Contact Thermal Conductance Estimation Method and Contact Electrical Resistance Estimation Method

Abstract

To provide a contact thermal conductance estimation method capable of accurately estimating a contact thermal conductance hc (ε) even when contact pressure P at the contact surface S is very high.SOLUTION: In a contact thermal conductance estimation method, a first object Ω1 has a surface S1 with fine unevenness and M layer(s) (M=0, 1 or 2) of a first plating layer C1M applied to a base material in order from the surface S1 side, and a second object Ω2 has a surface S2 with fine unevenness and N layer(s) (N=0, 1 or 2) of a second plating layer C2N applied to a base material in order from the surface S2 side. A substantially flat contact surface S is shared by the surface S1 and the surface S2. The method estimates a contact thermal conductance at the contact surface S when the first object Ω1 and the second object Ω2 are in contact with each other at a contact pressure P which is greater than 0 and contact heat transfer occurs between both objects through the contact surface S by using following equation (2), which expresses a contact area ratio ε2.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a contact thermal conductance estimation method for estimating the contact thermal conductance at the contact surface between a first object having a surface with minute irregularities and a second object having a surface with minute irregularities, and a contact electrical resistance estimation method using the same. In particular, the present invention relates to a case where a plating layer is provided on at least one of the surfaces of the first object and the second object, and the contact pressure at the contact surface between the first object and the second object that come into contact with each other is extremely large, such as when hot rolling, hot forging, resistance spot welding, etc. are performed. The present invention relates to a contact thermal conductance estimation method capable of accurately estimating the contact thermal conductance, and a contact electrical resistance estimation method using the same.

Background Art

[0002] Conventionally, for example, Non-Patent Document 1 has reported research on the contact thermal conductance at the contact surface between a first object having a surface with minute irregularities and a second object having a surface with minute irregularities.

[0003] In Non-Patent Document 1, a first object M1 having a surface S1 with minute irregularities and a second object M2 having a surface S2 with minute irregularities are in contact with each other at a substantially flat contact surface S shared by the surface S1 and the surface S2 with a contact pressure P greater than 0, and contact heat transfer occurs between the first object M1 and the second object M2 through the contact surface S. The contact thermal conductance h at the contact surface S c As an estimation formula for estimating, the following formula (eq1) has been proposed.

Equation

[0004] As described in Non-Patent Document 1, although the contact thermal conductance h c estimated using the above formulas (eq1) to (eq6) is considered to have high estimation accuracy under specific conditions, it has the following problems 1 and 2. (1) Problem 1 It is considered that the constriction parameter ψ(ε) represented by the above formula (eq3) has deteriorated estimation accuracy in the range where ε is large (0.6 or more), and it is necessary to use a more appropriate estimation formula for the constriction parameter ψ(ε) according to the magnitude of ε. (2) Problem 2 The contact area ratio ε represented by the above formula (eq2) 2 does not consider the influence of the volume change of the convex part crushed (or smoothed) by the contact between the surface S1 and the surface S2 on the shape change of the non-contact surface (for example, the concave part adjacent to the convex part). The above problems 1 and 2 occur when the contact pressure P on the contact surface S between the first object M1 and the second object M2 is very large, such as when performing hot rolling, hot forging, resistance spot welding, etc. For example, when the contact pressure P is so large that it exceeds the yield stress of the first object M1 and the second object M2, the contact thermal conductance h c becomes a major factor deteriorating the estimation accuracy. In addition, Non-Patent Document 1 does not propose a method for estimating the contact thermal conductance h on the contact surface S when a plating layer is provided on at least one of the surfaces of the surface S1 and the surface S2. c has not been proposed.

[0005] Note that Non-Patent Documents 3 and 4 report research on the contact thermal conductance at the contact surface between a first object with a plating layer on the surface side and a second object with a plating layer on the surface side. However, also in Non-Patent Documents 3 and 4, similar to Non-Patent Document 1, the case where the contact pressure P on the contact surface S between the first object M1 and the second object M2 is very large is not considered.

[0006] In addition, Non-Patent Documents 5 to 7 describe methods for estimating the hardness of the surface of an object with a plating layer on the surface side.

Prior Art Documents

Non-Patent Documents

[0007]

Non-Patent Document 1

[0008] The present invention has been made to solve the problems of the prior art as described above. Among the surfaces of the first object Ω1 and the second object Ω2, a plating layer is provided on at least one of the surface sides. Even when the contact pressure P at the contact surface S between the first object Ω1 and the second object Ω2 is very large, the contact thermal conductance h c (ε) is to provide a contact thermal conductance estimation method capable of accurately estimating, and a contact electrical resistance estimation method using the same. [Means for Solving the Problems]

[0009] To solve the above problems, the inventor of the present invention incorporated the ideas described in Non-Patent Documents 2 to 4 so that the contact thermal conductance h 2 for any contact pressure P, and thus any contact area ratio ε c (ε) can be accurately estimated, and earnestly studied to improve the estimation method of the contact thermal conductance h c described in Non-Patent Document 1, and completed the present invention. That is, in order to solve the above problems, the present invention provides a contact thermal conductance estimation method for estimating the contact thermal conductance h(ε) at a substantially flat contact surface S shared by a first object Ω1 having a surface S1 with minute irregularities and a second object Ω2 having a surface S2 with minute irregularities, when the first object Ω1 and the second object Ω2 are in contact with each other at a contact pressure P greater than 0 and contact heat transfer occurs between the first object Ω1 and the second object Ω2 through the contact surface S. On the surface S1 side of the first object Ω1, M layers (M = 0, 1 or 2) of a first plating layer C1 are provided in order from the surface S1 side with respect to the base material of the first object Ω1. c On the surface S2 side of the second object Ω2, N layers (N = 0, 1 or 2) of a second plating layer C2 are provided in order from the surface S2 side with respect to the base material of the second object Ω2 (however, except for the case where M = N = 0). The film thickness and thermal conductivity of the first plating layer C1 are respectively denoted as t and k, and the film thickness and thermal conductivity of the second plating layer C2 are respectively denoted as t and k. The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively denoted as k, k, the RMS roughnesses of the surfaces S1 and S2 are respectively denoted as σ, σ, the average inclinations of the convex portions of the surfaces S1 and S2 are respectively denoted as m, m, and the hardnesses of the surfaces S1 and S2 are respectively denoted as H, H. When these are set, the contact thermal conductance h(ε) at the contact surface S is estimated using the following formulas (1) to (17). M On the surface S2 side of the second object Ω2, N layers (N = 0, 1 or 2) of a second plating layer C2 are provided in order from the surface S2 side with respect to the base material of the second object Ω2 (however, except for the case where M = N = 0). N The film thickness and thermal conductivity of the first plating layer C1 are respectively denoted as t and k, and the film thickness and thermal conductivity of the second plating layer C2 are respectively denoted as t and k. The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively denoted as k, k, the RMS roughnesses of the surfaces S1 and S2 are respectively denoted as σ, σ, the average inclinations of the convex portions of the surfaces S1 and S2 are respectively denoted as m, m, and the hardnesses of the surfaces S1 and S2 are respectively denoted as H, H. When these are set, the contact thermal conductance h(ε) at the contact surface S is estimated using the following formulas (1) to (17). M The film thickness and thermal conductivity of the first plating layer C1 are respectively denoted as t and k, and the film thickness and thermal conductivity of the second plating layer C2 are respectively denoted as t and k. The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively denoted as k, k, the RMS roughnesses of the surfaces S1 and S2 are respectively denoted as σ, σ, the average inclinations of the convex portions of the surfaces S1 and S2 are respectively denoted as m, m, and the hardnesses of the surfaces S1 and S2 are respectively denoted as H, H. When these are set, the contact thermal conductance h(ε) at the contact surface S is estimated using the following formulas (1) to (17). M (1) and k M (1) The film thickness and thermal conductivity of the first plating layer C1 are respectively denoted as t and k, and the film thickness and thermal conductivity of the second plating layer C2 are respectively denoted as t and k. The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively denoted as k, k, the RMS roughnesses of the surfaces S1 and S2 are respectively denoted as σ, σ, the average inclinations of the convex portions of the surfaces S1 and S2 are respectively denoted as m, m, and the hardnesses of the surfaces S1 and S2 are respectively denoted as H, H. When these are set, the contact thermal conductance h(ε) at the contact surface S is estimated using the following formulas (1) to (17). N The film thickness and thermal conductivity of the first plating layer C1 are respectively denoted as t and k, and the film thickness and thermal conductivity of the second plating layer C2 are respectively denoted as t and k. The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively denoted as k, k, the RMS roughnesses of the surfaces S1 and S2 are respectively denoted as σ, σ, the average inclinations of the convex portions of the surfaces S1 and S2 are respectively denoted as m, m, and the hardnesses of the surfaces S1 and S2 are respectively denoted as H, H. When these are set, the contact thermal conductance h(ε) at the contact surface S is estimated using the following formulas (1) to (17). N (2) and k N (2) The film thickness and thermal conductivity of the first plating layer C1 are respectively denoted as t and k, and the film thickness and thermal conductivity of the second plating layer C2 are respectively denoted as t and k. The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively denoted as k, k, the RMS roughnesses of the surfaces S1 and S2 are respectively denoted as σ, σ, the average inclinations of the convex portions of the surfaces S1 and S2 are respectively denoted as m, m, and the hardnesses of the surfaces S1 and S2 are respectively denoted as H, H. When these are set, the contact thermal conductance h(ε) at the contact surface S is estimated using the following formulas (1) to (17). (1) k (2) k (1) σ (2) σ (1) m (2) m c,film (1) H c,film (2) H c A contact thermal conductance estimation method is provided, which is characterized by estimating the contact thermal conductance h(ε) at the contact surface S using the following formulas (1) to (17). [Number] In the above formulas (3) and (15), erfc -1 is the inverse function of the complementary error function, and in the above formula (5), erfc is the complementary error function. In the above formulas (3) and (15), π is the ratio of a circle's circumference to its diameter. In formulas (5), (6), and (11) to (14), i = 1 or 2. Also, in the above formulas (1), (5), (6), (9) to (14), (16), and (17), the superscript (1) means it is a value related to the first object Ω1 or the first plating layer C1 M and the superscript (2) means it is a value related to the second object Ω2 or the second plating layer C2 N . Also, when M = 1 (that is, when a single layer of the first plating layer C11 is applied to the first object Ω1), the following formula (18) holds, and when N = 1 (that is, when a single layer of the second plating layer C21 is applied to the second object Ω2), the following formula (19) holds. When M is 0 (that is, when no first plating layer is applied to the first object Ω1), CL (1) (ε) represented by the above formula (5) is 1, and when N is 0 (that is, when no second plating layer is applied to the second object Ω2), CL (2) (ε) represented by the above formula (5) is 1. k2 (1) = k (1) , t2 (1) = 0 ···(18) k2 (2) = k (2) , t2 (2) = 0 ···(19)

[0010] In the present invention, formula (3) is equivalent to the aforementioned formula (eq1). Formulas (10), (16), and (17) are equivalent to the aforementioned formulas (eq4) to (eq6), respectively. In the present invention, "the first plating layer C1 of M layers M"is applied" means that when M = 1, a single layer of the first plating layer C11 is applied to the surface S1 side of the first object Ω1, and when M = 2, two layers of the first plating layers C11 and C12 are applied to the surface S1 side of the first object Ω1. And, "the first plating layer C1 M The film thickness and thermal conductivity of are respectively t M (1) and k M (1) "is set as" means that when M = 1, the film thickness and thermal conductivity of the first plating layer C11 are respectively t1 (1) and k1 (1) and when M = 2, the film thickness and thermal conductivity of the first plating layer C11 are respectively t1 (1) , k1 (1) and H1 (1) and the film thickness and thermal conductivity of the first plating layer C12 are respectively t2 (1) and k2 (1) which means setting them as such. Similarly, in the present invention, "N layers of the second plating layer C2 N is applied" means that when N = 1, a single layer of the second plating layer C21 is applied to the surface S2 side of the second object Ω2, and when N = 2, two layers of the second plating layers C21 and C22 are applied to the surface S1 side of the second object Ω2. And, "the second plating layer C2 N The film thickness and thermal conductivity of are respectively t N (2) and k N (2) "is set as" means that when N = 1, the film thickness and thermal conductivity of the second plating layer C21 are respectively t1 (2) and k1 (2) and when N = 2, the film thickness and thermal conductivity of the second plating layer C21 are respectively t1 (2) and k1 (2) and the film thickness and thermal conductivity of the second plating layer C22 are respectively t2 (2) and k2 (2) which means setting them as such. According to the present invention, when a plating layer is applied to at least one of the surfaces of the first object Ω1 and the second object Ω2, as will be described later, the above-described problems 1 and 2 can be solved.

[0011] Also, in order to solve the above problems, in the present invention, the first object Ω1 and the second object Ω2 are metals, and the contact thermal conductance h c (ε) on the contact surface S estimated by the contact thermal conductance estimation method and the following formula (23) are used to estimate the contact electrical resistance R c (ε) on the contact surface S, and a contact electrical resistance estimation method is also provided, which is characterized in that. R c (ε) = LT / h c (ε) ···(23) In the above formula (23), L is the Lorentz number, and T is the absolute temperature of the contact surface S.

Advantages of the Invention

[0012] According to the present invention, even when the contact pressure P on the contact surface S between the first object Ω1 and the second object Ω2, on which a plating layer is provided on at least one of the surface sides, is very large, the contact thermal conductance h c (ε) can be accurately estimated.

Brief Description of the Drawings

[0013]

Figure 1

Figure 2

Embodiments for Carrying Out the Invention

[0014] Hereinafter, the contact thermal conductance estimation method according to an embodiment of the present invention will be described. FIG. 1 is a diagram schematically showing an object for estimating the contact thermal conductance by the contact thermal conductance estimation method according to the present embodiment. As shown in FIG. 1, the contact thermal conductance estimation method according to this embodiment is such that a first object Ω1 having a surface S1 with minute irregularities and a second object Ω2 having a surface S2 with minute irregularities are in contact with each other at a substantially flat contact surface S shared by the surfaces S1 and S2 with a contact pressure P greater than 0, and when contact heat transfer occurs between the first object Ω1 and the second object Ω2 through the contact surface S, the contact thermal conductance h c (ε) of the contact surface S is estimated.

[0015] Note that in FIG. 1, on the surface S1 side of the first object Ω1 (the lower side in the example shown in FIG. 1), two layers (M = 2) of first plating layers C11 and C12 are sequentially applied from the surface S1 side to the base material of the first object Ω1 (the hatched portion in FIG. 1), and on the surface S2 side of the second object Ω2 (the upper side in the example shown in FIG. 1), two layers (N = 2) of second plating layers C21 and C22 are sequentially applied from the surface S2 side to the base material of the second object Ω2 (the hatched portion in FIG. 1). This case is illustrated as an example. At this time, as shown in FIG. 1, the film thickness, thermal conductivity, and hardness of the first plating layer C11 are t1 (1) , k1 (1) and H1 (1) respectively, and the film thickness, thermal conductivity, and hardness of the first plating layer C12 are t2 (1) , k2 (1) and H2 (1) respectively. Also, the film thickness, thermal conductivity, and hardness of the second plating layer C21 are t1 (2) , k1 (2) and H1 (2) respectively, and the film thickness, thermal conductivity, and hardness of the second plating layer C22 are t2 (2) , k2 (2) and H2 (2) respectively. Further, as shown in FIG. 1, the thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are k (1) , k (2) respectively, and the hardnesses of the base materials of the first object Ω1 and the second object Ω2 are H (1) , H (2) respectively. Furthermore, although not shown, the RMS roughnesses of the surfaces S1 and S2 are σ (1) , σ(2) and the average inclinations of the convex portions of the surfaces S1 and S2 are m (1) and m (2) respectively, and the hardnesses of the surfaces S1 and S2 are H c,film (1) and H c,film (2) respectively. Note that the hardness in this specification means microhardness (Vickers hardness or micro-Vickers hardness). In FIG. 1, a case is exemplified in which two layers of first plating layers C11 and C12 are provided on the surface S1 side of the first object Ω1, and two layers of second plating layers C21 and C22 are provided on the surface S2 side of the second object Ω2. However, the present invention is not limited to this, and it is applicable when a plating layer is provided on at least one of the surfaces of the surface S1 of the first object Ω1 and the surface S2 of the second object Ω2.

[0016] The method for estimating the contact thermal conductance according to the present embodiment is a method for estimating the contact thermal conductance h c (ε) using the above-described formulas (1) to (17).

[0017] In the case where a plating layer is provided on at least one of the surfaces of the surface of the first object Ω1 and the surface of the second object Ω2, in order to solve the above-described problems 1 and 2, the process of deriving the method for estimating the contact thermal conductance according to the present embodiment is as follows. First, based on the concepts described in Non-Patent Documents 3 and 4, the present inventor expressed the contact thermal conductance h c (ε) by Equation (1). Specifically, the contact thermal conductance h c (ε) is expressed by Equation (1) using the contact thermal conductance h c,bare (ε) (see Equation (3)) when no plating layer is provided, the constriction parameter ψ film (i) (ε) when a plating layer is provided, and the constriction parameter correction coefficient C bare (ε) which is represented by the ratio of the constriction parameter ψ L (i) (ε) when no plating layer is provided (see the following Equation (eq7)). [Mathematics]

[0018] Then, as described above, in order to solve Problem 1 that the estimation accuracy of the necking parameter ψ(ε) represented by Equation (eq3) deteriorates in a range where ε is large, the present inventor considered the necking parameter ψ when no plating layer is applied bare (ε), according to the change of ε (ε: 0 → 1), the contact area ratio ε 2 when it is small (ε → 0), the necking parameter ψ bare (ε), from the theoretical solution of the contact area ratio ε 2 when it is large (ε → 1), the necking parameter ψ bare (ε), and introduced a function β(ε) of ε representing the change, thinking that it continuously transitions to the theoretical solution of the necking parameter ψ bare (ε), and came up with representing the necking parameter ψ [Mathematics]

[0019] Next, heat transfer finite element analysis of two contact cylinders (flux tubes) without a plating layer, with ε varied variously from 0 to 1, was performed, and the necking parameter ψ bare (ε) calculated from the analysis results and the necking parameter ψ bare (ε) calculated from Equation (eq8) were made to approximately match, and β(ε) represented by Equation (eq9) was derived by least squares approximation. [Mathematics]

[0020] Also, by taking into account the ideas described in Non-Patent Documents 3 and 4 in a similar way to the necking parameter ψ bare (ε) when no plating layer is applied, the necking parameter ψ film (i)(ε) was expressed by the following equation (eq10).

Number

Number

[0021] In addition, the inventor considered that the volume change of the convex part crushed (or smoothed) by the contact between the surface S1 and the surface S2 of the contact area ratio ε 2 expressed by the equation (eq2) has no influence on the shape change of the non-contact surface (for example, the concave part adjacent to the convex part). To solve the problem 2, based on the idea described in Non-Patent Document 2, the contact area ratio ε 2 is represented by the equation (2) instead of the equation (eq2). H c,film shown in the equation (2) means the softer hardness among the hardness H c,film (1) of the surface S1 of the first object Ω1 provided with the first plating layer and the hardness H c,film (2) of the surface S2 of the second object Ω2 provided with the second plating layer, as shown in the equation (9).

[0022] According to the above idea, when a plating layer is provided on at least one of the surfaces of the first object Ω1 and the second object Ω2, the above problems 1 and 2 can be solved. Therefore, even when the contact pressure P on the contact surface S is very large, the contact thermal conductance h c (ε) can be accurately estimated. However, since the above equations (eq8) and (eq10) include the sum with n = ∞, estimating using these equations requires a huge number of numerical operations including solving for the zeros of the first-kind Bessel function of the first order, and the computational load is excessive. Therefore, as a result of further intensive studies by the present inventor, when the film thicknesses and thermal conductivities of the first plating layer C1 M and the second plating layer C2 N are within a certain range, it has been found that there are characteristics in the distribution of the constriction parameter correction coefficient C L (i) (ε), and as an approximate formula that minimizes the error from the theoretical solution of the constriction parameter correction coefficient C L (i) (ε) calculated by the above equations (eq7) to (eq12) (the solution calculated by terminating the calculation at n (for example, n = 10000) where the sum converges within a certain range), Equation (5) has been derived. By using this approximate formula (5), since a huge number of numerical operations are not required, the computational load is small, and since the above-mentioned problems 1 and 2 can be solved, even when the contact pressure P at the contact surface S is very large, the contact thermal conductance h c (ε) can be accurately and simply estimated.

[0023] Incidentally, according to the findings of the present inventor, the hardness H of the surface S1 c,film (1) and the hardness H of the surface S2 c,film (2) can be obtained as the solution of the system of simultaneous equations represented by the following equations (20) to (22) with reference to the concepts described in Non-Patent Documents 5 and 6, for example.

Equation

[0024] The hardness H of the surface S1 c,film (1) and the hardness H of the surface S2 c,film (2) As a method for obtaining the above, as long as the method can consider the influence of the plating layer, it is not limited to the above example. For example, instead of the above formulas (20) and (22), it is also possible to obtain the values using the estimation formulas described in Non-Patent Document 7.

[0025] In addition, when both the first object Ω1 and the second object Ω2 are metals, generally, between the contact thermal conductance h(ε) and the contact electrical resistance R(ε), the Wiedemann-Franz law expressed by the following formula (23) holds. c (ε) and the contact electrical resistance R c (ε), the Wiedemann-Franz law represented by the following formula (23) holds. R c (ε) = LT / h(ε) ···(23) c (ε) ···(23) In the above formula (23), L is the Lorentz number, T is the absolute temperature of the contact surface S, and the average temperature of the absolute temperature of the surface S1 and the absolute temperature of the surface S2 can be used. Therefore, when both the first object Ω1 and the second object Ω2 are metals, the contact electrical resistance R(ε) on the contact surface S can also be estimated using the contact thermal conductance h(ε) estimated by the contact thermal conductance estimation method according to the present embodiment and the formula (23). c (ε) and the formula (23). c (ε) can be estimated.

[0026] Hereinafter, an example of the result of comparing the case of using the contact thermal conductance estimation method described in Non-Patent Document 3 with the case of using the contact thermal conductance estimation method according to the present embodiment will be described. Even in the contact thermal conductance estimation method described in Non-Patent Document 3, although a formula similar to formula (1) in the contact thermal conductance estimation method according to the present embodiment is used, the constriction parameter correction coefficient C in formula (1) L (i)(ε) is calculated in a significantly different way. In the estimation method according to this embodiment, as described above, the constriction parameter correction coefficient C is calculated using expressions such as expression (5) that do not require a huge number of numerical operations. L (i) In contrast, in the estimation method described in Non-Patent Document 3, a huge number of numerical operations similar to the above-described expression (eq8) and expression (eq10) are required to calculate the constriction parameter correction coefficient C L (i) (ε).

[0027] FIG. 2 shows an example of the constriction parameter correction coefficient C L (1) (ε) calculated by the estimation method of the contact thermal conductance described in Non-Patent Document 3 and the estimation method of the contact thermal conductance according to this embodiment when a first plating layer C11 of one layer is applied to the first object Ω1. FIG. 2(a) shows an example of the constriction parameter correction coefficient C L (1) (ε) calculated by the estimation method described in Non-Patent Document 3, and FIG. 2(b) shows an example of the constriction parameter correction coefficient C L (1) (ε) calculated by the estimation method according to this embodiment. In both cases, ε = 0.1, and τ1 (1) represented by expression (13) and K 21 (1) represented by expression (11) are changed to calculate the constriction parameter correction coefficient C L (1) (ε). As can be seen from FIG. 2, the values of the constriction parameter correction coefficient C L (1) (ε) calculated by both estimation methods are equivalent. Therefore, according to the estimation method according to this embodiment, the constriction parameter correction coefficient C L (1) (ε) can be accurately calculated with a significantly small computational load, and thus it can be said that the contact thermal conductance h c (ε) can be accurately estimated.

Explanation of Signs

[0028] Ω1 ··· First object Ω2 ··· Second object S... Contact surface S1, S2... Surfaces P... Contact pressure h c (ε)... Contact thermal conductance ε 2 ... Contact area ratio

Claims

1. A first object Ω1 having a surface S1 with minute irregularities and a second object Ω2 having a surface S2 with minute irregularities are in contact with each other at a contact pressure P greater than 0 on a substantially flat contact surface S shared by the surface S1 and the surface S2, and contact heat transfer occurs between the first object Ω1 and the second object Ω2 through the contact surface S. The contact thermal conductance h ｃ (ε) of the contact surface S is estimated by a contact thermal conductance estimation method, On the surface S1 side of the first object Ω1, M layers (M = 0, 1, or 2) of a first plating layer C1 are sequentially provided from the surface S1 side with respect to the base material of the first object Ω1 Ｍ On the surface S2 side of the second object Ω2, N layers (N = 0, 1, or 2) of a second plating layer C2 are sequentially provided from the surface S2 side with respect to the base material of the second object Ω2 Ｎ (provided that the case where M = N = 0 is excluded), The film thickness and thermal conductivity of the first plating layer C1 Ｍ are respectively t Ｍ （１） and k Ｍ （１） and the film thickness and thermal conductivity of the second plating layer C2 Ｎ are respectively t Ｎ （２） and k Ｎ （２） The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively k （１） and k （２） The RMS roughnesses of the surface S1 and the surface S2 are respectively σ （１） and σ （２） The average inclinations of the convex portions of the surface S1 and the surface S2 are respectively m （１） and m （２） The hardnesses of the surface S1 and the surface S2 are respectively H ｃ，ｆｉｌｍ （１） and H ｃ，ｆｉｌｍ （２） When it is set as, the contact thermal conductance h ｃ (ε) of the contact surface S is estimated using the following formulas (1) to (17). A method for estimating contact thermal conductance, characterized by the following. 【Equation 12】 In the above equations (3) and (15), erf c －１ is the inverse function of the complementary error function. In the above equation (5), erf c is the complementary error function. In the above equations (3) and (15), π is the ratio of a circle's circumference to its diameter. In equations (5), (6), and (11) to (14), i = 1 or 2. Also, in the above equations (1), (5), (6), (9) to (14), (16), and (17), the superscript (1) means a value related to the first object Ω1 or the first plating layer C1 Ｍ and the superscript (2) means a value related to the second object Ω2 or the second plating layer C2 Ｎ When M = 1 (i.e., when the first object Ω1 is provided with one layer of the first plating layer C1 １ ), the following equation (18) holds. When N = 1 (i.e., when the second object Ω2 is provided with one layer of the second plating layer C2 １ ), the following equation (19) holds. When M = 0 (i.e., when the first object Ω1 is not provided with the first plating layer), CL （１） represented by the above equation (5) is 1. When N = 0 (i.e., when the second object Ω2 is not provided with the second plating layer), CL （２） represented by the above equation (5) is 1. k ２ （１） = k （１） , t ２ （１） = 0... (18) k ２ （２） = k （２） , t ２ （２） = 0... (19)

2. The first object Ω1 and the second object Ω2 are metals, and the contact thermal conductance h at the contact surface S estimated by the contact thermal conductance estimation method according to Claim 1 ｃUsing (ε) and the following formula (23), the contact electrical resistance R at the contact surface S ｃ is estimated, A contact electrical resistance estimation method characterized by this. R ｃ (ε) = LT / h ｃ (ε) ··· (23) In the above formula (23), L is the Lorentz number, and T is the absolute temperature of the contact surface S.

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