Research Papers

A Stick-Slip Interactions Model of Soft-Solid Frictional Contacts

[+] Author and Article Information
Hongbiao Xiang

Tianjin Key Laboratory for Advanced Mechatronic
System Design and Intelligent Control,
Tianjin University of Technology,
Tianjin 300384, China
e-mail: xhb@tju.edu.cn

Mitja Trkov

Department of Mechanical Engineering,
University of Utah,
Salt Lake City, UT 84112
e-mail: m.trkov@utah.edu

Kaiyan Yu

Department of Mechanical Engineering,
Binghamton University,
Binghamton, NY 13902
e-mail: kyu@binghamton.edu

Jingang Yi

Fellow ASME
Department of Mechanical and
Aerospace Engineering,
Rutgers University,
Piscataway, NJ 08854
e-mail: jgyi@rutgers.edu

1H. X. and M. T. equally contributed to the paper.

2Present address: Tianjin Eco-City Information Park Investment and Development Co., Ltd., Tianjin, 300467, China.

3The author was a visiting scholar with the Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854.

4Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received November 7, 2017; final manuscript received December 5, 2018; published online January 14, 2019. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 141(4), 041015 (Jan 14, 2019) (10 pages) Paper No: DS-17-1556; doi: 10.1115/1.4042247 History: Received November 07, 2017; Revised December 05, 2018

Modeling of the soft-solid frictional interactions plays an important role in many robotic and mechatronic systems design. We present a new model that characterizes the two-dimensional (2D) soft-solid contact interactions. The new computational approach integrates the LuGre dynamic friction model with the beam network structure of the soft-solid contact. The LuGre dynamic friction model uses the bristle deformation to capture the friction characteristics and dynamics, while the beam network structure represents the elastic contact interactions. We also present a model simplification to facilitate analysis of model properties. The model prediction and validation results are demonstrated with the experiments. The experimental results confirm the effectiveness of the modeling development. We further use the model to compute the influence of the normal load and sliding velocity on the stick-slip interaction patterns and properties. These results explain and provide analytical foundation for the reported experiments in the literature.

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Fig. 1

(a) Tire–road contact example [4] and (b) a fingertip contact example [23]

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Fig. 2

A schematic of the beam-spring network model for soft-solid contact: (a) top view of the contact patch and the beams, (b) side view of the three beams and their elastic connections, and (c) forces acting on the individual beam

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Fig. 3

Top view schematic of the IUB computation method on the contact patch

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Fig. 4

(a) Three different patterns of the steady stick-slip behaviors and (b) relationship between λ and damping coefficient cb

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Fig. 5

Transfer function block diagram of the steady-state single-IUB friction model

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Fig. 6

Experimental setup for dynamic sliding motion of a fingertip-like rubber against transparent acrylic plate: (a) the entire system of two degrees-of-freedom linear stage, (b) laser line generators setup [25], and (c) schematics of rubber dimensions

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Fig. 7

Normal load distribution on the contact patch with a normal load Fz = 88 N and no applied horizontal external force. The thin solid circular curve shows the contact contour.

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Fig. 8

Total friction force Ff from experiments and simulation under constant normal load FZ = 88 N and velocity s˙=7.5×10−4 m/s. (a) Comparison of the model predictions under the MLBNM and the LBNM. (b) Zoomed-in comparison results of the transient performance. (c) Zoomed-in comparison results of the steady-state performance.

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Fig. 9

Deformation evolution of a very initial stick to slip transition with time increments of 0.1 s. Deformations are magnified five times.

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Fig. 10

Experimental (a)–(e) and simulation (f)–(j) results of deformation evolution of a single stick-slip oscillation during sliding. Time increment between images is 0.04 s. Deformations are magnified five times.

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Fig. 11

Simulation results of friction force distribution Ffx along the x-axis direction at y =0 from initial loading until steady-state sliding

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Fig. 12

Effect of velocity and normal force variations on the stick-slip friction force oscillation amplitudes and periods with the MLBNM. (a)–(d) Experimental results of rubber VytaFlex 60. (e)–(h) Experimental results of rubber VytaFlex 40. (a) Amplitude variation with velocity s˙ under FZ = 88 N. (b) Period (tss) variation with velocity s˙ under FZ = 88 N. (c) Amplitude variation with normal load FZ under s˙=7.5×10−4 m/s. (d) Period variation with normal load FZ under s˙=7.5×10−4 m/s. (e) Amplitude variation with velocity s˙ under FZ = 88 N. (f) Period variation with velocity s˙ under FZ = 88 N. (g) Amplitude variation with normal load FZ under s˙=1.25×10−4 m/s. (h) Period (tss) variation with normal load FZ under s˙=1.25×10−4 m/s.

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Fig. 13

Comparison of the beam tip velocity profiles between the model (13) and the LuGre/beam model for stick-slip motion with (a) pattern I (σ = 204 in model (13) and cb = 590), (b) pattern II (σ = 52 in model (13) and cb = 148) and (c) pattern III (σ = 2.6 in model (13) and cb = 7.4) for a single oscillation period. (d) Relationship between model parameters σ in model (13) and cb.

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Fig. 14

Stick-slip friction map as the function of the sliding velocity s˙ and normal force Fz. (a) Rubber VytaFlex 60 and (b) Rubber VytaFlex 40. The dash lines in both figures show the model prediction of the critical values of the sliding velocity and the normal load below which stick-slip motion appears.



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