JP7353148B2 - How to manufacture a heat sink - Google Patents

Description

The present invention relates to a method for manufacturing a heat sink used for heat dissipation in electronic devices such as computers.

Conventional heat sinks have a structure in which multiple plate-shaped fins are provided parallel to each other on one side of a base material, and are made of materials such as aluminum with high thermal conductivity, and are processed by casting, extrusion molding, machining, etc. (For example, Patent Documents 1 and 2). In this heat sink, a large number of fins having the same shape are arranged at regular intervals, thereby forming an air flow along the fins, contributing to improvement in heat dissipation efficiency.

Japanese Unexamined Patent Publication No. 57-193049 Japanese Unexamined Patent Publication No. 63-235031

However, conventional heat sinks have a structure in which a large number of fins are arranged over the entire surface of a base material in order to obtain a predetermined heat dissipation efficiency, which poses a problem of high material costs. Further, although there is a space between adjacent fins, the space actually occupies the same volume as a solid body with the fins at both ends serving as side walls and the base material serving as a bottom wall.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide a method for manufacturing a heat sink that can reduce the amount of material used for a heat dissipation element and suppress material costs. Further, the present invention provides a method for manufacturing a heat sink, which can eliminate the need for a heat dissipation element to substantially occupy the space on the base material, and can increase the degree of freedom in the arrangement of components other than the heat sink. It is an object.

In order to solve the above problems, the heat sink manufacturing method of the present invention is a method for manufacturing a heat sink in which one or more heat radiating elements extend from a base material, wherein the heat radiating elements are stretched in a cross section including the normal line of the base material. For the elongated shape of the heat dissipation element in the cross section, the total heat transfer amount of the heat sink and the material usage amount of the heat dissipation element in the cross section are used as the objective functions, and a genetic algorithm with two objective variables, the total heat transfer amount and the material usage amount. The feature is that the topology can be adjusted by using the response surface method and the response surface method together.

The heat sink manufacturing method of the present invention is characterized in that the response surface method uses a Kriging model.

In the heat sink manufacturing method of the present invention, the heat dissipation element is characterized in that, in cross section, a trunk extends from the base material and two or more branch portions extend from the trunk.

The heat sink manufacturing method of the present invention is characterized in that the thicknesses of the trunk and branches in cross section are set so that the flow rate of air is equal to or greater than a predetermined value.

The heat sink manufacturing method of the present invention is characterized in that adjacent heat radiating elements are provided so that their branch parts do not overlap when viewed along the normal line of the base material.

The heat sink manufacturing method of the present invention is characterized in that the total length of the heat dissipation elements in the stretching direction is used as the objective function instead of the amount of material used.

In the heat sink manufacturing method of the present invention, the heat sink is characterized in that at least the heat dissipation element is formed by additive manufacturing.

According to the present invention, the amount of material used for the heat dissipation element can be reduced and the material cost can be held down. Furthermore, it is possible to eliminate the heat radiating element from substantially occupying the space on the base material, and the degree of freedom in arranging components other than the heat sink can be increased.

FIG. 3 is a diagram showing an example of a heat sink according to an embodiment of the present invention. FIG. 3 is a diagram showing an example of a heat sink placed in a closed space in order to focus on the total amount of heat transfer Q and material cost. (a) is a diagram showing a cross-sectional shape of a heat sink according to a reference example, and (b) is a diagram showing a cross-sectional shape of a heat sink example according to an embodiment. It is a flowchart which shows the procedure of the optimization process in embodiment. (a) is a graph showing the calculation results of the local heat transfer coefficient at each position when using the object matching grid for the reference model, (b) is a graph showing the local heat transfer coefficient at each position when using the cut cell method (c) is a legend corresponding to (a) and (b), and (d) is a diagram showing the position shown on the horizontal axis of (a) and (b). It is a graph plotting the total amount of heat transfer against the total length of the branch and trunk for the initial sample, additional sample, and reference model.

Hereinafter, a method for manufacturing a heat sink according to an embodiment of the present invention will be described in detail with reference to the drawings.
The heat sink according to the present embodiment includes a base material and one or more heat dissipation elements extending from the base material. The heat dissipation element extends at least in a cross section that includes the normal line of the plate-shaped base material (a line along the direction perpendicular to the main plane of the base material). For example, as shown in the examples shown in FIGS. 1(a) to 1(f), the heat dissipation element extending in the Dimensionally extending configurations are also possible.

As explained below, the heat sink of the present embodiment has an objective function in which the total heat transfer amount Q of the heat sink and the amount of material used for the heat radiating element in the cross section or the total length L of the heat radiating element in the cross section are By using genetic algorithm and response surface methodology together with two objective variables: total heat transfer amount Q and material usage amount or total length L, the topology is adjusted and the material cost and total heat transfer amount Q are adjusted to the desired value. It is possible to optimize the combination.

In the heat sink whose topology has been optimized in this way, at least the heat dissipation element is formed by a 3D printer or other additive manufacturing method. Although the base material can be formed together with the heat dissipation element by an additive manufacturing method, it may be formed in advance by a method other than the additive manufacturing method before forming the heat dissipation element. Here, the total length L of the heat dissipation element is the total length of the trunk extending from the base material, the branches extending from the trunk, and the branches further extending from the branches. It is a separate numerical value from the thickness and outer circumference.

BACKGROUND OF THE INVENTION As the computing power of computers increases, numerical calculation techniques such as computational fluid dynamics (hereinafter referred to as "CFD") have come to be used in the design and optimization of engineering products. Design optimization can be roughly divided into three types: dimensional optimization, shape optimization, and topology optimization. Dimension optimization uses representative dimensions such as the length and thickness of the beam as design variables, so it cannot accommodate large changes in shape. Shape optimization is currently the most common method that uses the shapes of the outer and inner edges of a structure as design variables, but it cannot accommodate changes in topology such as the presence or absence of holes or the connectivity of regions. In particular, in fluid machines such as flow channels and heat exchangers, changes in topology have a large effect on performance, so optimization with a high degree of freedom in shape expression (topology optimization) is desired.

In view of the above points, the shape of the heat sink according to this embodiment is designed by tobological optimization. Many previous studies have focused on improving the performance of heat sinks, but here we will also focus on material costs and tackle multi-objective optimization. In the example described below, performance evaluation using CFD and multi-objective optimization will be performed on a two-dimensional branch form of the fins of a heat sink.

In design optimization problems for heat sinks and flow channels, it is known that the optimal structure is similar to natural objects such as tree branches, plant leaf veins, and bronchial tubes. In this embodiment, the fins of the heat sink are expressed using the Lindenmayer systems (hereinafter referred to as "L-systems") among topology methods that can express the structures of various natural objects with a small number of parameters.

L-systems is a grammar based on initial character strings and character replacement rules, and can express periodic self-similar structures (fractals) often seen in natural objects. The grammar is expressed in the form G={V,S,ω,P}. Here, V is a character that is sequentially replaced according to the replacement rule, and takes F or X. S is a set of constants, consisting of +, 1, [, ]. ω is a set of elements of V indicating an initial state. P is a set of substitution rules that change V. The number of iterations of P was set to 4 so that the branch form would fall within the design area.

The meaning of each symbol above is as follows.
(1) V
F Advance (stretch) in steps of length d
X Character that controls branch progression (2) S
+ : Rotate to the right by angle δ (dv ₁ ) - : Rotate to the left by angle δ (dv ₁ ) [ : Generate a new branch (heat dissipation element) (expressed by character string up to ])
]: Generate a new branch (heat dissipation element) (represented by a string from [)

(3)ω
X Same as X defined in (1) V above (4) P
F→FF
A string of 10 characters given by X → dv ₂ to dv ₁₁

Examples of heat sinks are shown in FIGS. 1(a) to 1(f). 1(a) is a cross-sectional view of the heat sink of Example 1, (b) is a perspective view of the heat sink of Example 1, (c) is a cross-sectional view of the heat sink of Example 2, (d) is a perspective view of the heat sink of Example 2, (e) is a sectional view of the heat sink of Example 3, and (f) is a perspective view of the heat sink of Example 3. 1(a), (c), and (e) are cross sections including the normal line of the base material 10. FIG. Here, the base material 10 is a plate material that extends in the XY plane shown in FIGS. 1(a) to 1(f), and its normal direction is along the Z direction.

In Example 1 shown in FIGS. 1(a) and 1(b), a trunk 11 extends from the base material 10 along the normal direction (Z direction), and two branches 12, 13 are separated from each other from this trunk 11. extending in the direction. Furthermore, two branches 21 and 22 extend from the one branch 12, and a further branch (numerical symbol omitted) extends at the tip of each branch. Regarding the other branch portion 13, two branch portions 23 and 24 extend as well, and a further branch portion (number omitted) extends at each tip.

Here, in FIGS. 1A to 1F, an example is shown in which the trunk 11 extends along the normal direction of the base material 10, but a configuration in which the trunk extends in a direction different from the normal direction is also possible. be.

In Example 2 shown in FIGS. 1(c) and 1(d), a trunk 11 extends from the base material 10 along the normal direction (Z direction), and two branches 12 and 13 are separated from each other from this trunk 11. extends in the direction of The trunk 11 extends further and a further branch 14 extends from its tip.

Also in Example 3 shown in FIGS. 1(e) and 1(f), a trunk 11 extends from the base material 10 along the normal direction (Z direction), and two branches 12 and 13 extend from the middle of this trunk 11. They extend in different directions. Further branches (not numbered) extend from these branches 12, 13. Further, the trunk 11 extends further upward (in the Z direction), and two branch portions 14 and 15 extend in mutually different directions, and a further branch portion (number omitted) extends from the branch portion 15.

In this embodiment, as shown in FIG. 2, we assume a heat sink placed in a closed space, and focus on the total amount of heat transfer Q [w] on the heat sink's heat dissipation surface and the material cost (volume of the heat dissipation element). . Here, we search for a shape that maximizes the total amount of heat transfer (heat radiation) of the heat sink while minimizing material costs. Here, the heat dissipation element is a flat fin in the reference example, and includes the trunk and branch portions of the fin in the heat sink of this embodiment.

In the following evaluation, the total length L [mm] of the trunk and branches of the fin on a two-dimensional cross section is used instead of the volume. There are a total of 11 design variables, where dv ₁ is the bending rotation angle of the branch, and dv ₂ to dv ₁₁ are given as discrete values in the range from 0 to 1 as shown below.

When 0≦dv _n <1/6: F
If 1/6≦dv _n <2/6: X
If 2/6≦dv _n <3/6: +
If 3/6≦dv _n <4/6: -
If 4/6≦dv _n <5/6: [
If 5/6≦dv _n ≦1: ]
However, n=2, 3,..., 11

Regarding optimization in this embodiment, the following definition is used.
(1) Objective function (objective function)
Maximization: Total heat transfer amount Q (unit: W)
Minimization: Total length L of trunk and branches (unit: mm)
(2) Design variable dv ₁ : Based on experimental values 0≦dv _n ≦1
However, n=2, 3,..., 11

As a reference example for comparison, F series 21F50 (model number) manufactured by LSI Cooler Co., Ltd., whose cross-sectional shape is shown in FIG. 3(a), was used. The size (cross-sectional shape) and specifications of each part of this heat sink are as follows.
(1) Base 101: width 50mm, height 6mm
(2) Fin 111 (heat dissipation element, flat plate): thickness 2.6 mm, interval 7.9 mm, height including base 101 21 mm
(3) Unit weight 1.513 kg/m, aluminum extrusion molded product

On the other hand, in the heat sink of this embodiment, as shown in FIG. 3(b) (cross-sectional view), the base (base material) was fixed in a plate shape with a width of 50 mm and a height of 6 mm. Furthermore, with the L-system, the fins (heat dissipation elements) extending from the center of the base are arranged in the external shape of the entire heat sink of the reference example shown in Fig. 3(a) (width 50 mm, base height 6 mm, height extending from the base 15 mm). ), constraints were placed on the design domain.

Furthermore, a three-dimensional shape is created by extending this cross-sectional shape by 50 mm in the depth direction (direction perpendicular to the plane of the paper in FIG. 3(b)), and the fins are optimized according to the above definition. In addition, during the optimization process, some individuals may have grammars such as +-, 1+, [], +], -] that are grammatically correct but have no meaning for the shape, or individuals whose last character is + or -]. , [, or individuals that do not have a branch form such as no X, no [ , ], +, or 1 are considered invalid individuals by giving 10,000 mm to the total length of the branch. Individuals in optimization will be described below.

In this embodiment, a genetic algorithm (hereinafter referred to as "GA"), which is an algorithm modeling the evolution of living things, is used. GA selects individuals from the current generation as parents, generates new individuals as children through crossover and mutation, and leaves superior individuals to the next generation.

GA is preferable for the following two reasons. First, unlike the gradient method, GA does not need to find the gradient of the objective function, and can achieve optimization by evaluating the objective function value itself. It can also be applied to design optimization problems. This leads to the excellent versatility of GA, as it does not require deep knowledge or experience in the mathematical background or theory of the application.

Second, unlike the gradient method, where the solution search is performed sequentially starting from one point, GA performs a population-based multi-point simultaneous search, so it is possible to find the global optimal solution without falling into a local optimal solution. There are many things that are expected to be discovered.
These characteristics make GA a powerful solution for optimization problems in which the objective function has strong nonlinearity and multimodality, such as tobological optimization of fluid problems.

In this embodiment, the Non-Dominated Sorting Genetic Algorithm (hereinafter referred to as "NSGA-II"), which is a famous GA for multi-objective optimization, is employed. As mentioned above, NSGA-II (GA) has an excellent ability to find global optimal solutions through group-based multi-point simultaneous search. Furthermore, NSGA-II is also excellent in that it can maintain the diversity of the solution population in order to search for a set of Pareto optimal solutions in a multi-objective optimization problem.

On the other hand, it is necessary to evaluate the objective function for each solution in the population, resulting in an enormous computational cost. Particularly in the case of evaluating the objective function by large-scale numerical calculations such as CFD as in this embodiment, it is not practical to use NSGA-II alone from the viewpoint of calculation cost. Therefore, in this embodiment, the response surface method is also used in order to reduce the calculation cost.

Response surface methodology is a method that evaluates (samples) the output (objective function value) in several cases with different inputs (design variable values), and then constructs an algebraic formula to interpolate these sample points. By using this algebraic formula for optimization, it is possible to instantly estimate the output for any input for which no sample points have been given, thereby significantly reducing the calculation time required for objective function evaluation and overall optimization.

In this embodiment, a Kriging model, which is a response surface method suitable for approximating nonlinear and multimodal functions, is used among response surface methods. While other response surface methods model only the estimated value of the objective function, the Kriging model can model both the estimated value ("Equation 1") and the uncertainty of the estimated value ("Equation 2"). Based on this uncertainty information, an index can be calculated to identify the location of the next sample point to be added to improve the model.

In this embodiment, for the objective function f(x) to be maximized, the expected value (Expected Improvement) of the amount of improvement I(x) from the current optimal value f _max is defined by the following equations (1) and (2). :EI) Calculate E[I(x)].

Here, F is a random variable that follows a normal distribution ("Equation 5"), and φ(F) is a probability density function of the variable F.

Instead of maximizing the original objective function f(x), a design variable value x that maximizes the EI value E[I(x)] of the objective function is searched on the Kriging model. After evaluating the value of the true objective function f(x) at this x, sample points are added and the Kriging model is updated. By repeating the above operations, it is possible to simultaneously search for a global optimal solution and improve the accuracy of the response surface.

FIG. 4 shows the optimization procedure in this embodiment. This procedure is a procedure related to adjusting (optimizing) the topology of the extended shape of the heat dissipation elements (branches and trunk) illustrated in FIG. 3(b) in the heat sink manufacturing method according to the present embodiment. In the process shown by the solid line frame (steps S1, S2) in FIG. ) is output.

Here, we use NSGA-II, which is one of the genetic algorithms (GA), to approximate the total heat transfer amount Q, which is the first objective function, using the Kriging model, which is one of the response surface methods. The total length L of the branches and trunk, which is the objective function of the eye, is analytically evaluated.

First, initial sample points (42 points in total) are uniformly created in the design space using Latin Hypercube Sampling (LHS) (14) (step S1). Subsequently, after performing CFD on each of the created points, a Kriging model that approximates the total amount of heat transfer Q is constructed (step S2).

Next, a Pareto optimal solution with the maximum EI value of Q and the minimum analytical value of L on the Kriging model is searched for using NSGA-II (population size 512, number of generations 100) (step S3). Among the countless Pareto optimal solutions obtained here, CFD is performed on samples of a total of three points, two points at both ends of the Pareto surface and one point in the center (step S4).

Subsequently, a convergence determination is performed (step S5). This convergence determination is made, for example, by determining whether the EI value has become less than a predetermined threshold and convergence has occurred, or whether the topology of the shape of the heat dissipation element has stopped being updated and has converged.

In the convergence determination, if it is determined that it has not converged (No in step S5), a sample is added to the current sample point and the Kriging model is updated (step S1).

On the other hand, in the convergence determination, if it is determined that convergence has been achieved (Yes in step S), the optimization process ends. With the above procedure, it is possible to efficiently search for a Pareto solution using the minimum necessary number of CFDs.

In this embodiment, the total heat transfer amount of the heat sink is evaluated using the pressure-based solver of the commercially available CFD software ANSYS FLUENT 17.2. The governing equations are the continuity equation, the steady incompressible Navier-Stokes equation, and the steady energy equation.

In addition, a pseudo transient algorithm is used to enable the pseudo-transient algorithm of the pressure-based coupled solver. As a result, unsteady terms are efficiently added to the analytical equations, improving stability and convergence.

Table 1 shows the calculation scheme used in this embodiment. The working fluid is air. The bottom surface of the heat sink is used as a heat source, and a constant temperature of 323.15 K is given as the first type temperature boundary condition.
A third type boundary condition is set for the area wall so that heat can be sufficiently released to the surroundings (293.15K). Here, Boussinesq approximation is used to model natural convection.

The CFD grid is generated by the cut cell method. Compared to the general object matching grid method, the cut cell method can automatically generate grids even for complex fin shapes explored during the topology optimization process. In addition, in contrast to the orthogonal lattice method, which expresses the object surface with simple step-like cells, the cut cell method, which extracts a lattice along the object by cutting cells that intersect with the object surface, can also be used next to a wall. is defined, so the conservation law is satisfied.

Figure 5(a) shows the results of calculating the local heat transfer coefficient at each position when using the object matching grid for the reference model, and Figure 5(b) shows the results of calculating the local heat transfer coefficient at each position when using the cut cell method. The results of calculating the local heat transfer coefficient are shown. In FIGS. 5(a) and 5(b), the vertical axis represents the local heat transfer coefficient (unit: W/m ⁻¹ ·K), and the horizontal axis represents the position of the model in one direction. Moreover, FIG. 5(c) shows a legend corresponding to FIGS. 5(a) and (b), and FIG. 5(d) is a diagram showing the position shown on the horizontal axis of FIGS. 5(a) and (b). . In FIGS. 5(a) and 5(b), the calculation results at position "Z+1" shown in FIG. The calculation results for `` are shown with squares.

When the object matching grid shown in FIG. 5(a) was used, calculations could be performed with high accuracy, but each case required approximately 1 hour for calculations. On the other hand, when the cut cell method shown in FIG. 5(b) was used, the calculation could be performed in about 10 minutes for one case. Therefore, it was found that by using the cut cell method, it is possible to capture the same tendency as the object matching grid while significantly reducing calculation time.

When the Kriging model was updated four times and 12 additional sample points were added according to the optimization procedure shown in FIG. 4, the results shown in FIG. 6 were obtained.

Figure 6 shows the initial sample, with the vertical axis as the first objective function, total heat transfer Q (unit: W), and the horizontal axis as the second objective function, total length L of the branches and trunk (unit: mm). ("Initial sample points" in Figure 6, circle mark), additional samples ("Additional sample points" in Figure 6, triangle mark), and reference model ("Reference model" in Figure 6, mark * (asterisk)). This is a graph plotting evaluation values.

In Figure 6, the two-dimensional cross-sectional shape (cross-section including the normal to the base material, however, the base material is not shown) is shown for four of the sample points (SA, SB, SC, SD) that are the Pareto optimal solution. They are also shown. Here, the total heat transfer amount Q and the total length L at each point are as follows.
SA: Total heat transfer amount Q: 0.6943W, total length L: 12.05mm
SB: Total heat transfer Q: 1.3268W, total length L: 73.86mm
SC: Total heat transfer amount Q: 1.4468W, total length L: 80.69mm
SD: Total heat transfer amount Q: 1.4351W, total length L: 100.66mm

As shown in FIG. 6, the average value of the total heat transfer amount Q of the model at the four points (SA, SB, SC, SD) is slightly inferior in performance compared to the reference model. Specifically, the total heat transfer amount Q in the sample shown at point SC is approximately 18% lower than that of the reference model. However, compared to the reference model in which a plurality of flat fins are arranged in parallel, the material cost can be reduced by about 30% in the sample shown at point SC.

Furthermore, regarding the above four points, the total heat transfer amount Q is significantly improved in the three samples SB, SC, and SD, which have multiple branches extending from the trunk, compared to sample SA, which has one branch to the trunk. ing. Furthermore, it can be seen that in the two samples SB and SC, the total heat transfer amount Q is significantly increased compared to the amount of increase in the total length L. From the above results, it can be seen that the optimal pareto solution is preferably a shape in which the branches extend widely to the left and right so that convection does not stagnate. Furthermore, it was found that the total amount of heat transfer Q can be significantly improved by adjusting the total length L of the branches and trunk.

Modifications will be explained below.
In the above explanation, the total length L of the branches and trunk was used as one of the objective functions, but instead of the total length L, it is assumed that the air flow rate in the heat sink is equal to or higher than a predetermined value, for example, the flow rate is in accordance with the specifications required for the heat sink. After considering the thickness of the heat sink, the amount of material used for the branches and trunk as heat dissipation elements can be set as an objective function.

In the above explanation, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) was taken as an example of the genetic algorithm, but other genetic algorithms such as Multi-Objective Genetic Algorithm (MOGA), Adaptive e Range Multi-Objective Genetic Algorithm (ARMOGA), Strength Pareto Evolutionary Algorithm (SPEA), etc. can also be used.

Although the present invention has been described with reference to the above embodiments, the present invention is not limited to the above embodiments, and improvements or changes can be made within the scope of the purpose of improvement or the idea of the present invention.

As described above, the method for manufacturing a heat sink according to the present invention is useful in that it is possible to reduce the amount of material used for the heat dissipation element and to suppress material costs.

10 Base material (base)
11 Executive (heat dissipation element)
12, 13, 21, 22, 23, 24 Branches (heat dissipation elements)
101 Base 111 Fin SA, SB, SC, SD Sample point

Claims (7)

A method for manufacturing a heat sink in which one or more heat dissipation elements extend from a base material, the method comprising:
The heat dissipation element extends in a cross section including the normal to the base material,
Regarding the stretched shape of the heat dissipation element in the cross section, the total heat transfer amount of the heat sink and the material usage amount of the heat dissipation element in the cross section are used as objective functions, and the two objective variables of the total heat transfer amount and the material usage amount are calculated. A method for manufacturing a heat sink, characterized by adjusting topology by using a combination of genetic algorithm and response surface methodology. 2. The method of manufacturing a heat sink according to claim 1, wherein the response surface method uses a Kriging model. Manufacturing the heat sink according to claim 1 or 2, wherein in the cross section, the heat dissipation element has a main body extending from the base material and two or more branch parts extending from the main body. Method. 4. The method of manufacturing a heat sink according to claim 3, wherein the thicknesses of the trunk and the branch portions in the cross section are set so that the flow rate of air is greater than or equal to a predetermined value. 2. The method of manufacturing a heat sink according to claim 1, wherein the adjacent heat dissipating elements are provided so that their branch parts do not overlap when viewed along the normal line of the base material. 2. The method of manufacturing a heat sink according to claim 1, wherein a total length of the heat dissipation elements in the stretching direction is used as the objective function instead of the amount of material used. 7. The method of manufacturing a heat sink according to claim 1, wherein at least the heat dissipation element of the heat sink is formed by an additive manufacturing method.

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