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.

## References

1.
Blok
,
H.
,
1937
, “
Theoretical Study of Temperature Rise at Surfaces of Actual Contact Under Oiliness Lubricating Conditions
,” General Discussion on Lubrication and Lubricants, London, Oct. 13–15, Institution of Mechanical Engineers, London, Vol. 2, pp.
222
235
.
2.
Jaeger
,
J. C.
,
1942
, “
Moving Sources of Heat and the Temperature at Sliding Contacts
,”
Proc. R. Soc. N. S. W.
,
76
, pp.
203
224
.
3.
Carslaw
,
H. S.
, and
Jaeger
,
J. C.
,
1959
,
Conduction of Heat in Solids
,
Oxford University Press
,
London
.
4.
Barber
,
J. R.
,
1971
, “
The Solution of Heated Punch Problems by Point Source Methods
,”
Int. J. Eng. Sci.
,
9
(
12
), pp.
1165
1170
.
5.
Barber
,
J. R.
,
1972
, “
The Transient Thermo-Elastic Contact of a Sphere Sliding on a Plane
,”
Wear
,
59
(
1980
), pp.
21
29
.
6.
Barber
,
J. R.
,
1972
, “
Distortion of the Semi-Infinite Solid Due to Transient Surface Heating
,”
Int. J. Mech. Sci.
,
14
(
6
), pp.
377
393
.
7.
Barber
,
J. R.
,
1973
, “
Indentation of a Semi-Infinite Solid by a Hot Sphere
,”
Int. J. Mech. Sci.
,
15
(
10
), pp.
813
819
.
8.
Tian
,
X.
, and
Kennedy
,
F. E.
,
1993
, “
Contact Surface Temperature Models for Finite Bodies in Dry and Boundary Lubricated Sliding
,”
ASME J. Tribol.
,
115
(
3
), pp.
411
418
.
9.
Chantrenne
,
P.
, and
Raynaud
,
M.
,
1996
, “
A Microscopic Thermal Model for Dry Sliding Contact
,”
Int. J. Heat Mass Transfer
,
40
(
5
), pp.
1083
1997
.
10.
Wang
,
Q.
, and
Liu
,
G.
,
1999
, “
A Thermoelastic Asperity Contact Model Considering Steady-State Heat Transfer
,”
Tribol. Trans.
,
42
(
4
), pp.
763
770
.
11.
Liu
,
S.
,
Wang
,
Q.
, and
Liu
,
G.
,
2001
, “
A Three-Dimensional Thermomechanical Model of Contact Between Non-Conforming Rough Surfaces
,”
ASME J. Tribol.
,
123
(
1
), pp.
17
26
.
12.
Liu
,
S.
,
Lannou
,
S.
,
Wang
,
Q.
, and
Keer
,
L.
,
2004
, “
Solutions for Temperature Rise in Stationary/Moving Bodies Caused by Surface Heating With Surface Convection
,”
ASME J. Heat Transfer
,
126
(
5
), pp.
776
785
.
13.
Lin
,
J.
,
Chung
,
J.
,
Chen
,
J.
, and
Liu
,
T.
,
2005
, “
Thermal Analysis of the Transient Temperatures Arising at the Contact Spots of Two Sliding Surfaces
,”
ASME J. Tribol.
,
127
(
4
), pp.
694
704
.
14.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
,
295
(
1442
), pp.
300
319
.
15.
Archard
,
J. F.
,
1959
, “
The Temperature of Rubbing Surfaces
,”
Wear
,
2
(
6
), pp.
438
454
.
16.
Gao
,
J. Q.
,
Lee
,
S. C.
, and
Ai
,
X. L.
,
2000
, “
An FFT-Based Transient Flash Temperature Model for General Three-Dimensional Rough Surface Contacts
,”
ASME J. Tribol.
,
122
(
3
), pp.
519
523
.
17.
McCool
,
J. I.
, and
John
,
J.
,
1988
, “
Flash Temperature on the Asperity Scale and Scuffing
,”
ASME J. Tribol.
,
110
(
4
), pp.
659
663
.
18.
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
.