CN102033077B - Method for testing contact thermal resistance of GH4169/K417 alloy - Google Patents

Abstract

The invention discloses a method for testing the contact thermal resistance of a GH4169/K417 alloy. The method comprises the following steps: first, confirming the reduced elastic moduli of two contact materials, and then modeling according to the plastic deformation theory of metal materials; simplifying models; confirming unknown parameters bo, b1, b2 and b3 through stepwise regression experiments, and obtaining an optimal regression equation; obtaining the contact thermal conduction of the GH4169/K417 alloy through regression analysis results, calculating the reciprocal of the contact thermal conduction, and obtaining the contact thermal resistance. When temperature is within the interval of 100-600 DEG C and independent variables choose the temperature and pressure value, hs=26.534T0.107P1.297, and when the independent variables only choose the pressure value, hs=41.43P1.291. By using the invention, the contact thermal conduction can be obtained according to a simple formula under the condition of randomly changing testing temperature and pressure only after the needed parameters b0, b1 and b3 are obtained through experiment data, and the testing process of the contact thermal resistance is simple and can be repeatedly used. Under the premise of ensuring engineering practicability and the accuracy of testing results, the testing process of the contact thermal conduction is greatly simplified.

Description

The thermal contact resistance method of testing that is used for the GH4169/K417 alloy

Technical field

The invention belongs to the high temperature metallic material technical field of measurement and test, be specifically related to a kind of thermal contact resistance method of testing of the GH4169/K417 of being used for 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 carry out through lot of test; Process of the test is to choose the sample that boundary material is processed into certain size, certain interface roughness; Be that the interface provides specific interface temperature and interfacial pressure through pressurization and the process of heating then, at last through interface temperature is fallen with sample in the contact conductane that measures two storerooms of heat flow density.

Though existing measuring technology obtains to the contact conductane under fixed temperature, pressure and the interface roughness condition more accurately; But because its test process is complicated; The test condition relative fixed; Can not satisfy temperature changeable in the practical applications and pressure condition, the contact conductane data at material interface place can't promptly and accurately be provided.

Summary of the invention

The present invention is the basis with the test, selects proper model through theoretical analysis, and the utilization mathematical statistic method draws the practical thermal contact resistance computing formula of engineering, and passes through the accuracy of demonstration test verification model.The present invention provides a kind of thermal contact resistance method of testing of the GH4169/K417 of being used for alloy, comprises the steps:

The first step is confirmed the reduction elastic modulus of two contact materials.

$E^{\′}=2{[(1-v_1^2)/E_1+(1-v_2^2)/E_2]}^{-1}$

E wherein ₁, E ₂Be respectively the elastic modulus of GH4169 and K417 alloy, v ₁, v ₂Be respectively the Poisson ratio of GH4169 and K417 alloy.

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

ψ＝(E′/H)tanθ。

Wherein, ψ is the plastic yield factor, and H is the K417 hardness of alloy, and tan θ is the absolute average pitch of contact interface profile.

According to theory of plastic strain in matrix, have:

h _s＝(1.13ktanθ/σ)(P/H) ^0.94

The 3rd step, model simplification.

(1) according to the theory of plastic strain in matrix of Mikic, the harmonic-mean k expression formula of the thermal conductivity coefficient of two thermal contact resistance test materials is:

k＝2k ₁k ₂/(k ₁+k ₂)

Because thermal conductivity coefficient k is proportional to temperature T, have

X wherein ₁Be coefficient to be determined.

(2) basis

The roughness of thermal contact resistance test material is σ; The average height of exosyndrome material contact interface profile; 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 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.

(3) for fixed two thermal contact resistance test materials, select less hardness H for calculating hardness, H is for confirming amount, so have

X wherein ₃Be parameter to be determined.

This moment, contact conductane can be expressed as:

$h_s=x_0{T}^{x_1}{\mathrm{\σ}}^{x_2}{P}^{x_3}$

Ask natural logarithm to get on the following formula both sides:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP

Make the lnh in the formula _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。

In the 4th step,, confirm unknown parameter b through 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/K417 alloy, contact conductane 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 through 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 in the practical applications, 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.

Thermal contact resistance method of testing provided by the invention realizes through following steps:

The first step is confirmed the reduction elastic modulus of two contact materials.

For GH4169/K417 alloy thermal contact resistance test sample, the reduction elastic modulus of two contact materials is:

$E^{\′}=2{[(1-v_1^2)/E_1+(1-v_2^2)/E_2]}^{-1}---\left(1\right)$

For GH4169 and K417 alloy material, as shown in table 1 is described alloy material temperature and the corresponding relation of elastic modulus in 100 ℃～600 ℃ intervals:

The elastic modulus of table 1GH4169 and K417 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 GH4169 and K417 alloy material with the variation of temperature relation is:

E ₁＝-0.0646T+208.27 (2)

E ₂＝-0.0651T+222.67 (3)

The Poisson ratio v of material ₁, v ₂Value is looked into " Chinese aeronautical material handbook the 2nd volume (the 2nd edition) " (Beijing: China Standard Press, 2001.8), is respectively v ₁=0.3, v ₂=0.29, so above-mentioned formula (1) further is written as:

$E^{\′}=2{[(1-v_1^2)/E_1+(1-v_2^2)/E_2]}^{-1}$

$=2{[\frac{{1-0.3}^2}{-0.0646T+208.27}+\frac{1-{0.29}^2}{-0.0651T+222.67}]}^{-1}---\left(4\right)$

Get T=600 ℃, try to achieve E '=195 * 10 ³MPa.

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

Theoretical according to plastic deformation of metal material, plastic yield factor ψ is:

ψ＝(E′/H)tanθ (5)

In the formula (5), 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:

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

H is the hardness of the softer material of the surface of contact of two thermal contact resistance test materials; Because the GH4169 hardness of alloy is H=400Mpa; The hardness of alloy K417 is H=370Mpa; So choose lower hardness number as H=370Mpa this moment, hardness of alloy H obtains through consulting " Chinese aeronautical material handbook the 2nd volume (the 2nd edition) ".

The preparation the contact material roughness of surveying between 0.1 and 3.0, get maximum conditions:

σ ₁＝σ ₂＝0.1μm；θ ₁＝θ ₂＝0.03°。

σ ₁, σ ₂Be respectively GH4169 and K417 alloy interface roughness, θ ₁, θ ₂Be respectively the average slope angle of contact interface profile, bring formula (6), material hardness H and formula (4) into formula (5), have:

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

$=\frac{195000}{370}\tan \mathrm{\θ}$

$=527\×\sqrt{{\mathrm{\θ}}_1^2+{\mathrm{\θ}}_2^2}---\left(7\right)$

$=527\×0.04242$

$=22.4$

Because ψ＞1, so this test findings also 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 (8)

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 harmonic-mean of the thermal conductivity coefficient of two thermal contact resistance test materials in the formula (8), and its expression formula is:

k＝2k ₁k ₂/(k ₁+k ₂) (9)

According to " Chinese aeronautical material handbook the 2nd volume (the 2nd edition) ", obtain the thermal conductivity coefficient of GH4169 and K417 alloy material under the different temperatures, like table 2:

The thermal conductivity coefficient of table 2GH4169 and K417 is with the variation of temperature value

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

k ₁＝0.0141T+13.221 (10)

k ₂＝0.0117T+9.3246 (11)

So formula (9) can further be written as:

$k=2k_1{k}_2/(k_1+k_2)$

$=\frac{2(0.0141T+13.221)(0.0117T+9.3246)}{0.0141T+13.221+0.0117T+9.3246}---\left(12\right)$

So thermal conductivity coefficient k is proportional to temperature T, according to formula (8),,

X wherein ₁Be coefficient to be determined.

(2) roughness according to

thermal contact resistance test material in the formula (6) is σ; 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; Therefore in other conditions one regularly, the absolute average pitch tan θ of profile and roughness σ positive correlation are in conjunction with formula

(8), can have

X wherein ₂Be coefficient to be determined.

(3), select less hardness H to be calculating hardness, so H confirm amount in the formula (8), in conjunction with formula (8), so have for fixed two thermal contact resistance test materials X wherein ₃Be parameter to be determined.

Formula this moment (8) can be expressed as:

$h_s=x_0{T}^{x_1}{\mathrm{\σ}}^{x_2}{P}^{x_3}---\left(13\right)$

Ask natural logarithm to get on formula (13) both sides:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP (14)

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

The explained variable (dependent variable) that adopts is the natural logarithm value (Y) of contact conductane, and explanatory variable (independent variable) is the natural logarithm value (X of interface temperature ₁), the natural logarithm value (X of interfacial pressure ₂) and the natural logarithm value (X of the compound roughness in interface ₃).Make the lnh in the formula (14) _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。(15)

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

In the present embodiment practical data all test from thermal contact resistance.Raw data is seen table 3:

Table 3 thermal contact resistance test figure

13 groups of data are handled in the his-and-hers watches 3, promptly respectively contact conductane value, interface mean temperature, contact stress and compound roughness are asked the natural logrithm 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; In engineering practice,, do not need to remeasure again to obtain as long as the roughness that guarantees material between 0.1-3.0, can meet the demands; 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 the value of b2 among the present invention.

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

Table 5 model gathers

A. predictive variable: (constant), X3, X1.

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 the R=0.933 of model in the last table is so make us more satisfied.Multiple correlation coefficient square value R ²(R Square) explains variation shared ratio in dependent variable of regression model independent variable, near 100% best, and R in the table ²=0.870 also is more satisfactory.The 4th classifies the multiple correlation coefficient square value adjustment R of correction as ²(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) explains 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|=4.761＞t _0.995(13)=3.0123

X ₃|t|＝8.186＞t _0.995(13)＝3.0123

Through checking us to see, the t value of model equation can reach requirement, explains that this model is reasonably on the whole, well fitting data.Principle according to progressively returning can know that the equation of model is an optimal regression equation.Promptly optimum progressively regression equation is:

Y＝3.278+0.107X ₁+1.297X ₃

Be Lnh _s=3.278+0.107LnT+1.297LnP

So: h _s=26.534T ^0.107P ^1.297

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

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

Table 7 model gathers

C. predictive variable: (constant), X3.

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=0.929 of model in the last table is so make us more satisfied.Multiple correlation coefficient square value R ²(R Square) explains variation shared ratio in dependent variable of regression model independent variable, near 100% best, and R in the table ²=0.863 also is more satisfactory.The 4th classifies the multiple correlation coefficient square value R of correction as ²(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) explains 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|=8.319＞t _0.995(13)=3.0123

Through checking us to see, the t value of model equation can reach requirement, explains that this model is reasonably on the whole, well fitting data.Principle according to progressively returning can know that the equation of model is an optimal regression equation.Promptly optimum progressively regression equation is:

Y＝3.724+1.291X ₃

Be Lnh _s=3.724+1.291LnP

So: h _s=41.43P ^1.291

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

Embodiment

For checking the correctness of definite thermal contact resistance model, carried out one group of proving test, result of the test sees Table 9:

Table 9 proving test data

(1) the thermal contact resistance experimental formula in order to confirm: h _s=26.534T ^0.107P ^1.297

Calculate h _s:

(2) the thermal contact resistance experimental formula in order to confirm: h _s=41.43P ^1.291

Calculate contact conductane h _s:

Can draw through above-mentioned instance; Method of testing provided by the invention can change or has only under the situation of pressure change at temperature and pressure simultaneously; Directly bringing the temperature and pressure data into formula just can draw two contact conductanes between the material GH4169/K417, and then obtains the contact thermal resistance.A large amount of test operations that when changing the temperature and pressure condition of work, need carry out have been avoided.The thermal contact resistance of certain the two kinds of material that obtains through above-mentioned formula is compared with the actual tests data, and error rate can well satisfy the demand of practical applications less than 8.32%.

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 _iTest point thermopair through on sample, being uniformly distributed with is gathered.The probe of said 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, confirm that through 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 order, 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 confirms 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 (1)

1. be used for the thermal contact resistance method of testing of GH4169/K417 alloy, it is characterized in that:

The first step, confirm the reduction elastic modulus of two contact materials:

$E^{\′}=2{[(1-v_1^2)/E_1+(1-v_2^2)/E_2]}^{-1}$

E wherein ₁, E ₂Be respectively the elastic modulus of GH4169 and K417 alloy, v ₁, v ₂Be respectively the Poisson ratio of GH4169 and K417 alloy; E ₁=-0.0646T+208.27, E ₂=-0.0651T+222.67; v ₁=0.3, v ₂=0.29;

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

ψ＝(E′/H)tanθ

Wherein, ψ is the plastic yield factor, and H is the K417 hardness of alloy, and tan θ is the absolute average pitch of contact interface profile, will

Material hardness H=370Mpa and reduction elastic modulus are brought following formula into, get θ ₁=θ ₂=0.03 °, have:

$\mathrm{\ψ}=\frac{2{[(1-v_1^2)/E_1+(1-v_2^2)/E_2]}^{-1}}{H}\×\sqrt{{\mathrm{\θ}}_1^2+{\mathrm{\θ}}_2^2}=22.4$

Because ψ>1, so, have according to theory of plastic strain in matrix:

h _s＝(1.13ktanθ/σ)(P/H) ^0.94；

The 3rd step, model simplification;

(1) according to the theory of plastic strain in matrix of Mikic, the harmonic-mean k expression formula of the thermal conductivity coefficient of two thermal contact resistance test materials is:

k＝2k ₁k ₂/(k ₁+k ₂)

K wherein ₁=0.0141T+13.221, k ₂=0.0117T+9.3246 is because thermal conductivity coefficient k ₁, k ₂Be proportional to temperature T, so have

X wherein ₁Be coefficient to be determined;

(2) basis The roughness of thermal contact resistance test material is σ; The average height of exosyndrome material contact interface profile; 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 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; The average slope angle θ of described material contact interface profile is 0.03 °, and roughness σ is between 0.1 and 3.0;

(3) for fixed two thermal contact resistance test materials, select less hardness H for calculating hardness, H is for confirming amount, so have

X wherein ₃Be parameter to be determined;

This moment, contact conductane was expressed as:

$h_s=x_0{T}^{x_1}{\mathrm{\σ}}^{x_2}{P}^{x_3}$

Ask natural logarithm to get on the following formula both sides:

lnh _s＝lnx ₀+x ₁lnT+x ₂lnσ+x ₃lnP

Make the lnh in the formula _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；

In the 4th step,, confirm unknown parameter b through 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/K417 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=26.534T ^0.107P ^1.297, independent variable is only during the selection pressure value, h _s=41.43P ^1.291