An Experimental Investigation on Thermal Contact ... - IEEE Xplore

An Experimental Investigation on Thermal Contact Resistance Across Metal Contact Interfaces Xiaobing LUO I ,2*, Han Feng I , Jv Liu I , Ming Lu Liu 3 and Sheng Liu 2 1 School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China, 430074 2 MOEMS Division, Wuhan National Optoelectronics Laboratory, Huazhong University of Science and Technology, Wuhan, China, 430074 3 School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, China, 430074 * Corresponding author: [email protected] Abstract Thermal contact resistance is an important parameter for the thermal management of electronics packaging. A type of test instrument for measuring thermal contact resistance was presented in this paper. Thermal contact resistance across a brass-brass (Cu-Cu) interface was investigated by the present instrument. The results show that the contact thermal resistance is at the magnitude of 10-4 for the present test samples. Experimental results were also compared with theoretical computation results, and the reasons for the difference between them discussed. Based on the experimental results, it was found that in most cases, the real contact surface is different to the contact area of the interface we usually assume in the prediction model. The complicated and different shapes of the real contact interfaces explain why there are differences between experimental results and theoretical prediction results. 1 Introduction In recent years, electronic products have developed with a focus on miniaturization and multi functionality, which results in extremely high heat flux density in electronic packaging. Therefore, thermal management for electronic devices has become an essential problem. To address the problem, the total thermal resistance of electronic devices needs to be reduced to a reasonable level. In the total thermal resistance, thermal contact resistance occupies a large amount of ratio, especially at the interface from electronic substrate such as printed circuit board (PCB) and chip packaging shell to heat sink. As heat flux density increases, this part of thermal resistance will play a critical role in transferring heat from chip packaging to the heat sink and ambient. Thus, it is necessary to evaluate thermal contact resistance theoretically and experimentally to provide reference for the thermal management of electronic devices. To study the fundamental theories behind thermal contact resistance, many researchers have been working on this topic for decades. In the majority of these investigations, there are just several theoretical studies on thermal contact conductance in the open literature. Some mathematical models have been established to predict thermal contact conductance. By using these models, we can predict thermal contact resistance somehow under a certain condition. The models include the ones for conforming surfaces given by Yovanovich et al. [1], sphere surfaces by Fletcher, et al. [2] and unloading models by Mikic [3].

To validate the predictions and obtain real results, there are different equipmental facilities available to measure thermal contact resistance. Milanez and Yovanovich [4] proposed an experimental setup: a test column of this instrument consisting of two test specimens and one ARMCO iron flux-meter, which is placed on the cold plate. The electrical heater is placed on the top of the ARMCO fluxmeter and can dissipate heat up to 60 W. Radiation heat losses from the test column are minimized by surrounding the column with a polished aluminum cylinder shell. The ARMCO flux-meter was used to determine the heat flux and independence of the two test specimens. Khounsary and Chojnowski [5] designed an experimental setup with a vacuum test chamber, the chamber basically consisting of a 30 em diameter glass cylinder and a stainless steel feedthrough port ring sandwiched between 2cm thick aluminum plates. The feedthrough ring is 13 em tall and has 30 em diameter with 12 ports distributed evenly around the perimeter. The 12 ports are used for the distribution of thermocouples, connecting electrical power wires for the heater, load cell signal wires, vacuum pump connections, water cooling lines for cold plate, and vacuum gauge connections. The top and bottom surfaces have gasket seating surfaces to seal against the glass cylinder and the bottom plate. Four threaded rods align and compress the assembly to create the vacuum chamber. Thus the heat flux is regarded as being equal to the heater's heating power since there are no heat losses under vacuum. This paper proposes a simple experimental setup to measure thermal contact resistance (TCR). The experimental setup consists of a temperature compensated system to prevent heat losses; such a compensation system does not use the vacuum chamber, which differs from previous studies. The error analysis for the present instrument was given. Using this instrument, the TCR of the copper-copper interface was studied with various interface pressures, the results were compared with theoretical computations based on Yovanovich's model, and the differences between the results obtained by the two kinds of methods were discussed, which can hopefully be used for the error analysis produced when using theoretical models to predict TCR. 2 Experimental setup The system is shown in Figure 1. Thermal contact resistance between metal-metal contact surfaces is measured by using a guarded flow methodology. The whole system

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contains four important parts: a pressure adjustment part, temperature and loading measurement part, heating and cooling part, and temperature compensation subsystem (TCS). The loading cells, the cold plate, the temperature test and TCS, and a heater are placed sequentially from the disk down to the outrigger's foundation plate. The pressure adjustment part is also called as load cell, and includes a screw device, which can provide contact pressure by whirling the turnplate. A disk is fixed under the screwed bar. Because the force of the turning screw depends on manual operation, the range of the pressure can be adjusted from about 0 to 3MPa. 2.1 Temperature and loading measurement As shown in the right part of Figure 1, the two same metal cylinders which directly contact each other are used for the heat flux meter and test specimens. Their heights and diameters are 60mm and 30mm, respectively. The K type thermocouples are positioned 10mm apart from each other along the longitudinal direction. The thermocouples' measured temperatures are read by digital computer-based data acquisition systems. Calibration of the thermocouples was performed prior to the experiment by placing them in an oven and establishing the resistance-temperature curve for each individual sensor. The load cell's measured weight can be transferred as electronic signals. By using a KQ-YB04 display instrument, the signals are converted to display numbers. Then, the contact pressure can be calculated with these measured values. 2.2 Heating and cooling There are three cartridge heaters, which are inserted in an aluminum block for heating supply. It is powered by 40W of heat through a variable transformer controller. Between the heater and the cylinder, there is a small brass ingot that has been cut to have the same cross section as the copper cylinders. To prevent heat from spreading outside, cotton is used for insulation. The rest space between the heater and the cotton are full of foam material. In this way, the heating area can be adjustable and a more uniform heat is achieved. To take heat away from the two cylinders, a cold plate is positioned on the upper copper cylinder. Heat-conducting cream has been smeared on the upper surface of the cylinder to enhance the heat transfer. The heat of the cold plate will be taken away by the water cooling system. 2.3 TCS There is a cotton layer around the copper cylinders. Outside the cotton are two iron sheet cylinder shells surrounded with heater strips. These iron cylinder shells have an approximate 60mm height, just like the copper cylinders, and their diameters are 90mm. For preventing heat transmission between the two iron cylinder shells, a synthetic glass ring was placed between them. Heater strip is wound around the two separate iron cylinder shells. A DC power supply was used to electrify the heater strips, with the input power able to be switched on automatically under the control of a Single Chip Micyoco (SCM). Therefore, according to the copper cylinders' temperature, the iron cylinder shells' temperatures can be changed in time and hold different

temperatures according to the respective copper cylinders. The temperature difference between copper cylinders and outer iron cylinder shells will be small. Thus, heat losses will be cut down efficiently.

Fig. 1 Diagram of experimental setup. 3 Principle and test procedures When heat flows across two contact surfaces, the temperature at the interface is not continuous, because of the imperfect contact of the two surfaces. Even for surfaces with the smallest flatness and roughness, the actual contact takes place over a fraction of the interface only [6]. Thus, there will be many gaps between the two contact surfaces, and the thermal conductivity at the interface is definitely not the same as that of the contact object. The resistance to heat flux at the interfaces of the two solids is used for defining thermal contact resistance. It is calculated through the temperature difference of the two contact surfaces divided by the heat flux through the interfaces. As seen in Figure 1, the heat insulation in this study was cotton, which was wrapped around the two brass cylinders along radical direction, used to prevent heat dissipating from the radial direction and make the radial direction adiabatic so that the heat transfer in the brass cylinders could be regarded as one-dimensional and linear heat transfer. Fourier's law could then be applied. In this experimental setup, the two cylinders were not only the test specimens but also the heat flux meters. Ten thermocouples were inserted in the holes drilled in the brass cylinders to measure the temperature distribution of the brass cylinders. The temperature gradient in the brass cylinders could then be calculated using the method of least squares. According to Fourier's Law, given the thermal conductivity of the brass and the temperature gradient in the cylinders, the heat-transfer rate can be calculated as below, q:=

aT ax

-k-

(1)

In this equation, k is the thermal conductivity of the test sample in experiments. After heating the cylinders for about two hours, we can obtain ten stable temperatures from the thermocouples. The temperature data is fitted by least square multiplication, and then reaches the line equation of the two respective cylinders. The partial derivative aT /ax is the slope of the temperature distribution line of the cylinder.

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According to Eq.(l), the heat flux through each cylinder can be calculated, and finally the averaging heat flux q can be regarded as the heat flux through the test samples and used for thermal contact resistance computation.

For the present measurement system, the theoretical basis for measurement is based on one dimensional Fourier equation. So to get good accuracy is to achieve onedimensional heat transfer characteristics along the axis of the metal cylinder. To prove the one-dimensional heat transfer characteristics, a finite element analysis of the system was done to see the heat flow in the brass cylinders. Because the entire system shown in Fig.l is symmetrical, we adapt a fully parameterized axisymmetric 3D model, only one quarter of the setup was used in the simulation for reducing calculation grids and time. The size and other relative parameters were the same as those in the experiments. Fig.3 shows the final result. As shown in figure 3, the streamlines of heat flow around the centre shaft of the brass cylinders is very straight. Figure 4 shows one set of our experimental data of the upper brass cylinder. It can be seen that the temperature distribution line almost overlapped with the fitting line, so based on Figs. 3 and 4, we can get good onedimensional heat conduction in the experiment.

Fig.2 Temperature distribution line of the two test samples. As shown in Figure 2, the lower line is the fitting line of the five temperature points of the upper cylinder, and the upper line is the fitting line of the five temperature values of the lower cylinder. The two cylinders' contact surfaces are at the position of 60mm. By substituting the position in each line equation, the upper surface temperature

1;.

and the lower

surface temperature T2 can be obtained. Therefore, the

R

thermal contact resistance

can be calculated by the

following Eq. (2), where the unit of R is K . m R

=:

1; - ~

2

/

W (2)

q

(1) Detailed procedures for the present experimental setup were as follows: (2) In order to prevent overheating, the first step is to turn on the water pump and begin water-cooling system operations, which then start to heat the bottom of the lower cylinder. (3) When the temperature distribution on the two cylinders is basically stable, we can activate the temperature compensation system. (4) According to the two cylinders' mean temperature, we can adjust the temperatures of the outside iron cylinder shells by SCM controller to get the best thermal insulation effect. (5) When the temperature fluctuation was less than O.2K over l5min, the temperatures appear to be stable and become apparent. After obtaining the temperature data, the abovementioned method was used to calculate thermal contact resistance.

4 Experimental uncertainty

Fig.3 Streamlines of heat flow in the experimental setup.

Fig.4 Temperature distribution of the upper cylinder. Even the present measurement get good one-dimensional heat transfer characteristics, there still exists experimental uncertainty. According to the measurement equation and method, the experimental inaccuracies depend on many


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factors, essentially consisting of the inaccuracy of temperature measurements, the extrapolated heat flux and the imperfect heat insulation of the temperature compensation system. As mentioned before, the temperatures of contact surfaces and the heat flux are all calculated from the fitting line of the cylinders' temperature distribution. For the two distribution lines obtained by the least squares technique, the measurement differential of the fitting line for five temperature points is very small and can be ignored. Regarding the cotton layer as a thick-walled cylinder, the temperature difference between the internal wall and the outer wall can be the calculated for heat losses in a horizontal direction. After all, it is caused by the imperfect heat insulation of the temperature compensation system. Assume the heat transfers through the cotton layer are all counted as the error of the heat flux rP , and it can be calculated with the correlation in Eq. (3)[7]: rjJ =

where

2nlkc (7;' - ~) In(r2 f'i)

(3)

I is the height of the brass cylinder, and kc is the

thermal conductivity of cotton.

1;' is

the temperature of the

inner side of the cotton layer, which can be replaced by the brass cylinder's mean temperature for approximate calculation. T~ is the temperature of the outside face cotton layer, which is actually the compensated temperature of the iron cylinder shell. r 2 and 'i are the radius of the cotton layer and the brass cylinders respectively. In order to validate the adiabatic process of the instrument, we take one set of those test data to calculate the heat loss. For the upper brass cylinder, 31.4°C, r 2 is 45mm and the heat loss is

1;.'

is 31.526 DC, T~ is

'i is 15mm. According to Eq. (3),

«. =2.115

x l 0-3W. For the lower brass

1;'

is 36.954 DC, T~ is 36.9 DC, r 2 is 45mm and 'i =15mm and the heat loss is rP/ow =0.906x 10-3W calculated

cylinder,

by Eq. (3) as well. In addition, the total heat provided by the heater is rP =4.557 W. Thus, the heat loss rate can be calculated as (2.115 x 10-3+O.906x 10-3)/4.557=0.0663%, which is so small that the instrument could be considered as adiabatic.

In Eq.(4), the (J and m are the effective root-meansquare (RMS) surface roughness and the effective absolute mean asperity slope, respectively. P is the apparent contact pressure. He is the contact microhardness, which can be measured by a Vickers microhardness tester. For a typical joint formed by two conforming rough surfaces, the two parameters are given by Eq. (5) and (6): (J

==

~(J12 + (J~ and m == ~m~ + m~

where

(Jl

and

(J 2

(5)

are the RMS surface roughness and the

mean absolute asperity slope of the contacting surfaces, respectively .

ks is the effective thermal conductivity of the

joint which is given by the relationship: 2k llpk/ow k s ==_---:......-kllP + k,ow where

(6)

kup and k, ow are the thermal conductivities of the

two contact solids. It has been demonstrated that the plastic contact conductance model shown in Eq.(4) predicts well for a range of surface roughness a / m, metal types and the relative contact pressure P f He [9-10]. 6 Experimental results and comparison with theoretical results In the present experiment, the two cylinder samples are made from brass, whose thermal conductivity is 109 W f(rn . K), as taken from the open literature. In fact, thermal conductivity will change with temperature variations. However, since the temperature variation of the brass cylinders in the test is very small, the thermal conductivity change of the brass can be ignored. The surface roughness (J" and the mean absolute asperity slope of the contact surfaces m were obtained by tests through a profilometer of which model name is Talysurf POI 830. Its measuring principle is based on the line waviness testing. The two metal surfaces were burnished with abrasive papers, and the surfaces profile parameters were given as follows:

5 Theoretical equations and computation Yovanovich et al. proposed an extended conforming rough surface model [1], called the extended Cooper-MikicYovanovich (CMY) model. This model is used to predict contact conductance he as described in Eq.(4)[8], where contact conductance is the reciprocal value of thermal contact resistance.

1.25(~. J

O95

he == m ks

(J"

He

.

(4)

Fig. 5 Result comparison between experimental data with extended CMY model (first test)


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0"1

=

0.780 Jllll

m1 = 0.0208

0"2

=

1.025Jllll

m2 = 0.0248

The microhardness He of brass H62 is 1300MPa, which is measured by a Vickers microhardness tester. Figure 5 shows the comparison between experimental results and theoretical results in our first test. Both the experimental values and the theoretical values decrease as the contact pressure increases. When the pressure increases, the contacting asperities will be deformed and the contact surfaces will become smoother. Therefore, the contact area is augmented, and thereby the thermal contact resistance will reduce. From Fig. 5, it is found that the trend of changes for experimental thermal resistance with pressure corresponds well with the data presented by theoretical computation. However, the theoretical results of contact resistance are much less than the experimental results at the same pressure. After the first experiment, the two test cylinders' surfaces were polished, and then used for the second test. The surfaces were measured again and the surface profile parameters of the two contact surfaces were: 0"1

=

0.35 Jllll

m1 = 0.035

0" 2

=

0.32Jllll

m 2 = 0.025

Figure 6 shows the comparison between the second experimental results and theoretical results. Compared with Figure 5, it is obvious that the experimental results were closer to the theoretical model results in the second test in which the surfaces are polished by machines. For both experiments, the theoretical results of thermal contact resistance were smaller than the experimental ones at the same contact pressure.

Fig. 6 Comparison of experimental data for brass H62 with extended CMY model (second test after polishing). 7 Analysis of difference between experiments and calculation In the first experiment, it is clear that the results of extended CMY model are greatly different from the experimental results. This can be explained as follows. In the CMY model, the surface profile of the contact surfaces was regarded as a flat surface. However, the actual situation is different. For an arbitrarily chosen line across the center of

the circle on the lower contact surface of our test sample, its profile can be obtained using profilometer. Figure 7 shows one of these surface contour curve lines. It can be seen that the height difference between the circumference and the center of circle is more than 25 J.1111, which cannot be identified by the naked eye. For the two contact surfaces in the experiments, the sketch map of their contact surface is shown in Figure 8.

Fig.7 Lower surface profile in the first experiment The extended CMY model is established based on the hypothesis of conforming solids joint. Thus, the flatness of the contact surfaces in the theoretical model is considered to be approximately zero in the model, but in practical situations, the surfaces in contact are not as flat and smooth as those in a theoretical assumption. It is actually like a flat surface contact with a concave surface, as shown in Fig.7. Therefore, there will be a macroscopic gap between these surfaces, which can cause an increase in thermal resistance.

Fig.8 Contact between concave surface and plane surface Based on the abovementioned analysis, we can conclude that when the surfaces are flatter, the theoretical results and the experimental results will become more uniform. The previous second experiment proves this, as shown in Fig. 6. The contour lines of the two contact surfaces in the second experiment are basically the same as those shown in Figure 9. Taking the contour curve of the upper surface as an example, the height difference between its highest point and lowest point is less than 10 J.1111. For ordinary machines, it is surely difficult to get a more flat surface. Thus, the condition that can perfectly match the extended CMY model's hypotheses is very hard to reach. For most solid contact situations in electronics packaging, the contact surfaces' precise shapes are difficult to predict or measured.


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Fig. 9 Surface profile of the upper surface in the second experiment after polishing 8 Conclusions An apparatus has been built for measuring thermal contact resistance. Two experiments measuring the thermal contact resistance of brass-brass contact were done and error analysis for the experiments was also conducted. Comparing to theoretical computations on the extended CMY model, the experimental results were higher than those made by the theoretical prediction. Profiles of surfaces consisted of the contact interface were examined and it was found that the surfaces were not as flat as expected and that a macroscopic gap exists when the surfaces come into contact together. This is different from the assumption of the theoretical model, which is the reason why the practical thermal contact resistance results are usually greater than those predicted by the extended CMY model.

7. 1. P. Holman, Heat Transfer, China Machine Press, Beijing, 2005. 8. M. G. Cooper, B. B. Mikic and M. M. Yovanovich, Thermal contact conductance, International Journal of Heat and Mass Transfer, Vol.12, pp: 279-300, 1969. 9. M. A. Lambert and L. S. Fletcher, Thermal contact conductance of spherical rugh metals, International Journal of Heat and Mass Transfer, Vol.l19, pp: 684690, 1997. 10. M.M. Yovanovich, Thermal contact correlations, in Proc, AIAA 16th Thermophysics Con£, Palo Alto, CA, pp: 8395, Jun.23-25,1981.

Acknowledgments The authors would like to acknowledge the financial support in part by 973 Project of The Ministry of Science and Technology of China (2009CB320203) and in part by New Century Excellent Talents Project of The Chinese Education Ministry (NCET-09-0387). References 1. M.M. Yovanovich, New contact and gap conductance correlations for conforming rough surfaces, in Proc, AIAA 16th Thermophysics Con£, Palo Alto, CA, Jun.2325,1981. 2. M. A. Lambert, and L. S. Fletcher, Thermal contact conductance of spherical rough surfaces, Journal of Heat Transfer, Vol.l19, No.4, pp: 684-690,1997. 3. B. B. Mikic, Analytical studies of contact of nominally flat surfaces:effect of previous loading, Journal of Lubrication Technology, Vol.93, No.4, pp:451--459,1971. 4. F. H. Milanez, M. M. Yovanovich and M. B. H. Mantelli, Thermal contact conductance at low contact pressures, Journal of Thermophysics and Heat Transfer, Vol. 18, No.1, pp: 37--44,2004. 5. A.M. Khounsary, D. Chojnowski, L. Assoufid, and W.M. Worek, Thermal contact resistance across a copper-silicon interface, Proc. SPIE, Vol.3151, No.45, pp: 45, Dec. 1997. 6. K. K. Tio and K. C. Toh, Thermal resistance of two solids in contact through a cylindrical joint , International Journal of Heat and Mass Transfer. Vol.41,No.13, pp:2013-2024, 1998.


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