Measurements of Thermal Contact M Rosochowska-2003

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Measurements of thermal contact conductance

M. Rosochowska, R. Balendra*, K. Chodnikiewicz Department of Design, Manufacture and Engineering Management, University of Strathclyde, James Weir Building,

75 Montrose Street, Glasgow G1 1XJ, UK

Abstract

During forging, the transfer of heat between the component, the tools and the environment has an impact on tool-life and the accuracy of the

formed component. Consequently, the measurement of thermal contact conductance is of increasing interest to researchers and industrial

engineers participating in the manufacture of high-precision components by plastic deformation. It is recognised that thermal contact

conductance is a function of several parameters, the dominant ones being the type of contacting materials, the macro- and micro-geometry of the contacting surfaces, temperature, the interfacial pressure, the type of lubricant or contaminant and its thickness. A new steady-state

method and measurement equipment areproposed in which the measurements areconducted on thin cylindrical specimens, which areretained

under pressure between two tools. A clear advantage of this method is the ability to measure the thermal contact conductance under precisely

controlled conditions. Due to the small aspect ratio of the specimen, the applied pressure may be of the same magnitude as that prevailing in

industrial bulk-metal forming processes. In the present paper some experimental results on the dependence of h on the pressure and the

specimen texture are presented.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Heat; Transfer; Coefficient

1. Introduction

The energy expended to plastically deform materials in

metal-forming processes is converted almost entirely into

heat, this energy increasing the temperature of the formed

component and the tools while some of it is dissipated to the

environment. The transfer of heat to the component and tools

has an impact on the accuracy of the formed component.

Consequently, heat transfer from the work-material to the

tool and the environment is of increasing interest to

researchers and engineers participating in the manufacture

of high-precision components by the plastic deformation of

engineering materials. At the initiation of manufacture, the

thermal conditions at the component–tool interface are in atransitional state: cycles of temperature change occur over

both the individual forming operation and the working day.

Many forming operations have to be completed for the tools

to acquire their saturation temperature. At this stage, each

successive operation provides a quantum of energy, which

equals that which is dissipated to the environment. A quasi-

steady-state is then maintained so long as the forming

parameters and the environmental conditions remain

unchanged [1].

The reliability of analytical approaches depends on the

accuracy of the material properties and the physical para-meters that influence heat transfer between solids [1–3]. The

latter refers to values for specific heat, thermal conductance

and coefficient of thermal expansion of both the component

and the tool materials; whilst a further consideration is the

allocation of a value for thermal contact conductance, since

this determines the thermal balance in the component/tool/

environment system.

Thermal contact conductance h, also known as the heat-

transfer coefficient, is defined as follows [4]:

h ¼q

DT (1)

in which DT is the temperature difference at the contacting

surfaces and q, the heat flux, defined as

q ¼d

d A

dQ

dt

(2)

It is recognised that thermal contact conductance is a func-

tion of several parameters, the dominant ones being the type

of contacting materials, the macro- and micro-geometry of

the contacting surfaces, the temperature, the interfacial

pressure, the type of lubricant or contaminant and its thick-

ness. The interfacial pressure between contacting surfaces

during plastic deformation (component/die, component/

Journal of Materials Processing Technology 135 (2003) 204–210

* Corresponding author.

E-mail address: [email protected] (R. Balendra).

0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 8 9 7 - X



punch and component/ejector) is often of an order higher

than the yield strength of the work-material. Further, the

variation of this interfacial pressure with time has a sig-

nificant influence on the thermal contact conductance. An

increasing trend in cold metal forming is to attempt to

manufacture the net shape of the component, which requires

a more complete understanding of the plastic deformation of engineering materials. To-date, several different thermody-

namic models have been used to compute the thermal

contact conductance [5–7].

Measurements of the coef ficient h have been carried out

while heat transfer was either in a steady-state [8] or

transient condition [9,10]. Experiments were conducted

using devices that contained two tools [9,10] or two tools

with a specimen sandwiched between them [9,11,12]. These

experiments were followed by an assessment of the thermal

contact conductance while the test specimen was deformed

plastically [9,11,12]: a further development involved the

incorporation of thermocouples in the specimen [13,14]. In

the simplest case of steady-state heat transfer, h may be

determined using Eq. (1). Another method is based on

matching the measured temperature distribution to analy-

tical or numerical solutions for various values of h [9–13].

While using this method, experiments are conducted to

establish temperature contours, which are then compared

to the results of numerical simulations. The thermal contact

conductance is assumed to be the value that provides the best

match between simulation and experimental results. A

further method is based on the solution of an inverse

problem. The sequential inverse method [14] has been used

to determine the thermal contact conductance in metal

forming processes. Review of publications [8–15] suggests

that values of h vary substantially, perhaps due to the fact

that these were derived using different experimental

approaches. Published values were derived from experi-

ments of different configurations, e.g. different materials,

surface preparation, lubricant, pressure and temperature,

thus disabling comparison. Values of h ¼ 7:5 and 17 kW/ m2 K were derived for an aluminium alloy (2024-0) by

compressing ring specimens between dies made of IN-

100 for a deformation speed of 1 mm/s and 56 m/s, respec-

tively, the lubricant used being Renite S52 [9]. Another

study, in which the dependence of h on the interfacial

pressure was taken into account, defined h ¼ 10 and

40 kW/m2 K under contact pressures of 6.9 and 110 MPa,

respectively. These tests were conducted using specimens

similar to those used in previous research, on dies made of

H-12 tool steel, lubricated with MoS2 [8]. Further, the

variation of thermal contact conductance with pressure

showed trends which appeared to depend on the work-

material and experimental conditions. From a more detailed

analysis [15] the thermal contact conductance was found to

be between 50 and 120 kW/m2 K for the cold upsetting of

non-lubricated aluminium, 80–220 kW/m2 K for the cold

upsetting of lubricated aluminium and 15–30 kW/m2 K for

the hot pressing of aluminium (billet at 200 8C) with tools at

room temperature. The reduction ranged from 14 to 50%. It

was proposed that under non-lubricated conditions an

approximate value for thermal contact conductance could

be 100 kW/m2 K for cold forming and 50 kW/m2 K for hot

forming operations.

It may be concluded that experiments used to determine

thermal contact conductance include ‘‘method-relatederrors’’. Results depend on the measuring devices used in

the experiments and on the method of processing the experi-

mental data.

A new approach for deriving values of thermal contact

conductance under differing interfacial conditions is pre-

sented, together with results on the dependence of h on

pressure and specimen texture. A clear advantage of this

method is the ability to measure the thermal contact con-

ductance under precisely controlled and continuously sus-

tained conditions.

2. Equipment and procedure

2.1. Test equipment

The proposed approach is based on steady-state heat flow

along two cylindrical tools and through a specimen [16]. The

distinct characteristic of this approach is the use of a thin

(d ¼ 2 mm) specimen of the same diameter as the tool. Due

to the small aspect ratio of the specimen, pressures of the

same magnitude as those prevailing in bulk-metal forming

processes may be applied. The experimental equipment is

shown schematically in Fig. 1. The lower part of the device

Nomenclature

A area of contact surface (m2)

h thermal contact conductance (W/(m2 K))

k s thermal conductivity of test specimen (W/

(m K))

k t thermal conductivity of tools (W/(m K))m temperature gradient in tool

q heat flux (W/m2)

Q heat (J)

t p process time

T C1 temperature at the upper tool surface (8C)

T C2 temperature at the lower tool surface (8C)

T S1 temperature at the upper surface of specimen

(8C)

T S2 temperature at the lower surface of specimen

(8C)

DT tÀs temperature difference at tool–specimen inter-

face (D 8C)

Greek symbols

d specimen thickness

y process relative time

M. Rosochowska et al. / Journal of Materials Processing Technology 135 (2003) 204–210 205



is attached to the press platen while the upper is attached to

the ram. The upper tool (1) is equipped with a heater (2)

while the lower tool (3) is fitted with a heat-sink (4). The test

specimen (marked black in Fig. 1) is located between these

tools. Two thermal barriers (passive and active) minimise

lateral heat-losses. A solid ceramic insulator (5), insulatingwool (6) and a reflective screen which surround these

elements (not shown in the figure) form the passive barrier.

The active barrier comprises a sleeve (7), compensating

heaters (8) and (9) and a heat-sink (10). These thermal-

compensation arrangements ensure a uniform and equal

temperature gradient along both tools. An insulating element

(11) insulates the load-cell (12). The heat-sinks (4) and (10)

are supplied from bath circulators.

Temperature control of the system in the range of 30–

300 8C was achieved using a bespoke control device. The

press possesses the capacity to exert a maximum interfacial

pressure of 800 MPa.

2.2. Materials

Tools were manufactured from tool steel, N1019, the

thermal conductance of which was measured at a National

Standards Laboratory. Cylindrical specimens (18 mm dia-

meter and 2 mm thickness) were made from Ma8 steel. Test

surfaces of all specimens were ground before imparting a

texture using electro-discharge machining. Two sets of

specimens with surface textures in the range Ra ¼0:27À5:95 mm were used in the trials. One set was used

in experiments with the main heater set at 200 8C and

applied pressures of 30, 60, 120, 180, 240, 300 and

420 MPa, whilst the second set was subjected to a similar

range of pressure with the main heater temperature set at

300 8C. These temperature settings resulted in interfacial

temperatures of approximately 90 and 130 8C, respectively.

2.3. Test procedure

The test specimens were located accurately between the

tools. The temperature settings of the main heater and the

cooling water were used to define the thermal conditions of

the experiments. The continuous change in temperature

along the tools was monitored until a steady-state condition

was achieved. At the point that the temperature distributions

along the tools were stable and the difference of heat fluxes

in both tools was within a specified limit, readings from the

thermocouples were used to compute the thermal contact

conductance. All experiments were conducted with dry

interfaces.

2.4. Computational considerations

As it has been already mentioned, heat flow was achieved

by applying a heat source to the upper tool and a heat sink to

the lower tool. The temperature distribution along the tools,

measured along their axis by four 0.5 mm type-K thermo-

couples in each tool, was used to calculate the heat flux and

temperature difference at the interface (Fig. 2). As both

punches were made from the same material and had the

same surface finish and hardness, it could be assumed that

Fig. 1. Layout of research equipment.

Fig. 2. Schematic diagram of equipment (a), temperature distribution (b).

206 M. Rosochowska et al. / Journal of Materials Processing Technology 135 (2003) 204 – 210



the temperature drop on both contact surfaces of the speci-

men with the punches was the same and could be defined by

DT tÀs ¼ðT C1 À T C2Þ À ðT S1 À T S2Þ

2(3)

Thus, using (1), the thermal contact conductance, as an

average of that in the two specimen–tool interfaces, maybe determined using the following equation:

h ¼2q

ðT C1 À T C2Þ À ðT S1 À T S2Þ(4)

in which the heat flux q was obtained from

q ¼ k tm (5)

Temperatures T C1 and T C2 were estimated by extrapolating

the temperature gradients in punches, which were computed

using the least-squares method. Using the relationship

T S1 À T S2 ¼ qd

k s(6)

the temperature difference ðT S1 À T S2Þ between the speci-

men surfaces was computed.

3. Results and discussion

3.1. Experimental results

The values of thermal contact conductance were com-

puted using Eq. (4). For the measured value of surface

texture, the variance of h with the applied pressure is shown

in Fig. 3. The thermal contact conductance is a function of pressure and surface roughness. Thermal contact conduc-

tance bears an exponential relationship to interfacial pres-

sure. This finding agrees with that reported [8] for

experiments with aluminium (Al 1100-O and Al 6061-O)

specimens under dry conditions. Further, it was found that

the magnitude of the thermal contact conductance increased

more rapidly with pressure for a finer textured specimen.

It should be stressed that data on contact conductance

published in the literature refers mainly to contact between

steel dies and specimens made from aluminium alloys.

Thermal contact conductance, for steel-to-steel contact,

was obtained from tool-to-tool experiments. Values ranging

from 0.75 to 9 kW/m2 K were established for H-13 tool steel

dies (temperatures of dies were 420 and 50 8C) subjected to

pressures ranging from 0 to 150 MPa [12]. Similar values

were obtained for IN-100 die [9]. For both cases, h attained a

saturation value. A value of h ¼ 100 kW/m2 K proposed

[15] for cold forming appears to be the nearest to the results

presented in Fig. 3.

3.2. FE application

The compression of a cylindrical specimen was simulated

to assess the influence of changes in the thermal contact

conductance on the temperature at the specimen and tool

contact surfaces. A 6 mm diameter specimen of 7.2 mmheight with thermo-mechanical properties of Ma8 and

cylindrical tools of 40 mm diameter and 25 mm height with

the properties of N1019 tool steel were used in simulations.

Friction between the specimen and the tool was assumed to

be zero to eliminate heat generation due to friction. The

lateral cylindrical surfaces of the tools and specimen dif-

fused heat by convection, the ambient temperature being

20 8C. The top surface of the upper tool and the bottom

surface of the lower were retained at a constant temperature

of 20 8C. Simulations were performed for the following

thermal contact conductance:

(i) 20 kW/m2 K, which was used for coupled thermo-mechanical analyses [17],

(ii) 100 kW/m2 K, which was recommended for cold

forming [15],

(iii) the pressure-dependent value of h (Table 1) derived

from presented experiments for an initial surface

roughness of Ra ¼ 2:0 mm was used as an alternative.

Ram velocities of 42, 2.1 and 0.42 mm/s were assumed to

reduce the height of the specimen by 58%. The temperature

at the end of the deformation process on both the tool and

specimen surfaces for nodes located on the axis of symmetry

are shown in Table 2. The table contains also the temperature

Fig. 3. Variation of thermal contact conductance with contact pressure.

M. Rosochowska et al. / Journal of Materials Processing Technology 135 (2003) 204 – 210 207



drop DT between the above-mentioned surfaces. Temperature

variations with time at these nodes are shown in Figs. 4–6 for

a velocity of 42.0, 2.1 and 0.42 mm/s, respectively. It follows

from Table 2 and Figs. 4–6 that

(a) The final temperatures at the specimen and die surface

are a function of deformation velocity; higher velocities

resulting in higher temperatures.

(b) For the same value of h, the final temperature

difference DT is higher for shorter process time t p.

(c) The final temperature drop DT across the interface is

higher for h ¼ 20 kW/m2 K than for h ¼ 100 kW/

m2 K.

(d) The temperature drop, DT , when the pressure-depen-

dent h is used is greater than when h ¼ 100 kW/m2 K:

this difference being even greater when h ¼ 20 kW/

m2 K.

The explanation for the first observation follows from this

FE model used, in which heat transfer to the environment

was taken into account. For lower deformation velocity, the

process time t p is longer and for this reason a greater amount

of heat is dissipated to the environment, resulting in a lower

final temperature.

The explanation of the remaining observations requires

the introduction of the relative time of the process:

y ¼t

t p(7)

Table 1

Pressure-dependent heat contact conductance

P (MPa) h (kW/m2

K)

0 5.0

30 18.3

120 58.8

180 87.0300 222

420 410

Table 2

Temperature at the die and specimen surface at the end of processes

h ¼ 20 kW/m2

K

0.42 mm/s 2.1 mm/s 42 mm/s

Specimen (8C) 45.9 79.7 100.6

Die (8C) 42.1 70.9 89.8

DT (8C) 3.8 8.8 10.8

h ¼ 100 kW/m2

K

Specimen (8C) 41.8 76.0 101.7

Die (8C) 41.2 74.5 99.7

DT (8C) 0.6 1.5 2.0

h ¼ f ð pÞ kW/m2 K

Specimen (8C) 40.94 75.2 101.9

Die (8C) 40.77 74.7 101.3

DT (8C) 0.17 0.5 0.6 Fig. 4. Variation of temperature with time at specimen and die surfaces for

ram velocity 42 mm/s.

Fig. 5. Variation of temperature with time at specimen and die surfaces for

press velocity 2.1 mm/s.




where t is the actual time. Introducing (7) into (2), after a

simple modification of (1), the following is derived:

DT ¼ 1t p

q

Ã

h(8)

where

qÃ ¼d

d A

dQ

dy

(9)

Observations (b) and (c) follow directly from (8). The

diagram shown in Fig. 7, which illustrates the relationship

between h and the relative time y, can be used to explain

observation (d). An average pressure-dependent value of h,

which was used in simulations, may be obtained from the

following equation:

hav ¼

Z 1

0

h dy (10)

The magnitude of this parameter is independent of process

time as long as the deformed material is not strain rate or

temperature sensitive: this is the case in the discussed model.

From the diagram (Fig. 7), it can be observed that

hav > 100 kW/m2 K and hav @ 20 kW/m2 K. Thus using

(8) it can be shown that DT hð pÞ < DT h¼100 as well as

DT hð pÞ ! DT h¼20. The influence of the pressure-dependent

h would be greater in processes where higher contact

pressures are encountered.

4. Conclusions

The conducted research enables the following conclu-

sions to be made:

1. A new method of determining thermal contact con-

ductance has been successfully used to measure the

dependence of thermal contact conductance on pressure

and surface texture.

2. Thermal contact conductance increases with pressure and

decreases with the surface roughness of the work material.

3. Increase of the value of thermal contact conductance

with pressure was more pronounced for specimens with

smooth surface finishes.

4. The temperature difference across the specimen–die

interface was smaller for the pressure-dependent h than

for 100 kW/m2 K, which has been recommended for

cold forming.

5. Differences in temperature distribution, resulting from

using different values of h in FE simulations, are more

noticeable for rapid plastic deformation processes.

6. The influence of the pressure-dependent thermal contact

conductance on the die and specimen surface tempera-

tures would be more prominent in processes where high

interface pressures occur.

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Fig. 7. Relationship between thermal contact conductance and relative

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Measurements of Thermal Contact M Rosochowska-2003