CN101980008A - Method for testing contact thermal resistance of GH4169/GH4169 by additional heating - Google Patents

Abstract

The invention discloses a method for testing the contact thermal resistance of GH4169/GH4169 by additional heating, which comprises the following steps of: firstly, determining a reduced elastic modulus between two materials; secondly, modeling according to a plastic deformation theory; thirdly, simplifying a model; and finally, determining unknown parameters through a stepwise regression test to obtain an optimal regression equation; obtaining contact thermal conductance hs according to a regression analysis result, wherein hs is 145583796.6T0.159P-1.932 when temperature and pressure values are independent variables and the temperature is between 100 and 600 DEG C, and hs is 165751460.8P-1.863 when only the pressure value is an independent variable; and obtaining the contact thermal resistance R according to a formula R=1/hs, wherein test data required by the regression test is obtained by a contact thermal resistance test, and temperature compensation is performed on a contact interface of two samples in the testing process. By the method, the required parameters can be obtained only according to the test data, and the contact thermal resistance can be obtained according to a simple formula under the condition of arbitrarily changing test temperature and test pressure, so that the contact thermal resistance testing process is simple and can be reused.

Description

The method of the thermal contact resistance of compensation heating test GH4169/GH4169

Technical field

The invention belongs to the thermal contact resistance technical field of measurement and test, be specifically related to a kind of method that compensates heating test GH4169/GH4169 thermal contact resistance.

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, select proper model by theoretical analysis, the utilization mathematical statistic method draws the thermal contact resistance computing formula of engineering practicality, and the accuracy by the verification experimental verification model, be compensated the method for heating test GH4169/GH4169 thermal contact resistance at last, this method specifically realizes as follows:

The first step is determined the reduction elastic modulus between two materials;

For GH4169/GH4169 thermal contact resistance testing experiment, the reduction elastic modulus of two contact materials is:

$E^{\′}=\frac{E}{1-v^2}$

In the formula, E is the elastic modulus of material, and v is a Poisson ratio;

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

If ψ＞1, the then theory of plastic strain in matrix modeling that proposes according to Mikic, its experimental formula is:

h _s＝(1.13ktanθ/σ)(P/H) ^0.94

In the formula, h _s, H, P, k, σ, tan θ be respectively the absolute average pitch of thermal conductance, hardness, test pressure, thermal conductivity coefficient, interface roughness and interface profile of thermal contact resistance test material;

The 3rd step, model simplification;

Contact conductane h _sThe formula both sides take from right logarithm, obtain following deformation formula:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP

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, Y is a dependent variable, X ₁, X ₂And X ₃Be respectively independent variable;

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=145583796.6T ^0.159P ^-1.932, independent variable is only during the selection pressure value, h _s=165751460.8P ^-1.863

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 method that is used to test the thermal contact resistance of same material GH4169/GH4169 under the temperature and pressure acting in conjunction, this method only need be passed through disposable test, just can obtain experimental formula, by this experimental formula, no matter how temperature and pressure changes, can obtain the thermal contact resistance between the two identical material GH4169/GH4169 very soon.Described method is specific implementation as follows:

The first step is determined the reduction elastic modulus between two materials.

For GH4169/GH4169 sample thermal contact resistance testing experiment, the reduction elastic modulus of 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:

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

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:

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

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) " (Beijing: China Standard Press, 2001.8).Get T=600 ℃, obtain E '=185 * 10 ³MPa.

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 H=400Mpa, the roughness of setting thermal contact resistance test material GH4169 is σ, the average height of exosyndrome material contact interface profile, according to the test needs, the roughness for preparing two thermal contact resistance test materials is got maximum conditions: σ=σ between 0.1 μ m and 3.0 μ m ₁=σ ₂=0.1 μ m; θ=θ ₁=θ ₂=0.03 °.σ wherein ₁And σ ₂Be respectively the roughness of two thermal contact resistance test materials, θ ₁And θ ₂Be respectively the interface profile average slope angle of two thermal contact resistance test materials.With H,

And formula (5) substitution formula (4) obtains the value of plastic yield factor ψ:

$\mathrm{\ψ}=(E^{\′}/H)\tan \mathrm{\θ}$

$=\frac{185000}{400}\tan \mathrm{\θ}$

$=462.5\×\sqrt{{\mathrm{\θ}}_1^2+{\mathrm{\θ}}_2^2}---\left(6\right)$

$=462.5\×0.04242$

$=19.62$

Because ψ＞1, so 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)

Wherein, h _sBe contact conductane, k is a thermal conductivity coefficient.

The 3rd step, model simplification.

(1) maximum conditions of test material meet the theory of plastic strain in matrix of Mikic, so all test findings all meet theory of plastic strain in matrix.Parameter k is the harmonic-mean of the thermal conductivity coefficient of two test materials in the formula (7), because two thermal contact resistance test materials are same material GH4169, therefore k=k is arranged ₁=k ₂, can obtain the thermal conductivity coefficient value of GH4169 by " Chinese aeronautical material handbook the 2nd volume (the 2nd edition) " (Beijing: China Standard Press, 2001.8).

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

Thermal conductivity coefficient in the his-and-hers watches 2 and temperature data carry out linear fit, obtain the relation of thermal conductivity coefficient and temperature:

k＝0.0141T+13.221 (8)

As seen, k is directly proportional with T, so have in conjunction with formula (7):

X wherein ₁Be coefficient to be determined.

(2) in the formula (7)

The average height of roughness σ exosyndrome material contact interface profile, θ ₁And θ ₂Be respectively the interface profile average slope angle of two thermal contact resistance test materials, tan θ is the absolute average pitch of material contact interface profile, therefore regularly in other conditions one, and the absolute average pitch tan θ of interface profile and roughness σ positive correlation, so, have in conjunction with formula (7)

X wherein ₂Be coefficient to be determined.

(3) for determining material GH4169, hardness H for determine or can directly measure, so in the formula (7) X wherein ₃Be parameter to be determined.

Formula this moment (7) can be expressed as:

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

Wherein, x ₀, x ₁, x ₂, x ₃Be parameter to be determined.

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.

The principal element that influences thermal contact resistance has surface of contact temperature, pressure and roughness 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.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.

Among the present invention practical data all from the thermal contact resistance test, in the process of the test,, obtain raw data and see Table 3 for the contact interface place of thermal contact resistance test material carrying out temperature compensation:

Table 3 thermal contact resistance testing experiment data

Data in the his-and-hers watches 3 are carried out the natural logarithm differentiate, obtain handling the back data and see Table 4:

Table 4 is handled the back data

(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, and the roughness of material is a microscopic quantity in addition, is difficult to direct acquisition in engineering practice, thus 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.

To carry out regretional analysis in the data input SPSS data processing software after handling in the table 4, when independent variable is selected temperature and force value, gained model summary such as table 5:

Table 5 model gathers

Model	R	R 2	Adjust R 2	The error that standard is estimated
					1	0.910 a	0.827	0.712	0.372607315

A. predictive variable: (constant), T, 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 5, and coefficient of multiple correlation R=0.910 of model in the last table is so make us more satisfied.Multiple correlation coefficient square value R ²(R Square) illustrates variation shared ratio in dependent variable of regression model independent variable, and near 100% best, this value is 0.827 also to be more satisfactory in the table.The 4th classifies the adjustment multiple correlation coefficient square value (Adjusted R Square) of correction as, is that the variable introduced is many more because secondary series is given 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 6 is the regression coefficient table of regression equation.

Table 6 regression coefficient ^b

B. dependent variable: Y

Can obtain by table 6:

The significance test X of variable ₁| t|=6.214＞t _0.995(6)=3.7074

X ₃|t|＝12.367＞t _0.995(6)＝3.7074

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＝18.796+0.159X ₁-1.932X ₃

Be Lnh _s=18.796+0.159LnT-1.932LnP

So: h _s=145583796.6T ^0.159P ^-1.932

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

Table 7 model gathers

Model	R	R 2	Adjust R 2	The error that standard is estimated
					1	.895 c	.801	.751	.346609008

C. predictive variable: (constant), X ₃

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 the R=0.895 of model in the last table is so make us more satisfied.Multiple correlation coefficient square value R ²(R Square) illustrates variation shared ratio in dependent variable of regression model independent variable, near 100% best, and R in the table ²=0.801 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 is given 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

D. dependent variable: Y

Can obtain by table 8:

The significance test X of variable ₃| t|=12.670＞t _0.995(6)=3.7074

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＝18.926-1.863X ₃

Be Lnh _s=18.926-1.863LnP

So: h _s=165751460.8P ^-1.863

Embodiment

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

Table 9 proving test data

(1) utilization fixed thermal contact resistance experimental formula: h _s=145583796.6T ^0.159P ^-1.932

Calculate:

(2) utilization fixed thermal contact resistance experimental formula: h _s=165751460.8P ^-1.863

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 meant:

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.

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.

According to the test needs, can adjust the heating-up temperature of heating arrangement or answer the loading stress of force loading device, repeat seven steps of the first step to the and can test thermal contact resistance under different temperatures and the stress condition.

Described temperature compensation test thermal contact resistance is meant that step of increase is as follows between the 3rd step and the 4th step:

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:

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

T ' carries out temperature compensation to the sample contact interface according to the medial temperature Δ.Heating-up temperature according to the medial temperature at sample contact interface place is regulated compensating heating device heats compensating heater in the sagittal plane at contact interface place, guarantee that the contact interface place keeps Δ T ' always.

Claims (2)

1. the method for the thermal contact resistance of GH4169/GH4169 is tested in the compensation heating, it is characterized in that following steps:

The first step is determined the reduction elastic modulus between two materials;

For GH4169/GH4169 thermal contact resistance testing experiment, the reduction elastic modulus of two contact materials is:

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

In the formula, E is the elastic modulus of material, 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 the plastic deformation of metal material theory, plastic yield factor ψ is:

ψ＝(E′/H)tanθ

With the reduction elastic modulus E ', 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 then theory of plastic strain in matrix modeling that proposes according to Mikic, its experimental formula is:

h _s＝(1.13ktanθ/σ)(P/H) ^0.94

In the formula, h _s, H, P, k, σ, tan θ be respectively the absolute average pitch of thermal conductance, hardness, test pressure, thermal conductivity coefficient, interface roughness and interface profile of thermal contact resistance test material;

The 3rd step, model simplification;

Contact conductane h _sThe formula both sides take from right logarithm, obtain following deformation formula:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP

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, Y is a dependent variable, X ₁, X ₂And X ₃Be respectively independent variable;

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 contact conductane h _s, in temperature is elected 100～600 intervals as, when independent variable is selected temperature and force value, h _s=145583796.6T ^0.159P ^-1.932, independent variable is only during the selection pressure value, h _s=165751460.8P ^-1.863, according to R=1/h _sObtain thermal contact resistance R; Described recurrence is tested required test figure and is obtained by the thermal contact resistance testing experiment, and the contact interface place to two samples in the process of the test carries out temperature compensation.

2. the method for the thermal contact resistance of compensation heating test GH4169/GH4169 according to claim 1, it is characterized in that: described material contact interface roughness σ is between 0.1 and 3.0.