering, China
University of Mining and Technology,
Xuzhou 221116, China

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received August 9, 2018; final manuscript received November 26, 2018; published online January 16, 2019. Assoc. Editor: Stephen Boedo.

J. Tribol 141(4), 041101 (Jan 16, 2019) (9 pages) Paper No: TRIB-18-1317; doi: 10.1115/1.4042199 History: Received August 09, 2018; Revised November 26, 2018

To describe the dynamic evolutionary law and tribological behavior of the tribopair AISI 52100-AISI 1045, rotational experiments were conducted by sliding a disk against a static pin. The multidimensional phase spaces were reconstructed based on the scalar time-series by the time-delay embedding technique, and the multivariate graph-based method was used to visualize the overall picture of the phase space. The evolution of radar plots and the corresponding multivariate graph centrobaric trajectory (MGCT) is consistent with the description of “running-in, steady-state and increasing friction stages,” and can serve as effective indicators for the friction state transitions. Results show that the radar plot can inform quantitative interpretations of friction process identification. Therefore, the multivariate graph-based method is a useful approach to characterize the nonlinear dynamics of tribological behaviors.

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Figures

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Fig. 2

Time-series of COF signals in different rotational tests

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Fig. 1

Schematic of the FTM_M20 tribometer: (a) tribometer and (b) friction pair

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Fig. 3

Bifurcation diagram of 100 generations of Logistic map for growth rates c varies from 2.4 to 4

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Fig. 4

Generation values of Logistic map with different growth rates: (a) c = 2.6, (b) c = 3.2, (c) c = 3.45, (d) c = 3.55, (e) c = 3.65, (f) c = 3.8, (g) c = 3.84, and (h) c = 4.0

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Fig. 5

Radar plots for different scalar time-series acquired from Logistic map: (a) c = 2.6, (b) c = 3.2, (c) c = 3.45, (d) c = 3.55, (e) c = 3.65, (f) c = 3.8, (g) c = 3.84, and (h) c = 4.0

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Fig. 7

Determination for time delay τ and embedding dimension m of four tests

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Fig. 8

Evolution of radar plots of COF signal during the friction process in Test 3: (a) 0-10 min, (b) 10-20 min, (c) 20-30 min, (d) 40-50 min, (e) 60-70 min, (f) 80-90 min, (g) 100-110 min, (h) 120-130 min, (i) 140-150 min, (j) 160-170 min, (k) 170-180 min, and (l) 180-195 min

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Fig. 9

Evolution of MGCT of the radar plots during the friction process in Test 3: (a) 0-10 min, (b) 10-20 min, (c) 20-30 min, (d) 40-50 min, (e) 60-70 min, (f) 80-90 min, (g) 100-110 min, (h) 120-130 min, (i) 140-150 min, (j) 160-170 min, (k) 170-180 min, and (l) 180-195 min

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Fig. 10

Evolution of the first rank moment quantity of MGCT throughout the friction process in test 3: (a) M0,1, (b) M1,1, (c) M2,1, (d) Mx,1, and (e) My,1

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Fig. 11

Evolution of moment quantity M0,1 of MGCT in four tests

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Fig. 6

Radar plots and MGCT for (a) Gaussian noise, (b) periodical-system, and (c) Lorenz system

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