JP2011106918A - Method and system for calculating heat conductivity - Google Patents

Abstract

A technique for accurately obtaining unknown thermal conductivity with a simple configuration is provided.
A thermal conductivity of a measurement target is calculated from a simulation result obtained by changing a temporary value of the thermal conductivity of the measurement target and an actual measurement result. At this time, the actual measurement environment is simplified, and the environment is easily reproduced by simulation. As a simple measurement environment, the influence of convection and radiation is suppressed and only conduction is dominant. Further, by using the temperature difference, the error of the boundary condition set during the simulation is canceled, and the simulation accuracy is further improved.
[Selection] Figure 4

Description

  The present invention relates to a technique for calculating an unknown thermal conductivity of an object.

  With the increasing complexity and miniaturization of electrical products and electronic equipment, thermal design that takes heat dissipation of components into account is becoming important. It is very important to obtain accurate thermophysical values of individual components when analyzing thermal fluid phenomena such as airflow and heat inside products. Among thermophysical values, in particular, grasping the thermal conductivity that contributes to temperature is regarded as important.

  In general, in order to measure the thermal conductivity of an object, a heater covered with a heat insulator, an object to be measured for thermal conductivity (measurement sample), and an object with a known thermal conductivity (known sample) are stacked. A method is used in which a thermocouple is attached between the two and calculation is performed using the output of the thermocouple (see, for example, Patent Document 1).

  However, an apparatus that realizes this technique is very expensive. For example, in the measurement of an object having a low thermal conductivity of about 0.01 to 50 W / mK, the hot wire probe method and the hot disk method are used among these methods. The price of a device that realizes this is about several million yen. A laser flash method is used for measuring an object having a high thermal conductivity of 400 W / mK or more. The price of a device that realizes this is tens of millions of yen.

  In thermal design, thermal fluid analysis software is used to calculate the heat distribution in an object when a heating element (heater) is attached to a part of the object and heated. Well-known ones include, for example, FLUENT (registered trademark) and CFdesign (registered trademark). By inputting boundary conditions such as heater power and air outside the case and the thermal properties of the object (thermal conductivity, emissivity, density, etc.) into these thermal fluid analysis software, and performing simulation, The distribution, that is, the temperature of each part of the object can be obtained.

JP 2001-21512 A

  It is conceivable that physical properties such as thermal conductivity can be obtained without using an expensive measuring device by fitting the measured temperature of the object with the simulation results of the thermal fluid analysis software. It was difficult to improve the performance. The reason is that even if the temperature of the object can be measured accurately, it is difficult to accurately input the boundary conditions used in the thermal fluid analysis software, and it is difficult to accurately reproduce and simulate the measurement state. It is thought that.

  The present invention has been made in view of the above circumstances, and an object thereof is to provide a technique for accurately obtaining unknown thermal conductivity with a simple configuration.

  In the present invention, the thermal conductivity of the measurement target is determined from the temperature obtained by simulation by changing the temporary value of the thermal conductivity of the measurement target, and the actually measured temperature. At this time, the actual measurement environment is simplified, the environment is easily reproduced by simulation, and the consistency between the actual measurement temperature and the temperature obtained by the simulation is enhanced.

  Specifically, a thermal conductivity calculation method for calculating the thermal conductivity of a measurement sample, the input power determination step for determining the power to be input to a heating element that supplies heat to the measurement sample, and the heating element The temperature of the measurement sample when the input power is turned on to generate heat is measured at a predetermined measurement point, and a temperature measurement step for obtaining an actual temperature, and a plurality of predetermined thermal conductivity setting values, respectively. A temperature estimation step for calculating the temperature of the corresponding measurement sample as an estimated temperature, and an approximate function calculation step for determining an approximate function for associating the thermal conductivity with the estimated temperature from the estimated temperature for each of the plurality of thermal conductivity setting values And a thermal conductivity calculation step for calculating the thermal conductivity of the measurement sample using the measured temperature on the approximate function, and a thermal conductivity calculation method comprising: To provide.

  Further, a thermal conductivity calculation system for calculating an unknown thermal conductivity of a measurement sample, the input power determining means for determining input power to be input to a heating element that supplies heat to the measurement sample, and the heating element The temperature of the measurement sample when heated to generate heat is measured at a predetermined measurement point and corresponds to each of a plurality of predetermined thermal conductivity setting values and temperature measurement means for obtaining an actual measurement temperature. Temperature estimation means for calculating the temperature of the measurement sample as an estimated temperature; and approximate function calculation means for determining an approximate function that associates thermal conductivity with the estimated temperature from the estimated temperature for each of the plurality of thermal conductivity setting values; There is provided a thermal conductivity calculation system comprising: thermal conductivity calculation means for calculating the thermal conductivity of the measurement sample using the measured temperature on the approximate function.

  According to the present invention, an unknown thermal conductivity can be obtained with high accuracy by a simple configuration.

It is a block diagram of the thermal conductivity calculation system of 1st embodiment. It is explanatory drawing for demonstrating the temperature measuring apparatus of 1st embodiment. It is a functional block diagram of the thermal conductivity calculation apparatus of 1st embodiment. It is a flowchart of the heat conductivity calculation process of 1st embodiment. It is a flowchart of the input electric power determination process of 1st embodiment. (A) is explanatory drawing for demonstrating the position of the measurement point of 1st embodiment, (b) is explanatory drawing for demonstrating the measurement result of the input electric power determination process of 1st embodiment. . It is a flowchart of the thermal fluid analysis process of 1st embodiment. It is a graph of the thermal fluid analysis result of 1st embodiment. It is explanatory drawing for demonstrating the temperature measurement point of 2nd embodiment. It is a flowchart of the thermal fluid analysis process of 2nd embodiment. It is a graph of the thermal fluid analysis result of 2nd embodiment. It is a graph after performing the process for approximate function preparation to the thermofluid analysis result of 3rd embodiment. 2 is a graph of Example 1. FIG. 10 is a graph of Example 2.

<< First Embodiment >>
Hereinafter, a first embodiment to which the present invention is applied will be described. In all the drawings for explaining the embodiments of the present invention, those having the same function are denoted by the same reference numerals, and repeated explanation thereof is omitted.

  In the thermal conductivity calculation system of the present embodiment, the desired thermal conductivity of the measurement target object (measurement sample) is obtained from the actual measurement value and the simulation result by the thermal fluid analysis software. Note that the measurement sample is a conductor, an insulator, or the like.

  Conventionally, it is known that the consistency between the simulation value and the actual measurement value in the thermal fluid analysis software is low. This is because it is difficult to input boundary conditions as described above, and it is difficult to reproduce the influence of convection and radiation affected by the boundary conditions. Further, among the calculated parameters, the convection / radiation parameters vary depending on the mesh size set in the operation. As a result, in an environment where the influence of convection / radiation is large, a calculation error due to the mesh size also occurs, in which the finally estimated temperature result varies depending on the mesh size. If the mesh size is made finer, the accuracy is improved, but since it is in a trade-off relationship with the calculation time, it is not realistic to make it extremely finer. In addition, with a certain mesh size, the amount of heat generation increases, and convection and reflection are promoted. Therefore, the influence of convection / radiation parameters on the calculation result increases, and the accuracy deteriorates. In other words, if the mesh size is appropriate, the difference from the actual measurement can be reduced as the calorific value is reduced. In the thermal conductivity estimation, it is desirable that the difference between the thermal fluid analysis result and the actual measurement is small. Therefore, it is only necessary to perform actual measurement and thermal fluid analysis with a minimum calorific value to improve accuracy. Therefore, in the present embodiment, a simulation using the thermal fluid analysis software is performed with the minimum calorific value, and the thermal conductivity is accurately obtained from the obtained simulation result and the actually measured value.

  Specifically, in the input power determination process of FIG. 4 to be described later, in calculating the thermal conductivity, it is assumed that a condition in which conduction is dominant with less influence of convection / radiation is realized in the heat sample. The input power that realizes the minimum heat generation amount among the heat generation amounts that cause a temperature difference is determined. Under the obtained conditions, actual measurement and simulation (thermal fluid analysis processing) are performed, and the simulation condition that matches the actual measurement value is set as the thermal conductivity of the measurement target.

  First, the structure of the whole thermal conductivity calculation system of this embodiment is demonstrated. FIG. 1 is a configuration diagram of a thermal conductivity calculation system 100 of the present embodiment. As shown in this figure, the thermal conductivity calculation system 100 of this embodiment includes a temperature measurement device 110 and a thermal conductivity calculation device 120. The temperature measurement device 110 measures the surface temperature of the measurement sample in accordance with an instruction from the thermal conductivity calculation device 120. The thermal conductivity calculation device 120 performs a thermal conductivity calculation process for calculating the thermal conductivity from the measurement result obtained by the temperature measurement device 110 and the simulation result using the thermal fluid analysis software stored in advance.

  FIG. 2 is a diagram for explaining the temperature measuring apparatus 110 of the present embodiment. As shown in the figure, the temperature measuring device 110 includes a resin case 112 in which a measurement sample 111 is installed, a heater 113 that heats the measurement sample 111, and a thermocouple that measures the temperature by contacting the measurement sample 111. 114 and a radiation thermometer 115 that measures the temperature of the surface of the measurement sample 111 by detecting the amount of radiant energy in a non-contact manner.

  Here, at least one radiation thermometer 115 is installed to face the measurement sample 111. The installation location is preferably installed in a portion that is not affected by radiant energy from a heating element such as the heater 113. Specifically, for example, when measuring a heat sink, a fin portion away from a heat source is measured.

  The temperature measurement device 110 according to the present embodiment inputs the electric power instructed from the thermal conductivity calculation device 120 to the heater 113, and sets the temperature at the measurement point instructed by the thermal conductivity calculation device 120 to the thermocouple 114 and / or radiation. It is measured by the thermometer 115 and output to the thermal conductivity calculator 120.

  The heater 113 is attached to the measurement sample 111 via a TIM (Thermal Interface Material) such as thermal conductive grease or a sheet.

  Further, the thermocouple 114 is installed at least at a measurement point for measuring the temperature on the predetermined measurement sample 111.

  The radiation thermometer 115 is installed at least in the vicinity of each measurement point by the thermocouple 114. The radiation thermometer 115 is used for obtaining emissivity as a parameter when performing simulation with the thermal fluid analysis software. Since the thermocouple 114 and the tape that fixes the thermocouple 114 cause an error in temperature measurement by the radiation thermometer 115, the measurement location is the surface of the measurement sample 111 and does not include these. Therefore, it is desirable that the radiation thermometer 115 can recognize the measurement range with a laser pointer.

  The resin case 112 is provided so as not to be affected by disturbance during temperature measurement. As the resin to be used, an insulating member having a low thermal conductivity, for example, acrylic or polycarbonate is selected. The size of the resin case 112 is set such that the air temperature in the resin case 112 does not rise significantly due to heat generated during measurement in order to reduce the influence of convection and radiation.

  FIG. 3 is a functional block diagram of the thermal conductivity calculation device 120 of the present embodiment. As shown in this figure, the thermal conductivity calculation device 120 of the present embodiment obtains the thermal conductivity from the measured temperature, the measured value of the thermal fluid analysis, and the simulation value by the thermal fluid analysis software. In order to realize this, the thermal conductivity calculation device 120 operates the input power determination unit 210 that determines the input power to be input to the heater 113 in order to cause the heater 113 to generate heat with a desired heat generation amount, and the temperature measurement device 110. A parameter determination unit 220 that measures the temperature of a predetermined temperature measurement point of the measurement sample 111 and calculates a parameter necessary for the simulation, and thermal fluid analysis software for each temporary set value of thermal conductivity prepared in advance. A thermal fluid analysis unit 230 that performs simulation and performs a thermofluid analysis to estimate the temperature at the temperature measurement point, and an approximate function creation unit 240 that creates an approximate function that identifies the relationship between thermal conductivity and temperature from the thermal fluid analysis result A thermal conductivity calculation unit 250 that calculates thermal conductivity from the approximate function, and a measurement value that receives and holds the measurement value from the temperature measurement device 110 It comprises a lifting unit 310, the temporary value retaining unit 320 for holding the temporarily set values of the unknown thermal conductivity of the measurement object to be used in the simulation, the. Here, the temporary set value holding unit 320 holds a plurality of different values inputted in advance as identification values that can be uniquely specified as temporary set values (thermal conductivity set values) of thermal conductivity. .

  The thermal conductivity calculation device 120 is configured by, for example, a general-purpose information processing device including a CPU, a memory, and a storage device. The input power determination unit 210, the parameter determination unit 220, the thermal fluid analysis unit 230, the approximate function creation unit 240, and the thermal conductivity calculation unit 250 are executed by the CPU loading a program stored in the storage device into the memory and executing it. It is realized by. Further, the measured value holding unit 310 and the temporary set value holding unit 320 are configured in a storage device. Various intermediate data generated during the thermal conductivity calculation process by the thermal conductivity calculation system 100 are also stored in the storage device.

  The flow of thermal conductivity calculation processing by the thermal conductivity calculation system 100 of the present embodiment will be described. FIG. 4 is a process flow of the thermal conductivity calculation process of the present embodiment.

  When a start instruction is received from the user, first, the input power determination unit 210 performs input power determination processing for determining input power to the heater 113 when measuring the temperature of the measurement sample 111 (step S1101). Thereby, as described above, the input power that realizes the heater heat generation amount in which conduction is dominant and the influence of convection and radiation is small is obtained. Further, this heater heat generation amount is used for thermal fluid analysis described later.

  Next, the parameter determination unit 220 causes the temperature measurement device 110 to input the input power determined in step S1101 to the heater 113, and the thermocouple 114 sets a predetermined measurement point (temperature measurement point) of the measurement sample 111. The temperature is measured (step S1102). Next, the emissivity at the temperature measurement point is changed by changing the emissivity input to the radiation thermometer so that the temperature at the measurement point measured by the radiation thermometer 115 is the same as the temperature measured by the thermocouple 114. Obtained (step S1103). In the present embodiment, the temperature measurement point is one point. The temperature measurement point is in the vicinity of the heater 113 which is a heat source. This is because the vicinity of the heat source is less affected by convection and radiation, and the environment can be easily reproduced by simulation. The parameter determination unit 220 stores the measured temperature in the measurement value holding unit 310 in association with the measurement point. Further, the calculated emissivity and the input power (heat generation amount) determined in step S1101 are also stored in the measured value holding unit 310.

  Next, the thermal fluid analysis unit 230 performs thermal fluid analysis processing using thermal fluid analysis software previously stored in a storage device (step S1104). At this time, among the input parameters, for the calorific value and emissivity, the data held in the measured value holding unit 310 is used, and for the thermal conductivity, a plurality of thermal conductivity setting values held in the temporary set value holding unit 320 are used. Use.

  Next, the approximate function creation unit 240 uses the thermal fluid analysis result to determine an approximate expression of a function indicating the relationship between thermal conductivity and temperature, and generates an approximate function (approximate function generation process: step S1105). Then, the thermal conductivity calculator 250 obtains the thermal conductivity of the measurement sample 111 by substituting the temperature actually measured in step S1102 for the approximate function (step S1106), and ends the process.

  Details of each process will be described below.

  First, input power determination processing by the input power determination unit 210 in step S1101 will be described. The input power determination unit 210 determines the input power while actually measuring the temperature using the temperature measurement device 110.

  As described above, it is difficult to improve the accuracy of the temperature (estimated temperature) calculated using the thermal fluid analysis software. One reason for this is that the thermal fluid analysis deals with a plurality of different forms of heat transfer such as conduction, convection, and radiation, and the phenomenon is complicated. By performing actual measurement in an environment in which one of the factors of heat transfer is dominant, the environment to be modeled is simplified and the environment can be easily reproduced by simulation.

  In the present embodiment, measurement is performed in an environment where conduction is dominant with little influence of convection and radiation. Such an environment can be realized by making the heat generation amount of the heater 113 as small as possible and causing a measurable temperature difference between two measurement points on the measurement sample 111. This is because the influence of convection and radiation in the measurement sample 111 can be reduced by reducing the amount of heat generated by the heater 113. Moreover, the influence of conduction in the measurement sample 111 can be confirmed by causing a measurable temperature difference between the measurement points. In this embodiment, the input power at which the temperature difference between the two measurement points of the measurement sample 111 is equal to or less than a predetermined value (for example, 10 ° C. or less) is obtained. The appropriate temperature difference varies depending on the size, material, etc. of the measurement sample 111, and is, for example, 2 ° C. for a 100 mm square 1 mm thick copper flat plate.

  Note that at least two measurement points are set for the input power determination process. One measurement point (first measurement point) is at a position near the heater 113, and the other measurement point (second measurement point) is as far as possible on the same axis due to heat conduction from the first measurement point. Install at a distance. This is because when there is no temperature difference (the temperature difference between the two points is 0 ° C.), the calculation of the thermal conductivity diverges and a solution cannot be obtained. When three or more measurement points are set, two points at both ends are set so as to satisfy this condition, and the remaining points are set at equal intervals therebetween.

  The measurement is performed at normal temperature and normal pressure, and after the heater 113 is turned on, the measurement sample 111 and the air temperature in the resin case 112 reach a steady state.

  FIG. 5 is a processing flow of input power determination processing according to the present embodiment. Here, a case where two measurement points are set will be described as an example. The initial power (PW0), the amount of change (ΔPW) in the input power (PW), and the threshold value ΔT0 used to determine whether there is a temperature difference are determined in advance and stored in the storage device.

  First, the input power determination unit 210 sets initial power (PW0) as the power (PW) to be input to the heater 113, and issues an instruction to the temperature measurement apparatus 110 to input the power (step S1201). In response to this, the temperature measuring device 110 sets the initial power (PW0) as the input power (PW) and heats the measurement sample 111 (step S1202). Then, the temperature measuring device 110 measures the temperatures at the two set measurement points (step S1203). The measurement point is set according to the above conditions. The temperature may be measured by either a contact method using a thermocouple 114 or a non-contact method using a radiation thermometer 115. Other methods may also be used.

  When receiving the measurement result from the temperature measurement device 110, the input power determination unit 210 determines whether or not a predetermined temperature difference (ΔT0) has occurred between the two measurement results (step S1204). Here, when the temperature difference ΔT between the two measurement points is equal to or greater than the threshold value ΔT0, it is determined that a temperature difference has occurred. If it is determined that a temperature difference has occurred, the power (PW) set at that time is determined as the input power (step S1205). Since the internal resistance of the heater 113 varies depending on the temperature, the power consumption smoothly decreases with time. Therefore, the final power value after the power consumption of the heater 113 is sufficiently reduced is used as the heat generation amount used in the thermal fluid analysis process described later.

  On the other hand, if it is determined in step S1204 that there is no temperature difference between the two measurement points, the power PW is increased by a predetermined change amount (ΔPW) (step S1206), and the process returns to step S1202.

  A specific example of determining the input power by the above procedure is shown in FIG. FIG. 6A is a diagram for explaining the positions of measurement points. Here, the measurement sample 111 is a 100 mm square 1 mm thick copper flat plate, the measurement point 11 (first measurement point) is installed at a position 20 mm from the end where the heater 113 is installed, and the measurement point 12 (first measurement point). The second measurement point) is installed at a position 80 mm from the same end. The initial power PW0 is 0.5 W, the change amount ΔPW is 0.5 W, and the threshold value ΔT0 used for determining whether there is a temperature difference is 2 ° C.

  FIG. 6B shows a temperature measurement result during execution of the input power determination process. From the results shown in this figure, under the above conditions, when the power PW is increased from 0.5 W in increments of 0.5 W, the temperature difference ΔT between the measurement point 11 and the measurement point 12 at the time of 2 W is 2 ° C. To reach. Therefore, in this case, the input power is determined to be 2W.

  Next, the thermal fluid analysis process by the thermal fluid analysis unit 230 in step S1104 of the thermal conductivity calculation process will be described. FIG. 7 is a processing flow of thermal fluid analysis processing.

  Here, commercially available thermal fluid analysis software (for example, FLUENT (registered trademark), CFdesign (registered trademark)) or the like is used. In addition, the temporary set value holding unit 320 has a rough value determined with reference to literature values and published values as the heat conductivity set value, and ± 30%, ± 60%, etc. positive / negative based on the rough value. Hold at least 3, preferably 5 or more different values, varied by the same width. Here, it is assumed that N (N is a natural number of 3 or more) different thermal conductivity setting values are held in association with numbers 1 to N. In the region where the temperature change is large with respect to the change in thermal conductivity (approximately 100 [W / (m · K)] or less), the value of the thermal conductivity to be held may be further added.

  When receiving the instruction to start the thermal fluid analysis process, the thermal fluid analysis unit 230 first sets the counter n to 1 (step S1301). The heater 113, TIM, measurement sample 111, resin case 112, air inside the resin case 112, and air outside the resin case 112 necessary for thermal fluid analysis are modeled by three-dimensional CAD to generate an analysis model (step S1302).

  At this time, the measured state is reproduced so that the difference between the analysis result and the actually measured temperature does not increase. This means that the actual temperature measurement environment and the environment used for the simulation are matched. As a specific procedure, first, in the actual temperature measurement, the measurement sample 111 is placed in the resin case 112 and measured so as not to be affected by disturbance. Here, examples of the disturbance include air convection and radiation from other heat sources. Also in simulation, modeling and condition setting are performed, and the actual measurement environment is reproduced as an environment used for the calculation.

  Next, pre-analysis processing is performed (step S1303). Here, as pre-analysis processing, a mesh that divides the analysis space specified by the analysis model is generated and set in the thermal fluid analysis software. Further, the thermal fluid analysis is performed on the boundary conditions such as the air temperature outside the resin case 112, the heat generation amount of the heater 113 calculated in step S1101, and the thermal conductivity other than the thermal conductivity such as emissivity and density calculated in step S1103. Set to soft. The density and the like are input in advance and stored in the storage device.

  Next, the thermal conductivity is set to the thermal conductivity of the thermal fluid analysis software (step S1304). Here, the nth thermal conductivity set value held in the temporary set value holding unit 320 is set.

  Then, the temperature of the temperature measurement point is calculated by simulation using thermal fluid analysis software (step S1305). The calculated temperature is stored in the storage device as the estimated temperature in association with the thermal conductivity setting value set in step S1304.

  It is determined whether the processing has been completed for all the thermal conductivity setting values (n = N?) (Step S1306). If completed, the process is terminated. On the other hand, if there is an unprocessed thermal conductivity setting value, the counter n is incremented by 1 (step S1307), the process proceeds to step S1304, and the process is continued.

  As described above, the thermal fluid analysis unit 230 according to the present embodiment can obtain the relationship between each thermal conductivity setting value and the estimated temperature at the temperature measurement point as the thermal fluid analysis result.

  Next, the approximate function creation process by the approximate function creation unit 240 in step S1105 of the thermal fluid analysis process will be described.

  Here, the thermal fluid analysis result is plotted on a graph with the horizontal axis representing thermal conductivity and the vertical axis representing temperature, and an expression (approximate expression) representing an approximate curve of the plotted result is determined. In FIG. 8, the plot result of the estimated temperature for every heat conductivity setting value is shown. Here, a case where five types of thermal conductivity setting values are held is illustrated. The approximate expression of this plot result is determined as an approximate function.

  The thermal conductivity calculator 250 substitutes the temperature (T) actually measured in step S1102 for the obtained function indicating the approximate curve f (x) in FIG. Conductivity) f (T) can be obtained.

  As described above, according to this embodiment, in calculating the unknown thermal conductivity using the measured temperature and the simulation result, the influence of convection and radiation is suppressed, and the temperature is controlled in an environment where conduction is dominant. Is actually measured. Such an environment can be easily reproduced by simulation using thermal fluid analysis software, and therefore errors due to the difference between the actual measurement environment and the simulation environment can be reduced. Therefore, the unknown thermal conductivity can be calculated with high accuracy.

  Further, the temperature measuring device 110 used at the time of actual measurement has a simple and inexpensive configuration. Therefore, according to this embodiment, an unknown thermal conductivity can be accurately obtained at low cost without using an expensive thermal conductivity measuring device.

  Furthermore, since the temperature measuring device 110 of the present embodiment does not need to use a heat insulating material used for an expensive thermal conductivity measuring device, it can reduce the environmental load.

  In the present embodiment, the temperature at the temperature measurement point of the measurement sample 111 is measured in the parameter determination process. However, the temperature at the measurement point near the heater 113 obtained in the input power determination process is not measured here. May be used. In this case, the measured temperature is stored in the measured value holding unit 310 in the input power determination process.

<< Second Embodiment >>
A second embodiment to which the present invention is applied will be described. This embodiment is basically the same as the first embodiment. However, in the first embodiment, one temperature measurement point for actually measuring the temperature is set as one point, but in this embodiment, a plurality of temperature measurement points are set. Thereby, the accuracy of the required thermal conductivity is improved. Hereinafter, the configuration of the present embodiment will be described focusing on the configuration different from the first embodiment.

  The thermal conductivity calculation system 100 of this embodiment basically has the same configuration as that of the first embodiment. However, in this embodiment, in order to measure a plurality of points on the measurement sample 111, the thermocouple 114 in the temperature measurement device 110 includes at least the number of temperature measurement points.

  The input power determination process by the input power determination unit 210 and the parameter determination process by the parameter determination unit 220 of the present embodiment are basically the same as those in the first embodiment. However, the parameter determination unit 230 of the present embodiment measures temperature at a plurality of measurement points. Then, the plurality of actually measured temperatures obtained are stored in the measured value holding unit 310 in association with the temperature measurement points. The emissivity is calculated at any one temperature measurement point.

  In this embodiment, the temperature measurement points may be two or more, but it is desirable to set three or more. When there are two temperature measurement points, one point is set in the vicinity of the heater 113 that is a heat source, and the other points are set at positions that are as far as possible from there. This is because the influence of the measurement error can be relatively reduced when the temperature difference between the temperature measurement points is as large as possible. When the temperature measurement points are three or more, the remaining points are provided at equal intervals between the two points set as described above. FIG. 9 illustrates a case where three temperature measurement points (point A, point B, and point C) are provided.

  Next, thermal fluid analysis processing by the thermal fluid analysis unit 230 of the present embodiment will be described. The thermal fluid analysis processing by the thermal fluid analysis unit 230 of this embodiment is basically the same as that of the first embodiment.

  The processing flow of the thermal fluid analysis process by the thermal fluid analysis part 230 of this embodiment is shown in FIG. Here, similarly to the first embodiment, N (N is a natural number of 3 or more) different thermal conductivity setting values are held, and M temperature measurement points (M is a natural number of 2 or more). And

  First, the counters n and m are set to 1 (step S1401). Then, an analysis model is generated by three-dimensional CAD (step S1402). Next, pre-analysis processing is performed (step S1403).

  Next, thermal conductivity is set (step S1404). Here, the nth thermal conductivity set value held in the temporary set value holding unit 320 is set.

  Then, the temperature of the temperature measurement point is calculated using thermal fluid analysis software (step S1406). The calculated temperature is stored in the storage device as the estimated temperature in association with the temperature measurement point and the thermal conductivity setting value set in step S1404.

  It is determined whether the processing has been completed for all the thermal conductivity setting values (n = N?) (Step S1406). If there is an unprocessed thermal conductivity setting value, n is incremented by 1 (step S1407), the process proceeds to step S1404, and the process is continued.

  On the other hand, if it is determined in step S1406 that the process has been completed for all the thermal conductivity setting values, it is determined whether the process has been completed for all temperature measurement points (m = M?) (Step S1408). If so, the process ends. On the other hand, if there is an unprocessed temperature measurement point, the counter m is incremented by 1 and the counter n is set to 1 (step S1409), the process proceeds to step S1404, and the process is continued.

  As described above, the thermal fluid analysis unit 230 of the present embodiment obtains an estimated temperature for each thermal conductivity setting value for each temperature measurement point as a thermal fluid analysis result.

  Next, an approximate function creation process by the approximate function creation unit 240 of the present embodiment will be described. The approximation function creation process is basically the same as that in the first embodiment, but in this embodiment, an approximation function is created for each measurement point.

  That is, the approximate function creation unit 240 of the present embodiment first plots the thermal fluid analysis result in a graph with the horizontal axis representing the thermal conductivity and the vertical axis representing the temperature, and approximates the plot result for each temperature measurement point. Determine the formula. FIG. 11 shows a plot result of the estimated temperature for each thermal conductivity setting value when there are three temperature measurement points (point A, point B, and point C). Then, the approximate function creation unit 240 according to the present embodiment determines an approximate function for each temperature measurement point from the plot result by the same method as in the first embodiment. Here, three approximation functions are obtained.

  Next, the thermal conductivity calculation process by the thermal conductivity calculation unit 250 of the present embodiment will be described. In this embodiment, a plurality of approximate functions are obtained. Assume that the measured temperatures at each temperature measurement point are TA, TB, and TC, respectively, and the approximate functions at each temperature measurement point shown in FIG. 11 are fA (x), fB (x), and fC (x), respectively (here X is thermal conductivity), and thermal conductivities corresponding to the actually measured temperatures are fA (TA), fB (TB), and fC (TC), respectively.

  When the thermal conductivity corresponding to the measured temperature is the same for each temperature measurement point, the thermal conductivity corresponding to the measured temperature on the approximate function is the thermal conductivity of the measurement sample 111 as in the first embodiment. Calculate with rate. That is, when fA (TA) = fB (TB) = fC (TC), the thermal conductivity calculator 250 sets fA (TA) as the thermal conductivity.

  On the other hand, when the thermal conductivity corresponding to the measured temperature calculated from any one of the approximate functions is different, the thermal conductivity calculation unit 250 uses the following method to minimize the difference between the measured temperature and the estimated temperature. To obtain the thermal conductivity of the measurement sample 111. A specific method will be described with an example in which there are three temperature measurement points.

First, for each temperature measurement point, the formulas FA (x), FB (x), and FC (x) for calculating the difference between the measured temperature and the estimated temperature obtained from the approximate function when the thermal conductivity is x are Ask. Here, FA (x), FB (x), and FC (x) are respectively
FA (x) = TA−fA (x)
FB (x) = TB−fB (x)
FC (x) = TC−fC (x)
It is expressed.

Then, the thermal conductivity calculator 250 calculates the sum of squares of FA (x), FB (x), and FC (x) (G (x) = (FA (x)) ² + (FB (x)) ² + X that minimizes (FC (x)) ² ) is calculated and set as the thermal conductivity of the measurement sample.

  As described above, according to the present embodiment, the temperature of the measurement sample 111 is measured in the same environment as in the first embodiment and the simulation by the thermal fluid analysis software is performed. Can be obtained.

  Furthermore, according to the present embodiment, the thermal conductivity is calculated using measured temperatures measured at a plurality of temperature measurement points. Since the influence of the measurement error on the calculation result can be reduced by increasing the number of measurements of the entire measurement sample 111, according to the present embodiment, the thermal conductivity of the measurement sample 111 can be obtained with higher accuracy. .

  Also in this embodiment, if the number of measurement points for measuring the temperature in the input power determination process is the same as the number of temperature measurement points, the temperature of the measurement point is again determined in the parameter determination process as in the first embodiment. The temperature measured in the input power determination process may be used without measuring the power.

  In the thermal conductivity calculation process, the process when the thermal conductivity corresponding to the actually measured temperature is different for each approximate function is not limited to the above method. For example, the average of the thermal conductivity obtained for each temperature measurement point may be calculated as the thermal conductivity of the measurement sample 111.

<< Third Embodiment >>
A third embodiment to which the present invention is applied will be described. This embodiment is basically the same as the second embodiment. However, in the second embodiment, the thermal conductivity is calculated by using the measured temperature and the estimated temperature as they are for each temperature measurement point, but in this embodiment, the temperature difference between each temperature measurement point is used. Calculate the thermal conductivity. This improves the accuracy of the required thermal conductivity. Hereinafter, the configuration of the present embodiment will be described focusing on the configuration different from the second embodiment.

  The thermal conductivity calculation system 100 of the present embodiment has basically the same configuration as that of the second embodiment. That is, the input power is determined by the same method as in the second embodiment, and the thermal fluid analysis result is obtained by the same method. However, as described above, in this embodiment, when calculating the thermal conductivity, the temperature difference between the measurement points is used, and therefore the approximation function creation process is different.

  An approximate function creation process by the approximate function creation unit 240 of this embodiment will be described. The approximate function creation unit 240 of this embodiment calculates an estimated temperature difference between each temperature measurement point for each thermal conductivity from the estimated temperature for each temperature measurement point obtained from the thermal fluid analysis result held in the storage device. To do. The estimated temperature difference is calculated for all combinations of temperature measurement points.

  For example, as in the second embodiment, when there are three temperature measurement points (point A, point B, and point C), the estimated temperature difference tAB between point A and point B, point A and point C, Is estimated temperature difference tAC, and estimated temperature difference tBC between points B and C is calculated. If the estimated temperatures at the temperature measurement points are tA, tB, and tC, respectively, tAB = tA−tB, tAC = tA−tC, and tBC = tB−tC.

  Each obtained temperature difference is plotted on a graph with the horizontal axis representing the thermal conductivity and the vertical axis representing the temperature difference for each temperature measurement point, and an approximate expression of the plotted result is determined. In FIG. 12, the plot result of the temperature difference of the estimated temperature for every thermal conductivity setting value in the case of three temperature measurement points is shown. Also in this embodiment, the case where five types of thermal conductivity setting values are held is illustrated. The approximate function creation unit 240 calculates an approximate expression of this plot result by the same method as in the above embodiments, and determines an approximate function for each temperature measurement point.

  Next, the thermal conductivity calculation process by the thermal conductivity calculation unit 250 of the present embodiment will be described. In the present embodiment, the thermal conductivity is estimated from a measured temperature difference between each temperature measurement point and a plurality of approximate functions obtained from the estimated temperature difference.

  For example, when there are two temperature measurement points, point A and point C, one approximate function is obtained. Therefore, as in the first embodiment, the thermal conductivity calculation unit 250 sets the thermal conductivity corresponding to the temperature difference between the actually measured temperatures as the thermal conductivity of the measurement sample 111 on this approximate function.

  On the other hand, when there are three temperature measurement points (point A, point B, and point C), first, an actually measured temperature difference between the temperature measurement points is calculated. If the measured temperatures at each temperature measurement point are TA, TB, and TC, respectively, the measured temperature difference TAB between point A and point B is TA-TB, and the measured temperature difference TAC between point A and point C is TA-TC, the measured temperature difference TBC between point B and point C is obtained as TB-TC. Here, if the approximate functions calculated from the relationship between the temperature difference at each measurement point and the thermal conductivity setting value shown in FIG. 12 are fAB (x), fAC (x), and fBC (x), respectively (here And x is the thermal conductivity), and the thermal conductivities corresponding to the actually measured temperature differences between the temperature measurement points are fAC (TAC), fAB (TAB), and fBC (TBC), respectively.

  As in the second embodiment, when the thermal conductivity corresponding to the measured temperature difference between each temperature measurement point is the same in each approximate function, the measured temperature difference is calculated on the approximate function as in the second embodiment. The corresponding thermal conductivity is taken as the thermal conductivity of the measurement sample. That is, when fAC (TAC) = fAB (TAB) = fBC (TBC), the thermal conductivity calculation unit 250 sets fAC (TAC) as the thermal conductivity.

  On the other hand, when the thermal conductivity corresponding to the measured temperature difference is different for each approximate function, the thermal conductivity calculation unit 250 uses the following method to conduct the heat conduction that minimizes the difference between the measured temperature difference and the estimated temperature difference. The rate is obtained and set as the thermal conductivity of the measurement sample 111.

First, for each temperature measurement point, the formulas FAB (x), FAC (x), FBC (x) for calculating the difference between the measured temperature difference and the estimated temperature difference obtained from the approximate function when the thermal conductivity is x. ) The formulas FAB (x), FAC (x) and FBC (x) are respectively
FAB (x) = TAB−fAB (x)
FAC (x) = TAC-fAC (x)
FBC (x) = TBC-fBC (x)
It becomes.

Then, the thermal conductivity calculator 250 calculates the sum of squares of FAB (x), FAC (x), and FBC (x) (GG (x) = (FAB (x)) ² + (FAC (x)) ² + X that minimizes (FBC (x)) ² ) is calculated and set as the thermal conductivity of the measurement sample 111.

  As described above, according to the present embodiment, the temperature of the measurement sample 111 is actually measured in the same environment as the above-described embodiments and the simulation by the thermal fluid analysis software is performed. be able to.

  Further, according to the present embodiment, the approximate function is determined from the temperature difference between the temperature measurement points for the estimated temperature at the plurality of temperature measurement points, and the thermal conductivity is measured at the temperature difference and the plurality of temperature measurement points. It calculates using the temperature difference between the temperature measurement points of actual measurement temperature. Thereby, the difference between the simulation result and the actual measurement can be further reduced, and the accuracy of the obtained thermal conductivity is increased.

  In general, it is known that it is very difficult to suppress the difference between the simulation result by the thermal fluid analysis software and the actual measurement result to such an extent that the thermal conductivity can be calculated (within ± 5 ° C.). Such a difference between the simulation result and the actual measurement result is considered to be caused by parameters of convection and radiation. On the other hand, heat conduction, which is heat transfer inside the member, is a parameter that hardly affects both results. Therefore, as in the present embodiment, not the absolute value of the temperature but the temperature difference (heat conduction inside the measurement sample 111) is used to determine the approximate curve and calculate the thermal conductivity based on the approximate curve and the actually measured value. The thermal conductivity can be calculated in a state where there is little error between the actual measurement result and the simulation result. For this reason, it is possible to calculate the thermal conductivity with high accuracy.

  In the thermal conductivity calculation process, the process when the thermal conductivity corresponding to the actually measured temperature is different for each approximate function is not limited to the above method. For example, the average of the thermal conductivity obtained for each temperature measurement point may be calculated as the thermal conductivity of the measurement sample 111.

  Also in this embodiment, if the number of measurement points for measuring the temperature in the input power determination process is the same as the number of temperature measurement points, the temperature of the measurement point is again determined in the parameter determination process as in the first embodiment. The temperature measured in the input power determination process may be used without measuring the power.

<< Example 1 >>
Examples of the present invention will be described below. First, examples of the first and second embodiments will be described. Here, a molded product of a 100 mm square × 1 mm copper flat plate (390 W / mK) and a 150 mm × 50 mm × 50 mm aluminum alloy (170 W / mK) is used as an object to be measured (measurement sample) 111, and the input power is the temperature at the measurement point. The difference was 2 W at 2 ° C. Further, five types of heat conductivity set values of 200 W / mK, 300 W / mK, 400 W / mK, 500 W / mK, and 600 W / mK were used. The temperature measurement points were three points shown in FIG. 9 (points A, B, and C, respectively). CFdesign (registered trademark) was used as thermal fluid analysis software.

  FIG. 13 is a graph of an approximate curve obtained by fitting the estimated temperature for each thermal conductivity set value obtained by performing thermal conductivity calculation processing and simulating according to the method of the second embodiment, for each temperature measurement point. It is.

  At this time, the actually measured temperature at the temperature measuring point A was 46.9 ° C. Further, the actual temperature at the measurement point B was 45.7 ° C., and the actual temperature at the measurement point C was 45.2 ° C. From the result of the temperature measurement point A in the vicinity of the heat source, about 62.5 W / mK was obtained as the thermal conductivity of the measurement sample 111 from the graph of FIG. Here, a molded product made of an aluminum alloy having a high thermal conductivity of 390 W / mK, which is a published value of thermal conductivity, was used. The accuracy of the thermal conductivity estimation according to the temperature of the second embodiment is further enhanced.

<< Example 2 >>
Next, an example of the third embodiment will be described. The measurement sample 111, input power, used thermal conductivity setting value, temperature measurement point, and used thermal fluid analysis software were the same as those in Example 1.

  FIG. 14 shows an estimated temperature difference between point A and point B for each thermal conductivity setting value obtained by performing thermal conductivity calculation processing and simulating according to the method of the third embodiment, It is a graph of the approximate curve of each estimated temperature difference with C point, and each estimated temperature difference with B point and C point.

  The measured temperature at each point is as in the second embodiment. Therefore, 456 W / mK is obtained as the thermal conductivity of the measurement sample 111. This value is 17% different from the published value of 390 W / mK, and it can be seen that even if the measurement object has a high thermal conductivity, it can be measured with higher accuracy than in Example 1.

11: measurement point, 12: measurement point, 100: thermal conductivity calculation system, 110: temperature measurement device, 111: measurement sample, 112: resin case, 113: heater, 114: thermocouple, 115: radiation thermometer, 120 : Thermal conductivity calculation device, 210: input power determination unit, 220: parameter determination unit, 230: thermal fluid analysis unit, 240: approximate function creation unit, 250: thermal conductivity calculation unit, 310: measurement value holding unit, 320 : Temporary set value holding section

Claims (11)

A thermal conductivity calculation method for calculating the thermal conductivity of a measurement sample,
An input power determination step for determining power to be input to a heating element that supplies heat to the measurement sample;
A temperature measurement step of measuring the temperature of the measurement sample when the input power is supplied to the heating element and generating heat, at a predetermined measurement point, and obtaining an actual temperature;
A temperature estimation step of calculating the temperature of the measurement sample corresponding to each of a plurality of predetermined thermal conductivity setting values as an estimated temperature;
An approximate function calculating step for determining an approximate function for associating the thermal conductivity with the estimated temperature from the estimated temperature for each of the plurality of thermal conductivity setting values;
A thermal conductivity calculation step of calculating the thermal conductivity of the measurement sample using the measured temperature on the approximate function. The thermal conductivity calculation method according to claim 1,
In the thermal conductivity calculation step, the thermal conductivity corresponding to the measured temperature on the approximate function is set as the thermal conductivity of the measurement sample. The thermal conductivity calculation method according to claim 1,
There are a plurality of measurement points for obtaining the actual temperature in the temperature measurement step,
In the temperature estimation step, an estimated temperature of each of the plurality of measurement points is calculated,
In the approximate function calculating step, the approximate function is determined for each of the plurality of measurement points,
In the thermal conductivity calculation step, the thermal conductivity of the measurement sample is calculated using the measured temperature on the approximate function for each measurement point. The thermal conductivity calculation method according to claim 3,
In the thermal conductivity calculation step, the thermal conductivity that minimizes the sum of squares of the difference between the approximate temperature corresponding to the thermal conductivity and the actually measured temperature on the approximate function obtained for each of the plurality of measurement points is A method for calculating thermal conductivity, characterized in that the thermal conductivity of a measurement sample is used. The thermal conductivity calculation method according to claim 1,
The temperature measurement step has a plurality of measurement points to obtain the actual temperature,
In the temperature estimation step, an estimated temperature of each of the plurality of measurement points is calculated,
In the approximate function calculating step, an estimated temperature difference that is an estimated temperature difference between the plurality of measurement points is calculated, and the approximate function is determined as a function that associates thermal conductivity and the estimated temperature difference between the measurement points. And
In the thermal conductivity calculation step, an actual temperature difference that is a difference in actual temperature between the plurality of measurement points is calculated, and the actual temperature difference of the measurement sample is calculated using the actual temperature difference on an approximate function between the measurement points. A method for calculating thermal conductivity, comprising calculating thermal conductivity. The thermal conductivity calculation method according to claim 5,
The measurement point at which the temperature measurement step obtains the actual temperature is 3 or more,
In the thermal conductivity calculation step, the thermal conductivity that minimizes the sum of squares of the difference between the approximate temperature difference corresponding to the thermal conductivity and the measured temperature difference on the approximate function obtained for each of the plurality of measurement points. Is defined as the thermal conductivity of the measurement sample. The thermal conductivity calculation method according to claim 1, wherein:
In the input power determination step, the minimum power is determined as the input power, which is a power at which a temperature difference between a position closest to the heating element and a position farthest from the heating element on the measurement sample is a predetermined value or more. The thermal conductivity calculation method characterized by this. The thermal conductivity calculation method according to claim 1, wherein
An emissivity calculating means for calculating the emissivity of the surface of the measurement sample immediately after the temperature measuring step;
In the temperature estimation step, the estimated temperature is calculated in consideration of the emissivity. A thermal conductivity calculation method according to any one of claims 1 to 8,
In the temperature estimation step, the estimated temperature is calculated using thermal fluid analysis software. A thermal conductivity calculation system for calculating an unknown thermal conductivity of a measurement sample,
Input power determining means for determining input power to be input to a heating element for supplying heat to the measurement sample;
Temperature measurement means for measuring the temperature of the measurement sample when the power is applied to the heating element to generate heat, and measuring the temperature at a predetermined measurement point;
Temperature estimation means for calculating the temperature of the measurement sample corresponding to each of a plurality of predetermined thermal conductivity setting values as an estimated temperature;
An approximate function calculating means for determining an approximate function for associating the thermal conductivity with the estimated temperature from the estimated temperature for each of the plurality of thermal conductivity setting values;
And a thermal conductivity calculating means for calculating the thermal conductivity of the measurement sample using the measured temperature on the approximate function. Computer
Input power determining means for determining input power to be input to a heating element that supplies heat to the measurement sample;
Temperature measurement means for measuring the temperature of the measurement sample when the power is applied to the heating element to generate heat, and measuring the temperature at a predetermined measurement point;
Temperature estimation means for calculating the temperature of the measurement sample corresponding to each of a plurality of predetermined set values of unknown thermal conductivity of the measurement sample as an estimated temperature;
An approximate function calculating means for determining an approximate function that associates thermal conductivity and estimated temperature from the estimated temperature for each of the plurality of set values;
A program for functioning as thermal conductivity calculation means for calculating the thermal conductivity of the measurement sample using the measured temperature on the approximate function.

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