JP2008191772A - Method for preparing analysis model of golf ball - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily reproduce a dimple on the surface of an analysis model, and to make an analysis result more approximate to that of an actual golf ball. <P>SOLUTION: This method for preparing an analysis model 1 of a golf ball to be used in executing the numerical analysis of a golf ball includes: a process for preparing a three-dimensional outer layer model 2 with a plurality of dimples D on the surface arranged at the outermost side by using finite pieces of tetrahedra elements e4; a process for preparing a spherical inner layer model 3 arranged inside the outer layer model 2 by using finite pieces of hexahedron elements e6; and a process for connecting an inner peripheral face 2i of the outer layer model 2 to an outer peripheral face 3o of the inner layer model 3 so that their relative distance can be prevented from being changed. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method of creating an analysis model used when performing numerical analysis of a golf ball using a computer.

  In recent years, numerical analysis (simulation) of a golf ball using a computer has been performed. In this analysis, for example, a golf ball is divided into a finite number of elements to create an analysis model, given a predetermined boundary condition, and the deformation calculation is performed every minute time. Based on the result of deformation calculation output every minute time, for example, the deformation behavior when the golf ball collides with the club head is visualized. The prior art includes the following.

Japanese Patent Application Laid-Open No. 2004-13652

  The surface of a golf ball is usually provided with a large number of dimples having a circular or polygonal outline and recessed at a small depth. Such dimples have a great influence on the flight distance and spin performance of a golf ball depending on the depth, shape, number and arrangement thereof. However, since conventional golf ball analysis models have not been provided with dimples on the surface thereof, for example, spin performance of golf balls obtained by numerical analysis of such analysis models and actual dimples. There was a large discrepancy between the experimental results of golf balls having a golf ball.

  The present invention has been devised in view of the above circumstances, and has a process of creating an outer layer model having a plurality of dimples on the surface and arranged on the outermost side using a finite number of tetrahedral elements, Including a step of creating an inner layer model arranged inside the outer layer model using a finite number of hexahedral elements, for example, a dimple having a circular contour can be easily formed on the surface of the analysis model, and the analysis result is The main object is to provide a method for creating an analysis model of a golf ball that can be approximated by that of an actual golf ball.

  The invention according to claim 1 of the present invention is a method of creating an analysis model of a golf ball used when performing numerical analysis of the golf ball, and a plurality of finite tetrahedral elements are used on the surface. Creating a three-dimensional outer layer model having dimples and being arranged on the outermost side, creating a spherical inner layer model arranged inside the outer layer model using a finite number of hexahedral elements, and the outer layer And combining these surfaces so that the relative distance between the inner peripheral surface of the model and the outer peripheral surface of the inner layer model does not change.

  According to a second aspect of the present invention, in the outer layer model, the golf ball according to the first aspect, wherein a plurality of shell-like layers formed by connecting the tetrahedral elements in the circumferential direction are stacked in the radial direction. This is a method of creating an analysis model.

  The invention according to claim 3 is the golf ball analysis model creation method according to claim 2, wherein the number of elements of each shell-like layer is larger than the number of elements appearing on the outer peripheral surface of the inner layer model. .

According to a fourth aspect of the present invention, the inner layer model is formed by using a regular hexahedron element and is arranged at the center of the golf ball analysis model, and between the cube core portion and the outer layer model. 2. The mid section is formed of a plurality of mid layers stacked in the radial direction, and the number of elements of the mid layer decreases stepwise inward in the radial direction. 4. A method for creating an analysis model for a golf ball according to any one of items 1 to 3.

  In the golf ball analysis model creation method of the present invention, an outer layer model having a plurality of dimples on the surface and arranged on the outermost side is created using a finite number of tetrahedral elements. Dimples are composed of various shapes, such as those having a circular contour and recessed in a spherical shape, and those having a polygonal contour and recessed in a conical shape, but the tetrahedral element is compared to the hexahedral element. The complicated three-dimensional shape described above can be easily created. Therefore, it is possible to form dimples on the surface of the analysis model with high accuracy, and the analysis result can be approximated by that of an actual golf ball.

  Also, the inner layer model arranged inside the outer layer model is created using a finite number of hexahedral elements. Since such an inner layer model is a sphere without dimples, it can be easily formed using hexahedral elements. Further, since the amount of deformation of the golf ball at the time of hitting is smaller toward the inner side, it is not necessary to divide the element finely. Nevertheless, when the inner layer model is made of tetrahedral elements, the number of elements may increase excessively and require a lot of calculation time. However, the present invention can prevent such a problem.

  Further, both models are coupled so that the relative distance between the inner peripheral surface of the outer layer model and the outer peripheral surface of the inner layer model does not change. For this reason, since force and deformation are transmitted between the outer layer model and the inner layer model, the deformation behavior of the golf ball can be accurately calculated.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a cross-sectional perspective view of a golf ball analysis model 1 (hereinafter, simply referred to as “analysis model”) according to the present embodiment visualized and cut along a plane passing through the center thereof. Moreover, the top view of the surface is shown by FIG.

  The analysis model 1 is used when performing a numerical analysis of a golf ball using a computer (not shown). The analysis model 1 is given as numerical data that can be handled by a computer. Specifically, it is an aggregate of a small finite number of elements, and the node coordinate values, element numbers, shapes and material properties (such as density, Young's modulus and / or damping coefficient) of each element are stored as numerical data in the computer. Stored on the medium. In the numerical analysis, for example, a predetermined boundary condition is given to the analysis model 1, and the deformation calculation for each minute time is performed by a computer based on the finite element method or the like. Based on this result, the general performance of various golf balls can be compared and evaluated without actually making a prototype.

  In the method of creating the analysis model 1 of the present invention, a step of creating a three-dimensional outer layer model 2 having a plurality of dimples D and being arranged on the outermost side using a finite number of tetrahedral elements e4, Forming a spherical inner layer model 3 disposed inside the outer layer model 2 using the hexahedral element e6. Any of these steps may be performed first or simultaneously. The spherical shape includes not only a substantial sphere but also a part thereof (for example, a hemisphere).

  The outer layer model 2 is created based on the outer diameter, material, thickness, etc. of the golf ball cover to be evaluated. Here, it does not matter whether or not the golf ball to be evaluated actually exists. The cover is a thin outer layer made of the same material covering the surface of the ball. The outer layer model 2 of this embodiment is formed with a thickness T substantially equal to the golf ball cover to be evaluated. The thickness T of the outer layer model 2 can be variously determined in accordance with the golf ball to be analyzed. However, as in a solid golf ball in recent years, for example, it is 3.5 mm or less, preferably 3.0 mm or less, more preferably Is desirably 2.0 mm or less. On the other hand, the thickness T of the outer layer model is preferably 0.2 mm or more, more preferably 0.5 mm or more, and even more preferably, because it is necessary to make it larger (thicker) than the maximum depth d of the dimple D. Is preferably 0.8 mm or more.

  In addition, a material property value equal to the material of the cover is defined for the tetrahedron element e4 constituting the outer layer model 2. The material physical property values include specific gravity and elastic modulus. The thickness T is substantially the same except for the dimple D.

  Further, the outer layer model 2 is all divided into a finite number using the tetrahedral element e4. As shown in FIGS. 3A and 3B, the tetrahedral element e4 is a three-dimensional continuum element in which the sides of the four triangular planes P1 are connected to each other. As shown in FIG. 5A, the tetrahedral element e4 may be a primary element having a node n1 only at the vertex of each plane P1, or in addition to the node n1, at a midpoint between adjacent vertices. It may be a secondary element having a node n2. In order to express the bending deformation more accurately, a secondary element is more preferably used in the outer layer model 2.

  The size of the tetrahedral element e4 constituting the outer layer model 2 is not particularly limited, but in order to analyze the deformation behavior of the cover in more detail, the length of one side of the tetrahedral element e4 is preferably 0.3 mm or less, More preferably, it is 0.2 mm or less. On the other hand, if the length of one side of the tetrahedral element e4 is too small, a large amount of calculation time is required due to the increase in the number of elements. From such a viewpoint, the length of one side of the tetrahedral element e4 of the outer layer model 2 is preferably 0.05 mm or more, more preferably 0.1 mm or more.

  A plurality of dimples D are provided on the surface of the outer layer model 2. The size, the number of types, and the shape of the dimples are set for the dimples D, for example, based on the dimples provided on the golf ball to be evaluated. As an example, it is desirable that the dimples D are formed with 250 or more and 500 or less.

  Since the tetrahedron element e4 has a triangular surface P1, as shown by hatching in FIG. 2, a substantially hexagonal surface H can be easily formed by arranging around one point. Then, by arranging the tetrahedron elements e4 side by side around the hexagonal surface H, it is possible to easily form dimples having a circular outline. Further, as apparent from FIG. 2, a triangular space S having a sharp tip is formed between the dimples Dc and Dc sharing the edge with each other. Such a space S can be easily arranged.

  FIG. 4 shows a cross-sectional view of the outer layer model 2 at a position including the dimple D. The outer layer model 2 is formed by superimposing a plurality of shell-like layers formed by connecting tetrahedral elements e4 in the circumferential direction, in this embodiment, three layers 2a, 2b, and 2c in the radial direction. In FIG. 4, the intermediate layer 2b is colored for easy understanding. Thus, forming the outer layer model 2 with a plurality of layers increases the degree of freedom of deformation of the outer layer model 2 and helps to perform more detailed and accurate deformation calculation. As an example, when the thickness of the cover is about 0.8 to 3.4 mm, the outer layer model 2 is preferably formed of 3 or more and 10 or less layers.

  Further, the dimple D is easily formed as a depression that is recessed from the surface, for example, by reducing the height in the radial direction of the tetrahedron element e4 located on the radially inner side. As described above, the outer layer model 2 is formed with a thickness T larger than the depth d of the dimple D so as to include all of the dimple D. Further, in the present embodiment, the dimple D and the other portions are each provided with the three layers 2a, 2b or 2c extending inside thereof.

  In addition, the outer layer model 2 of the present embodiment has the side that passes from an arbitrary node n1 on the surface to the node on the inner peripheral surface 2i of the outer layer model 2 through only the side of the tetrahedral element e4. The shortest number includes at least a first portion z1 that is n (where n is an integer that is arbitrarily determined as 2 or more) and a second portion z2 that is n + 1.

  For example, in the radially inner region of the dimple D, the thickness of the outer layer model 2 is reduced, but by including at least one first portion z1 in the region, the volume of the tetrahedral element e4 is significantly reduced. Thus, the shape of the dimple D can be maintained. This helps to prevent a decrease in calculation accuracy. On the other hand, in the outer layer model 2, a region having a sufficiently radial thickness is configured by the second portion z2, thereby increasing the degree of freedom of deformation of the outer layer model 2 and providing more complex and detailed deformation behavior. Can be expressed. Note that the outer layer model 2 of the present embodiment is mainly configured by the second portion z2.

  Here, the number of types of the shortest number of sides of the tetrahedral element e4 passing from the surface of the outer layer model 2 to the outer peripheral surface of the inner layer model 3 is preferably 2 or more, more preferably 3 or more. On the other hand, if the number of types is too large, there is a concern about an increase in calculation cost due to an increase in the number of elements. Therefore, it is preferably 5 or less, more preferably 4 or less. In the above embodiment, the case where the number of types is 2 and n is 2 is shown, but the present invention is not limited to this.

  As shown in FIG. 1, the inner layer model 3 is arranged on the inner side of the outer layer model 2 and is made based on an inner portion covered with a golf ball cover to be analyzed. Further, the inner layer model 3 is entirely composed of hexahedral elements e6.

  As shown in FIGS. 5A and 5B, the hexahedron element e6 is a continuous body element having a rectangular parallelepiped shape in which six quadrilateral (not to mention other than square) surfaces P2 are connected. . Further, in the hexahedral element e6, as shown in FIG. 5A, in addition to the primary element or the node n1 having the node n1 only at the vertex of each plane P2, as in the tetrahedral element e4, between the adjacent vertices. A secondary element having a node n2 at the midpoint may also be used.

  As shown in FIG. 2, the inner layer model 3 includes a cube core portion 4 that is formed using a regular hexahedron element e6t in which all the planes P2 form a square and is arranged at the center of the analysis model 1, and the cube core portion. 4 and the mid part 5 arranged between the outer layer model 2. That is, the step of creating the inner layer model 3 includes the step of setting the cube core portion 4 and the step of setting the mid portion 5.

  As shown in FIG. 6, the cube core portion 4 is formed as a cube as a whole by connecting regular hexahedron elements e6t in a multi-stage multi-row arrangement. The cube core portion 4 is arranged so that the center CC thereof is aligned with the center BC of the analysis model 1 that forms a sphere.

  The mid part 5 is formed from a plurality of mid layers 7 which are stacked in the radial direction. The mid layer 7 is formed as a hollow shell-like layer in which the hexahedron elements e6 are arranged without gaps in the circumferential direction.

  In FIG. 7, in order to explain an example of the process of setting the mid part 5, the analysis model 1 is set to 8 etc. on three planes (XY, YZ, and ZX planes) that pass through the center BC of the analysis model 1 and are orthogonal to each other. A perspective view of the divided 1/8 model is shown. First, a plurality of virtual small spheres k1, k2,... Centered on the center BC of the analysis model 1 (this is the center CC of the cube core part 4) and have a different radius while surrounding the cube core part 4. The small spheres k1, k2,... Can be set, for example, while increasing the radius by a fixed distance or a random distance.

  Next, a radius line r1 extending outward from the center CC through the node n1 appearing on the outer surface of the cube core portion 4 is calculated, and an intersection U between the radius line r1 and each of the small spheres k1, k2,. . Then, by connecting the intersection point U as the node n1, the shell-like mids in which the hexahedron element e6 is connected in the circumferential direction between the virtual spheres k1 and k1 or between the cube core part 4 and the virtual sphere k1. Each layer 7 can be formed.

  By the way, when the mid part 5 is formed by such a method, as shown in FIG. 8, the volume of the hexahedral element e6 of the mid layer 7 is larger as the mid layer 7 on the radially outer side and the mid layer on the radially inner side. As small as 7. In the finite element method, in order to improve the calculation accuracy, it is important to divide a portion with large deformation more finely. However, the mid part 5 made with such a volume balance has room for improvement in view of the fact that the amount of deformation of the golf ball at the time of hitting is larger toward the outside in the radial direction. That is, in the mid layer 7 on the radially outer side, the degree of freedom of deformation is lowered, and there is a possibility that the reproducibility of the deformation behavior is not sufficient. In order to prevent this, each regular hexahedron element e6t of the cube core part 4 can be further reduced to reduce the volume of the hexahedron element of the mid layer 7 on the radially outer side. The number of elements of model 1 is unnecessarily increased, which is not preferable.

  In the present embodiment, in view of such a situation, in the step of forming the mid part 5, the volume of the hexahedron element e6 of the mid layer 7 that is sequentially divided and generated is calculated. If the volume exceeds a predetermined threshold value, as shown in FIG. 9, the surface of the hexahedral element e6 facing the small sphere kn has a grid shape of m × m (m is an integer of 2 or more), etc. A process of dividing and setting a new node n3 is performed. A radius line r2 (which passes through the center CC) extending radially outward from the new node n3 is drawn, and the intersection of the radius line r2 and the virtual small sphere kn + 1, kn + 2,. Add as Then, by subdividing using these nodes n1 and n2, the subsequent mid layer 7 can be further divided into elements.

  By repeating the above processing, as shown in FIG. 6, the mid portion 5 of the present embodiment is provided in a radially outer region and a plurality of mid layers having the same number of hexahedral elements e6 in one layer. A first layer group 5a in which seven layers overlap, a second layer group 5b in which a plurality of mid layers 7 having a smaller number of hexahedral elements e6 included in one layer than the first layer group 5a overlap, The third layer group 5b includes a plurality of mid layers 7 in which the number of hexahedral elements e6 included in one layer is smaller than that of the second layer group 5b. That is, the number of elements included in the mid layer 7 decreases stepwise toward the inside in the radial direction.

  Such a mid part 5 forms a large number of mid layers 7 in the radial direction, while the volume Vi of the hexahedral element of the radially innermost mid layer 7 and the hexahedral element of the radially outermost mid layer 7. An increase in the difference from the volume Vo can be effectively prevented. Therefore, the detailed deformation behavior of the inner layer model 3 can be expressed with a good balance. Moreover, since it is not necessary to make the hexahedral element of the cube core part 4 excessively small, it is possible to suppress an unnecessary increase in the number of elements. Although not particularly limited, the number of the mid layers 7 is preferably 20 or more and 50 or less in order to improve the analysis accuracy. The volume ratio (Vo / Vi) is preferably 0.5 or more, more preferably 0.9 or more, and preferably 1.2 or less, more preferably 1.1 or less. Furthermore, it is desirable that the mid part 5 includes about 3 to 5 groups having different numbers of elements.

  In addition, although material properties are appropriately defined for each hexahedral element e6 of the mid portion 5, one or more material properties can be set as the values based on the material properties of the golf ball to be analyzed. .

  In the present invention, the step of combining these surfaces is performed so that the relative distance between the inner peripheral surface 2 i of the outer layer model 2 and the outer peripheral surface 3 o of the inner layer model 3 does not change. Thereby, the analysis model 1 which shows an integral behavior in the interface of the outer layer model 2 and the inner layer model 3 can be obtained.

  As described above, the analysis model 1 of the present embodiment can easily form dimples on the surface of the outer layer model 3 by using the tetrahedron element e4. become. Further, by making the inner layer model 3 with the hexahedral element e6, it is possible to suppress an increase in the number of elements as a whole and to prevent an increase in calculation time. Note that the analysis model 1 of the present invention does not need to be a perfect sphere, and it is sufficient if a region necessary for the analysis is created. Therefore, if the analysis model 1 is three-dimensional, for example, it can be made in various forms such as a hemisphere or a quarter of a sphere.

  In order to confirm the effects of the present invention, golf ball analysis models having the specifications shown in Table 1 were created, and natural frequency analysis and collision simulation were performed, respectively.

In Table 1, Examples 1 to 5 are analysis models including an outer layer model having dimples made of tetrahedral elements. The dimple specifications are as follows.
Total number of dimples: 312 Number of types of dimples: 3 types Diameter of dimple 1: 3.930 mm
Dimple 1 depth: 0.150 mm
Number of dimples 1: 2

Dimple 2 diameter: 3.060 mm
Dimple 2 depth: 0.163 mm
Number of dimples 2: 10

Dimple 3 diameter: 4.068 mm
Dimple 3 depth: 0.178 mm
Number of dimples 3: 300 FIG. 4 is a cross-sectional perspective view of the model of Example 4 visualized.

  In addition, Comparative Examples 1 to 4 are analysis models including an outer layer model without a dimple made of hexahedral elements.

  The natural frequency analysis was performed based on the natural frequency measurement method under the one-end fixed boundary condition of an actual golf ball, as described in JP-A-2005-261754. Briefly, first, an analysis model of a golf ball is fixed to one end by fixing a surface node included in a surface diameter of 10 mm to a virtual shaker so that it cannot be displaced. Then, a vibration is applied to the analysis model from a virtual shaker, and the time history of the vibration speed of the analysis model at that time is calculated. Next, the frequency transfer function of the analysis model of the golf ball was calculated from these calculation results, and the frequency having the maximum peak in the range of 100 to 2000 Hz was obtained as the primary natural frequency.

  Further, the collision simulation was performed based on an actual golf ball collision test method as described in JP-A-2006-343139. Briefly, a golf ball analysis model was collided at a speed of 34 m / s with a tilted plate fixed at 34 degrees with respect to a vertical plane, and the backspin amount at the time of repulsion was calculated. The friction coefficient between the golf ball analysis model and the inclined plate was constant at 0.3.

  Each numerical analysis was performed by an SGI workstation using engineering analysis application software (LS-DYNA developed and improved by Livermore Software Technology, USA) using the finite element method. .

  Further, the same experiment was performed on an actual golf ball, and the natural frequency and the backspin amount were measured. Then, an error between the calculated value obtained by the numerical analysis and these experimental values was calculated. Table 1 shows the test results.

  As a result of the test, in the analysis model of the example, it can be confirmed that the deviation from the actual experimental result of the golf ball is small with respect to the natural frequency and the backspin amount. In particular, it was confirmed that the analysis accuracy was greatly improved with respect to the amount of backspin that was greatly influenced by dimples. Although an attempt was made to create an outer layer model with dimples using only hexahedral elements, a model that could complete numerical analysis could not be created.

It is a section perspective view of an analysis model of a golf ball of an embodiment of the present invention. It is the elements on larger scale of the surface. (A), (b) is a perspective view of a tetrahedral element. It is sectional drawing of the outer layer model including a dimple. (A), (b) is a perspective view of a hexahedral element. It is a fragmentary sectional view of the analysis model of a golf ball. It is a perspective view explaining the process of setting a mid part. It is a perspective view explaining the process of setting a mid part. It is a perspective view of the hexahedron element explaining the process of setting a mid part. It is a cross-sectional perspective view which shows another Example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Golf ball analysis model 2 Outer layer model 2i Inner surface 3 of outer layer model Inner layer model 3o Outer surface of inner layer model 4 Cube core part 5 Mid part 5a First group 5b Second group 5c Third group 7 Mid layer D dimple e4 tetrahedral element e6 hexahedral element

Claims (4)

A method of creating an analysis model of a golf ball used when performing numerical analysis of a golf ball,
Using a finite number of tetrahedral elements to create a three-dimensional outer layer model having a plurality of dimples on the surface and disposed on the outermost side;
Creating a spherical inner layer model arranged inside the outer layer model using a finite number of hexahedral elements;
A method for creating an analysis model for a golf ball, comprising: combining the inner peripheral surface of the outer layer model and these surfaces so that the relative distance between the outer peripheral surface of the inner layer model does not change.   2. The golf ball analysis model creation method according to claim 1, wherein the outer layer model is formed by overlapping a plurality of shell-like layers formed in a circumferential direction by connecting the tetrahedral elements in a circumferential direction.   The golf ball analysis model creation method according to claim 2, wherein the number of elements of each shell-like layer is larger than the number of elements appearing on the outer peripheral surface of the inner layer model. The inner layer model is made of a regular hexahedron element and is arranged at the center of the golf ball analysis model,
It consists of a mid part arranged between the cube core part and the outer layer model,
4. The golf ball according to claim 1, wherein the mid portion includes a plurality of mid layers stacked in the radial direction, and the number of elements of the mid layer decreases stepwise inward in the radial direction. To create an analysis model.