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RESEARCH PAPERS

A Non-Phenomenological Account of Friction/Vibration Interaction in Rotary Systems

[+] Author and Article Information
Kambiz Farhang

Department of Mechanical Engineering and Energy Processes, Southern Illinois University at Carbondale, Carbondale, Illinois 62901-6603farhang@siu.edu

Aik-Liang Lim

Department of Mechanical Engineering and Energy Processes, Southern Illinois University at Carbondale, Carbondale, Illinois 62901-6603

J. Tribol 128(1), 103-112 (Jun 12, 2005) (10 pages) doi:10.1115/1.2000978 History: Received February 25, 2004; Revised June 12, 2005

Using a nonlinear model of a two disk brake system, coupled equations of motion are found for their frictional interaction. The mathematical formulation relates the tribological events at micron scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a viscoelastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macroscale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macrosystem’s dynamics and contact, there are combinations of parameters at the micro- and macroscale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to decrease with decrease in the normal load and/or increase in structural damping of the system.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of the two-disk model

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Figure 2

Free body diagram for (a) normal and (b) torsional motions

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Figure 3

Asperity shoulder contact at positive and negative interference slopes

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Figure 4

Maximum possible static friction of asperities

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Figure 9

Case 2A: friction torque versus velocity, β=100 to 104.5

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Figure 10

Case 2B: friction torque versus velocity at β=100 to 102.5

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Figure 5

Case 1A: friction torque versus angular velocity at β=100 to 101

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Figure 6

Case 1A: friction torque versus angular velocity at β=138.5 to 140

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Figure 8

Case 1B: friction torque versus velocity, β=135 to 140

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Figure 19

(a) Case 4: friction torque versus angular velocity at β=100 to 105; (b) case 4: friction torque versus angular velocity at β=137 to 140

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Figure 11

The Stribeck curve (1)

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Figure 12

Case 1A: angular speed versus normalized separation at β=100 to 140

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Figure 13

Case 1A: angular speed coefficient (2nd term of torque function) versus normalized separation, h

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Figure 14

Negative damping versus β: (a) Case 1; (b) case 2

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Figure 15

Case 1B: elastic friction torque at fs=0.3

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Figure 16

Critical speed at various h versus β: (a) Case 1B; and (b) case 2B

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Figure 17

Effect of β on negative damping at various maximum torque separations, h

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Figure 7

Case 1B: friction torque versus angular velocity at β=100 to 105

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Figure 18

(a) Case 3: friction torque versus angular velocity at β=100 to 102; (b) case 3: friction torque versus angular velocity at β=112.5 to 114.5; (c) case 3: friction torque versus angular velocity at β=118 to 119

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