JP2002116166A - Measuring method and measuring instrument for thermal resistance and biot number of laminated material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a measuring method and a measuring instrument for the thermal resistance and Biot number of a laminated material, capable of accurately determining the thermal resistance of an interlayer part when an interlayer indefinable in thickness exists between layers of a laminated material having a first layer and a second layer, and capable of determining the Biot number of the laminated material. SOLUTION: This method comprises a first process for finding a measured surface temperature of one surface of the laminated material 13 when the other surface of the material 13 is heated instantly, a second process for finding a theoretical surface temperature of one surface of the material 13 when the other surface of the material 13 is heated instantly by calculating from the solution of a non-steady heat conduction equation taking boundary conditions into consideration, and a third process for determining the thermal resistance and Biot number from conditions for minimizing the deviation of the measured surface temperature from the theoretical surface temperature.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring the thermal resistance existing between layers of a laminated material having a first layer and a second layer and the number of biot of the laminated material and a measuring apparatus therefor. The present invention relates to a method and apparatus for measuring the thermal resistance of a laminated material having an interlayer whose thickness cannot be clearly defined and the biot number of the laminated material at that time.

[0002]

2. Description of the Related Art The application range of materials, such as formation of an oxidation-resistant film for improving the oxidation resistance of heat-resistant metals and non-oxide-based materials, and formation of a thermal barrier coating layer for improving the heat resistance of the material, is increased. In order to enlarge the material, multilayering of a material for improving characteristics of a material by laminating another material on a surface of a material to be a base material has been widely studied. In particular, in a multilayer material used at a high temperature, the heat conduction property is an important physical property value in the material design, and among them, the thermal resistance generated between the layers of the multilayer material is a particularly important factor in the material design of the high temperature material. . Therefore, conventionally, for example, in a laminated material in which an oxidation-resistant film or a thermal barrier coating layer is formed on the base material surface, the thickness between layers formed between the base material surface and the formed layer can be clearly defined. When the lever portion can be considered as the intermediate layer, the thermal resistance existing between the layers can be obtained by, for example, a multilayer material analysis method using a laser flash method.

In the multilayer material analysis method using the laser flash method, first, one surface of a laminated material is irradiated with a laser beam for instantaneous heating, and the temperature of the other surface due to the conduction of the heat at that time. The change is measured by, for example, an infrared detector to determine an actually measured surface temperature. In addition, the temperature change on the other surface when one side of the laminated material is irradiated with laser light is obtained by solving the heat conduction equation, and this analytical solution is used to determine the density, thickness, thermophysical properties, etc. of each layer of the laminated material. Substituting the data, further assuming the thermal resistance of the intermediate layer formed between the layers, performing a numerical calculation using a computer, and obtaining the theoretical surface temperature of the other surface. Next, the thermal resistance of the intermediate layer was determined from the condition that minimizes the square deviation between the measured surface temperature and the theoretical surface temperature obtained by numerical calculation, and this value was used as the thermal resistance of the intermediate layer.

[0004] For example, the thickness of both the first layer and the third layer is 1 m.
m, a second layer which is an intermediate layer formed between the first layer and the third layer.
Using a sample with a layer thickness of 0.005 to 1 mm,
One pulse of laser light with a pulse width of 1 ms and a triangular waveform
Irradiates one surface and heats it based on temperature changes on the other surface.
When determining the resistance, the accuracy of the determined thermal resistance and the thermal resistance
When the relation of the thickness of the generated intermediate layer is obtained, FIGS.
The result shown in FIG. 4 and 5, the horizontal axis represents the intermediate layer.
Thickness of the second layer (ΔL_Two ) And the thickness of the laminated material (L _Three )When
It is expressed as the ratio of In addition, laser flash method
Temperature measurement is 10 μs, pulse waveform measurement
The measurement is performed at a sampling rate of 1 μs.
The thermal diffusivity of the first layer is 1.0 × 10^-Fourm^Two / S, second
1.1 × 10 layers^-Fourm^Two / S, the third layer is 1.2 × 10^-Four
m^Two / S, specific heat of the first layer is 1.0 kJ / kg / K,
1.1 kJ / kg / K for the layer, 1.2 kJ / kg for the third layer
/ K, density of the first layer is 1000 kg / m^Three , The second layer is 1
100kg / m^Three , The third layer is 1200 kg / m^Three age
Therefore, the Biot number indicating the radiation loss is the same for both the first and third layers.
It was set to 0.01. FIG. 4 shows the pulse waveform of the laser.
Considering the thickness of the second layer (ΔL
_Two ) And the thickness of the laminated material (L_Three ) As the parameter
Figure 5 shows the change in accuracy of the determined thermal resistance when
Intermediate layer in the case of the center of gravity method with waveform approximated by delta function
Of the second layer (ΔL_Two ) And the thickness of the laminated material (L
_Three ) And the determined thermal resistance as a parameter
Changes in accuracy are shown.

[0005]

As shown in FIGS. 4 and 5, the ratio of the thickness (ΔL ₂ ) of the second layer as the intermediate layer to the thickness (L ₃ ) of the laminated material is small. In other words, as the thickness (ΔL ₂ ) of the second layer, which is the intermediate layer, decreases, the accuracy of the determined thermal resistance gradually decreases. For example, when the pulse waveform of the laser shown in FIG. 4 is considered, an error occurs when the ratio of the thickness (ΔL ₂ ) of the second layer as the intermediate layer to the thickness (L ₃ ) of the laminated material is less than 0.05. rapidly increased, when the pulse waveform in FIG. 5 of the delta function approximation center of gravity method, the ratio of the thickness of the second layer is an intermediate layer ([delta] L ₂₎ to the thickness of the laminate material (L ₃₎ is 0. If it becomes less than 1, the error will increase sharply. As described above, when the thickness (ΔL ₂ ) of the second layer, which is the intermediate layer, becomes thinner than the thickness (L ₃ ) of the laminated material, the thermal resistance determined by the multilayer material analysis method using the laser flash method. The thermal resistance between the layers where the first and third layers partially contact and the interlayer thickness disappears and the interlayer thickness cannot be clearly defined is reduced by the laser flash method. It is impossible to accurately determine from the used multi-layer analysis method.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has a thermal resistance of an interlayer portion when a layer whose thickness cannot be clearly defined exists between layers of a laminated material having a first layer and a second layer. It is an object of the present invention to provide a method and an apparatus for measuring the thermal resistance and the biot number of the laminated material, which can determine the Biot number of the laminated material with high accuracy.

[0007]

According to the present invention, there is provided a method for measuring a thermal resistance and a biot number of a laminated material according to the present invention, which comprises a plate-shaped laminated material having a first layer and a second layer. A method for measuring the thermal resistance and biot number of the laminated material, which measures the thermal resistance of the interlayer portion between the second layer and the biot number indicating the degree of heat radiation loss of the laminated material, A first step of obtaining the measured surface temperature of the other surface of the laminated material when one surface is instantaneously heated, and the other step of the laminated material when one surface of the laminated material is instantaneously heated. A second step of calculating the theoretical surface temperature of the surface from the solution of the unsteady heat conduction equation in consideration of the boundary condition, and the heat resistance from the condition of minimizing the deviation between the measured surface temperature and the theoretical surface temperature. And a third step of determining the biot number.

[0008] One surface of the laminated material is instantaneously heated,
Since the temperature of the other surface at that time is measured in an unsteady state, the time required for the measurement can be extremely shortened, and the temperature change reflecting the thermal characteristics of the laminated material without being affected by surrounding disturbances. It can be measured accurately. Also, by solving the unsteady heat conduction equation considering the heating condition and the boundary condition when the one surface of the laminated material is instantaneously heated, the thermal resistance and the biot number can be used as variables. It is possible to obtain the theoretical surface temperature by calculation in a form that includes it. Therefore, by calculating the theoretical surface temperature while changing the thermal resistance and the Biot number, it becomes possible to make the theoretical surface temperature coincide with the measured surface temperature. Therefore, the values of the thermal resistance and the biot number when the theoretical surface temperature matches the measured surface temperature can be considered to be the thermal resistance of the interlayer portion of the laminated material and the biot number of the laminated material. here,
The agreement between the theoretical surface temperature and the measured surface temperature is determined from the condition that minimizes the deviation between the measured surface temperature and the theoretical surface temperature, so the thermal resistance and biot number are determined from repeated calculations using the thermal resistance and biot number as parameters. can do.

In the method for measuring the thermal resistance and biot number of a laminated material according to the present invention, the measured surface temperature is a Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the other surface, and the theoretical surface temperature is the unsteady heat. It is a calculated value based on an analytical solution obtained by Laplace transforming the conduction equation, and the deviation may be a square deviation between the Laplace conversion temperature and the calculated value. The Laplace transform makes it possible to easily and analytically solve the unsteady heat conduction equation having the boundary condition. In addition, the thermal resistance and biot number are determined under the condition that the square deviation between the Laplace conversion temperature and the calculated value based on the analytical solution is minimized, so the amount of calculation required to determine the thermal resistance and biot number is greatly reduced. Can be done.

In the method for measuring the thermal resistance and biot number of a laminated material according to the present invention, the measured surface temperature is a Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the other surface, and the theoretical surface temperature is the unsteady heat. It is a calculated value based on an analytical solution obtained by Laplace transforming the conduction equation, and the deviation is preferably a square deviation of the reciprocal of the Laplace conversion temperature and the reciprocal of the calculated value. If the calculated value based on the analytic solution is in fractional format and is configured in a format that includes the thermal resistance and Biot number required by the denominator, adopting the reciprocal of the calculated value allows the thermal resistance and Biot number to be determined from the denominator Move to Therefore, if the square deviation between the reciprocal of the Laplace conversion temperature and the reciprocal of the calculated value is adopted, the calculation of the fractional formula in the calculation formula of the squared deviation is eliminated, and the heat resistance and the biot number are avoided by avoiding complicated calculation processing. Can be determined.

In the method for measuring the thermal resistance and the Biot number of a laminated material according to the present invention, the condition for minimizing the square deviation is determined by setting the measured decay time constant obtained from the change in the measured surface temperature to the theoretical surface temperature. It can also be obtained under an additional condition that makes the same value as the theoretical decay time constant obtained from the change. By providing additional conditions, the thermal resistance and biot number
One independent variable can be one independent variable of thermal resistance or Biot number, and the amount of calculation for determining the variable can be greatly reduced.

Subsequently, a laminated material having a first layer and a second layer
More details on the method of measuring the thermal resistance and biot number of materials
explain. Thermal resistance R exists between the first layer and the second layer
Instantly heat the surface of the first layer of the plate-shaped laminated material,
Heat from the surface of the first layer to the surface of the second layer (the back side of the laminated material)
If it can be approximated to move only to
One-dimensional unsteady heat conduction equation and the boundary condition for degree T
It can be described by the following equations (1) to (8). Where t is
Time, x is in the laminated material from the surface with reference to the surface of the first layer
Distance that entered the part, α ₁ , Α_Two Are the first layer and the second layer, respectively.
Thermal diffusivity of the layer, k₁ , K_Two Are the first and second layers, respectively.
Thermal conductivity, L₁ , L_Two Is the thickness of the first and second layers, respectively.
H₀ , H₁ Is the number of bios in the first and second layers, respectively.
Q is the maximum absorbed energy when the first layer surface is pulse-heated
-, F (t) is the pulse for pulse heating the surface of the first layer
6 shows a time change of a waveform.

[0013]

(Equation 1)

When the above-mentioned one-dimensional transient heat conduction equation and equations (1) to (8) showing boundary conditions are Laplace transformed,
Expressions (9) to (16) are obtained.

[0015]

(Equation 2)

The general solution of the differential equation (9) is A _i , B _i
Is given by the following equations (17) and (18) as a constant. Here, r _i = (p / α _i ) ^1/2 and i = 1 is the first
The layer, i = 2, indicates the second layer.

[0017]

(Equation 3)

Next, the boundary conditions (11) and (1)
Substituting general solutions into (2), (13), and (16) and rearranging them gives equations (19) and (22).

[0019]

(Equation 4)

Further, when the equations (19) and (22) are arranged, the equations (23) and (24) are obtained.

[0021]

(Equation 5)

Next, according to equations (20) and (21), the constant A
The relationship between ₁ , B ₁ and A ₂ , B ₂ is determined. (20),
Equation (21) can be rearranged and expressed using A ₁ , B ₁ , A ₂ , and B _2, as shown in equations (25) and (26).
7) It is summarized in the form of the equation.

[0023]

(Equation 6)

Further, from the expressions (24) and (27), A ₁ ,
When the relationship between B ₁ and A ₂ is derived, equations (28) and (29) are obtained.

[0025]

(Equation 7)

Further, (28), and the equation (30) leads to the A ₂ is substituted into the (23) equation (29) below.

[0027]

(Equation 8)

From this, the temperature of the back surface of the laminated material is (31)
It is expressed by an equation.

[0029]

(Equation 9)

In the equation (31), when the inside of the brackets ([]) of the numerator is transformed, the equation (32) is obtained.

[0031]

(Equation 10)

In equation (31), the brackets ([]) of the denominator are modified. First, when c + dγ and a + bγ are transformed, equations (33) and (34) are obtained, respectively.

[0033]

[Equation 11]

Using (33) and (34), the molecular
R caused by the transformation in brackets_Two -H ₁ / L_Two Taking into account
Then, by rearranging and rearranging the brackets of the denominator of equation (31),
(35).

[0035]

(Equation 12)

Accordingly, when the temperature of the back surface of the laminated material is obtained by using the equations (31), (32), and (35), the equation (36) is obtained.

[0037]

(Equation 13)

Next, a description will be given of a method of determining the thermal resistance generated between the layers when the thermophysical properties of the first and second layers are known. A square deviation is formed by using a theoretical expression representing the measured surface temperature and the theoretical surface temperature of the back surface of the laminated material, and the thermal resistance R and the Biot number h are determined to minimize the square deviation. There are direct method and time constant method. In the direct method, both the thermal resistance R and the Biot number h are independent variables, and both variables are sequentially moved in a direction in which the square deviation is reduced to obtain the thermal resistance R and the Biot number h that minimize the square deviation. . On the other hand, the time constant method measures the decay time constant τ in the decay region of the measured surface temperature of the back surface of the laminated material in the time space, and calculates a theoretical equation representing the measured decay time constant τ and the theoretical surface temperature of the back surface of the laminated material. The minimum value of the squared deviation is obtained under an additional condition that makes the calculated theoretical decay time constant the same value. The additional conditional expression relating to this time constant is an expression representing the relationship between the thermal resistance R and the Biot number h.
Here, it is assumed that the biot numbers of the first layer surface and the second layer surface are equal. If h ₀ = h ₁ = h and the equation (36) is modified, the equation (37) is obtained.

[0039]

[Equation 14]

Equation (37) is obtained by dividing equation (37) by the Laplace transform equation f (p) of the time-varying portion of the pulse waveform to obtain equation (38).

[0041]

(Equation 15)

Subsequently, a square deviation is formed by using a theoretical formula representing the measured surface temperature and the theoretical surface temperature of the back surface of the laminated material,
The thermal resistance R and the Biot number h that minimize the squared deviation will be obtained. A square deviation using a reciprocal may be used. Here, since the thermal resistance R and the Biot number h found in the equation that gives the theoretical surface temperature are present in the denominator, the square deviation using the reciprocal is used. The square deviation between the reciprocal of the measured surface temperature of the second layer surface, which is the back surface of the laminated material, and the reciprocal of the theoretical surface temperature obtained in (37) is given by Expression (39). Here, the value obtained by Laplace transforming the measured surface temperature of the surface of the second layer is E _j , and the reciprocal thereof is v _j . Here, n is the number of Laplace variables.

[0043]

(Equation 16)

First, the maximum absorption energy Q is obtained from equation (40).

[0045]

[Equation 17]

Next, since the thermal resistance R can be determined as the value of R that minimizes the square deviation S, the value obtained by partially differentiating with R is set to 0 to obtain the square deviation S shown in the equation (41). R
Is obtained.

[0047]

(Equation 18)

Therefore, the thermal resistance R is determined from the equation (42).

[0049]

[Equation 19]

When the biot number is small and negligible, (4
The thermal resistance R is determined by substituting a _0j and b _0j for a _j and b _j in the expression 2). In the case of the direct method, the thermal resistance R when the Biot number h is not negligible is calculated by sequentially moving the thermal resistance R and the Biot number h in a direction in which the square deviation is reduced, and finally the minimum value of the square deviation. , And the biot number h can be obtained. In the case of the time constant method,
When determining the thermal resistance R and the Biot number h from the condition that minimizes the square deviation, the time constant calculated from the actually measured temperature decay process of the second layer surface, which is the back surface of the laminated material, is the thermal resistance R.
And the additional condition that it is a function of the Biot number h, the two independent variables of the thermal resistance R and the Biot number h are the thermal resistance R
Alternatively, it becomes one of the independent variables of the biot number h, and the calculation becomes easy. Therefore, the case where the time constant method is used will be described here. Therefore, the theoretical time constant is calculated using the equation (36). First, the (36) when expanded to the third order terms denominator in parentheses as (p) ^1/2 = x of formula (43) below.

[0051]

(Equation 20)

From this, the time constant τ of the temperature decay on the surface of the second layer
Is given by equation (44).

[0053]

(Equation 21)

When the time constant τ is arranged with respect to the Biot number and the thermal resistance R, the denominator and the numerator of the equation (44) are expressed by the equations (45) and (46), respectively.

[0055]

(Equation 22)

Accordingly, the time constant τ is expressed by the following equation (47) using the equations (45) and (46). Here, when the biot number is small, the biot number is obtained from equation (47) as equation (48).

[0057]

(Equation 23)

Further, the thermal resistance R is obtained by equation (49).

[0059]

(Equation 24)

From the above, the time constant τ is specifically obtained from the decay process of the measured surface temperature, and the Bioe number can be specifically determined by making the equations (42) and (49) the same value. The thermal resistance R is obtained by substituting the determined Biot number into (42). Further, the thermal resistance R can be obtained by using the approximate expression of the expression (42). The approximate expression of the expression (42) is obtained by using the expression (50) in which each term of the expression (42) is expanded and expressed as a function of the Biot number.

[0061]

(Equation 25)

That is, substituting the equation (50) into the equation (42) and rearranging the denominator and the numerator of the equation (45) up to the first order term of the Biot number, the equation (51) is obtained, and the equation (51) is used. The thermal resistance R can be determined.

[0063]

(Equation 26)

According to the present invention, there is provided an apparatus for measuring the thermal resistance and biot number of a laminated material according to the present invention, comprising a first layer and a second layer, wherein an interlayer is provided between the first layer and the second layer. Pulse heating means for instantaneously heating one surface of the plate-shaped laminated material in which there is present, temperature measuring means for obtaining the measured surface temperature of the other surface of the laminated material, and said one surface being heated instantaneously. Calculating the theoretical surface temperature of the other surface at the time of the determination and matching the theoretical surface temperature to the measured surface temperature to determine the thermal resistance of the interlayer portion of the laminated material and the number of bios of the laminated material. Processing means. The provision of the pulse heating means for instantaneously heating one surface of the laminated material enables measurement in an unsteady state. Further, the provision of the temperature measuring means for measuring the temperature of the other surface of the laminated material enables accurate temperature measurement of the surface. Further, the provision of the arithmetic processing means enables continuous recording of the measured temperature of the other surface, calculation of the theoretical surface temperature, and determination of the thermal resistance and the number of bios of the laminated material. .

[0065]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, embodiments of the present invention will be described with reference to the accompanying drawings to provide an understanding of the present invention. Here, FIG. 1 is a configuration diagram of an apparatus for measuring a thermal resistance and a biot number of a laminated material according to an embodiment of the present invention, and FIG. 2 is a thermal resistance and a biot number of the laminated material according to an embodiment of the present invention. FIG. 3 is an explanatory view showing the accuracy of the thermal resistance value determined by applying the measurement method of FIG. 3, and FIG. FIG. 9 is an explanatory diagram showing the accuracy of the thermal resistance determined as follows.

As shown in FIG. 1, a laser flash device 10 which is an example of an apparatus for measuring the thermal resistance and biot number of a laminated material according to one embodiment of the present invention has a pulse capable of generating a laser pulse. A laser pulse generating means 11 which is an example of a heating means, and a half mirror 14 which distributes the generated laser pulse into a laser pulse directed to a laser pulse detecting means 12 for detecting a laser pulse waveform and a laser pulse for irradiating a laminated material 13.
A temperature measuring unit 15 for measuring the temperature of the back surface of the laminated material 13 irradiated with the laser pulse; a signal from the laser pulse detecting unit 12 and a signal from the temperature measuring unit 15 as input signals; It has an arithmetic processing means 16 for analyzing the number of biot, and an output means 17 for displaying an analysis result by the arithmetic processing means 16. Hereinafter, these will be described in detail.

As the laser pulse generating means 11, for example, a ruby laser oscillator capable of injecting thermal energy exceeding the thermal fluctuation of the atmosphere into the surface of the laminated material 13 even when the sample is kept in a high temperature atmosphere is used. be able to. The size of the laminated material 13 is determined by the size of the sample holder 18 provided in the laser flash device 10, and is, for example, 8 to 12 mm in diameter and 2 to 3 m in thickness.
A disc-shaped laminated material of about m can be used. The half mirror 14 has a configuration in which a coating layer that reflects a predetermined amount of light from a ruby laser incident on the surface of a substrate having a material having a very low ruby laser absorptivity and a very high transmissivity is provided, For example, 50% of the incident light amount of the ruby laser can be reflected and 50% can be transmitted. Therefore, by adjusting the optical axis of the light receiving section of the laser pulse detecting means 12 so that the laser generated from the laser pulse generating means 11 is reflected by the half mirror 14 and reaches the light receiving section of the laser pulse detecting means 12, the laser pulse is adjusted. A part of the laser light emitted from the generator 11 is introduced into the laser pulse detector 12 so that the laser pulse waveform can be measured by the laser pulse detector 12. Further, by aligning the optical axis of the laser generated from the laser pulse generating means 11 and transmitted through the half mirror 14 with the central axis of the laminated material 13, the surface of the laminated material 13 can be reliably irradiated with the laser pulse. . With such a configuration,
When one surface of the laminated material 13 is irradiated with a ruby laser pulse, the temperature change of the laminated material 13 can be described by a one-dimensional transient heat conduction equation.

The temperature measuring means 15 needs to have a function of measuring the temperature change on the back surface of the laminated material 13 irradiated with the laser pulse at high speed and with high accuracy. For example, the temperature measuring means 15 is provided with an infrared detector as a temperature detecting sensor. A measuring instrument can be used. The arithmetic processing means 16 includes, for example, 1) a function of recording a signal from the laser pulse detecting means 12 and Laplace transforming the pulse waveform, and 2) a temperature measuring means 15
A function of recording the signal of the measured surface temperature of the back surface of the laminated material 13 from, and performing Laplace conversion of the measured surface temperature,
3) Using the various physical property values of the first and second layers constituting the laminated material 13 and the dimensions of the laminated material 13, a one-dimensional transient heat conduction equation is obtained from the boundary conditions of the laminated material 13. A function of calculating the theoretical surface temperature of the back surface of the laminated material 13 by solving analytically by the conversion, 4) calculating the Laplace transform of the measured surface temperature and the square deviation of the theoretical surface temperature, and calculating the heat from the condition that minimizes the square deviation. It has a function of determining the resistance and the number of bios, and 5) a function of displaying the determined thermal resistance and the number of bios on the display means. For example, a personal computer can be used as the arithmetic processing means 16. The output means 17 has a function of displaying the determined thermal resistance and biot number. For example, a display device for a personal computer can be used.

Next, a method for measuring the thermal resistance and the number of bios of a laminated material according to one embodiment of the present invention will be described in detail. For example, from a material formed by pressing the first layer and the second layer, a diameter of 10 mm, a thickness of the first layer and a second layer of 1 mm each around the boundary between the first layer and the second layer, and an overall thickness of 1 mm. A disk-shaped laminated material 13 having a thickness of 2 mm is prepared, and a sample holder 1 provided in a sample chamber of the laser flash device 10 is prepared.
8, for example, with the first layer side facing upward. Subsequently, the sample chamber is set to a predetermined atmosphere such as a vacuum, the temperature in the sample chamber is controlled, and a laser pulse is emitted from the laser pulse generating means 11 toward the half mirror 14 when the laminated material 13 is stabilized at the predetermined temperature. I do. The emitted laser pulse reaches the half mirror 14 and the half mirror 14
For example, 50% of the light amount of the laser pulse is reflected and reaches the laser pulse detecting means 12 to determine the waveform of the laser pulse.
Is forwarded to The laser pulse transmitted through the half mirror 14 reaches the surface of the first layer of the laminated material 13 and instantaneously heats the surface.

The first of the laminated materials 13 is generated by a laser pulse.
When the layer surface is heated, the heat at that time is conducted to the second layer side, so that the temperature of the second layer surface (the back surface of the laminated material 13) gradually increases. However, since heat is also dissipated from the surface of the laminated material 13 at the same time, the rear surface temperature gradually decreases after passing through the maximum temperature. The temperature change at this time is measured by, for example, temperature measuring means 15 having an infrared detector, and the measured value is transferred to arithmetic processing means 16. First, the arithmetic processing means 16 records the signal of the measured surface temperature of the back surface of the laminated material 13 transferred from the temperature measuring means 15 and performs the Laplace conversion of the measured surface temperature to record the Laplace conversion temperature. Next, the one-dimensional unsteady heat conduction equation is analytically solved by Laplace transform from the boundary conditions of the laminated material 13, and a pulse waveform absorbed by the surface of the laminated material 13 by a signal from the laser pulse detecting means 12 is recorded. The pulse waveform is subjected to Laplace conversion, and the Laplace space on the back surface of the laminated material 13 is obtained using various physical property values of the first and second layers constituting the laminated material 13 and the dimensions of the first and second layers. The theoretical surface temperature at is determined. Thereafter, a square deviation between the recorded Laplace conversion temperature of the actually measured surface temperature and the theoretical surface temperature in the Laplace space is obtained, and the thermal resistance and the Biot number are determined from the condition for minimizing the square deviation. Finally, the specified contents such as the determined thermal resistance and biot number, and the measured data are displayed on a display device for a personal computer, for example.

Next, the accuracy of the thermal resistance and the biot number determined by the method for measuring the thermal resistance and the biot number of the laminated material of the present invention will be described. First, various physical property values including the thermophysical property values of the first layer and the second layer of the laminated material 13, sample size, biot number, and thermal resistance generated between the first layer and the second layer are set. The temperature of the surface of the second layer (back surface) when the surface of the first layer is heated using a laser pulse is analytically determined from a one-dimensional transient heat conduction equation in consideration of boundary conditions.
Here, several types of thermal resistances were arbitrarily set on condition that the values were within a reasonable range, and the biot number was also set to a reasonable value as being the same for the first layer and the second layer. next,
The temperature of the back surface obtained analytically is set as the virtual actually measured surface temperature, and the heating conditions by the laser pulse are the same, and the laminated material 1
The theoretical surface temperature in the Laplace space is obtained by equation (36) using various physical property values including the thermophysical property values of the first layer and the second layer of No. 3 and sample dimensions. Subsequently, the squared deviation between the Laplace conversion value of the virtual measured surface temperature and the theoretical surface temperature is obtained, and the thermal resistance and the biot number are determined from the condition that minimizes the squared deviation. By comparing the determined thermal resistance and Biot number with the values of the thermal resistance and Biot number set at the time of obtaining the virtual measured surface temperature, Expression (36) was used from the degree of coincidence, that is, the lamination of the present invention. The accuracy of the thermal resistance and Biot number determined by the method of measuring the thermal resistance and Biot number of the material can be evaluated.

For example, the first layer may be provided with a density of 1000 kg / m
^Three , Specific heat: 1.00 kJ / kg / K, thermal diffusivity: 1.0
× 10^-Fourm^Two / S, layer thickness: 1.0 mm, the second layer
Density: 1200 kg / m^Three , Specific heat: 1.20 kJ / kg
/ K, thermal diffusivity: 1.2 × 10 ^-Fourm^Two / S, layer thickness:
1.0mm, Bior number 0.01, set thermal resistance
(R ₀ ) Is changed to 11 values shown in Table 1.
Find the surface temperature and find the Laplace transform value of the virtual measured surface temperature
Was. Furthermore, for the virtual measured surface temperature,
Various physical properties, including thermophysical properties of the first and second layers,
Theoretical surface temperature is calculated from equation (36) using the material dimensions.
The Laplace transform value of the virtual measured surface temperature and the theoretical surface temperature
The thermal resistance and biot number from the condition that minimizes the square deviation of
Were determined. The determined thermal resistance value is referred to as thermal resistance analysis value (R).
And set thermal resistance (R₀ ) Are listed in Table 1. What
The thermal resistance and the number of bios are determined by using the equation (36).
The center of the laser pulse waveform absorbed by the surface of the first layer
Approximation (center of gravity method) and when considering the pulse waveform
(Pulse correction method).

[0073]

[Table 1]

Further, as shown in FIG. 2, the vertical axis represents the ratio between the set thermal resistance value (R ₀ ) and the thermal resistance analysis value (R) determined to minimize the square deviation, and the horizontal axis represents the horizontal axis. Sum of the set thermal resistance (R ₀ ) and the thermal resistance of the first and second layers (R ₁ + R
₂ ) and the characteristics of the thermal resistance analysis value (R) were examined. Here, R ₁ and R ₂ are obtained by dividing the thickness of the first layer and the second layer by the thermal conductivity of each layer. Table 1 and FIG.
According to the method of measuring the thermal resistance and the biot number of the laminated material using the square deviation, the heat of the interlayer portion when there is an interlayer portion whose thickness cannot be clearly defined between the first layer and the second layer It has been found that the resistance can be determined accurately. Furthermore, in order to accurately determine the thermal resistance, the ratio of the determined thermal resistance to the sum of the thermal resistances of the first layer and the second layer is determined by:
It was also found that it was necessary to be 0.05 or more.
Furthermore, it has been found that the pulse correction method (●) considering the pulse waveform can determine the thermal resistance with higher accuracy than the pulse centroid method (〇). The examination of the accuracy of the thermal resistance and the Biot number determined using the square deviation was specifically shown for the case of thermal resistance, but the square of the Laplace transform value of the virtual measured surface temperature and the theoretical surface temperature was shown. Because the thermal resistance and biot number are determined from the condition that minimizes the deviation,
The accuracy of the determined Biot number has the same accuracy as the thermal resistance.

The method for measuring the thermal resistance of the laminated material according to the present invention
Is a laminated material having a first layer, a second layer, and a third layer.
The thermal diffusivity of the two layers is compared with the thermal diffusivities of the first and third layers.
To determine the thermal resistance when acting as a small thermal resistance layer
Has also been found to be applicable. For example, close the first layer
Degree: 1100kg / m^Three , Specific heat: 1.00 kJ / kg /
K, thermal diffusivity: 1.0 × 10^-Fourm^Two / S, layer thickness: 1.
0 mm, and the density of the third layer is 1200 kg / m.^Three ,ratio
Heat: 1.20 kJ / kg / K, Thermal diffusivity: 1.2 × 10
^-Fourm^Two / S, layer thickness: 1.0 mm, thermal diffusion of the second layer
Rate: 1.1 × 10^-6m^Two / S, specific heat: 1.10 kJ / k
g / K, the biot number is 0.01, and the thickness of the second layer is changed.
By changing the thermal resistance to five values, three layers
Calculate the theoretical surface temperature from the theoretical equation of
Thermal resistance of the laminated material according to the present invention with respect to the measured surface temperature
Was applied to determine the thermal resistance of the second layer. That
FIG. 3 shows the results in the same manner as in FIG. From FIG.
As can be seen, the thermal diffusivity of the second layer is higher than that of the first and third layers.
If the spreading factor is 1/100 or less, use the pulse correction method
Then, the determined thermal resistance (R_Two ) And first and third layers
The sum of the thermal resistances (R₁ + R _Three ) Is greater than 0.05
In this case, the thermal resistance of the second layer is determined with an accuracy within 5%.
be able to.

The embodiment of the present invention has been described above.
The present invention is not limited to this embodiment,
For example, although a laser pulse generating means is used as a pulse heating means in a measuring device for measuring the thermal resistance and biot number of a laminated material, a pulse heating means using a halogen lamp such as a xenon lamp may be used. In addition, as a square deviation between the Laplace conversion value of the measured surface temperature and the theoretical surface temperature, a square deviation obtained by squaring the deviation of each reciprocal was obtained as an example. It is also possible to use a squared deviation obtained by squaring the deviation of the surface temperature.

[0077]

According to the method for measuring the thermal resistance and biot number of a laminated material according to the present invention, the measured surface temperature of the other surface of the laminated material when one surface of the laminated material is instantaneously heated. And the theoretical surface temperature of the other surface of the laminated material when one surface of the laminated material is instantaneously heated is calculated from the solution of the unsteady heat conduction equation in consideration of the boundary conditions. Since the method includes the second step and the third step of determining the thermal resistance and the biot number from the condition of minimizing the deviation between the measured surface temperature and the theoretical surface temperature, the determination of the thermal resistance and the biot number requires skill in measurement. It can be performed with high accuracy without need. Furthermore, because the measurement is in an unsteady state,
Measurement can be easily performed in a wide temperature range from a low temperature to a high temperature.

In particular, in the method for measuring the thermal resistance and the biot number of a laminated material according to the second aspect, the measured surface temperature is the Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the other surface, and the theoretical surface temperature is the unsteady heat. This is a calculated value based on the analytical solution obtained by Laplace transform of the conduction equation, and the deviation is the square deviation of the Laplace transform temperature and the calculated value. In addition, since the thermal resistance and Biot number are determined from the condition that minimizes the squared deviation, the process from measurement to determination of the thermal resistance and Biot number can be automated, and the thermal resistance and Biot number can be accurately determined in a short time. Can be determined.

In the method for measuring the thermal resistance and biot number of a laminated material according to the third aspect, the measured surface temperature is the Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the other surface, and the theoretical surface temperature is the unsteady heat conduction equation. Is the calculated value based on the analytical solution obtained by Laplace transform, and the deviation is the square deviation of the reciprocal of the Laplace conversion temperature and the calculated value, so the thermal resistance and Biot number are determined from the condition that minimizes the squared deviation. In doing so, complicated calculations of fractional expressions can be avoided, and the thermal resistance and Biot number can be determined in a shorter time with high accuracy.

According to a fourth aspect of the present invention, in the method for measuring the thermal resistance and the biot number of a laminated material, the condition for minimizing the squared deviation is determined by changing the measured attenuation time constant and the theoretical surface temperature obtained from the measured surface temperature change. The two independent variables are set to 1
By using two independent variables, the amount of calculation can be greatly reduced, and the thermal resistance and Biot number can be determined in a shorter time with higher accuracy.

According to a fifth aspect of the present invention, there is provided an apparatus for measuring thermal resistance and biot number of a laminated material, comprising a first layer and a second layer.
A pulse heating means for instantaneously heating one surface of a plate-shaped laminated material having an interlayer portion between the layer and the second layer; a temperature measuring means for obtaining a measured surface temperature of the other surface of the laminated material; By calculating the theoretical surface temperature of the other surface when one surface is instantaneously heated and matching the theoretical surface temperature to the measured surface temperature, the thermal resistance of the interlayer portion of the laminated material and the biot number of the laminated material are determined. Since it has an arithmetic processing means for determining, even a person who is not skilled in measurement can perform the measurement, and can determine the thermal resistance and the biot number with high accuracy. In addition, the measurement can be performed on a sample having a very small size.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an apparatus for measuring the thermal resistance and biot number of a laminated material according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram showing accuracy of a thermal resistance value determined by applying a method for measuring a thermal resistance and a biot number of a laminated material according to an embodiment of the present invention.

FIG. 3 is an explanatory diagram showing the accuracy of thermal resistance determined by applying the method for measuring the thermal resistance and biot number of the laminated material to a three-layer laminated material in which an intermediate layer acts as a thermal resistance layer.

FIG. 4 is a graph showing the relationship between the accuracy of the thermal resistance determined by a multilayer material analysis method and the thickness of the intermediate layer in a three-layer laminated material in which the intermediate layer acts as a heat resistance layer in consideration of the laser pulse waveform. .

FIG. 5 shows the relationship between the accuracy of the thermal resistance determined by the multilayer material analysis method and the thickness of the intermediate layer in a three-layer laminated material in which the intermediate layer acts as a thermal resistance layer when the laser pulse waveform is approximated by the center of gravity method. It is a graph.

[Explanation of symbols]

10: laser flash device (measuring device for thermal resistance and biot number of laminated material), 11: laser pulse generating means (pulse heating means), 12: laser pulse detecting means,
13: laminated material, 14: half mirror, 15: temperature measuring means, 16: arithmetic processing means, 17: output means, 18: sample holder

Claims (5)

[Claims] 1. A thermal resistance of a plate-shaped laminated material having a first layer and a second layer in an interlayer portion between the first layer and the second layer.
And a method for measuring the thermal resistance and biot number of the laminated material for measuring the Biot number indicating the degree of heat radiation loss of the laminated material, wherein the laminated material when one surface of the laminated material is instantaneously heated A first step of determining the measured surface temperature of the other surface of the, and the theoretical surface temperature of the other surface of the laminated material when one surface of the laminated material is momentarily heated,
Determining the thermal resistance and the biot number from the second step of calculating and calculating from the solution of the unsteady heat conduction equation in consideration of the boundary condition, and the condition of minimizing the deviation between the measured surface temperature and the theoretical surface temperature. A method for measuring the thermal resistance and biot number of a laminated material, comprising a third step. 2. The method for measuring the thermal resistance and biot number of a laminated material according to claim 1, wherein the measured surface temperature is a Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the other surface, and the theoretical surface temperature is the Laplace conversion temperature. Thermal resistance of the laminated material, wherein the deviation is a square deviation between the Laplace conversion temperature and the calculated value, which is a calculated value based on an analytical solution obtained by Laplace transforming the transient heat conduction equation. How to measure numbers. 3. The method for measuring the thermal resistance and biot number of a laminated material according to claim 1, wherein the measured surface temperature is a Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the other surface, and the theoretical surface temperature is the Laplace conversion temperature. It is a calculated value based on an analytical solution obtained by Laplace transform of the unsteady heat conduction equation, wherein the deviation is a squared deviation of the reciprocal of the Laplace conversion temperature and the reciprocal of the calculated value. How to measure thermal resistance and biot number. 4. The method for measuring the thermal resistance and Biot number of a laminated material according to claim 2 or 3, wherein the condition for minimizing the squared deviation is determined by a measured decay time constant obtained from a change in the measured surface temperature. A method for measuring the thermal resistance and biot number of a laminated material, wherein the thermal resistance and the biot number of the laminated material are obtained under additional conditions that make the theoretical decay time constant obtained from the change in the theoretical surface temperature the same. 5. A pulse for instantaneously heating one surface of a plate-shaped laminated material having a first layer and a second layer and having an interlayer between the first layer and the second layer. Heating means, temperature measuring means for measuring the measured surface temperature of the other surface of the laminated material, and calculating the theoretical surface temperature of the other surface when the one surface is instantaneously heated, the theoretical surface temperature The thermal resistance of the interlayer portion of the laminated material and the arithmetic processing means for determining the number of bios of the laminated material by matching the measured surface temperature and the thermal resistance of the laminated material and the number of bios measuring device.