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 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, or resistance spot welding is 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 reports 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 contact pressure P greater than 0 at a substantially flat contact surface S shared by the surface S1 and the surface S2. When contact heat transfer occurs between the first object M1 and the second object M2 through the contact surface S, the contact thermal conductance h c at the contact surface S is proposed as an estimation formula as follows (eq1).

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 provided on the surface side and a second object with a plating layer provided 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 provided 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) provides 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 method for estimating the contact thermal conductance h(ε) at a contact surface S when 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 at 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. c (ε), which is a method for estimating contact thermal conductance, wherein 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. 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, the case where M = N = 0 is excluded). N The film thickness and thermal conductivity of the first plating layer C1 are respectively denoted as t M and k M (1) The film thickness and thermal conductivity of the second plating layer C2 are respectively denoted as t M (1) and k N The thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively denoted as k N (2) and k N (2) The RMS roughnesses of the surface S1 and the surface S2 are respectively denoted as σ (1) and σ (2) The average inclinations of the convex portions of the surface S1 and the surface S2 are respectively denoted as m (1) and m (2) The hardnesses of the surface S1 and the surface S2 are respectively denoted as H (1) and H (2) When the above are used, the contact thermal conductance h(ε) at the contact surface S is estimated using the following formulas (1) to (17). c,film (1) and H c,film (2) and H c Provided is a method for estimating contact thermal conductance, characterized by the above.

Equation

[0010] In the present invention, Equation (3) is an equation equivalent to the aforementioned Equation (eq1). Equation (10), Equation (16), and Equation (17) are equations equivalent to the aforementioned Equations (eq4) to (eq6), respectively. In the present invention, "the first plating layer C1 of the M layer M is applied" means that when M = 1, one 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 layer C11 and C12 are applied to the surface S1 side of the first object Ω1. And, "the film thickness and thermal conductivity of the first plating layer C1 M are respectively t M (1) and k M (1) are 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) are set as, and when M = 2, the film thickness and thermal conductivity of the first plating layer C11 are respectively t1 (1) and k1 (1) are set as, and the film thickness and thermal conductivity of the first plating layer C12 are respectively t2 (1) and k2 (1) are set as. Similarly, in the present invention, "the second plating layer C2 of the N layer N is applied" means that when N = 1, one 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 layer C21 and C22 are applied to the surface S1 side of the second object Ω2. And, "the film thickness and thermal conductivity of the second plating layer C2 N are respectively t N (2) and k N (2) are 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 the thermal conductivity of the second plating layer C21 are t1 (2) and k1 (2) respectively, and the film thickness and the thermal conductivity of the second plating layer C22 are t2 (2) and k2 (2) respectively. According to the present invention, when a plating layer is provided on at least one of the surfaces of the first object Ω1 and the second object Ω2, as described below, the above-described problems 1 and 2 can be solved.

[0011] Further, 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) at the contact surface S estimated by the contact thermal conductance estimation method and the following formula (24) are used to estimate the contact electrical resistance R c (ε) at the contact surface S. The present invention is also provided as a contact electrical resistance estimation method characterized by this. R c (ε)=LT / h c (ε) ···(24) In the above formula (24), 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 at 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 surfaces, is very large, the contact thermal conductance h c (ε) can be accurately estimated.

Brief Description of the Drawings

[0013]

Figure 1

Figure 2

Mode for Carrying Out the Invention

[0014] Hereinafter, a 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 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 the present embodiment includes 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 surfaces S1 and S2 are in contact with each other at a contact pressure P greater than 0 at a substantially flat contact surface S shared by the surfaces S1 and S2 and contact heat transfer occurs between the first object Ω1 and the second object Ω2 through the contact surface S, it is a method for estimating the contact thermal conductance h c (ε) at the contact surface S.

[0015] 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). 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). 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) where the film thickness, thermal conductivity, and hardness of the second plating layer C22 are t2 (2) , k2 (2) and H2 (2) respectively. Also, 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) respectively, the average inclinations of the convex portions of the surfaces S1 and S2 are m (1) , m (2) respectively, and the hardnesses of the surfaces S1 and S2 are H c,film (1) , H c,film (2) respectively. Note that the hardness in this specification means microhardness (Vickers hardness or micro-Vickers hardness). In FIG. 1, the case where two layers of the first plating layers C11 and C12 are applied to the surface S1 side of the first object Ω1 and two layers of the second plating layers C21 and C22 are applied to the surface S2 side of the second object Ω2 is taken as an example. However, the present invention is not limited to this, and it is applicable when a plating layer is applied to at least one of the surfaces S1 of the first object Ω1 and S2 of the second object Ω2.

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

[0017] In the case where a plating layer is applied to at least one of the surfaces of the first object Ω1 and the second object Ω2, in order to solve the above-mentioned problems 1 and 2, the process of deriving the method for estimating the contact thermal conductance according to this embodiment is as follows. Based on the ideas described in Non-Patent Documents 3 and 4, the inventor first decided to represent the contact thermal conductance h c (ε) by Equation (1). Specifically, the contact thermal conductance h c (ε) is represented by Equation (1) using the contact thermal conductance h c,bare (ε) (see Equation (3)) when no plating layer is applied, or the constriction parameter ψ film (i) (ε) when a plating layer is applied, and the constriction parameter ψ bare (ε) when no plating layer is applied, and the constriction parameter correction coefficient C L (i) (ε) (see Equation (4)), etc. Then, as described above, in order to solve Problem 1 that the estimation accuracy of the constriction parameter ψ(ε) represented by Equation (eq3) deteriorates in the range where ε is large, the constriction parameter ψ bare (ε) when no plating layer is applied is considered to continuously transition from the theoretical solution of the constriction parameter ψ 2 (ε) when the contact area ratio ε bare is small (ε→0) to the theoretical solution of the constriction parameter ψ 2 (ε) when the contact area ratio ε bare is large (ε→1) as ε changes (ε: 0→1). A function β(ε) of ε representing this change is introduced, and as shown in Equation (5), the constriction parameter ψ bare (ε) is conceived to be represented by a linear mixture of the above two theoretical solutions. Next, heat transfer finite element analysis of two non-plated contact cylinders (flux tubes) with ε varied variously from 0 to 1 was performed, and the constriction parameter ψ bare (ε) calculated from the analysis results and the constriction parameter ψ bare (ε) calculated from Equation (5) were made to approximately coincide, and β(ε) represented by Equation (7) was derived by least squares approximation. Also, the constriction parameter ψ bareBy applying the concept similar to (ε) and incorporating the concepts described in Non-Patent Documents 3 and 4, the constriction parameter ψ when a plating layer is provided film (i) (ε) was expressed by Equation (6).

[0018] In addition, the inventor considered that the contact area ratio ε expressed by Equation (eq2) 2 does not take into account the influence of the volume change of the convex portions 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 portion adjacent to the convex portion). To solve Problem 2, based on the concept described in Non-Patent Document 2, the contact area ratio ε 2 was replaced with Equation (2) instead of Equation (eq2). The H shown in Equation (2) c,film means the hardness H of the surface S1 of the first object Ω1 provided with the first plating layer, as shown in Equation (20) c,film (1) and the hardness H of the surface S2 of the second object Ω2 provided with the second plating layer c,film (2) means the softer hardness among them.

[0019] According to the findings of the 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, for example, as the solutions of the simultaneous equations represented by the following Equations (21) to (23) with reference to the concepts described in Non-Patent Documents 5 and 6.

Equation

[0020] Hardness H of surface S1 c,film (1) and hardness H of 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 (21) and (23), it is also possible to obtain them using the estimation formulas described in Non-Patent Document 7.

[0021] As described above, the contact thermal conductance estimation method according to the present embodiment is derived to solve the above-mentioned problems 1 and 2 when a plating layer is provided on at least one of the surfaces of the first object Ω1 and the second object Ω2. 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.

[0022] When organizing the matters considered in the contact thermal conductance estimation method according to the present embodiment and the contact thermal conductance estimation methods described in Non-Patent Documents 3 and 4, it becomes as shown in Table 1 below.

Table 1

[0023] When both the first object Ω1 and the second object Ω2 are metals, generally, between the contact thermal conductance h c (ε) and the contact electrical resistance R c (ε), the Wiedemann-Franz law expressed by the following equation (24) holds. R c (ε)=LT / h c (ε) ···(24) In the above equation (24), 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, using the contact thermal conductance h c (ε) estimated by the contact thermal conductance estimation method according to the present embodiment and equation (24), it is also possible to estimate the contact electrical resistance R c (ε) on the contact surface S.

[0024] The contact thermal conductance estimation method according to the present embodiment uses the above-mentioned equations (1) to (17) to apply a maximum of two first plating layers C1 to the surface S1 side of the first object Ω1 M and a maximum of two second plating layers C1 to the surface S2 side of the second object Ω2 N to estimate the contact thermal conductance h c (ε). By extending the same concept, it is also possible to estimate the contact thermal conductance h c (ε) when three or more plating layers are applied to each surface side of the first object Ω1 and / or the second object Ω2.

[0025] Figure 2 shows the contact thermal conductance h estimated by the contact thermal conductance estimation method according to the present embodiment for various contact pressures Pc (ε) and the contact thermal conductance h estimated by the estimation method described in Non-Patent Document 3 c An example of the result of comparing (ε) is shown. Specifically, when an arbitrary single-layer first plating layer C11 that satisfies the following formula (25) for the right side of formula (6) is provided on the surface S1 side of the first object Ω1, and an arbitrary single-layer second plating layer C21 that satisfies the following formula (26) for the right side of formula (6) is provided on the surface S2 side of the second object Ω2, the contact thermal conductance h at the substantially flat contact surface S shared by the surface S1 and the surface S2 c An example of the result of comparing (ε) is shown.

Number

Number

[0026] As can be seen from FIG. 2, the dimensionless contact thermal conductance C of the comparative example c is under the condition that the contact pressure P is large (dimensionless contact pressure log(P / H c,film) > 0), the dimensionless contact thermal conductance C of the example c became smaller than that, and an error Er of up to about 48% occurred compared with the example. Therefore, according to the contact thermal conductance estimation method according to the present embodiment, even when the contact pressure P is large, the contact thermal conductance h c (ε) can be accurately estimated.

Explanation of symbols

[0027] 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) on 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 provided in order 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 provided in order from the surface S2 side with respect to the base material of the second object Ω2 Ｎ (except for the case where M = N = 0), 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） k （２） The RMS roughnesses of the surface S1 and the surface S2 are respectively σ （１） σ （２） The average inclinations of the convex portions of the surface S1 and the surface S2 are respectively m （１） m （２） The hardnesses of the surface S1 and the surface S2 are respectively H ｃ，ｆｉｌｍ （１） H ｃ，ｆｉｌｍ （２） When this is the case, the contact thermal conductance h ｃ (ε) on 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 9] In the above equations (3) and (15), erf c －１ is the inverse function of the complementary error function. In the above equations (5) and (6), J ０ , J １ are the Bessel functions of the first kind of order 0 and 1 respectively, and δ ｎ is the zero of the Bessel function of the first kind of order 1 (i.e., J １ (δ ｎ ) = 0), and n is a natural number. In the above equations (3), (5), (6), and (15), π is the ratio of a circle's circumference to its diameter. In equations (4), (6), (8), (9), and (11) - (14), i = 1 or 2. Also, in the above equations (1), (4), (6), (8) - (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 a single layer of the first plating layer C1 is applied to the first object Ω1 １ ), the following equation (18) holds. When N = 1 (i.e., when a single layer of the second plating layer C2 is applied to the second object Ω2 １ ), the following equation (19) holds. When M = 0 (i.e., when no first plating layer is applied to the first object Ω1), CL （１） (ε) represented by the above equation (4) is 1. When N = 0 (i.e., when no second plating layer is applied to the second object Ω2), CL （２） (ε) represented by the above equation (4) is 1. Further, in the above equation (2), H ｃ，ｆｉｌｍ is a value represented by the following equation (20). k ２ （１） = k （１） , t ２ （１） = 0... (18) k ２ （２） = k （２） , t ２ （２） = 0 ··· (19) H ｃ，ｆｉｌｍ = min(H ｃ，ｆｉｌｍ （１） , H ｃ，ｆｉｌｍ （２） ) ··· (20)

2. The first object Ω1 and the second object Ω2 are metals, The thermal contact conductance h ｃ (ε) at the contact surface S estimated by the thermal contact conductance estimation method according to Claim 1, and the electrical contact resistance R ｃ (ε) at the contact surface S is estimated using the following formula (24): A method for estimating electrical contact resistance, characterized by this. R ｃ (ε) = LT / h ｃ (ε) ··· (24) In the above formula (24), L is the Lorentz number, and T is the absolute temperature of the contact surface S.

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