JP7624657B2 - Method for manufacturing heat sink and heat sink - Google Patents

Description

The present invention relates to a method for manufacturing a heat sink used to dissipate heat from electronic devices such as computers, and a heat sink that can be manufactured using this method.

Conventional heat sinks have a structure in which multiple plate-shaped fins are provided parallel to one another on one side of a base material, and are formed by casting, extrusion molding, machining, or other methods using materials with high thermal conductivity, such as aluminum (see, for example, Patent Documents 1 and 2). In these heat sinks, many fins of the same shape are arranged at regular intervals, which creates an air flow along the fins, contributing to improved heat dissipation efficiency.

In conventional heat sinks like this, numerous fins are arranged across one surface of the base material to achieve a certain level of heat dissipation efficiency, so although there is space between adjacent fins, the fins on both ends essentially form side walls, occupying a volume equivalent to that of a solid body with the base material as its bottom wall.

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

In response to this, the inventors are actively conducting research into configuring heat dissipation elements as three-dimensional structures based on graph theory, with a set of edges (lines connecting points) connecting sets of nodes (points) arranged three-dimensionally, in order to increase the amount of heat dissipation while keeping the volume of the space in which the heat dissipation elements are arranged small.

The present invention therefore aims to provide a method for manufacturing a heat sink that enables a heat sink with a three-dimensional structure to be manufactured as a three-dimensional structure that reproduces the design shape with high precision, and a heat sink that can be manufactured by this manufacturing method. A further object of the present invention is to provide a heat sink that can exhibit stable heat dissipation performance regardless of the position at the time of installation, and a manufacturing method for this heat sink.

In order to solve the above problems, the manufacturing method of the heat sink of the present invention is a manufacturing method of a heat sink equipped with a heat dissipation element having a three-dimensional structure in which a set of three-dimensionally arranged nodes is connected by a set of edges, and includes a manufacturing data generation process for generating manufacturing data that can be molded by additive manufacturing based on design values of the nodes and edges, a modeling process analysis process for generating mesh structure data based on the manufacturing data and calculating the shape deviation between the mesh structure data and the manufacturing data, and the maximum principal stress value at a predetermined position on the mesh structure data, and a first predetermined range for the shape deviation and a second predetermined range for the maximum principal stress value, which are set to realize a three-dimensional structure corresponding to the design values for the shape deviation and maximum principal stress value calculated in the modeling process analysis process. The method is characterized by comprising a printing defect diagnosis process for predicting a portion that will cause a printing defect by exceeding the range; a printing limit setting process for setting a printing limit to be considered in the manufacturing data generation process in order to eliminate the printing defect predicted in the printing defect diagnosis process based on the results of the printing process analysis process and a predetermined range set in advance for the printing limit; and an additive manufacturing process for repeating the manufacturing data generation process, the printing process analysis process, the printing defect diagnosis process, and the printing limit setting process when a new printing limit is obtained in the printing limit setting process, and for performing additive manufacturing based on the manufacturing data at that time to manufacture the heat sink when both the shape deviation and the maximum principal stress value fall within the first and second predetermined ranges, respectively, in the printing defect diagnosis process.

The heat sink of the present invention is a heat sink equipped with a heat dissipation element, the heat dissipation element having a set of edges connecting a set of nodes arranged three-dimensionally, a part of the set of nodes being arranged on a substrate, the substrate having a three-dimensional lattice structure in which a plurality of layers are stacked in the out-of-plane direction of the substrate surface, the edges being arranged more densely in the central part than in the outer part in the in-plane direction of the substrate surface as the layer is further from the substrate, a first ventilation hole is formed in the farthest layer farthest from the substrate, and a second ventilation hole is formed in the outer part of the layer closer to the substrate than the farthest layer.

The heat sink of the present invention is a heat sink equipped with a heat dissipation element, the heat dissipation element having a set of edges connecting a set of nodes arranged three-dimensionally, a part of the set of nodes being arranged on a substrate, and having a three-dimensional lattice structure in which a plurality of layers are stacked in the out-of-plane direction of the surface of the substrate, the edges are arranged more densely in the central part than in the outer part in the in-plane direction of the surface as the layer is further from the substrate, a first vent is formed in the farthest layer farthest from the substrate, a second vent is formed in the outer part of a layer closer to the substrate than the farthest layer, and air heated by a heat source close to the heat sink is discharged from the vent that is located higher in the vertical direction out of the first vent and the second vent, and air flows in from the vent that is located lower in the vertical direction out of the first vent and the second vent, depending on the attitude of the heat sink.

The heat sink manufacturing method of the present invention makes it possible to manufacture a heat sink with a designed three-dimensional structure as a three-dimensional structure that reproduces the design shape with high precision. This manufacturing method makes it possible to reduce the volume of the space in which the heat dissipation elements are placed while increasing the amount of heat dissipation, and to realize a heat sink that exhibits stable heat dissipation performance regardless of the installation position.

4 is a flowchart showing a flow of a method for manufacturing a heat sink according to an embodiment of the present invention. FIG. 1 is a block diagram showing an example of the configuration of a calculation device that can be used in an embodiment of the present invention. FIG. 13 is a diagram showing an example of a groove pattern engraved in a flow channel expressed by graph theory. FIG. 2 is a diagram showing an example of a three-dimensional lattice structure in an embodiment of the present invention. 1 is a flowchart showing a procedure of optimization calculation in an embodiment of the present invention. FIG. 2 is a diagram showing a model of a target region and boundary conditions of a thermal fluid analysis according to an embodiment of the present invention. 1 is a graph in which a scatter diagram of sample data searched by an optimization calculation in an embodiment of the present invention is plotted in an objective function space. This is a visualization of the structure of a ready-made heat sink and the generated flow field. This is a visualization of the structure and generated flow field of sample 09-001, among the heat sinks related to the two-objective optimum solution with a three-dimensional lattice structure in an embodiment of the present invention. This is a diagram visualizing the structure and generated flow field of sample 08-001, among the heat sinks related to the two-objective optimum solution with a three-dimensional lattice structure in an embodiment of the present invention. This is a visualization of the structure and generated flow field of sample 10-002, one of the heat sinks related to a two-objective optimum solution with a three-dimensional lattice structure in an embodiment of the present invention. FIG. 2 is a diagram showing the appearance of a model used in a simulation for analyzing a modeling process. FIG. FIG. 13 is a diagram showing the maximum principal stress distribution during molding. FIG. 13 is a diagram showing the maximum principal stress distribution during molding. FIG. 1 is a diagram showing the appearance of a model used in a heat transfer performance experiment. FIG. 1 is a visualization of the thermal boundary layer. FIG. 13 is a diagram showing an apparatus configuration when a natural convection cooling experiment is performed as a heat transfer performance experiment with a heat sink arranged vertically. FIG. 13 is a diagram showing an apparatus configuration for conducting a natural convection cooling experiment as a heat transfer performance experiment with a heat sink placed flat. 20 is a graph showing the relationship between the position in the X direction and the temperature obtained in a natural convection cooling experiment in which the heat sink 44 was placed flat using the device shown in FIG. 19 .

Hereinafter, a method for manufacturing a heat sink and a heat sink according to an embodiment of the present invention will be described in detail with reference to the drawings.
Fig. 1 is a flow chart showing the flow of a method for manufacturing a heat sink according to this embodiment. Fig. 2 is a block diagram showing an example of the configuration of a computing device that can be used in this embodiment. In this embodiment, a heat sink is manufactured through each process shown in Fig. 1. Here, the flow of each process will be described with reference to Fig. 1, and experimental results of each process will be described later.

The heat dissipation elements of a heat sink can be designed in a variety of ways, but here we will take a design based on graph theory as an example. In the design process (step S11), design values are calculated for each of the nodes and edges of the heat dissipation elements of the heat sink. The heat dissipation elements of the heat sink have a three-dimensional structure with a set of edges that connect a set of three-dimensionally arranged nodes. A node is a nodal point or vertex that constitutes the start point and end point of each heat dissipation element. An edge is a branch-like, side-like, linear, or columnar element that connects two nodes that constitute one heat dissipation element. The thickness of the edge and the cross-sectional shape perpendicular to the direction in which the edge extends can be set according to the specifications of the heat sink, the tolerances in the manufacturing process, etc.

The design values are calculated in the calculation device shown in FIG. 2, e.g., a computer, based on information input from the input unit 15 and design information previously stored in the memory unit 14, under the control of the control circuit 11. The information input from the input unit 15, the design information used in the calculation, the progress and results of the calculation, etc. are displayed on the display unit 16. In the calculation, for example, nodes connected by edges are selected in the calculation circuit 12, and the topology of the three-dimensional structure of the nodes is adjusted and optimized by the adjustment circuit 13 using a predetermined optimization algorithm, e.g., an optimization algorithm based on a population search. The calculation results by the calculation circuit 12 and the calculation results by the adjustment circuit 13 are stored in the memory unit 14 each time a calculation is performed, and are read out by the control circuit 11 during adjustment by the adjustment circuit 13.

Next, in the manufacturing data generation process (step S12), manufacturing data, for example CAD data, for modeling by additive manufacturing (AM modeling), for example modeling by a 3D printer, is generated based on the design values of the nodes and edges calculated in the design process (step S11). The manufacturing data is generated by the arithmetic circuit 12 under the control of the control circuit 11, based on the generation information previously stored in the memory unit 14, and the generated data is saved in the memory unit 14.

In the three-dimensional structure designed in the design process (step S11), an edge where one of the nodes is not supported by the base material of the heat sink or an edge on the lower layer constitutes an overhanging portion. For this reason, in the manufacturing data generation process (step S12), the overhanging portion is identified, and a support edge for supporting the overhanging portion by the base material or the edge on the lower layer is added to the manufacturing data. This ensures that the heat sink can be manufactured reliably in the subsequent additive manufacturing process (step S17).

Next, in the modeling process analysis step (step S13), mesh structure data is generated based on the manufacturing data generated in the manufacturing data generation step (step S12), and the shape deviation between the mesh structure data and the manufacturing data, and the maximum principal stress value at a predetermined position on the mesh structure data are calculated. The mesh structure data is generated by the arithmetic circuit 12 under the control of the control circuit 11, based on the generation information previously stored in the memory unit 14, and the generated data is saved in the memory unit 14.

In the modeling process analysis step (step S13), the inherent strain method is used to calculate the shape deviation between the mesh structure data and the manufacturing data, and the maximum principal stress value at a specified position on the mesh structure data.

The next molding defect diagnosis process (step S14) predicts the parts that will cause molding defects by exceeding the first predetermined range for shape deviation and the second predetermined range for maximum principal stress value, which are set to realize a three-dimensional structure corresponding to the design values, for the shape deviation and maximum principal stress value calculated in the molding process analysis process (step S13). The diagnosis of molding defects is performed by the arithmetic circuit 12 under the control of the control circuit 11 based on the diagnosis information previously stored in the memory unit 14, and the diagnosis result is saved in the memory unit 14.

If a modeling defect is diagnosed in the modeling defect diagnosis process (step S14) (YES in step S15), the modeling limit setting process (step S16) is executed, and then the design process (step S11), manufacturing data generation process (step S12), modeling process analysis process (step S13), and modeling defect diagnosis process (step S14) are executed until the modeling defect is eliminated.

In the modeling limit setting process (step S16), the modeling limits to be considered in the manufacturing data generation process are set based on the results of the modeling process analysis process and a predetermined range for the modeling limits in order to eliminate the modeling defects predicted in the modeling defect diagnosis process (step S14). The modeling limits are set by the arithmetic circuit 12 under the control of the control circuit 11 based on the setting information previously stored in the memory unit 14, and the setting results are saved in the memory unit 14.

If it is determined in the above-mentioned molding defect diagnosis process (step S14) that there is no molding defect (NO in step S15), the additive manufacturing process (step S17) is executed. In the additive manufacturing process (step S17), additive manufacturing is executed based on the manufacturing data at that time to manufacture the heat sink. For example, the manufacturing is performed by giving a manufacturing instruction signal corresponding to the manufacturing data to a 3D printer connected to the arithmetic unit shown in FIG. 2 based on the control of the control circuit 11, and molding is performed based on this signal. The overhang portion is removed after molding (step S18).

Next, in the heat transfer performance experiment process (step S19), a heat transfer performance experiment is performed on the heat sink manufactured in the additive manufacturing process (step S17) using a heat source in a natural convection environment. In the subsequent heat transfer performance analysis process (step S20), the heat transfer performance obtained in the heat transfer performance experiment is analyzed, and the analysis results are fed back to the design process (step S11) to improve the prediction accuracy of the heat transfer performance in the design process. The heat transfer performance experiment is performed using the experimental equipment described below (Figures 18 and 19), and the results are input to the calculation device shown in Figure 2, the heat transfer performance analysis is performed by the calculation circuit 12, and the analysis results are stored in the memory unit 14.

Next, in the inherent strain test process (step S21), an inherent strain experiment is performed by heating and cooling a test piece made of the material used for the heat dissipation element. In the subsequent inherent strain analysis process (step S22), the inherent strain value obtained in the inherent strain experiment is analyzed, and the analysis results are fed back to the modeling process analysis process (step S13) to improve the accuracy of defect diagnosis in the modeling process analysis process (step S13) and the subsequent modeling defect diagnosis process (step S14). The results of the inherent strain test are input to the calculation device shown in Figure 2, and inherent strain analysis is performed by the calculation circuit 12, and the analysis results are stored in the memory unit 14.

Next, a performance convergence judgment (step S23) is performed. For example, the total heat transfer amount (amount of heat) and volume of the manufactured heat sink are measured, and compared with the total heat transfer amount (amount of heat) and volume as the objective function when the topology is optimized in the design process (step S11), and it is judged whether or not each of them converges within a preset range. The judgment is performed by changing the object to be measured, for example, the total heat transfer amount and the volume, according to the objective function in the design process (step S11). The performance convergence judgment is performed by the arithmetic circuit 12 under the control of the control circuit 11 based on judgment information including the set range that is pre-stored in the memory unit 14, and the diagnosis result is saved in the memory unit 14.

If the total heat transfer amount and volume have converged within the set range in the performance convergence judgment (step S23) (YES in step S24), it is determined that a heat sink with optimized topology has been manufactured, and the manufacturing process is terminated.

On the other hand, if the performance convergence determination (step S23) determines that the total heat transfer amount and volume have not converged within the set range (NO in step S24), it is determined that the performance has not converged, and the design process (step S11) is performed again based on the measured total heat transfer amount and volume.

<Heat sink configuration>
As described above, the heat sink according to the present embodiment has a three-dimensional structure, and has a three-dimensional lattice structure in which multiple layers are stacked in the out-of-plane direction of the surface of the substrate, for example, in the normal direction of the surface. In a configuration stacked along the normal direction, a set of nodes arranged on a plane perpendicular to the normal direction forms one layer. In the three-dimensional lattice structure, the edges in the central part have a higher edge arrangement density than the outer part in the plane direction of the surface as the layer is further away from the substrate. Here, when looking at the change in edge arrangement density from the layer closest to the substrate to the furthest layer, the edge arrangement density in adjacent layers above and below is also included. The arrangement density being the same means that the density has the same numerical value, as well as that the difference in density is small enough that the air inside the heat sink, which is warmed by being close to the heat source, does not change the direction or flow rate of the air flow flowing vertically upward.

In the three-dimensional lattice structure, the first ventilation hole is formed in the farthest layer farthest from the substrate, and the second ventilation hole is formed in the outer part of the layer closer to the substrate than the farthest layer. For example, in the case of a three-layered structure, the second ventilation hole is provided in one or both of the layer closest to the substrate and the layer farthest from this layer. More specifically, in the three-dimensional lattice structure shown in Figures 9 to 11, a plurality of voids that become the first ventilation hole Gt are provided in the farthest layer L3 that is farthest from the substrate 20 in the normal direction Dn. Also, in the layer L1 that is closest to the substrate 20, voids that become the second ventilation hole Gb are provided in the outer part, that is, in the range corresponding to each of the four sides of the substrate 20 that forms a square when viewed from above in the normal direction Dn. The first ventilation hole Gt is formed in quadrangular symmetry when viewed from above in the normal direction Dn, and the second ventilation hole Gb is also formed in quadrangular symmetry.

In a heat sink with a three-dimensional lattice structure as described above, depending on the posture, which differs depending on the object, orientation, method, etc. to be installed, air heated by a heat source close to the heat sink is released from the first ventilation opening Gt or the second ventilation opening Gb, whichever is higher in the vertical direction, and surrounding air flows in from the first ventilation opening Gt or the second ventilation opening Gb, whichever is lower in the vertical direction.

For example, when a heat sink is placed flat with the stacking direction of its multiple layers aligned vertically, air heated by a heat source close to the heat sink is released from the first ventilation opening Gt of the farthest layer, and air flows in through the second ventilation opening Gb.

On the other hand, when the heat sink is placed vertically so that the stacking direction of its multiple layers is horizontal, air heated by a heat source close to the heat sink is released from the first ventilation opening Gt or the second ventilation opening Gb, whichever is higher in the vertical direction, and air flows in from the first ventilation opening Gt or the second ventilation opening Gb, whichever is lower in the vertical direction.

The overhang portion H is formed in any layer from the layer immediately above the layer closest to the substrate to the layer furthest from the layer closest to the substrate. The position of the overhang portion H corresponds to the position of the second ventilation port Gb, and the gap formed by the overhang portion H increases the opening area of the second ventilation port Gb, and the flow rate of air passing through the second ventilation port Gb is increased.

<Design process (step S11)>
The arrangement of a set of nodes connected by a set of edges can be performed by various methods. For example, by selecting a set of nodes and a set of edges based on the graph theory described below and using a population search-based optimization algorithm in combination with response surface methodology, it is possible to adjust the topology of a three-dimensional structure and optimize the topology.

As a population search-based optimization algorithm, any algorithm can be used, for example, the genetic algorithm described below, as well as the memetic algorithm, path recombination method, ant colony method, particle swarm optimization, and differential evolution method.

The set of nodes can be one in which the nodes are distributed in a three-dimensional space, or one in which some or all of the nodes are arranged at any position on the substrate. The shape of the substrate is not particularly limited, but examples include a plate with a flat surface, a shape with a curved surface, a sphere, a hemisphere, and the like. Furthermore, arranging the nodes on the substrate can include arranging the nodes on the surface of the substrate, as well as on the back surface, side surface, or inner surface opposite the surface.

When some nodes are placed on the substrate, the remaining nodes are placed in three-dimensional space away from the substrate. The edges are set to extend in any out-of-plane direction relative to the surface of the substrate. Here, the out-of-plane direction of the substrate surface means the direction away from the surface, and more specifically, for nodes placed on the substrate surface, the direction away from the surface at the placement position. In addition, the out-of-plane direction can be the same for all nodes placed on the substrate surface, but it may also be different for some or all of the nodes placed on the surface.

In the configuration in which some of the nodes are arranged on the substrate as described above, the remaining nodes can be arranged so that multiple layers are stacked in the out-of-plane direction of the substrate surface, forming a three-dimensional lattice structure (grid-like structure) as a whole. The number of layers can be set as desired.

The shape of the substrate in plan view from the normal direction of the surface can be any shape as long as the topology of the three-dimensional structure is adjusted. Examples of such plan view shapes include squares, triangles, other regular polygons, and circles.

Furthermore, in a configuration in which some of the nodes are arranged on the substrate, the set of edges is composed of a first edge that starts at a node arranged on the surface of the substrate, and a second edge that is connected to the first edge directly or via another edge. In a three-dimensional lattice configuration in which the set of nodes is arranged so that multiple layers are stacked in the out-of-plane direction of the substrate surface, the first edge and the second edge are each set to extend at a predetermined angle or less, for example, 45 degrees or less, with respect to the stacking direction.

The above topology is adjusted to maximize or minimize based on an objective function related to the heat sink. The number of objective functions can be set arbitrarily depending on the specifications of the heat sink, etc. Examples of objective functions include an index representing the heat dissipation efficiency of the heat sink, an index representing the material cost of the heat sink, and an index representing the thermal fluid performance related to the heat sink. These indices can be used alone as objective functions, or two or more can be used in combination. When an index representing the heat dissipation efficiency of the heat sink is used, the topology is adjusted to maximize this index, and when an index representing the material cost of the heat sink is used, the topology is adjusted to minimize this index. The index representing the thermal fluid performance is adjusted to maximize, for example, the flow rate per unit time.

Indicators representing the heat dissipation efficiency of a heat sink and thermal fluid performance related to the fluid associated with the heat sink include, for example, the total heat transfer amount Q of the heat sink, the temperature gradient, and the shape ratio (intake/exhaust ratio) between the vent at the bottom of the heat sink and the vent at the top of the heat sink, while indicators representing the material cost of the heat sink include the volume V of the material constituting the heat sink and the unit price of the material. The respective indicators are not limited to the above examples, and for example, the volume V of the material may be used as an indicator of the heat dissipation efficiency of a heat sink. Also, each indicator can be combined in any ratio. The total heat transfer amount Q is evaluated, for example, with the base material as the heat source and air as the working fluid.

When considering the manufacture of the heat sink, it is preferable that the topology adjustment also includes the identification of the modeling limits for the design values of the set of nodes and the set of edges. When the heat sink is manufactured by a 3D printer or other additive manufacturing, the identification of the modeling limits in additive manufacturing is included, and for example, feedback based on experimental results of the heat transfer performance and inherent distortion of the heat sink manufactured by additive manufacturing is included.

As a response surface methodology used to adjust the topology, for example, the Kriging model can be used.

In this embodiment, a heat sink used to remove heat from electronic devices such as computers is designed by topology optimization. Although many previous studies have focused on improving the performance of heat sinks, here we also focus on material costs and tackle multi-objective optimization. In the past, the inventors have considered the two-dimensional extrusion structure of heat sink fins as a structure similar to natural objects (such as tree branches, plant veins, and bronchi), and expressed this using a recursive data format grammar called Lindenmayer Systems (L-systems). Through multi-objective optimization, they have created a new heat sink that has equivalent performance to existing designs but can significantly reduce material costs.

In contrast, this embodiment focuses on the three-dimensional lattice structure of the heat sink and represents it using graph theory to achieve multi-objective optimization of more complex and fine heat sinks.

<Graph Theory>
Graph theory is a theory that abstracts how nodes are connected by a set of nodes (junctions, vertices) and a set of edges (branches, sides) that connect them. For example, when looking at a route map for a train or bus, the issue is how the stations (nodes) are connected by the routes (edges), but the specific curves of the tracks are often not an essential issue. In other words, the main important information is how the stations are connected, and this is the role of graph theory.

Here, an example of a pattern of grooves (micromixers) carved into a flow channel expressed by graph theory is shown in Figures 3(a) and (b). If the groove pattern shown in Figure 3(b) is expressed as edges connecting 3 x 3 = 9 nodes as shown in Figure 3(a), the total number of edges when all nodes are connected is _9C2 = 36. This graph is expressed using the following ₉ x 9 adjacency matrix A.

In the adjacency matrix A, A _ij =1 means that an edge connecting nodes i and j exists, and A _ij =0 means that there is no edge. Also, the diagonal terms represented by A _ij =. have no meaning. In this example, edges that do not affect the mixing efficiency, specifically, nine grooves parallel to the flow direction and represented by A _ij =*, can be excluded, so that 27 edges ultimately remain. In other words, the groove pattern can be expressed by 27 parameters (design variables).

<Definition of the optimization problem>
In this embodiment, the three-dimensional lattice structure of the heat sink is expressed as edges connecting 7×7×3=147 nodes (node spacing=8.3 mm) as shown in FIG. 4(a). In other words, the nodes arranged in 7×7 are stacked in three layers on the surface 21 of the base material 20 in the stacking direction Ds along the normal direction Dn of the surface 21. Considering the symmetry of the flow occurring in the flat-laid heat sink, the design area can be reduced to 1/8 (10 nodes, represented by light gray areas) in each layer (7×7=49 nodes) as shown in FIG. 4(b). Furthermore, the first and second layers (10×2=20 nodes, represented by large circles P1) and the second and third layers (10×2=20 nodes, represented by small circles P2) are designed independently.

As shown in Fig. 4(c), from _{the 20C2} = 190 edges connecting each layer, only 34 edges are left that can be molded, i.e., the angle between them and the stacking direction Ds is 45 degrees or less, as shown in Fig. 4(d). As a result, 34 x 2 = 68 edges remain. Therefore, a 3D lattice structure can be expressed by 68 design variables.

The design variables are given as real numbers between 0 and 1, and when they are between 0 and 0.2 it is determined that there is no edge, and when they are between 0.2 and 1 it is determined that there is an edge. Each edge is replaced with a solid cylinder with a diameter of 2.6 mm. By cutting off the part that protrudes from the design domain (50 mm x 50 mm x 15 mm) and attaching a base part 30 (50 mm x 50 mm x 6 mm) to the bottom, solid data such as that shown in Figure 4 (e) can be obtained.

The objective functions include an index representing the heat dissipation efficiency as a performance of the heat sink, and an index representing the material cost. In this embodiment, the topology is maximized based on the total heat transfer amount Q, and is minimized based on the lattice volume V (volume of the three-dimensional lattice structure). The total heat transfer amount Q is evaluated by thermal fluid analysis, and the lattice volume V is replaced with the total edge length and analytically evaluated using a self-made code. In addition, a constraint is taken into account that all edges are connected to the base portion 30 so that all edges contribute to heat transfer.

In this embodiment, a genetic algorithm (hereinafter referred to as "GA"), which is a population search-based optimization algorithm that simulates the evolution of living organisms, is used as a calculation method for optimization. GA can be applied to various optimization problems regardless of the nature of the objective function (differentiability, nonlinearity, multimodality, etc.), and is expected to discover a global optimum without falling into a local optimum. GA is a powerful solution method for thermo-fluid dynamics problems described by nonlinear governing equations, which are the subject of this embodiment, and optimization problems in which performance changes sensitively (i.e., multimodal) due to changes in the topology of the structure. A wide variety of GAs have been proposed so far, but here we use Non-Dominated Sorting Genetic Algorithm II (hereinafter referred to as "NSGA-II"), which is the most famous in the world and has many performance verifications and applications.

On the other hand, GA requires the evaluation of the objective function for a large number of solutions that make up the population, so the total cost required for optimization calculations is enormous. In particular, when evaluating the objective function using large-scale numerical calculations such as thermal fluid analysis, using GA alone is not realistic in terms of calculation costs. Therefore, in order to reduce calculation costs, a response surface (also known as a surrogate model) is used in combination (response surface methodology). A response surface is an approximation of the response of f(x), which is a black box, as the algebraic formula B shown below, by learning sample data of the output (objective function) f(x) in response to the input (design variable) x.

By using algebraic formula B, the output value for any input value can be instantly estimated, which can significantly reduce the calculation time required for objective function evaluation and the entire optimization. However, since the response surface is only an approximation of the objective function, and any errors that occur there will affect the quality of the optimal solution ultimately obtained, approximation errors must be handled carefully during the solution search process.

In this embodiment, the Kriging response surface is used as the response surface. While other response surfaces model only the algebraic expression B, which is an approximation of the objective function f(x), Kriging can model both the approximation (algebraic expression B) and its uncertainty, i.e., the approximation error (shown in the following equation).

By referring to the information on the uncertainty C, it is possible to probabilistically identify the position on the response surface where the global optimum is expected to exist. Here, for the objective function f(x) to be maximized, the expected improvement EI[f(x)] (Expected Improvement) of the objective function from the optimum value _fmax of the objective function found up to now is calculated by the following formula:

Here, F is a probability distribution that follows a normal distribution with mean B and variance C, and PDF(F) is the probability density distribution of F. Instead of maximizing the original objective function f(x), a solution x* that maximizes the expected value EI[f(x)] on the Kriging response surface is searched for by optimization calculation. The objective function f(x*) evaluated at this x* is added as new sample data, and the Kriging response surface is then updated. By repeatedly adding sample data in this manner, it is possible to simultaneously search for a global optimum solution and improve the accuracy of the response surface.

The procedure for optimization calculation in this embodiment is shown in Figure 5. The first objective function, the total heat transfer amount Q, is evaluated by thermal fluid analysis when sample data is given, and is approximately evaluated using the Kriging response surface under other conditions. The second objective function, the lattice volume V, is replaced with the total edge length and analytically evaluated using a self-made code.

In the procedure shown in FIG. 5, first, initial sample data (total of 98 points) is created uniformly within the 68 design variable space using Latin Hypercube Sampling (LHS) (step S31). Then, heat sink structural data corresponding to each point is created and Q is evaluated using thermal fluid analysis, after which a Kriging response surface that approximates Q is constructed (step S32).

Next, the Pareto optimal solution that maximizes EI[Q] estimated on the Kriging response surface and minimizes the volume V (analysis value of the entire edge length) is searched for using NSGA-II (population size 200, number of generations 200, mutation rate approximately 1.5%) (step S33). Here, the Pareto optimal solution means a solution that is not inferior to any other solution for all objective functions. From the countless Pareto optimal solution sets obtained in the two-objective function space, thermal fluid analysis is performed on two limit solutions, the maximum solution of expected value EI[Q] and the minimum solution of volume V, and the three solutions closest to the centers of gravity when the remaining solution set is divided into three by the K-means method, and these results (up to a total of five points) are added to the sample data, and the Kriging response surface is updated (step S34). By repeating the above update work, the Pareto optimal solution is efficiently searched for with the minimum number of thermal fluid analyses (i.e., the number of sample points).

Next, a convergence determination is performed (step S35). For example, the convergence determination is performed by determining whether EI[Q] has converged to be less than a predetermined threshold value, or whether the topology of the shape of the edge heat dissipation element has ceased to be updated and convergence has occurred.

If it is determined that convergence has not occurred (No in step S35), a sample is added to the current sample point and the Kriging model is updated (step S31).

On the other hand, if it is determined that convergence has occurred (Yes in step S35), the optimization process ends. By following the above procedure, it is possible to efficiently search for a Pareto solution with the minimum number of iterations required.

<Thermal fluid analysis>
The thermal fluid analysis is performed in the region A1 and boundary conditions shown in a cube in FIG. 6. The working fluid is air. The bottom surface of the heat sink (bottom surface Ab of region A1) is used as the heat source, and a constant temperature of 323.15 K is given as the first type boundary condition. Around region A1, a third type boundary condition (293.15 K) is set so that heat is sufficiently dissipated. Here, the Boussinesq approximation is used to model natural convection. The total heat transfer amount Q of the heat sink is evaluated using the pressure-based solver of the commercially available fluid analysis software "ANSYS Fluent 2019 R1.2". The governing equations are the continuity equation, the steady incompressible Navier-Stokes equation, and the steady energy equation. In addition, the pseudo-unsteady algorithm of the pressure-based coupled solver is enabled using the Pseudo Transient method. As a result, an unsteady term is efficiently added to the governing equation, improving stability and convergence. Table 1 shows the calculation scheme used in this embodiment.

The computational grid for thermal fluid analysis is generated using the cut cell method (minimum element size 0.2 mm). Compared to common object-fitting grid methods, the cut cell method can automatically generate grids even for complex structures explored during topology optimization. Also, unlike the Cartesian grid method, which represents the object surface with simple stepped cells, the cut cell method cuts cells that intersect with the object surface to extract a grid that follows the object, and has the characteristic that conservation laws are satisfied because the inspection volume is defined even next to walls.

<Results and Discussion>
FIG. 7 shows a scatter diagram of the initial sample data (point P11) and the additional sample data searched by the optimization calculation, plotted in the objective function space (horizontal axis: total heat transfer amount Q (unit: W), vertical axis: volume V (unit: ^m3 )). The additional sample data are (a) the result of two-objective optimization (point P12) of maximizing the total heat transfer amount Q and minimizing the volume V (response surface updated 10 times), and (b) the result of one-objective optimization (point P13) of maximizing only the total heat transfer amount Q (response surface updated 18 times). In the two-objective optimization (a) above, the response surface was updated 10 times, and in the one-objective optimization (b) above, the response surface was updated 18 times.

Among these sample data, the heat sink of the embodiment that is the Pareto optimal solution is indicated by a small circle P14. In addition, as a comparative example, a ready-made heat sink (21F50) with comb-tooth shaped heat dissipation elements and a two-dimensional fin structure formed by extrusion molding, as shown in Figure 8, is indicated by point P15. The heat sink indicated by point P15 has the same size as the heat sink of the embodiment that is the Pareto optimal solution, as shown by point P14, with a fin section of 50 mm x 50 mm x 15 mm and a base section of 50 mm x 50 mm x 6 mm. Furthermore, data for a structure with lattices arranged on all edges (full lattice structure) as shown in Figure 4(e) is also plotted as point P16.

As shown in FIG. 7, the two-objective optimal solution (point P14) has improved both the total heat transfer amount Q and the volume V compared to the initial sample data (P11). For example, the two-objective Pareto optimal solution with the largest Q (09-001, meaning the first additional sample data obtained in the ninth update) (hereinafter referred to as the sample name "Lattice3") has improved (increased) the total heat transfer amount Q by 22% and reduced (decreased) the volume V by 53% compared to the ready-made product (P15). In addition, the distribution of the additional sample data (point P14) by two-objective optimization showed that there is a trade-off relationship between maximizing the total heat transfer amount Q and minimizing the volume V. Next, when we look at the point (14-001) with the largest total heat transfer amount Q among the one-objective optimal solutions (point P13), it is located near the sample of the two-objective optimal solution (09-001) (the sample shown in FIG. 9). From this, we can say that the two-objective optimal solution (09-001) has roughly reached the design limit for maximizing the total heat transfer amount Q, in other words, it is impossible to maximize the total heat transfer amount Q any further.

Next, a representative optimum solution and a ready-made product will be described. The structure of the heat sink and visualization of the flow field generated by the heat sink are shown in Figs. 8 to 11. Fig. 8 shows a ready-made product (shown as sample name "21F50" in Fig. 7) in which multiple plate-like fins F are arranged parallel to each other, and Figs. 9 to 11 show a two-objective optimum solution with a three-dimensional lattice structure. The sample shown in Figs. 9 to 11 has a three-dimensional lattice structure in which a heat dissipation element with a set of edges E has three layers L1, L2, and L3 stacked in order from the substrate 20 side in the normal direction Dn of the surface 21 of the substrate 20. Furthermore, when this sample is viewed along the normal direction Dn of the surface 21 of the substrate 20, it has a quadrilaterally symmetrical shape that is symmetrical with respect to the four directions D1, D2, D3, and D4 corresponding to the four sides of the square substrate 20.

Figure 9 shows the first piece of additional sample data obtained in the ninth update (shown as "sample name 09-001" in Figure 7), Figure 10 shows the first piece of additional sample data obtained in the eighth update (shown as "08-001" in Figure 7), and Figure 11 shows the second piece of additional sample data obtained in the tenth update (shown as "10-002" in Figure 7).

In each of Figures 8 to 11, (a) is a perspective view showing the overall shape of the sample, and (b) to (d) show the heat distribution in the range described below. The higher the density of the black, the higher the temperature.

In FIG. 8, (b) shows the heat distribution in a height range close to the substrate 120 in the normal direction Dn of the substrate 120, (c) shows the heat distribution in an intermediate height range between the range shown in (b) and the range shown in (d), and (d) shows the heat distribution in the highest range.

In each of Figures 9 to 11, (b) shows the heat distribution in the lower layer of the lattice structure, i.e., the first layer L1 and second layer L2 on the substrate 20 side, (c) shows the heat distribution in the upper layer of the lattice structure, i.e., the second layer L2 and third layer L3, and (d) shows the heat distribution in the third layer L3 (the farthest layer).

In the ready-made product (sample name: 21F50) shown in Figure 8, the surrounding cold air enters the heat sink along the gaps between adjacent fins F, i.e., from only two directions Da and Db along the direction in which the fins F extend, and as can be seen from (b), (c), and (d), the air that is heated by heat from the heat sink rises away from the base material 120. In the ready-made product shown in Figure 8, air is taken in only from the directions Da and Db that correspond to the two sides of the square-shaped base material 120 in a plan view along the normal direction Dn of the base material 120, so the heat absorption and dissipation performance is easily affected by the posture and direction in which the heat sink is attached.

On the other hand, in the dual-objective optimized solution shown in Figures 9 to 11, the heat sink structure is symmetrical in all four directions, D1, D2, D3, and D4, which correspond to the four sides of the base material 20, so that the surrounding cold air is taken in from all four directions D1, D2, D3, and D4, which correspond to the four sides of the base material 20. As shown in (b) and (c) of each figure, the taken-in air is heated in the center and is released from the third layer L3 as shown in (d). From this, it can be seen that the mounting direction has less effect on the performance of the optimized heat sink shown in Figures 9 to 11 compared to the ready-made product shown in Figure 8, and it can be said that a robust design has been achieved.

Furthermore, the dual-objective optimal solutions in Figures 9 to 11 are compared. A common configuration of these lattice structures is that there are gaps Gb (intakes, vents) on the sides of the first layer L1 to second layer L2, which are the lower layers of the lattice structure, and the lattice is dense in the center of the second layer L2 to third layer L3, which are the upper layers of the lattice structure. The arrangement density of the edges E is higher in the center than in the outer parts of the surface direction of the surface 21 of the substrate 20 in the layers farther from the substrate 20, that is, from the first layer L1 to the third layer L3. In addition, the third layer L3 has gaps Gt (vents) that open upward in the normal direction Dn of the substrate 20.

The above-mentioned intakes (gap Gb) allow the surrounding cold air to be taken in from all four sides of the heat sink (four directions D1 to D4), which is thought to ensure that air can reach the center of the heat sink sufficiently. In contrast, in the ready-made product shown in FIG. 8, the intakes are only at positions corresponding to two sides of the base material 120, which is rectangular in plan view, and depending on the surrounding air flow, it is possible that air will only flow in from one of the intakes, so it is not easy for the air taken in from the surroundings to reach the center of the heat sink.

In the heat sink of the dual-objective optimal solution shown in Figures 9 to 11, dense lattices are concentrated in the center where most of the air passes so that the air taken in can sufficiently remove heat from the heat sink. This prevents the air that has entered from escaping through the gap Gb (intake) and makes it easier to form a flow toward the third layer L3, making it easier to release the warm air that has removed heat from the heat sink to the outside through the third layer L3, which is thought to be a significant effect on improving heat dissipation performance. Furthermore, in the heat sink of the dual-objective optimal solution shown in Figures 9 to 11, the layer below the lattice structure has a gap Gb (vent) as an intake, and while satisfying the configuration in which the lattices are densely arranged in the center of the third layer L3, the lattices can be appropriately thinned out to adjust the balance between performance (Q) and material cost (V). In addition, in the dual-objective optimal solution shown in Figures 9 to 11, an overhang portion H is formed, which contributes to increasing the opening area of the gap Gb.

In contrast, the existing product shown in Figure 8, as mentioned above, makes it difficult for the incoming air to reach the center, and does not have a structure to suppress the air flow in the center and make it easier for the air to escape upwards. Therefore, near the intake, the air that has flowed in from the periphery and the air that has been warmed inside the heat sink mix, and the air flow stagnates, making it difficult to achieve sufficient heat dissipation performance.

As described above, in this embodiment, multi-objective optimization was performed on the three-dimensional lattice structure of the heat sink, aiming at improving performance and reducing material costs. As a result, the optimization calculations could be efficiently realized by optimizing the lattice structure expressed by graph theory using GA and Kriging response surfaces in combination. Furthermore, a three-dimensional lattice structure was found that can improve performance and reduce material costs compared to existing products (two-dimensional extrusion fin structures). This three-dimensional lattice structure is innovative in that it combines heat dissipation performance with low material costs, something not seen in conventional heat sinks. Furthermore, the characteristics of the lattice structure for improving performance and the thermal fluid phenomena that support it were identified.

<Modeling process analysis (step S13), modeling defect diagnosis (step S14)>
The simulation of the modeling process analysis (step S13) and the modeling defect diagnosis (step S14) will be described with reference to FIGS.
In this embodiment, a modeling simulation calculation and analysis were performed for the case where a heat sink having a heat dissipation element made of an aluminum alloy was modeled by a 3D printer based on the manufacturing data generated in the manufacturing data generation process (step S12). For the simulation calculation and analysis, stress analysis software corresponding to the simulation of a metal additive manufacturing process was used.

Figures 12(a) and (b) show the appearance of the model used in the above simulation, with (a) being a perspective view from the side and (b) being a perspective view from above. This model is a sample (09-001, Lattice 3) shown in Figure 9, with supports S provided as supporting edges that support the overhanging portion H from the substrate 20 side. Supports S are provided at 12 locations indicated by circled numbers in Figure 12(b).

In the above stress analysis software, the shape of the external shape of the object is approximated by a voxel mesh (a collection of regular hexahedral elements). In this embodiment, the voxel mesh was created with a size of 0.2 mm on each side. The total number of voxel meshes was approximately 2.83 million.

The simulation calculations were performed in the following order: (1) molding, (2) separation from the base plate, and (3) removal of support S.

(1) In the modeling process, voxel meshes are layered from the surface of the substrate 20 (base plate). The inherent strain was determined using values obtained from an inherent strain identification test and calibration using the above-mentioned stress analysis software.

(2) Separation from the substrate 20 was a procedure in which the molded object was separated from the substrate 20 after the above-mentioned modeling was completed. The separation position was the boundary between the molded object and the base plate. The effect of the wire diameter on the separation was not taken into consideration.

(3) The support removal was carried out by removing the support S after the object was separated from the substrate 20.

Figures 13(a), (b), and (c) are perspective views showing the shaping process. Figure 13(a) is a diagram showing the shaping process, and (b) is a diagram showing the shape after removal of supports S has been completed, with the deformation magnification displayed as 10. Figure 13(c) is a diagram comparing the shape in the state of Figure 13(b) with the shape of the data (CAD data) generated in the manufacturing data generation process (step S12), superimposed, with the distribution of shape deviations shown by shades of color. In Figure 13(c), the deviation is at most about 0.04 mm, and the amount of deformation is kept small compared to the manufacturing data. There was almost no change in shape during the support removal process.

14(a), (b), (c), (d) and FIG. 15 are diagrams showing the maximum principal stress distribution during molding, where the normal direction (stacking direction) of the substrate 20 is the Z direction, and the directions corresponding to the two mutually perpendicular sides of the rectangular substrate 20 in a plane perpendicular to the Z direction are the X direction and the Y direction, respectively. FIG. 14(a) is a cross-sectional view of the cross-sectional area A perpendicular to the Y direction, (b) is an enlarged view of (a), (c) is a cross-sectional view of the cross-sectional area B perpendicular to the X direction, and (d) is an enlarged view of (c). FIG. 15 is an enlarged view of the cross-sectional area A as viewed along the arrow AL in FIG. 14(a), and the value of the maximum principal stress (tensile component) is shown in the figure. In FIG. 14(a), (b), (c), (d) and FIG. 15, the difference in the strength of only the tensile component of the maximum principal stress is expressed by the color density.

By comparing the maximum value of the maximum principal stress with the tensile strength of the material, the possibility of breakage during molding can be investigated. In the molding of this embodiment, tensile stress exceeding the tensile strength (about 460 MPa) of a general AlSi10Mg alloy (JIS standard H5202) was generated in a part of the base material 20 (base) and the base of the edge E (branch). The value was a maximum of 574 MPa, which is 1.25 times the tensile strength, and it can be seen that the occurrence of tensile stress is also suppressed because the deformation also decreases with the decrease in inherent strain. In addition, the tensile stress is high only in a part of the base of the edge E (branch). Compared to the tensile strength of a general AlSi10Mg alloy (about 460 MPa), it can be suppressed to 1.25 times.

As shown in Figure 15, it was confirmed that during molding, a maximum tensile stress of approximately 570 MPa acts at the base of the edge E (branch) of the molded object, which exceeds the tensile strength of a typical AlSi10Mg alloy of 460 MPa.

It was found that locations where tensile stress is high have the following characteristics (1) to (3).
(1) The root of edge E (branch) parallel to the XZ cross section.
Due to the inherent strain used, it shrinks more in the Y direction than in the X direction, so the stress is higher at the base parallel to the XZ cross section than at the YZ cross section.

(2) Overhanging portions H are adjacent to each other, and the distance to the intersection (node) between edges E and E is long.
It is believed that the overhanging portion H is supported by a pillar called a support S, which weakens its rigidity. In addition, the edge E of the corresponding portion is farther from the node, so it is believed to have weaker rigidity than other portions.

(3) There is a free branch.
There is an edge E that extends vertically in the center, but it is not connected to the node at the top and is in a free state. Furthermore, the edge E that extends individually from the center has a long distance to the node. Therefore, it is considered that the rigidity is weaker than other parts.

From the above results, the shape after the support S has been removed, i.e., the shape of the molded product, had a maximum shape deviation of about 0.04 mm from the CAD shape (manufacturing data). It was found that if no breakage problems occurred during molding, a shape equivalent to the CAD shape could be obtained. It was also confirmed that during molding, a tensile stress of up to about 570 MPa, which exceeds the tensile strength of a typical AlSi10Mg alloy of 460 MPa, acts on a part of the base of the edge E of the molded product. Furthermore, except for the base of the base 20 and the edge E, the tensile stress was generally lower than the tensile strength. From the above, it can be inferred that the risk of breakage can be reduced by providing a rounded (R) to the base of the edge E attached to the base 20 (base).

<Heat transfer performance experiment (step S19), heat transfer performance analysis (step S20)>
The heat transfer performance experiment (step S19) and the heat transfer performance analysis (step S20) will be described with reference to Figs. 16 to 20. Figs. 16(a) and (b) are diagrams showing the external appearance of the model that is the subject of the heat transfer performance experiment. The model shown in Figs. 16(a) and (b) corresponds to the sample (09-001, Lattice 3) shown in Fig. 9.

Figures 17(a), (b), (c), and (d) are visualizations of the thermal boundary layer (internal space and surrounding temperature field of the heat sink). Figures 17(a) and (b) show the case of the sample (09-001, Lattice 3) shown in Figure 9, and (c) and (d) show the case of the ready-made heat sink (21F50) shown in Figure 8. Figures 17(a) and (c) are visualizations of the thermal boundary layer in the actual heat sink using an interferometer, and Figures 17(b) and (d) are results obtained by numerical calculation. As can be seen from Figures 17(a), (b), (c), and (d), in sample Lattice 3, high-temperature air is emitted from the center of the farthest layer (the top layer in Figures 17(a) and (b)). In addition, the outer edge of the layer on the substrate side (the bottom layer in Figures 17(a) and (b)) is low temperature, and it can be seen that outside air flows in from this part and is released from the farthest layer, resulting in efficient circulation.

Figures 18(a), (b), and (c) are diagrams showing the device configuration when conducting a natural convection cooling experiment as a heat transfer performance experiment with the heat sink placed vertically, and Figure 19 is a diagram showing the device configuration when conducting a natural convection cooling experiment as a heat transfer performance experiment with the heat sink placed flat. Figures 18(a) and 19 are side views of the internal configuration, Figure 18(b) is a front view (viewed from the right side of Figure 18(a)), and Figure 18(c) is a perspective view seen from above. In Figures 18(a), (b), (c), and 19, the vertical direction is indicated as the Z direction.

18(a), (b), and (c), an aluminum block 42 made of aluminum is placed horizontally in a heat insulating material 41 that is placed horizontally, that is, extending in the X direction (the left-right direction in FIG. 18(a)). The aluminum block 42 is placed so that a first end face 42a, which is one end face in the X direction, is flush with one end face 41b in the longitudinal direction of the heat insulating material 41, and a second end face 42b, which is the other end face, is placed inside the heat insulating material 41. A heat sink 44 is fixed in a vertical position to the first end face 42a of the aluminum block 42, and a heater 43 is fixed to the second end face 42b as a heat source. The heater 43 generates heat by driving a power source 45 placed outside the heat insulating material 41.

Thermocouples are arranged in three positions, TC ₁ , TC ₂ , and TC ₃ , in the X direction on the aluminum block 42. Furthermore, thermocouples are also arranged in two positions, TC _b and TC _f , in the base material portion and the farthest layer portion of the heat sink 44, in the X direction, and at a position TC _∞ outside the heat sink 44. The detection results by each thermocouple are output to a circuit not shown.

In the configurations shown in Figures 18(a), (b), and (c), airflow is supplied to the heat sink 44 as natural convection in the direction indicated by the arrows. The airflow velocity is 6.78 ± 0.02 m/s.

The configuration shown in FIG. 19 is the same as the configuration shown in FIG. 18(a), except that the heat insulating material 41 is placed vertically so that the heat sink 44 is located vertically above, and the heat sink 44 is placed flat.

Figure 20 is a graph showing the relationship between temperature and vertical position in Figure 19, obtained in a natural convection cooling experiment with the heat sink 44 laid flat using the device shown in Figure 19. The position shown on the horizontal axis is set with the position where the heater 43 is installed as the origin, and the numerical value increases the further up in Figure 19, with positions 0 to 90 mm corresponding to the aluminum block 42, and positions 90 mm to approximately 123 mm corresponding to the heat sink 44. In Figure 20, the results for sample Lattice 3 are shown with circles, and the results for a ready-made heat sink (21F50) used as a reference are shown with diamonds.

As shown in Figure 20, in sample Lattice 3, similar to the reference heat sink, no sudden change is observed between the temperature gradient in the aluminum block 42 and the temperature gradient in the heat sink 44. Therefore, it can be seen that in sample Lattice 3, high heat transfer performance from the aluminum block 42 to the heat sink 44 is achieved under natural convection, at the same level as the reference.

As shown in Figure 19, the heat quantity was 5.92 W when sample Lattice 3 was placed flat, and 5.18 W when heat sink 44 was placed vertically as shown in Figure 18. Although a graph like that of Figure 20 is not shown here, it was confirmed that when heat sink 44 was placed vertically as in Figure 18, there was no sudden change in the temperature gradient within aluminum block 42 and the temperature gradient within heat sink 44, just as in the case of placing it flat, and heat transfer performance equivalent to that of placing it flat was achieved. This shows that sample Lattice 3 is capable of achieving stable heat dissipation performance regardless of the installation position.

<Inherent Distortion Test (Step S21), Inherent Distortion Analysis (Step S22)>
In actual additive manufacturing, material shrinks due to heating by laser irradiation and cooling. This shrinkage rate is not constant, but changes in relation to the direction of laser irradiation. In stress analysis software that supports simulations of metal additive manufacturing, this shrinkage rate is parameterized as "intrinsic strain" and calculations and analysis are performed by replacing simulations related to thermal phenomena with mechanical simulations.

Inherent strain varies depending on additive manufacturing parameters and materials. To perform accurate calculations and analysis, it is necessary to identify the inherent strain. Here, we conducted an experiment to identify the inherent strain to be used in the calculations and analysis of actual molding (hereinafter referred to as "intrinsic strain testing") and obtained the inherent strain to be used in the molding simulation.

The inherent strain test and inherent strain analysis can be carried out, for example, by the following steps (1) to (3).
(1) A test piece is created using additive manufacturing (AM modeling), and the amount of deformation caused by residual strain is measured.
(2) Using the above-mentioned stress analysis software, the same test piece as in (1) is fabricated under the same conditions as in (1), and the inherent strain value is calibrated until the deformation amount coincides with the result of (1).
(3) The inherent strain value obtained in (2) is incorporated into the material properties of the AlSi10Mg alloy and applied to the subsequent molding process analysis for the heat sink shape.

In the inherent strain analysis, the test piece shape, material properties, and deformation amount are given as input to the stress analysis software, and the inherent strain value is obtained as output by performing calibration using the stress analysis software. The obtained inherent strain value is fed back to the modeling process analysis step (step S13).

REFERENCE SIGNS LIST 11 Control circuit 12 Arithmetic circuit 13 Adjustment circuit 14 Memory section 15 Input section 16 Display section 20, 120 Substrate 21 Surface of substrate 30 Base section 41 Insulating material 41b End surface of insulating material 42 Aluminum block 42a First end surface 42b Second end surface 43 Heater (heat source)
44 Heat sink 45 Power supply A1 Area Ab Bottom surface D1, D2, D3, D4, Da, Db Direction Dn Normal direction Ds Stacking direction E Edge F Fin Gb Air gap (second ventilation hole)
Gt gap (first vent)
H: Overhanging part L1, L2, L3: Layers of 3D lattice structure S: Support (support edge)

Claims (3)

A method for manufacturing a heat sink having a heat dissipation element having a three-dimensional structure in which a set of three-dimensionally arranged nodes are connected by a set of edges, comprising:
A manufacturing data generation process for generating manufacturing data that can be modeled by additive manufacturing based on design values of the nodes and the edges;
a modeling process analysis step of generating mesh structure data based on the manufacturing data, and calculating a shape deviation between the mesh structure data and the manufacturing data, and a maximum principal stress value at a predetermined position on the mesh structure data;
a molding defect diagnosis process for predicting a portion that will cause a molding defect due to the shape deviation and the maximum principal stress value calculated in the molding process analysis process exceeding a first predetermined range for the shape deviation and a second predetermined range for the maximum principal stress value, the first predetermined range and the second predetermined range for the maximum principal stress value being set in order to realize the three-dimensional structure corresponding to the design values;
a printing limit setting step of setting a printing limit to be considered in the manufacturing data generating step in order to eliminate the printing defect predicted in the printing defect diagnosis step, based on the result of the printing process analysis step and a predetermined range set in advance for the printing limit;
and when a new modeling limit is obtained in the modeling limit setting process, the manufacturing data generation process, the modeling process analysis process, the modeling defect diagnosis process, and the modeling limit setting process are repeated, and when both the shape deviation and the maximum principal stress value fall within the first predetermined range and the second predetermined range, respectively, in the modeling defect diagnosis process, additive manufacturing is performed based on the manufacturing data at that time to manufacture the heat sink. A heat sink having a heat dissipation element,
The heat dissipation element includes a set of edges connecting a set of three-dimensionally arranged nodes, a portion of the set of nodes is arranged on a substrate, and has a three-dimensional lattice structure in which a plurality of layers are stacked in an out-of-plane direction of a surface of the substrate;
the edge is arranged at a higher density in a central portion than in an outer portion in a planar direction of the surface in a layer farther from the base material;
A first ventilation hole is formed in the farthest layer farthest from the base material,
A heat sink, characterized in that a second ventilation hole is formed in the outer portion in a layer closer to the base material than the farthest layer. A heat sink having a heat dissipation element,
The heat dissipation element includes a set of edges connecting a set of three-dimensionally arranged nodes, a portion of the set of nodes is arranged on a substrate, and has a three-dimensional lattice structure in which a plurality of layers are stacked in an out-of-plane direction of a surface of the substrate;
the edge is arranged at a higher density in a central portion than in an outer portion in a planar direction of the surface in a layer farther from the base material;
A first ventilation hole is formed in the farthest layer farthest from the base material,
a second ventilation hole is formed in the outer portion of a layer closer to the base material than the farthest layer,
Depending on the attitude of the heat sink,
Air heated by a heat source adjacent to the heat sink is discharged from one of the first and second vents which is located higher in the vertical direction, and
A heat sink, wherein air flows in through one of the first vent hole and the second vent hole which is located lower in the vertical direction.

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