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Research Papers

# Two-Dimensional Thermal Model of Asperity Heating in a Disk Pair in Dry Friction Between Two Rough Surfaces

[+] Author and Article Information
A. Elhomani

Department of Innovation
Altec Industries,
Midwest Division,
St. Joseph, MO 64507-9799
e-mail: dellelhomani@gmail.com

K. Farhang

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

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received December 16, 2014; final manuscript received July 6, 2015; published online September 16, 2015. Assoc. Editor: Bengt Sunden.

J. Thermal Sci. Eng. Appl 7(4), 041018 (Sep 16, 2015) (10 pages) Paper No: TSEA-14-1280; doi: 10.1115/1.4031358 History: Received December 16, 2014; Revised July 06, 2015

## Abstract

In this paper, a formulation for the rate of heat generation due to the contact of one asperity with asperities on a second surface is proposed. A statistical approach is used to obtain the heat generation rate due to one asperity and employed to develop the equation for generation of heat rate between two rough surfaces. This heat rate formulation between the two rough surfaces has been incorporated into the 2D lumped parameter model of disk pair in dry friction developed by Elhomani and Farhang (2010, “A 2D Lumped Parameter Model for Prediction of Temperature in C/C Composite Disk Pair in Dry Friction Contact,” ASME J. Therm. Sci. Eng. Appl., 2(2), p. 021001). In this paper, the disk brake is viewed as consisting of three main regions: (1) the surface contact, (2) the friction interface, and (3) the bulk. Both surfaces of the disk brake are subjected to frictional heating. This model is considered to be a necessary step for simulating the aircraft braking system that consists of a stack of multiple disks.

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## References

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Elhomani, A. , and Farhang, K. , 2010, “ A 2D Lumped Parameter Model for Prediction of Temperature in C/C Composite Disk Pair in Dry Friction Contact,” ASME J. Therm. Sci. Eng. Appl., 2(2), p. 021001.

## Figures

Fig. 6

Thermal representation of a disk using lumped thermal elements

Fig. 7

Heat flow in the first layer (a) and last layer (b)—in a friction cell

Fig. 5

Division of a disk into n rings and m layers

Fig. 4

Percent error in Pa(h)

Fig. 3

Integral function P in Eq. (1.16) and its approximation Pa in Eq. (1.17)

Fig. 2

Integral function f in Eq. (1.4) and its approximation fa in Eq. (1.6)

Fig. 1

Sliding of two asperities

Fig. 8

Lumped resistance and capacitance

Fig. 9

Contact surface A temperatures during braking—at time equal 10 s

Fig. 10

Contact surface B temperatures during braking—at time equal 10 s

Fig. 13

Bulk temperatures in layer 1

Fig. 14

Bulk temperatures in layer 2

Fig. 15

Bulk temperatures in layer 3

Fig. 16

Bulk temperatures in layer 4

Fig. 17

Bulk temperatures in layer 5

Fig. 11

Interface A temperatures—stop time 35 s

Fig. 12

Interface B temperatures—stop time 35 s

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