CN101975795A - Contact thermal resistance test method applied to GH4169/GH4169 high temperature alloy - Google Patents

Abstract

The invention discloses a contact thermal resistance test method applied to a GH4169/GH4169 high temperature alloy, comprising the following steps of: modeling through the reduced elastic moduli of two contact materials according to the plastic deformation theory, simplifying a model, and finally determining unknown parameters through a stepwise regression test to obtain an optimal regression equation. The contact thermal conductance of the GH4169/GH4169 high temperature alloy is obtained according to a regression analysis result, and the reciprocal of the contact thermal conductance is fetched to obtain contact thermal resistance. Within the temperature interval of 100-600 DEG C, when a temperature value and a pressure value are selected as independent variables, hs is equal to 0.1566T0.371P2.061, and when only the pressure value is selected as the independent variable, hs is equal to 0.5013P2.18. In the invention, the practical engineering contact thermal resistance test method is obtained on the base of test data through selecting a proper theoretical model by applying a mathematical statistics method. Only by obtaining the required parameters through the test data, the invention can obtain the contact thermal resistance according to a simple formula under any condition of changing the test temperature and pressure, and thereby the contact thermal resistance test process is simple and can be repeatedly used.

Description

A kind of thermal contact resistance method of testing that is applied to the GH4169/GH4169 high temperature alloy

Technical field

The invention belongs to high temperature alloy thermal contact resistance technical field of measurement and test, be specifically related to a kind of thermal contact resistance method of testing of the GH4169/GH4169 of being applied to high temperature alloy.

Background technology

There are the model, experience and the semi-empirical relation that much are used to predict contact conductane to be suggested in the past few decades.Classical model has the Mikic elastic model, CMY (Cooper, Mikic and Yovanovich) plasticity model and by the elastic-plastic deformation model of Sridar and Yovanovich.Theoretical research at home is mainly reflected in the numerical simulation of thermal contact resistance.

Thermal contact resistance test for two high-temperature materials in the prior art all is to be undertaken by a large amount of tests, process of the test is to choose the sample that boundary material is processed into certain size, certain interface roughness, provide specific interface temperature and interfacial pressure by the pressurization and the process of heating for the interface then, at last by interface temperature is fallen with sample in the contact conductane that measures two storerooms of heat flow density.

Though existing measuring technology obtains more accurately to the contact conductane under fixed temperature, pressure and the interface roughness condition, but because its test process complexity, the test condition relative fixed, can not satisfy changeable temperature and pressure condition in the engineering application, the contact conductane data at material interface place can't promptly and accurately be provided.

Summary of the invention

The present invention is based on test figure, and by selecting suitable theoretical model, the utilization mathematical statistic method draws the thermal contact resistance method of testing of engineering practicality, and passes through the accuracy of demonstration test verification model.

Described thermal contact resistance method of testing realizes as follows:

The first step, determine the reduction elastic modulus E of two contact materials '.

$E^{\′}=\frac{E}{1-v^2}$

Wherein E is the elastic modulus of GH4169, and v is a Poisson ratio.

Second step is according to the theory of plastic strain in matrix modeling.

According to the absolute average pitch tan θ of the micro-profile at the contact interface place of material hardness H and thermal contact resistance test material, the plastic yield factor ψ that obtains material is:

ψ＝(E′/H)tanθ，

If ψ＞1, the theory of plastic strain in matrix modeling of then selecting for use Mikic to propose obtains the contact conductane h of thermal contact resistance test material _sFor:

h _s＝(1.13ktanθ/σ)(P/H) ^0.94；

Otherwise reselect other theoretical modeling.

In the following formula, tan θ is the absolute average pitch of micro-profile at the contact interface place of thermal contact resistance test material, and σ is the roughness of thermal contact resistance test material, and k is the thermal conductivity coefficient of thermal contact resistance test material, P is the thermal contact resistance test pressure, and H is the hardness of thermal contact resistance test material.

The 3rd step, model simplification.

Because be identical two storeroom thermo-resistance measurements, so contact conductane h _sFormula following distortion is arranged:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP

Y=lnh in other following formula _s, X ₁=lnT, X ₂=lnP, X ₃=ln σ, b ₀=lnx ₀, b ₁=x ₁, b ₂=x ₂, b ₃=x ₃, then following formula further is written as:

Y＝b ₀+b ₁X ₁+b ₂X ₂+b ₃X ₃

B in the formula ₀, b ₁, b ₂And b ₃Be unknown parameter.

In the 4th step,, determine unknown parameter b by progressively returning test ₀, b ₁, b ₂And b ₃, obtain optimal regression equation; According to the regretional analysis result, when independent variable is selected temperature and force value, h _s=0.1566T ^0.371P ^2.061, independent variable is only during the selection pressure value, h _s=0.5013P ^2.18Thermal conductance is got inverse obtain thermal contact resistance.

The invention has the advantages that:

Thermal contact resistance method of testing provided by the invention only need obtain the parameter b that needs by test figure ₀, b ₁And b ₃, just can obtain contact conductane according to simple formula changing under the condition of probe temperature and pressure arbitrarily, make the thermal contact resistance test process simply also can reuse.Because the contact conductane of storeroom can't be realized the comprehensive measurement under all temps, the pressure condition during engineering was used, method provided by the invention has been simplified the test process of contact conductane greatly under the prerequisite that guarantees engineering practicability and test result accuracy.

Embodiment

Below in conjunction with embodiment thermal contact resistance method of testing provided by the invention is elaborated.

The invention provides a kind of thermal contact resistance method of testing, especially be applicable to the thermal contact resistance method of testing between the GH4169/GH4169 material, specifically realize by the following method:

The first step, determine the reduction elastic modulus E of two contact materials '.

Because be the thermal contact resistance test between the same material GH4169, therefore the elastic modulus E of two test materials is identical, for the reduction elastic modulus of GH4169/GH4169 two contact materials is:

$E^{\′}=2{[(1-v^2)/E+(1-v^2)/E]}^{-1}=\frac{E}{1-v^2},---\left(1\right)$

For the GH4169 alloy material, as shown in table 1 is this alloy material in 100 ℃～600 ℃ intervals temperature and the corresponding relation of elastic modulus, corresponding relation to above-mentioned temperature and elastic modulus carries out linear fit, and the elastic modulus that obtains the GH4169 alloy material closes with variation of temperature and is:

E＝-0.0646T+208.27 (2)

Therefore formula (1) can further be written as:

$E^{\′}=\frac{E}{1-v^2}=\frac{-0.0646T+208.27}{1-v^2}=\frac{-0.0646T+208.27}{1-{0.3}^2}---\left(3\right)$

Wherein, E is the elastic modulus of GH4169, and v is a Poisson ratio, obtains by looking into " Chinese aeronautical material handbook the 2nd volume (the 2nd edition) ".Get T=600 ℃, obtain E '=185 * 10 ³MPa.

The elastic modulus of table 1GH4169 is with the variation of temperature value

Second step is according to the theory of plastic strain in matrix modeling.

According to the plastic deformation of metal material theory, plastic yield factor ψ is:

ψ＝(E′/H)tanθ (4)

In the formula (4), tan θ is the absolute average pitch of material contact interface profile, and θ is the average slope angle of material contact interface profile, therefore has:

$\tan \mathrm{\θ}=\sqrt{{2\mathrm{\θ}}^2}=\sqrt{2}\mathrm{\θ}---\left(5\right)$

The hardness H of GH4169 is by consulting " Chinese aeronautical material handbook the 2nd volume (the 2nd edition) " (Beijing: China Standard Press, 2001.8) be HBS346～450, the roughness of setting thermal contact resistance test material GH4169 is σ, it is the average height of material contact interface profile, according to the test needs, get roughness σ between 0.1 μ m and 3.0 μ m, get maximum conditions:

σ ₁＝σ ₂＝0.1μm；θ ₁＝θ ₂＝0.03°。

H, σ and formula (5) substitution formula (4) are obtained the value of plastic yield factor ψ:

$\mathrm{\ψ}=(E^{\′}/H)\tan \mathrm{\θ}=(E^{\′}/H)\sqrt{2}\mathrm{\θ}=\frac{-0.0646T+208.27}{H(1-v^2)}\×\sqrt{2}\mathrm{\θ}$

$=\frac{185000}{400}\×\sqrt{2}\mathrm{\θ}$

$=462.5\×\sqrt{2}\mathrm{\θ}---\left(6\right)$

$=462.5\×0.04242$

$=19.62$

Get H=400, σ=0.1 μ m, θ=0.03 ° then has:

$\mathrm{\ψ}=\frac{185000}{400}\×\sqrt{2}\mathrm{\θ}$

$=19.62$

Because ψ＞1, so according to theory of plastic strain in matrix, this test findings should meet the theory of plastic strain in matrix that Mikic proposes, its experimental formula is:

h _s＝(1.13ktanθ/σ)(P/H) ^0.94 (7)

In the formula (7), h _sBe the contact conductane of material, σ is the roughness of thermal contact resistance test material, and k is the thermal conductivity coefficient of thermal contact resistance test material, and P is the thermal contact resistance test pressure, and H is the hardness of thermal contact resistance test material.

By verification experimental verification, in the interval of 100 ℃～600 ℃ of probe temperatures, test findings all meets the theory of plastic strain in matrix that Mikic proposes.

The 3rd step, model simplification.

The principal element that influences thermal contact resistance has surface of contact temperature T, pressure P and roughness σ etc., and choosing above three factors among the present invention is explanatory variable, adopts the method for regretional analysis, studies its degree of influence to thermal contact resistance.

(1) according to the theory of plastic strain in matrix of Mikic, parameter k is the mediation value of the thermal conductivity coefficient of two thermal contact resistance test materials, i.e. k=2k in the formula (7) ₁k ₂/ (k ₁+ k ₂), because k ₁=k ₂So,, k=k ₁=k ₂, can obtain the thermal conductivity coefficient k value of GH4169 by " Chinese aeronautical material handbook the 2nd volume (the 2nd edition) ".

According to the thermal conductivity coefficient of GH4169 under the different temperatures, as table 2:

The thermal conductivity coefficient of table 2GH4169 is with the variation of temperature value

Data are carried out the relation that linear fit obtains thermal conductivity coefficient and temperature in the his-and-hers watches 2:

k＝0.0141T+13.221 (8)

So according to formula (7),

X wherein ₁Be coefficient to be determined.

(2) roughness of preparation thermal contact resistance test material GH4169 is σ, the average height of roughness σ exosyndrome material contact interface profile, tan θ is the absolute average pitch of material contact interface profile, θ is the average slope angle of material contact interface profile, therefore regularly in other conditions one, the absolute average pitch tan θ of profile and roughness σ positive correlation in conjunction with formula (7), can have

X wherein ₂Be coefficient to be determined.

(3) for determining material GH4169, hardness H is what determine, in conjunction with formula (7), so have

X wherein ₃Be parameter to be determined.

Formula this moment (7) can be expressed as:

$h_s=x_0{T}^{x_1}{\mathrm{\σ}}^{x_2}{P}^{x_3}---\left(9\right)$

x ₀Be constant, ask logarithm to get on formula (9) both sides:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP (10)

So far each parameter h _s, set up linear relationship between T, σ and the P, utilize the method for regretional analysis to determine that each unknown parameter can obtain the experimental formula of thermal contact resistance.

Among the present invention, explained variable (dependent variable) is the natural logarithm value lnh of contact conductane _sExplanatory variable (independent variable) is the natural logarithm value ln σ of the compound roughness of natural logarithm value lnP and interface of natural logarithm value lnT, the interfacial pressure of interface temperature, makes the lnh in the formula (10) _s=Y, lnT=X ₁, ln σ=X ₂, lnP=X ₃, and make b ₀=lnx ₀, b ₁=x ₁, b ₂=x ₂, b ₃=x ₃, then initial model is set up as follows:

Y＝b ₀+b ₁X ₁+b ₂X ₂+b ₃X ₃。(11)

In the 4th step,, determine unknown parameter b by progressively returning test ₀, b ₁, b ₂And b ₃, obtain optimal regression equation.

Progressively returning is a kind of method of choice variable subclass.This method is by the check to sum of squares of partial regression, when it is remarkable, in original variable subset, add new variable, and in case after having new variable to add, need again the sum of squares of partial regression of original variable is checked once more, in case will be deleted immediately after inapparent variable is arranged, till not having variable to delete not have variable to add again yet, use the variable subset of being chosen to set up regression equation at last, do not contain the inapparent variable of coefficient in the regression equation that the method that usefulness progressively returns is set up.Concise and to the point step is as follows: 1. consider all possible simple linear regression, find out the variable that can explain largest portion Y variation.What 2. the next one was put into model is that the conspicuousness of contribution is determined by the F check to the most significant variable of regression sum of square contribution.If 3. a new variable adds model, then utilize F to check the conspicuousness of each variable to the regression sum of square contribution.4. repeating step 2. with step 3., up to the variable that might increase all not remarkable, the variable that might reject all significantly the time till.

Employed data are all from the thermal contact resistance testing experiment in the present embodiment.Raw data sees Table 3:

Table 3 thermal contact resistance testing experiment data

26 groups of data are handled in the his-and-hers watches 1, promptly respectively contact conductane value, interface medial temperature, contact stress and compound roughness are asked the natural logarithm computing, the results are shown in Table 4 after the processing.

Table 4 is handled the back data

Carry out regretional analysis below:

(1) find according to data analysis in the table 4: Ln σ is at Lnh _sNumerical value in the constant interval is stable, just Ln σ and Lnh _sCorrelativity is relatively poor relatively, the roughness of material is a microscopic quantity in addition, the roughness that needs only the assurance material in engineering practice is between 0.1-3.0 μ m, can meet the demands, do not need to remeasure again and obtain, so consider the engineering practicability of correlation of variables and formula, in follow-up regretional analysis with variables L n σ=X ₂Reject, promptly only to linear equation Y=b ₀+ b ₁X ₁+ b ₃X ₃Carry out regretional analysis, so need not calculate b among the present invention ₂Value.

With data (data in the table 4) Lnh after handling _s, carry out regretional analysis in LnT and the LnP input SPSS data processing software, when independent variable is selected temperature T and pressure value P, gained model summary such as table 5:

Table 5 model summary

Model	R	R 2	Adjust R 2	The standard error of estimating
					1	0.941 a	0.885	0.875	0.204968261

Annotate: a. predictive variable is constant.

On behalf of the linear combination of independent variable or independent variable, coefficient of multiple correlation R can explain dependent variable on much degree in the table 5, the coefficient of multiple correlation R of model=0.941 in the table 5, so make us more satisfied, just independent variable (temperature T and pressure value P) is explained dependent variable on can be largely.Multiple correlation coefficient square value R ²Variation shared ratio in dependent variable of size description regression model independent variable, near 100% best, R in the table 5 ²=0.885 also is more satisfactory, and the variation that is to say independent variable shared ratio in dependent variable is very big.The 4th row are adjusted R ²Be multiple correlation coefficient square value (the Adjusted R that revises ²), because the variable that the size description of secondary series coefficient of multiple correlation R is introduced is many more, coefficient of multiple correlation R is big more, in order to eliminate this influence, provides the multiple correlation coefficient square value R of correction ², the influence of independent variable for dependent variable is described by variation shared ratio in dependent variable of independent variable.The standard error of estimating (Std.Error of the Estimate) illustrates that dependent variable much can not be explained by regression equation in addition, therefore the standard error of the estimation here is very little, can think that the selected independent variable temperature and pressure of the present invention can well explain dependent variable Y.

Following table 6 is the regression coefficient table of the regression equation that carries out regretional analysis by the SPSS data processing software and obtain:

Table 6 regression coefficient ^b

Annotate: b. dependent variable Y

By table 6,, can obtain in conjunction with looking into the t distribution table:

The significance test X of independent variable ₁| t|=5.946＞t _0.995(26)=2.7787

X ₃|t|＝11.651＞t _0.995(26)＝2.7787

By checking us to see, the t value of model equation can reach requirement, illustrates that this model is reasonably on the whole, well fitting data.According to the principle that progressively returns as can be known, model equation is an optimal regression equation.In the above-mentioned table 6, the constant term b of model equation ₀=-1.854, X ₁Coefficient b ₁=0.371, X ₃Coefficient b ₃=2.061, so obtain optimum progressively regression equation be:

Y＝-1.854+0.371X ₁+2.061X ₃

Be Lnh _s=-1.854+0.371LnT+2.061LnP

So: h _s=0.1566T ^0.371P ^2.061

(2) carry out regretional analysis in the data input SPSS data processing software in the table 4 after will handling, independent variable is only during selection pressure value P, gained model summary such as table 7

Table 7 model summary

Model	R	R 2	Adjust R 2	The error that standard is estimated
					1	0.930 c	0.866	0.860	0.216545765

Annotate: c is a predictive variable, and predictive variable is a constant, and variable only is a pressure P.

On behalf of the linear combination of independent variable or independent variable, coefficient of multiple correlation R can explain dependent variable on much degree in the table 7, and dependent variable so make us more satisfied, can be explained with the linear combination of independent variable or independent variable in the coefficient of multiple correlation R of model=0.930 in the last table 7.Multiple correlation coefficient square value R ²Variation shared ratio in dependent variable of regression model independent variable is described, near 100% best, R in the table 7 ²=0.866 also is more satisfactory.The 4th row are adjusted R ²The multiple correlation coefficient square value of be revising (Adjusted R Square) is that the variable introduced is many more because secondary series R gives people's a impression, and multiple correlation coefficient is big more, in order to eliminate this influence, provides the multiple correlation coefficient square value of correction.The standard deviation of estimating (Std.Error of the Estimate) illustrates that dependent variable much can not be explained by regression equation in addition.It also is to have only relative meaning, does not have absolute sense.

Following table 8 is the regression coefficient table of regression equation.

Table 8 regression coefficient ^d

Annotate: d-dependent variable Y

Can obtain by table 8:

The significance test X of variable ₃| t|=12.441＞t _0.995(26)=2.7787

By checking us to see, the t value of model equation can reach requirement, illustrates that this model is reasonably on the whole, well fitting data.According to the principle that progressively returns as can be known, the equation of model is an optimal regression equation.Promptly Zui You progressively regression equation is:

Y＝-0.691+2.180X ₃

Be Lnh _s=-0.691+2.18LnP

So: h _s=0.5013P ^2.18

According to thermal conductance h _s, obtain thermal resistance R=1/h _s

Embodiment

By the correctness of the definite contact conductane model of checking, carried out one group of proving test, test findings sees Table 9,

Table 9 proving test data

(1) utilization fixed contact conductane experimental formula: h _s=0.1566T ^0.371P ^2.061

When temperature and pressure applies simultaneously, calculate table 10 data:

Table 10 contact conductane data

(2) utilization fixed contact conductane experimental formula: h _s=0.5013P ^2.18

When only considering pressure influence, calculate table 11 data:

Table 11 contact conductane data

Can draw through above-mentioned example, method of testing provided by the invention can change simultaneously or has only under the situation of pressure change at temperature and pressure, directly the temperature and pressure data are brought into formula and just can draw contact conductane between identical two material GH4169/GH4169, and then obtain the thermal contact resistance value.A large amount of test operations of having avoided same material when changing the temperature and pressure condition of work, need carry out.

Described thermal contact resistance testing experiment is:

The first step, process at least three samples, comprise a heat flow meter sample and two test samples, be installed in the bottom heating arrangement and the top is answered between the force loading device with three samples are vertically coaxial, described sample is provided with thermopair, thermopair is connected with data acquisition system (DAS), is used for the axial temperature of test sample.

In second step, to the sample heating, specimen temperature begins the collecting test temperature after reaching and stablizing.Described probe temperature comprises the test point temperature T of the test point on each sample _i, i=1 ... n, n are test point number on the sample.Described test point temperature T _iGather by test point thermopair uniform on sample.The probe of described test point thermopair is arranged on the axis of sample, guarantees the accuracy of thermometric.

In the 3rd step, the temperature on each test point on the sample is gathered and stored, and pass through the temperature variation curve at computer drawing test point place.

On per two adjacent samples, the temperature of two thermopairs nearest apart from contact interface is T _nAnd T _N+1, the medial temperature Δ T ' at then per two sample contact interface places is:

${\mathrm{\ΔT}}^{\′}=\frac{T_n+T_{n+1}}{2}.$

In the 4th step, determine that by the extrapolation thermograde Δ T falls in the temperature at adjacent samples contact interface place:

$\mathrm{\ΔT}=(T_n-\frac{(T_1-T_n)}{(n-1)\·l/n}\×l/2n)-(T_{n+1}+\frac{(T_{n+1}-T_{2n})}{(n-1)\·l/n}\×l/2n)$

$=(T_n-\frac{2(T_1-T_n)}{n-1})-(T_{n+1}+\frac{2(T_{n+1}-T_{2n})}{n-1})$

Wherein, l is a specimen length, and n is a number of checkpoints on each sample, from top to bottom the test point on each sample is numbered in turn, then T ₁, T _n, T _N+1, T _2nThe temperature of the 1st of first tested sample of difference, the temperature of a n test point, second tested sample n+1 and 2n test point.

The 5th goes on foot, and determines the axial hot-fluid of sample according to selected heat flow meter.

Ignore the lateral heat flow loss of sample, as heat flow meter, be prepared into the heat flow meter sample with the same size of sample with metallic copper, then axially hot-fluid is:

$q={\mathrm{\λ}}_T\frac{\mathrm{dt}}{\mathrm{dx}}={\mathrm{\λ}}_T(T_1-T_n)/m$

λ wherein _TThermal conductivity for copper; T ₁, T _nTemperature for first test point and n test point on the heat flow meter sample; M is the distance between first test point and n the test point on the heat flow meter sample.

In the 6th step, calculate contact conductane and thermal contact resistance.

According to the axial hot-fluid in the 5th step, the contact conductane h in obtaining testing _sAs follows:

$h_s=\frac{q}{\mathrm{\ΔT}}=\frac{{\mathrm{\λ}}_T(T_1-T_n)/m}{(T_n-\frac{2(T_1-T_n)}{n-1})-(T_{n+1}+\frac{2(T_{n+1}-T_{2n})}{n-1})}$

Fall Δ T according to the temperature at per two sample contact interface places and calculate thermal contact resistance R.

Described thermal contact resistance R is:

$R=\frac{1}{h_s}=\frac{\mathrm{\ΔT}}{q}$

Wherein q is axial hot-fluid.

Claims (2)

1. thermal contact resistance method of testing that is applied to the GH4169/GH4169 high temperature alloy, it is characterized in that: described thermal contact resistance method of testing realizes as follows:

The first step, determine the reduction elastic modulus E of two contact materials ':

$E^{\′}=\frac{E}{1-v^2}=\frac{-0.0646T+208.27}{1-v^2}$

Wherein E is the elastic modulus of GH4169 high temperature alloy, and v is a Poisson ratio, and T is a probe temperature;

Second step is according to the theory of plastic strain in matrix modeling;

According to theory of plastic strain in matrix, the plastic yield factor ψ that obtains material is:

ψ＝(E′/H)tanθ，

With reduction elastic modulus, hardness H=400MPa and Bring following formula into, get θ=0.03 °, T=600 ℃, obtain:

$\mathrm{\ψ}=(E^{\′}/H)\sqrt{2}\mathrm{\θ}=\frac{-0.0646T+208.27}{H(1-v^2)}\×\sqrt{2}\mathrm{\θ}$

$=19.62$

In the following formula, ψ＞1, the theory of plastic strain in matrix modeling of then selecting for use Mikic to propose obtains the contact conductane h of thermal contact resistance test material _sFor:

h _s＝(1.13ktanθ/σ)(P/H) ^0.94；

In the formula, tan θ and θ are respectively the absolute average pitch and the average slope angle of micro-profile at the contact interface place of thermal contact resistance test material, and σ, k, P and H are respectively the hardness of surfaceness, thermal conductivity coefficient, test pressure and the material of thermal contact resistance test material;

The 3rd step, model simplification;

Relation to material thermal conductivity coefficient under the different temperatures and temperature is carried out linear fit, obtains:

k＝0.0141T+13.221

So have

X wherein ₁Be coefficient to be determined;

σ is the roughness of thermal contact resistance test material GH4169, the average height of exosyndrome material contact interface profile, tan θ is the absolute average pitch of material contact interface profile, θ is the average slope angle of material contact interface profile, in other conditions one regularly, the absolute average pitch tan θ of profile and roughness σ positive correlation are so have

X wherein ₂Be coefficient to be determined;

Again X wherein ₃Be parameter to be determined; So to contact conductane h _sFormula equal sign both sides do natural logarithm, obtain following distortion:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP

X wherein ₀Be unknown parameter, make Y=lnh in the following formula _s, X ₁=lnT, X ₂=ln σ, X ₃=lnP, b ₀=lnx ₀, b ₁=x ₁, b ₂=x ₂, b ₃=x ₃, then following formula further is written as:

Y＝b ₀+b ₁X ₁+b ₂X ₂+b ₃X ₃

B in the formula ₀, b ₁, b ₂And b ₃Be unknown parameter;

In the 4th step,, determine unknown parameter b by progressively returning test ₀, b ₁, b ₂And b ₃, obtain optimal regression equation; According to the regretional analysis result, obtain the contact conductane of GH4169/GH4169 high temperature alloy, contact conductane is got inverse, obtain thermal contact resistance; In temperature is 100～600 ℃ of intervals, when independent variable is selected temperature and force value, h _s=0.1566T ^0.371P ^2.061, independent variable is only during the selection pressure value, h _s=0.5013P ^2.18

2. the thermal contact resistance method of testing that is applied to the GH4169/GH4169 high temperature alloy according to claim 1 is characterized in that: described material contact interface roughness σ is between 0.1 and 3.0.