Measurement and Modeling of Dynamic Rolling Friction in Linear Microball Bearings

[+] Author and Article Information
Xiaobo Tan

Department of Electrical & Computer Engineering,  Michigan State University, East Lansing, MI 48824xbtan@msu.edu

Alireza Modafe

Department of Electrical & Computer Engineering, and Institute for Systems Research,  University of Maryland, College Park, MD 20742modafe@glue.umd.edu

Reza Ghodssi

Department of Electrical & Computer Engineering, and Institute for Systems Research,  University of Maryland, College Park, MD 20742ghodssi@glue.umd.edu

The COF computed from the viscoelastic model will depend on the normal load. The results reported are based on the load used in the experiments.

J. Dyn. Sys., Meas., Control 128(4), 891-898 (Apr 09, 2006) (8 pages) doi:10.1115/1.2362786 History: Received June 14, 2005; Revised April 09, 2006

In prior work of the authors and co-workers, a vision-based system was developed for characterizing the tribological behavior of silicon-micromachined linear microball bearings. Plain difference methods introduce amplitude and/or phase distortion in computing the derivative signals (e.g., velocity and acceleration) based on the position snapshots. In this paper frequency-dependent amplitude and phase compensation algorithms are developed for both the forward difference and the central difference methods to retrieve without distortion the friction and the relative velocity between bearing elements. Processing of experimental data with these techniques reveals nonlinear, viscous frictional behavior in the bearing. A viscoelastic model based on a continuum of mass-spring-damper elements is then proposed for the ball-groove interaction. Numerical results show that this model captures the nonlinear velocity dependence of the rolling friction observed in experiments.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic of a linear microball bearing (11)

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Figure 2

Vision-based experimental setup

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Figure 3

The three-stage data processing algorithm, applicable to both the forward difference method and the central forward method

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Figure 4

Comparison of difference methods: (a) forward difference method, (b) forward-difference-based three-stage algorithm, (c) central difference method, and (d) central-difference-based three-stage algorithm

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Figure 5

Effect of amplitude compensation on the approximation error

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Figure 6

Experimentally measured trajectories of the slider (top), the stator (center), and their relative position (bottom)

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Figure 7

Slider acceleration (friction) versus relative velocity under different data processing schemes. (a) Low-pass filtering followed by forward difference; (b) three-stage algorithm based on forward difference; and (c) three-stage algorithm based on central difference

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Figure 8

The Langevin approximation to experimental data

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Figure 9

Simulated position trajectories of xslid, xstat, and xslid−xstat

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Figure 10

A viscous ball rolling on a viscous plane

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Figure 11

Characterization of the projection AC of the contact area

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Figure 12

Computed COF versus experimental measurement

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Figure 13

Computed COF for a larger velocity range

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Figure 14

Computed penetration depth



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