US20070015601A1

US20070015601A1 - Method of designing golf club and golf club head

Info

Publication number: US20070015601A1
Application number: US11/414,292
Authority: US
Inventors: Masaya Tsunoda; Masayoshi Nishio
Original assignee: SRI Sports Ltd
Current assignee: Dunlop Sports Co Ltd
Priority date: 2005-07-12
Filing date: 2006-05-01
Publication date: 2007-01-18
Also published as: JP2007025761A

Abstract

A method for designing a golf club head by using a computer. A golf club head model in which the rear surface of a face part is provided with reinforcing ribs and a golf ball model to be analyzed by using a finite element method (FEM) are prepared. Conditions including the positions of the reinforcing ribs and the configurations thereof including the sectional areas and heights are adjusted to set the maximum value of the Mises stresses generated by the collision between the golf ball model and the golf club head model at any off-center positions of said front surface of said face part thereof to less than 1.3 times the maximum value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the center of said front surface of said face part thereof.

Description

This nonprovisional application claims priority under 35 U.S.C. §119(a) on Patent Application No(s). 2005-202727 filed in Japan on Jul. 12, 2005, the entire contents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention
The present invention relates to a method of designing a golf club head by utilizing a computer. The present invention also relates to a golf club head. More particularly, the present invention relates to a method of efficiently designing a golf club head having a sufficient strength and excellent restitution characteristics. To do so, a golf ball model and a golf club head model both composed of a plurality of finite elements are used. Further reinforcing ribs are formed on the rear surface of the face part of the golf club head model. By changing conditions of the reinforcing ribs, ball-hitting simulation is executed to make stresses generated at any hitting positions of the face part uniform.
2. Description of the Related Art
Conventionally, a metal plate is disposed on the face part of a wood head of a golf club. To improve the restitution characteristic of the wood head at the time when a golf ball is hit with the wood head, it is effective to thin the metal plate disposed on the face part of the wood head to approximate the natural frequency of the face part to that of the golf ball, based on an impedance matching theory.
Therefore in recent years, there is a tendency for the face part to be thinned. However, thinning the face part causes the strength of the wood head to be low. Thus as a method of thinning the face part and enhancing the strength of the face part, a method of providing the rear surface of the face part with a reinforcing rib is adopted.
For example, in the golf club head disclosed in Japanese Patent Application Laid-Open No. 2003-290396 (patent document 1), a plurality of reinforcing ribs is vertically mounted on the rear surface of the face part, with the reinforcing ribs becoming gradually lower toward the toe and the heel and longitudinally equal or gradually higher toward the bottom (sole) of the golf club head.
Because all the reinforcing ribs extend vertically in the golf club head disclosed in the patent document 1, the reinforcing ribs disposed at the toe and the heel make the rigidity of the face part excessively high. Thus at the time of collision between a golf ball and the face part, the face part is excessively restrained from vibrating, thus having insufficient restitution performance. In addition, although the reinforcing ribs have a large volume (weight), they provide the face part with an insufficient reinforcing effect.
In designing the golf club head, it is desirable to provide it with a high degree of strength and a possible highest restitution performance. The conventional method of designing the golf club head depends greatly on experience and perception and requires immense trial-and-error investigations. Thus it takes much time to design the golf club head. In addition, there is a variation in the guiding principle in designing the golf club head. Therefore various proposals for efficiently designing the golf club head excellent in various properties such as the restitution performance, strength, and the like have been made.
For example, as disclosed in Japanese Patent Application Laid-Open No. 9-149954 (patent document 2), the present applicant proposed the following method serviceable for designing the golf club head: The three-dimensional configuration of the golf club head is measured by using a three-dimensional configuration measuring apparatus. Based on the data of measured three-dimensional configuration, the golf club head model is formed by using a finite element method (FEM) and a construction-analyzing pre-program. By using an analyzing software commercially available, the inertial main shaft of the golf club head model and the main inertial moment thereof are computed.
In the above-described designing method, the inertial main shaft and the main inertial moment of the golf club head model in the initial configuration thereof are computed to make them serviceable for designing the golf club head. However, the method has room for improvement in designing the golf club head having a high restitution characteristics and strength.
Patent document 1: Japanese Patent Application Laid-Open No. 2003-290396
Patent document 2: Japanese Patent Application Laid-Open No. 9-149954

SUMMARY OF THE INVENTION

The present invention has been made in view of the above-described problems. Therefore it is an object of the present invention to provide a method of efficiently designing a golf club head having a sufficient strength and a superior restitution characteristic. To achieve the above-described object, a golf ball model and a golf club head model are used. The rear surface of the face part of the golf club head model is provided with reinforcing ribs. In addition, a finite element method is used to make stresses generated at different hitting positions of the face part uniform.
To achieve the above-described object, the present invention provides a method of designing a golf club head by using a computer. The designing method includes the steps of preparing a ball model and a club head model obtained by dividing a golf ball and a golf club head into a plurality of finite elements respectively. The club head model is provided with a central reinforcing rib formed at a central portion of a rear surface of a face part thereof and a plurality of belt-shaped reinforcing ribs extended radially from the central reinforcing rib toward a peripheral edge of the rear surface of the face part. The designing method further includes the step of executing simulation of collision between the ball model and the club head model at a plurality of positions of a front surface of the face part thereof to determine a Mises stress generated at each of the collision positions; and the step of changing setting conditions of the central reinforcing rib and the belt-shaped reinforcing ribs to set a maximum value of Mises stresses generated at off-center positions of the front surface of the face part to less than 1.3 times a maximum value of a Mises stress generated at a center of the front surface of the face part.
In the above-described construction, by using the golf ball model and the golf club head model divided into a plurality of finite elements respectively, conditions including the positions of the reinforcing ribs, and the configurations thereof including the sectional areas and heights are inputted to the computer to execute ball-hitting simulation. Approximation of the stress generated by the collision between the ball model and the golf club head model at an arbitrary off-center position of the front surface of the face part to the stress generated by the collision therebetween at the center of the front surface thereof is set as the objective function. The positions of the reinforcing ribs and the sectional areas and heights thereof are set as the design variables. Thereby the maximum Mises stress generated by the collision between the golf ball model and the golf club head model at the center of the front surface of the face part thereof and the maximum Mises stress generated by the collision between the golf ball model and the golf club head model at the arbitrary off-center position of the front surface of the face part are compared with each other.
Owing to the comparison, the conditions of the positions of the reinforcing ribs and the configurations thereof including the sectional areas and heights are adjusted to set the maximum value of the Mises stresses generated by the collision between the golf ball model and the golf club head model at any off-center positions to less than 1.3 times the maximum value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the center.
As described above, as the reinforcing rib to be formed on the rear surface of the face part, there are formed the central reinforcing rib and a plurality of the belt-shaped reinforcing ribs extended from the central reinforcing rib toward the peripheral edge of the rear surface of the face part. Therefore the center of the face part subjected to a highest degree of shock has an enhanced rigidity. Further since the belt-shaped reinforcing ribs are extended radially from the central reinforcing rib toward the peripheral edge of the rear surface of the face part, the rigidity of the face part can be prevented from being excessively increased, and the stress acting on the face part can be uniformly dispersed.
The maximum value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the off-center positions of the front surface of the face part thereof is set to less than 1.3 times the maximum value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the center of the front surface of the face part thereof. Therefore the restitution performance of the golf club head model generated by the collision between the golf ball model and the golf club head model at the off-center positions of the front surface of the face part thereof is similar to that of the golf club head model generated by the collision between the golf ball model and the golf club head model at the center (sweet area) of the front surface of the face part thereof.
The ratio of the maximum Mises stress generated at the off-center position of the face part to that generated at the center thereof is set to less than 1.3. But it is preferable to approximate the above-described ratio to one. Thus it is preferable to set the above-described ratio to not less than 1 and less than 1.3.
The golf club-designing method of the present invention is carried out based on the stress value computed by using the finite element method. Thus it is very easy to design the golf club head without performing steps of making actual golf club heads on an experimental basis or measuring the stress value. Further because the computer is used, the configuration and material of the golf club head can be changed by merely altering input data. Thus it is easy to design the face part of the golf club head having various patterns in an imaginary space by using the computer.
More specifically, the club head model is a wood club head model. When the maximum value of the Mises stress generated when the ball model collides with the golf club head model at the off-center positions of the face part thereof is more than 1.3 times the maximum value of the Mises stress generated when the golf ball collides with the golf club head model at the off-center positions of the face part thereof, the sectional areas of the reinforcing ribs, disposed on the rear surface of the face part, which correspond to the collision positions, the width or/and the height thereof are set large, whereas when the above-described ratio is less than 1.0 time, the sectional areas of the reinforcing ribs, disposed on the rear surface of the face part, which correspond to the collision positions, the width or/and the height thereof are set small.
The number of the belt-shaped reinforcing ribs formed on the rear surface of the face part is set to not less than four nor more than 10.
When the number of the belt-shaped reinforcing ribs is less than four, the face part has a wide region where the belt-shaped reinforcing ribs are not formed. Thus the region has an insufficient strength. On the other hand, when the number of the belt-shaped reinforcing ribs is more than 10, the face part has a very high rigidity. Consequently the face part is excessively restrained from vibrating and has a low restitution performance, thus providing little reinforcing effect.
The Mises stress generated in each of the elements when the ball model collides with the club head model is computed from a main stress value at an integration point of each of the elements, and the maximum value of the Mises stress at each of the collision positions is computed from a change of the time series of the determined Mises stress. The Mises stress can be computed by analyses based on the finite element method (FEM). One value of the Mises stress is obtained for one element. The value of the Mises stress is optimum for determining whether the material of the face part is destroyed.
When the ball model collides with the golf club head model at an initial speed of 40 m/second, the maximum value of the Mises stress generated in the face part is computed. The initial speed of 40 m/s is generated when an ordinary golfer hits a golf ball with a wood golf club head. When the difference between the maximum values of the Mises stress falls in the above-described range at the initial speed of 40 m/second, it is possible to make the stresses of the entire face part uniform and sufficiently hold the strength of the face part when the golf ball is hit at other head speeds.
The off-center collision positions, namely, positions other than the center position of the front surface of the face part means the region surrounding the geometrical center of the front surface thereof. It is favorable that at least four positions including positions upward and downward from the center position and left-hand and right-hand positions thereof surrounding the center position of the front surface of the face part are set as the collision positions. It is more favorable that a portion of the front surface of the face part corresponding to a portion of the rear surface thereof where the reinforcing rib is formed and a portion of the front surface thereof corresponding to a portion of the rear surface thereof where the reinforcing rib is not formed, which is sandwiched between the adjacent reinforcing ribs, are set as collision positions.
As the number of the collision positions increases, it is possible to design the golf club head with higher precision, but the period of time required to perform computations increases. If the off-center positions close to the center position are set as the collision positions, stress values generated at the off-center positions are almost equal to those generated at the center positions by computations. Thus it is preferable that the off-center collision positions are spaced at equal intervals from the center position.
The designing method of the present invention is suitably applied to the wood head having various configurations such as the wood head having a hollow portion. The designing method of the present invention is effective for designing the head of a driver and the head of fairway wood clubs #1 through #9.
The designing method of the present invention which is carried out by utilizing a computer is also applicable to designing of an iron head to approximate the stress generated outside the sweet area to that generated in the sweet area.
The designing method of the present invention forms a model of the configuration of the face part of the golf club head by using a computer. Thus the designing method is capable of forming various configurations of the face part. For example, the face part is allowed to have the shape of an approximately flat plate having a flat surface or/and a curved surface. The face part can be made of metal such as titanium and alloys of titanium or the like. The material for a portion of the face part of the head model can be altered from that of the other portion thereof. It is necessary to input values indicating the properties of the material for the portion of the face part to be altered.
The golf ball model can be made of materials that have been hitherto used. Thus rubbers, polymer compositions containing synthetic resin, and the like can be used to compose the golf ball model.
The golf club head model can be composed of solid elements. As the number of elements of the head model increases, computations can be performed with higher accuracy. In consideration of design efficiency, the number of the solid elements is preferably 60,000 to 200,000 when a tetrahedral solid element is used. The above-described range is set in consideration of the ability of the present-day computer. As the performance of the computer is improved, the period of time required to perform computations becomes shorter. Thus the head model can be composed of more elements in the future. The deformed configuration of the golf club head at a hitting time may be displayed from coordinate values of nodal points of each element. Thereby the deformed configuration of the golf club head at a ball hitting time can be evaluated, which is effective for designing the golf club head.
In the present invention, it is preferable to use tetrahedral secondary elements or hexagonal elements, when the size of one side of each element cannot be made sufficiently small in dividing the golf club head model and the golf ball model into finite elements. When the size of one side of each element can be made sufficiently small, tetrahedral primary elements may be used.
When the tetrahedral elements are used, the angle of an edge thereof is set to not less than 20 degrees nor more than 120 degrees.
It is preferable that the face part has not less than two layers in the thickness direction thereof. When the tetrahedral secondary elements are used, it is preferable that the length of one side of each of the tetrahedral secondary elements is set to not less than 1.0 mm nor more than 3.0 mm.
When the tetrahedral primary elements are used, it is conceivable that the length of one side thereof is half of the length of one side of the tetrahedral secondary element to improve accuracy. But in consideration of a computing period of time, it is preferable that the length of one side thereof is not less than 0.5 mm nor more than 1.25 mm.
The present invention provides the following three types of golf club heads.
The golf club head of the first present invention is designed by the first designing method.
The second golf club head is not limited to the first designing method, but may be designed by other designing methods. In the second golf club head, a central reinforcing rib is formed at a central portion of a rear surface of a face part and not less than four nor more than 10 belt-shaped reinforcing ribs are extended radially from the central reinforcing rib toward a peripheral edge of the rear surface of the face part. Values of Mises stresses generated by collision between a golf ball and the golf club head at off-center positions of a front surface of the face part thereof is set to less than 1.3 times a value of a Mises stress generated by collision between the golf ball and the golf club head at a center of the front surface of the face part thereof.
In the third golf club head, a central reinforcing rib is formed at a central portion of a rear surface of a face part and not less than four nor more than 10 belt-shaped reinforcing ribs are extended radially from the central reinforcing rib toward a peripheral edge of the rear surface of the face part. A ratio (W/t) of a width W of each of the belt-shaped reinforcing ribs to a thickness (height) t thereof is set to not less than 15 nor more than 40. Each of the belt-shaped reinforcing ribs forms an intersection angle of not less than 100 degrees nor more than 160 degrees with respect to a reference plane of the rear surface of the face part.
In any of the above-described golf club heads, the central portion of the rear surface of the face part is the region surrounding the geometrical center of the rear surface of the face part. A plurality of the belt-shaped reinforcing ribs is confluent with each other in the central portion of the rear surface of the face part. The central reinforcing rib is circular, elliptic or polygonal in a sectional view. The configuration of the central reinforcing rib is varied according to the extended direction and the like of the belt-shaped reinforcing ribs. The sectional area of the central reinforcing rib is also varied according to the values of the Mises stresses.
The belt-shaped reinforcing ribs may be extended radially from the central reinforcing rib to the peripheral edge of the rear surface of the face part. But they do not have to be necessarily extended to peripheral edge of the rear surface of the face part. The belt-shaped reinforcing ribs are approximately linearly extended in a predetermined width to the peripheral edge of the rear surface of the face part. But they may be partly bent or curved.
In the first and second golf club heads, the values of the Mises stresses generated by the collision between the golf ball model and the golf club head model at the positions other the center position of the front surface of the face part are set to less than 1.3 times the maximum value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the center of the front surface of the face part thereof.
In the third golf club head, as described above, not less than four nor more than 10 belt-shaped reinforcing ribs are extended radially from the central reinforcing rib toward the peripheral edge of the rear surface of the face part. The ratio of the width of each of the belt-shaped reinforcing ribs to the thickness (height) thereof is set to the above-described specified range. Further each of the belt-shaped reinforcing ribs forms the above-described specified intersection angle with respect to the reference plane of the rear surface of the face part. Similarly to the first and second inventions, the values of the Mises stresses generated by the collision between the golf ball model and the golf club head model at the off-center positions of the front surface of the face part thereof are set to less than 1.3 times the maximum value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the center position of the front surface of the face part thereof.
The reason the ratio (W/t) of the width W of each of the belt-shaped reinforcing ribs to the height t thereof is set to not less than 15 nor more than 40 is as follows: When the ratio of W/t is less than 15, a high stress is generated at the boundary between the reinforcing ribs and the rear surface of the face part and a stress concentrates on the boundary. Thereby the stress cannot be made uniform. On the other hand, if the ratio of W/t is more than 40, the reinforcing rib has an insufficient reinforcing effect.
The reason each of the belt-shaped reinforcing ribs forms the intersection angle of not less than 100 degrees nor more than 160 degrees with respect to the reference plane of the rear surface of the face part is as follows: If the intersection angle is less than 100 degrees, a stress is generated at the boundary between the belt-shaped reinforcing ribs and the rear surface of the face part. Thereby there is a possibility that the face part cracks. On the other hand, if the intersection angle is more than 160 degrees, the belt-shaped reinforcing ribs provide an insufficient reinforcing strength.
It is preferable that any of the first through third golf club heads are wood heads. The face part is composed of a metal plate. The reinforcing ribs are formed on the rear surface of the metal plate.
It is preferable that the area of the central reinforcing rib formed on the rear surface of the face part is set to not less than 20% nor more than 90% of the area of the entire rear surface of the face part.
When the area of the central reinforcing rib is out of the above-described range, it is impossible to set the values of the Mises stresses generated by the collision between the golf ball model and the golf club head model at the off-center positions of the front surface of the face part thereof to less than 1.3 times the value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the center of the front surface of the face part thereof.
It is preferable that in any of the first through third golf club heads, the height, namely, the thickness (thickness of the face part and that of reinforcing rib) obtained by the addition of the thickness of the face part and that of the reinforcing rib is uniform. It is preferable that the projected end surfaces of the reinforcing ribs are on the same level.
Therefore the thickness of the reinforcing rib is set large in a portion where the thickness of the face part is small, and the thickness of the reinforcing rib is set small in a portion where the thickness of the face part is large. Because the thickness of the face part is large in the central portion thereof, the thickness of the central reinforcing rib is small.
It is preferable that the thickness of the face part made of the metal plate is set to not less than 0.5 mm nor more than 3.5 mm. When the thickness of the face part is less than 0.5 mm, the face part has an insufficient strength. On the other hand, when the thickness of the face part is more than 3.5 mm, the face part has a very high rigidity and thus a low restitution performance.
It is favorable that the thickness of the central reinforcing rib is not less than 2.6 mm nor more than 5.0 mm and that the area of the central reinforcing rib is not less than 10 mm²nor more than 1000 mm².
When the thickness of the central region is less than 2.6 mm, the face part has an insufficient strength. On the other hand, when the thickness of the central region is more than 5.0 mm, the face part has a very high rigidity and thus a low restitution performance. It is more favorable that the thickness of the central region is not less than 2 mm nor more than 4 mm.
It is preferable that the sectional area of the belt-shaped reinforcing rib is 2.0 mm²to 10 mm², that the width thereof is 3 mm to 14 mm, and that the height thereof is 0.3 mm to 1.5 mm. When the sectional area of the belt-shaped reinforcing rib, the width thereof, and the height thereof are less than 2.0 mm², 3 mm, and 0.3 mm respectively, the face part has an insufficient strength, and a stress concentration is liable to occur. On the other hand, when the sectional area of the belt-shaped reinforcing rib, the width thereof, and the height thereof are more than 10 mm², 14 mm, and 1.5 mm respectively, the face part has a high rigidity and thus a low restitution performance.
A portion where the adjacent belt-shaped reinforcing ribs intersect with each other is rounded. The ratio (θ/R) of an intersection angle θ (degree) formed between the adjacent belt-shaped reinforcing ribs to a radius of curvature R (mm) of the rounded portion is set to favorably not less than three nor more than 50 and more favorably not less than 6 nor more than 22.
When the ratio (θ/R) is in the above-described range, a stress does not concentrate on the rounded portion disposed at the boundary between the adjacent belt-shaped reinforcing ribs, but disperses. Thereby the face part has a high durability.
When the ratio of the intersection angle θ formed between the adjacent belt-shaped reinforcing ribs to the radius of curvature R is less than three, the radius of curvature R is large with respect to the intersection angle θ. Thereby the thick portion of the face part increases too much, which decreases the coefficient of restitution thereof. On the other hand, when the ratio (θ/R) becomes large and exceeds 50, the radius of curvature R is small with respect to the intersection angle θ. Thereby a stress concentrates on the portion where the adjacent belt-shaped reinforcing ribs intersect with each other and thus the durability of the face part deteriorates.
As described above, according to the method of the present invention for designing the golf club head carried out by using the golf club head model and the golf ball model, simulation is executed in an imaginary space by using a computer to set the maximum value of the Mises stresses generated by the collision between the golf ball model and the golf club head model at any off-center positions of the front surface of the face part thereof to less than 1.3 times the maximum value of the Mises stress generated by the collision between the golf ball model and the golf club head model at the center of the front surface of the face part thereof. To do so, the positions of the reinforcing ribs and the configurations thereof including the sectional areas and the heights are changed. That is, the designing method of the present invention allows the golf club head to be designed very easily without performing steps of making actual golf club heads on an experimental basis or measuring values of generated stresses. Therefore the designing method of the present invention reduces the expense and the period of time required to execute computations.
In the golf club head formed based on the above-described designing method and the second and third golf club heads, it is possible to make stresses generated at any positions of the face part thereof uniform. Further the stress generated by the collision between the golf ball and the golf club head at the off-center positions of the front surface of the face part thereof is approximated to the stress generated by the collision between the golf ball and the golf club head at the center of the front surface of the face part thereof. Thereby the sweet area can be enlarged. Therefore at the time ball-hitting at positions other than the center of the face part (off-center shot), the golf club head has a high strength and a superior restitution characteristic.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a flowchart showing the method of the present invention of designing a golf club head.
FIG. 2A is a perspective view showing a golf club head model.
FIG. 2B is a front view showing the golf club head model.
FIG. 3 is a schematic view showing a golf ball model.
FIGS. 4A, 4B, and 4C are explanatory views showing a situation in which the golf ball head model and the golf club head model collide with each other.
FIG. 5 is a graph showing a change of a stress generated in a certain element with the elapse of time when the golf club head model hits the golf ball model.
FIG. 6 shows a golf club head according to an embodiment of the present invention, in which FIG. 6A is a plan view showing a rear surface of a face part; and FIG. 6B is a perspective view showing the entire face part.
FIG. 7A is an explanatory view for explaining the definition of an intersection angle α of a reinforcing rib with respect to a reference plane of the rear surface of the face part.
FIG. 7B is an enlarged view showing a portion surround with a rectangle of FIG. 7A.
FIG. 8A is an explanatory view for explaining the sectional area of the reinforcing rib.
FIG. 8B shows the width and height of the reinforcing rib.
FIG. 9 is an enlarged view showing a boundary portion between adjacent belt-shaped reinforcing ribs adjacent to a central reinforcing rib.
FIG. 10 is a plan view showing a rear surface of a face part of an example 1.
FIG. 11 is a plan view showing a rear surface of a face part of an example 2.
FIG. 12 is a plan view showing a rear surface of a face part of an example 3.
FIG. 13 is a plan view showing a rear surface of a face part of an example 4.
FIG. 14 shows an intersection angle of a reinforcing rib of an example 5.
FIG. 15 shows an intersection angle of a reinforcing rib of an example 6.
FIG. 16 is a plan view showing a rear surface of a face part of an example 7.
FIG. 17 is a plan view showing a rear surface of a face part of an example 8.
FIG. 18 shows an intersection angle of a reinforcing rib of a comparison example 1.
FIG. 19 shows an intersection angle of a reinforcing rib of a comparison example 2.
FIG. 20 is a plan view showing a rear surface of a face part of a comparison example 3.
FIG. 21 is a plan view showing a rear surface of a face part of a comparison example 4.
FIG. 22 is a graph showing results of analysis of a Mises stress of the example 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The embodiments of the present invention will be described below with reference to drawings.
FIG. 1 is a flowchart showing the method of the present invention of designing a golf club head. The designing method will be schematically described below based on the flowchart.
Initially at step #1, from CAD data, a golf club head model and a golf ball model to be analyzed by using a finite element method (FEM) are prepared. That is, the wood golf club head model and the golf ball model divided into finite elements are prepared. In the golf club head model, a central reinforcing rib is formed at the central portion of the rear surface of the face part, and a plurality of belt-shaped reinforcing ribs is extended radially from the central portion of the rear surface of the face part toward the peripheral edge of the rear surface thereof. The positions of the reinforcing ribs, the dimensions thereof such as widths and heights, and the properties of a material of the face part are specified.
At step #2, supposing that a golf ball collides with a golf club head, simulation of hitting the golf ball model with the golf club head model at the face center located at the geometrical center of the face part of the golf club head model and at a plurality of positions other than the face center is executed.
At step #3, computations are performed by using the finite element method (FEM) to obtain a maximum value of Mises stresses generated in finite elements of the front surface of the face part of the club head model at each position of collision between the golf ball model and the golf club head model.
At step #4, the difference in situations or values of stresses generated on the face part according to hitting positions is evaluated.
At step #5, when a maximum value of Mises stresses generated by hitting the golf ball model with the golf club head model at arbitrary positions of the front surface of the face part is less than 1.3 times (less than 1.2 times preferably) a maximum value of a Mises stress generated by hitting the golf ball model with therewith at the center of the front surface of the face part, the designing finishes and wood golf club heads are made on an experimental basis and evaluated.
At step #6, if the situations or values of stresses generated on the face part are out of the specified range, simulation is executed again by changing the positions of the reinforcing ribs and the configurations thereof including the sectional areas and the heights in dependence on stress values. Until the situations or values of generated stresses falls in an allowable range, the positions of the reinforcing ribs and the configurations thereof including the sectional areas and the heights are controlled and hitting simulation are executed repeatedly.
The designing method will be described in detail below.
Initially, golf club head model having the reinforcing ribs formed on the rear surface of the face and the golf ball model are prepared by using the computer, and an initial condition is set.
FIGS. 2A and 2B show the wood golf club head model (hereinafter referred to as merely head model) 1 used in the simulation. The head model 1 is hollow. The face part 2 of the head model 1 is plate-shaped and approximately elliptic. A plurality of reinforcing ribs is formed at the central portion of the rear surface of the face part 2 and in the region from the central portion toward the peripheral edge of the rear surface thereof.
The head model 1 is divided into 64,247 tetrahedral primary elements 1 a, and a large number of nodal points 3 is obtained. The average length of one side of each finite element is about 2.0 mm in the face part and about 2.5 mm in the body part. The face part 2 is divided into 27,412 tetrahedral elements and has two layers. Titanium is used as the material of the head model 1. As the property of the material of the head model, the property of titanium is inputted to the computer.
The head model 1 has a volume of 420 cc and weighs 191.0 g.
FIG. 3 shows a golf ball model (hereinafter referred to as merely ball model) 5 used in the simulation. The ball model 5 is made of an elastic material divided into solid elements each having eight nodal points. The modulus of elasticity of the ball model 5 is so adjusted that the static compression characteristic thereof is similar to that of a “HI-BRID everio” (manufactured by Sumitomo Rubber Industries Inc.). The dimension and weight of the ball model 5 are also so adjusted that they are similar to those of the “HI-BRID everio”. The ball model 5 is divided into 11800 hexahedral primary elements 5 a, and a large number of nodal points 5 b is obtained. The length of one side of the finite element is 0.2 mm to 2 mm. As the property of the material of the ball model 5, the modulus of elasticity and the Poisson's ratio are inputted to the computer.
By using the head model 1 and the ball model 5, as shown in FIGS. 4A, 4B, and 4C, simulation is conducted, supposing that a golf ball is hit with a golf club head.
More specifically, after the ball model 5 is disposed near a portion of the head model 1 at which the ball model 5 is hit with the head model 1, the head model 1 collides with the ball model 5 at an initial speed of 40 m/second. A stress generated in each element of the face part 2 of the head model 1 at the time of collision is analyzed by using the finite element method (FEM).
FIG. 5 shows a situation in which a stress is generated in a certain element at the time when the ball model 5 is hit with the head model 1. As shown in FIG. 5, the value of generated stress changes with the elapse of time (analysis step), the value of the stress becomes maximum at about the middle point of the time period of contact between the head model 1 and the ball model 5.
The stress is computed from the time of when the ball model 5 is hit with the head model 1 until the time when the ball model 5 separates completely from the head model 1. The coefficient of the dynamic friction and that of the static friction at the time of the contact therebetween are set to 0.3.
In this embodiment, the collision positions are set to a face center position (CEN) and an off-center position on the periphery of the center of the front surface 2 a of the face part 2 with respect to a reference position, namely, the face center point which is the geometrical center of the front surface 2 a of the face part 2. As the off-center collision position, the following eight positions are set: a position at an interval of 10 mm upward from the center position CEN, a position at an interval of 10 mm downward from the center position CEN, a heel-side position spaced at an interval of 20 mm from the center position CEN to the heel side, a toe-side position spaced at an interval of 20 mm from the center position CEN to the toe side, a heel-side obliquely upward position spaced at an interval of 20 mm from the center position CEN to the heel side and upward at an interval of 10 mm from the center position CEN, a heel-side obliquely downward position spaced at an interval of 20 mm from the center position CEN to the heel side and downward at an interval of 10 mm from the center position CEN, a toe-side obliquely upward position spaced at an interval of 20 mm from the center position CEN to the toe side and upward at an interval of 10 mm from the center position CEN, and a toe-side obliquely downward position spaced at an interval of 20 mm from the center position CEN to the toe side and downward at an interval of 10 mm from the center position CEN.
Stresses generated in each element of the face part of the head model 1 when the head model collides with the ball model at the center position and the off-center positions are computed by analyses based on the finite element method.
More specifically, an equation 1 shown below is used to determine the Mises stress generated in each element of the face part at each collision position based on a main stress value at an integration point of each element of the face part. In the equation 1, σe is the Mises stress, σ1 is a maximum main stress, σ2 is an intermediate main stress, and σ3 is a minimum main stress. $\begin{matrix} σ_{e} = \frac{1}{2} {({(σ_{1} - σ_{2})}^{2} - {(σ_{2} - σ_{3})}^{2} - {(σ_{3} - σ_{1})}^{2})}^{\frac{1}{2}} & Equation 1 \end{matrix}$
A maximum value of the Mises stress generated in each element is determined from a change in time series. The number of integration points in the thickness direction thereof is set to two. The maximum value of the Mises stress at all integration points is determined. By carrying out this method, the maximum value of the Mises stress generated in the face part is determined at each of eight hitting positions.
When the maximum value of the Mises stress generated at the off-center collision positions (positions on the periphery of the face center) is not less than 1.3 times the maximum value of the Mises stress generated at the face center collision position, the conditions including the positions of the reinforcing ribs and the configurations thereof including the sectional areas and the heights are adjusted and hitting simulation are executed repeatedly until the maximum value of the Mises stress generated at the off-center positions becomes less than 1.3 times and preferably less than 1.2 times the maximum value of the Mises stress generated at the face center.
As an analysis software for simulation, an LS-DYNA (manufactured by LSTC Inc.) is used. In addition, an ABAQUS Explicit (manufactured by HKS Inc.) and a RAM-CRASH (manufactured by ESI Inc.) can be used.
As the finite element model, a beam element, a shell element, a solid element, and a combination of these elements can be used. Analysis conditions can be altered appropriately.
The embodiment of the golf club head of the present invention formed by using the above-described designing method is described with reference to FIGS. 6 through 8.
The golf club head of the present invention may be formed by using designing methods other than the above-described designing method.
The wood golf club head 10 shown in FIGS. 6 through 9 has a face part 12 for hitting a ball, a crown portion 13 extended from the upper edge of the face part 12 to the rear upper edge of the golf club head, a sole portion 14 extended from the lower edge of the face part 12 to the rear lower edge of the golf club head, a side portion 15 extended between the crown portion 13 and the sole portion 14, and a hosel portion having a shaft hole (not shown) to which a shaft (not shown) is bonded after the shaft is inserted thereinto.
The golf club head 10 is made of metal such as a titanium alloy. The golf club head 10 is composed of the face part 12 and a body part 19 disposed rearward therefrom. The face part 12 and the body part 19 are joined with each other at a boundary line K. The face part 12 is formed by a forging method. The body part 19 is formed by a lost wax precision casting method.
The material for the golf club head is not limited to a titanium alloy, but it is possible to use one or more kinds of metal materials including titanium, stainless steel alloy, aluminum alloy, and magnesium alloy, and carbon fiber reinforced plastic.
The face part 12 of the hollow golf club head 10 is composed of a front surface portion 12 a which contacts a ball when the ball is hit with the golf club head 10 and a rear surface portion 12 b disposed rearward from front surface portion 12 a, with a hollow portion interposed therebetween. FIG. 6A is a rear view showing the rear surface portion 12 b of the face part 12. The hatched portion in FIG. 6A shows a peripheral edge gs of the face part 12 that is welded to the body part 19.
As shown in FIG. 6, a central reinforcing rib 70 approximately elliptic in a sectional view is formed at the central portion of the rear surface of the face part 12. In addition, belt-shaped reinforcing ribs 71 through 76 are extended radially from the periphery of the central reinforcing rib 70 toward the peripheral edge of the rear surface of the face part 12. In this embodiment, six belt-shaped reinforcing ribs 71 through 76 are formed, but not less than four nor more than 10 belt-shaped reinforcing ribs may be provided. The belt-shaped reinforcing ribs 71 through 76 have the same sectional specification (sectional area, sectional configuration, width, height) and are extended substantially straight.
As shown in FIGS. 7A and 7B, each of the belt-shaped reinforcing ribs 71 through 76 forms an intersection angle of α to the reference plane of the rear surface of the face part 12. The intersection angle α is set to not less than 100 degrees nor more than 160 degrees to prevent a stress from concentrating on a proximal portion of each of the belt-shaped reinforcing ribs.
The intersection angle α is defined as follows:
As shown in FIG. 7A, in the section of the belt-shaped reinforcing rib, a boundary point P3 between the belt-shaped reinforcing rib having a width W and the rear surface of the face part is set. At a position spaced by W/7 from the boundary point P3, a line is drawn vertically to the rear surface of the face part. As shown in FIG. 7B, the point at which the vertical line and the front surface of the belt-shaped reinforcing rib intersect with each other is denoted by P1. The point at which the vertical line and the rear surface of the face part of the face part intersect with each other is denoted by P2. The intersection angle α is obtained by subtracting ∠P1P3P2 from 180 degrees.
The sectional area of each of the belt-shaped reinforcing ribs 71 through 76 is set to 2.0 mm²to 10 mm². The sectional area of each of the belt-shaped reinforcing ribs 71 through 76 is set as follow: For example, with reference to FIG. 8A, a position spaced by 40% of a whole length L of the belt-shaped reinforcing rib 72 from a center position 72 c thereof in a longitudinal direction thereof toward one end thereof is denoted by 72 d. Similarly a position spaced by 40% of the whole length L of the belt-shaped reinforcing rib 72 from the center position 72 c thereof in a longitudinal direction thereof toward the other end thereof is denoted by 72 e. The average of sectional areas of each position in the longitudinal direction of the belt-shaped reinforcing rib 72 in the range from the position 72 d to the position 72 e is set as the sectional area of the belt-shaped reinforcing rib 72.
As shown in FIG. 8B, the height t of each of the belt-shaped reinforcing ribs 71 through 76 and the width W thereof are set to 0.3 to 2.0 mm and 8 to 22 mm respectively. The ratio (W/t) of the width W to the height t is set to not less than 5.3 nor more than 74.
The height (thickness) of the central reinforcing rib 70 is set to not less than 2.6 mm nor more than 5.0 mm. The sectional area of the central reinforcing rib is set to not less than 10 mm²nor more than 1000 mm². That is, the sectional area of the central reinforcing rib is set to not less than 20% nor more than 90% of the area of the entire rear surface of the face part 12.
The intersection angle θ (θ1 to θ6) formed between the adjacent belt-shaped reinforcing ribs 71 through 76 is set to less than 90 degrees. At positions where the belt-shaped reinforcing ribs 71 through 76 are continuous with the central reinforcing rib 70, the adjacent belt-shaped reinforcing ribs intersect with each other. A required radius of curvature R (R1 to R6) is set at each of the positions where the adjacent belt-shaped reinforcing ribs intersect with each other to allow the belt-shaped reinforcing ribs 71 through 76 to be continuous with each other smoothly.
The ratio (θ/R) of the intersection angle θ (degree) formed between the adjacent belt-shaped reinforcing ribs 71 through 76 to the radius of curvature R (mm) is set to not less than three nor more than 50.
As shown in FIG. 9, the relationship between the radius of curvature R and the intersection angle θ is as follows: at a portion where a boundary line rk of the belt-shaped reinforcing rib 72 and a boundary line rk of the belt-shaped reinforcing rib 73 intersect with each other, as the ratio (θ/R) of the intersection angle θ formed between the belt-shaped reinforcing ribs 72 and 73 to the radius of curvature R becomes smaller, a radial line (m2) of the radius of curvature R becomes increasingly far from the position rc where the center lines of the belt-shaped reinforcing ribs 72 and 73 intersect with each other. On the other hand, as the ratio (θ/R) becomes larger, a radial line (m1) of the radius of curvature R becomes increasingly close to the position rc where the center lines of the belt-shaped reinforcing ribs 72 and 73 intersect with each other.
When the ratio (θ/R) becomes small and less than three, the thick portion of the face part increases owing to an increase of the area of the belt-shaped reinforcing rib. Thereby the golf club head 10 has a low coefficient of restitution. On the other hand, when the ratio (θ/R) becomes large and exceeds 50, a stress concentrates on the portion where the adjacent belt-shaped reinforcing ribs intersect with each other. Thus golf club head has a low durability. Therefore the ratio (θ/R) is set to not less than 3 nor more than 50.
In the wood golf club head 10 having the above-described construction, the positions, heights, widths, and sectional areas of the reinforcing ribs 70 through 76 are set so that the maximum value of the Mises stress generated at the off-center positions of the front surface of the face part 12 is less than 1.3 times the maximum value of the Mises stress generated at the center of the front surface of the face part 12.
In the designing method of the present invention and the golf club head designed by the designing method, it is possible to secure the reinforcing effect provided by the reinforcing rib and decrease the rigidity of the face part when the golf ball collides with the face part at the off-center positions thereof. Thereby it is possible to provide the golf club head with a high restitution characteristic owing to improvement of the impedance matching and enlarge the sweet area. Further the designing method allows the golf club head to be designed very easily without performing steps of making actual golf club heads on an experimental basis or measuring the stress value. Moreover because the computer is used, the configuration and material of the golf club head can be changed by merely altering input data. Thus it is easy to design the face part of the golf club head having various patterns in an imaginary space by using the computer.

EXAMPLES

Golf club head models of the examples 1 through 8 shown in table 1 and golf club head models of the comparison examples 1 through 4 shown in table 2 were formed by using a computer. Simulation was executed by collision between ball models and the golf club head models. The coefficient of restitution of each golf club head model was determined to evaluate the performance of the golf club head models.

Excluding the reinforcing ribs of the face part, the golf club head models of all the examples and the comparison examples were prepared by using the same specification. More specifically, similarly to the embodiments shown in FIGS. 6 through 9, each of the hollow golf club head models made of a titanium alloy was formed by joining the face and body parts with each other to make them approximately cup-shaped. The head had a volume of 405 cc. The face part has an area of 4100 mm². The thickness of the portion of the face part where the reinforcing ribs were not formed was set to 1.8 mm to 2.0 mm.

TABLE 1


Unit	E1	E2	E3	E4	E5	E6	E7	E8

Number of ribs		6	6	6	6	6	6	4	8
Drawing of rear surface of face	—
Height(t1)of section of rib	mm	0.56	0.59	0.54	0.54	0.56	0.56	0.62	0.5
Width(W1) of rib	mm	13	19	15	15	13	13	17	13
Height(t2)of section of rib	mm	0.53	0.47	0.56	0.55	0.53	0.53	0.67	0.53
Width(W2) of rib	mm	15	20	13	17	14	15	22	13
Height(t3)of section of rib	mm	0.53	0.49	0.56	0.55	0.53	0.53	0.62	0.53
Width(W3) of rib	mm	15	20	13	17	15	16	21	13
Height(t4)of section of rib	mm	0.54	0.54	0.54	0.54	0.54	0.54	0.67	0.53
Width(W4) of rib	mm	15	20	13	15	19	19	22	13
Height(t5)of section of rib	mm	0.55	0.6	0.55	0.56	0.55	0.55	—	0.55
Width(W5) of rib	mm	15	20	16	13	19	19	—	13
Height(t6)of section of rib	mm	0.61	0.58	0.55	0.56	0.61	0.61	—	0.53
Width(W6) of rib	mm	15	20	16	13	20	20	—	13
Height(t7)of section of rib	mm	—	—	—	—	—	—	—	0.53
Wiclth(W7) of rib	mm	—	—	—	—	—	—	—	13
Height(t8)of section of rib	mm	—	—	—	—	—	—	—	0.53
Width(W8)of rib	mm	—	—	—	—	—	—	—	13
Intersection angle(α1)	deg.	176	176	176	176	122	145	176	176
Intersection angle(α2)	deg.	176	176	176	176	122	145	176	176
Intersection angle(α3)	deg.	176	176	176	176	122	145	176	176
Intersection angle(α4)	deg.	176	176	176	176	122	145	176	176
Intersection angle(α5)	deg.	176	176	176	176	122	145	176	176
Intersection angle(α6)	deg.	176	176	176	176	122	145	—	176
Intersection angle(α7)	deg.	—	—	—	—	—	—	—	176
Intersection angle(α8)	deg.	—	—	—	—	—	—	—	176
R1	mm	10	10	10	10	10	10	10	7
R2	mm	3	3	3	3	3	3	10	4
R3	mm	7	7	7	7	7	7	10	4
R4	mm	4	4	4	4	4	4	10	10
R5	mm	3	3	3	3	3	3	—	7
R6	mm	10	10	10	10	10	10	—	4
R7	mm	—	—	—	—	—	—	—	4
R8	mm	—	—	—	—	—	—	—	10
θ1	deg.	65	65	65	65	65	65	90	45
θ2	deg.	40	40	40	40	40	40	90	45
θ3	deg.	75	75	75	75	75	75	90	45
θ4	deg.	65	65	65	65	65	65	90	45
θ5	deg.	40	40	40	40	40	40	—	45
θ6	deg.	75	75	75	75	75	75	—	45
θ7	deg.	—	—	—	—	—	—	—	45
θ8	deg.	—	—	—	—	—	—	—	45
Smax′/Smax	—	1.25	1.23	1.24	1.24	1.25	1.25	1.25	1.25
Thickness(H) of face center	mm	2.8	2.8	2.8	2.8	2.8	2.8	2.8	2.8
Area of thickness portion	mm²	78.5	113	80.1	78.2	78.2	78.2	78.2	78.2
Durability	—	⊚	⊚	⊚	⊚	⊚	◯	◯	◯

where E denotes example.

TABLE 2


Unit	CE1	CE2	CE3	CE4

Number of ribs		6	6	6	6
Drawing of rear surface	—
of face
Height(t1)of section of rib	mm	1.6	1	0.29	0.6
Width(W1) of rib	mm	7	2.4	14	14
Height(t2)of section of rib	mm	1.6	1	0.29	0.6
Width(W2) of rib	mm	4	2.4	14	14
Height(t3)of section of rib	mm	1.6	1	0.29	0.6
Width(W3) of rib	mm	7	2.4	14	14
Height(t4)of section of rib	mm	1.6	1	0.29	0.6
Width(W4) of rib	mm	7	2.4	14	14
Height(t5)of section of rib	mm	1.6	1	0.29	0.6
Width(W5) of rib	mm	7	2.4	14	14
Height(t6)of section of rib	mm	1.6	1	0.29	0.6
Width(W6) of rib	mm	7	2.4	14	14
Intersection angle(α1)	deg.	110	90	176	176
Intersection angle(α2)	deg.	110	90	176	176
Intersection angle(α3)	deg.	110	90	176	176
Intersection angle(α4)	deg.	110	90	176	176
Intersection angle(α5)	deg.	110	90	176	176
Intersection angle(α6)	deg.	110	90	176	176
R1	mm	6	6	6	6
R2	mm	6	6	6	6
R3	mm	6	6	6	6
R4	mm	6	6	6	6
R5	mm	6	6	6	6
R6	mm	6	6	6	6
θ1	deg.	65	65	65	65
θ2	deg.	40	40	40	40
θ3	deg.	75	75	75	75
θ4	deg.	65	65	65	65
θ5	deg.	40	40	40	40
θ6	deg.	75	75	75	75
Smax′/Smax	—	1.32	1.35	1.32	1.32
Thickness(H) of face center	mm	2.8	2.8	2.8	2.8
Area of thickness portion	mm²	78.5	75	78.5	78.5
Durability	—	Δ	X	Δ	Δ

where CE denotes comparison example.

In the tables 1 and 2, Smax denotes the maximum value of the Mises stress generated at the center of face part, and Smax′ denotes the maximum value of the Mises stresses generated at positions (off-center position) other than center of the face part.
In the tables 1 and 2, to evaluate durability of the face part of the golf club head of each of the examples 1 through 8 and the comparison examples 1 through 4, a shaft and a grip were mounted on each of the golf club heads to prepare golf clubs. By using a swing robot, 1000 golf balls were hit with each golf club at the center of the face part at a head speed of 50 m/second. The durability of the golf clubs were marked by ◯, Δ, and X. The golf club in which the depth of a concave formed by hitting was less than 0.1 mm was marked by ◯. The golf club in which the depth of a concave formed by hitting was not less than 0.1 mm was marked by Δ. The golf club whose face part was destroyed before not more than 1,000 balls were hit thereby was marked by X.
As shown in tables 1 and 2, the configuration of the rear surface of the face part of each of the examples 1, 2, 3, and 4 is shown in FIGS. 10, 11, 12, and 13 respectively. The entire construction of the rear surface of the face part of each of the examples 5 and 6 is the same as that of example 4. The intersection angle of the belt-shaped reinforcing rib of each of the examples 5 and 6 with respect to the reference plane of the rear surface of the face part is as shown in FIGS. 14 and 15 respectively. The construction of the rear surface of the face part of each of the examples 7 and 8 is shown in FIGS. 16 and 17 respectively.
The configuration of the golf club head of each of the comparison examples 1 and 2 is as shown in FIG. 2A. The reinforcing ribs of the comparison examples 1 and 2 formed 110° and 90° respectively to the reference plane of the rear surface of the face part. The configuration of the face part of each of the comparison example 3 and the comparison example 4 is as shown in FIGS. 20 and 21 respectively.
The head model of each of the examples 1 through 8 and the comparison examples 1 through 4 was prepared as shown in FIG. 2. In addition ball models were prepared. The ball models collided with the head models to analyze the Mises stresses generated at the collision positions.
FIG. 22 shows the results of analyzed stress generated by the head model of the example 1.
As the collision positions, the following eight positions are set: a center position CEN (a), a U10 position (b) upward at an interval of 10 mm from the center position CEN, a D10 position (c) downward at an interval of 10 mm from the center position CEN, a heel-side H20 position (d) spaced at an interval of 20 mm from the center position CEN to the heel side, a toe-side T20 position (e) spaced at an interval of 20 mm from the center position CEN to the toe side, a heel-side obliquely upward H20U10 position (f) spaced at an interval of 20 mm from the center position CEN to the heel side and upward at an interval of 10 mm from the center position CEN, a heel-side obliquely downward H20D10 position (g) spaced at 20 mm from the center position CEN to the heel side and downward at an interval of 10 mm from the center position CEN, a toe-side obliquely upward T20U10 position (h) spaced at an interval of 20 mm from the center position CEN to the toe side and upward at an interval of 10 mm from the center position CEN, and a toe-side obliquely downward T20d10 position (i) spaced at an interval of 20 mm from the center position CEN to the toe side and downward at an interval of 10 mm from the center position CEN.
In the head models of the examples 1 through 8 shown in table 1, Smax′/Smax were less than 1.3. Thus it could be confirmed that the restitution performance at the off-center positions of the face part was similar to that at the center (sweet area) of the face part. That is, it could be also confirmed that the sweet area could be enlarged. The durability of the head models of the examples 1 through 8 was favorably evaluated as ⊚ and ◯.
On the other hand, in the head models of the comparison examples 1 through 4 shown in table 2, Smax′/Smax exceeded 1.3. Thus it could be confirmed that the restitution performance at the off-center positions of the face part was different from that at the center (sweet area) of the face part. That is, the restitution performance obtained at the center position could not be obtained at the off-center positions. The durability of the head models of the comparison examples 1 through 4 was evaluated as Δ or X.

Claims

1. A method of designing a golf club head by using a computer, comprising the steps of:

preparing a ball model and a club head model obtained by dividing a golf ball and a golf club head into a plurality of finite elements respectively, wherein said club head model is provided with a central reinforcing rib formed at a central portion of a rear surface of a face part thereof and a plurality of belt-shaped reinforcing ribs extended radially from said central reinforcing rib toward a peripheral edge of said rear surface of said face part;

executing simulation of collision between said ball model and said club head model at a plurality of positions of a front surface of said face part thereof to determine a Mises stress generated at each of said collision positions; and

changing setting conditions of said central reinforcing rib and said belt-shaped reinforcing ribs to set a maximum value of Mises stresses generated at off-center positions of said front surface of said face part to less than 1.3 times a maximum value of a Mises stress generated at a center of said front surface of said face part.

2. The method according to claim 1, wherein not less than four nor more than 10 belt-shaped reinforcing ribs are formed on said rear surface of said face part; and said setting conditions of said belt-shaped reinforcing ribs include a number of said belt-shaped reinforcing ribs, positions thereof, sectional areas thereof, heights thereof, and widths thereof.

3. The method according to claim 1, wherein said club head model is a wood club head model; said reinforcing ribs are formed on a rear surface of a metal plate forming said face part; and when said maximum value of said Mises stresses generated by said collision between said ball model and said club head model at said off-center positions of said front surface of said face part is not less than 1.3 times said maximum value of said Mises stress generated by said collision between said ball model and said club head model at said center of said front surface of said face part, said sectional area, said width or/and said height of said reinforcing ribs, disposed on said rear surface of said face part, which correspond to said off-center positions are set large, whereas when said ratio is less than 1.0, said sectional area, said width or/and said height of said reinforcing ribs, disposed on said rear surface of said face part, which correspond to said off-center positions are set small.

4. The method according to claim 2, wherein said club head model is a wood club head model; said reinforcing ribs are formed on a rear surface of a metal plate forming said face part; and when said maximum value of said Mises stress generated by said collision between said ball model and said club head model at said off-center positions of said front surface of said face part is not less than 1.3 times said maximum value of said Mises stress generated by said collision between said ball model and said club head model at said center of said front surface of said face part, said sectional area, said width or/and said height of said reinforcing ribs, disposed on said rear surface of said face part, which correspond to said off-center positions are set large, whereas when said ratio is less than 1.0, said sectional area, said width or/and said height of said reinforcing ribs, disposed on said rear surface of said face part, which correspond to said off-center positions are set small.

5. The golf club head designed by a designing method according to claim 1.

6. A golf club head, wherein a central reinforcing rib is formed at a central portion of a rear surface of a face part and not less than four nor more than 10 belt-shaped reinforcing ribs are extended radially from said central reinforcing rib toward a peripheral edge of said rear surface of said face part; and

a maximum value of Mises stresses generated by collision between a golf ball and said golf club head at off-center positions of a front surface of said face part is set to less than 1.3 times a maximum value of a Mises stress generated by collision between said golf ball and said golf club head at a center of said front surface thereof.

7. A golf club head in which a central reinforcing rib is formed at a central portion of a rear surface of a face part and not less than four nor more than 10 belt-shaped reinforcing ribs are extended radially from said central reinforcing rib toward a peripheral edge of said rear surface of said face part; a ratio (W/t) of a width W of each of said belt-shaped reinforcing ribs to a height t thereof is set to not less than 15 nor more than 40; and each of said belt-shaped reinforcing ribs forms an intersection angle of not less than 100 degrees nor more than 160 degrees with respect to a reference plane of said rear surface of said face part.

8. The golf club head according to claim 5, wherein said reinforcing ribs are formed on a rear surface of a metal plate composing said face part; and a sectional area of said central reinforcing rib is set to not less than 20% nor more than 90% of an area of an entire rear surface of said face part.

9. The golf club head according to claim 6, wherein said reinforcing ribs are formed on a rear surface of a metal plate composing said face part; and a sectional area of said central reinforcing rib is set to not less than 20% nor more than 90% of an area of an entire rear surface of said face part.

10. The golf club head according to claim 7, wherein said reinforcing ribs are formed on a rear surface of a metal plate composing said face part; and a sectional area of said central reinforcing rib is set to not less than 20% nor more than 90% of an area of an entire rear surface of said face part.

11. The golf club head according to claim 8, wherein a thickness of said central reinforcing rib is set to not less than 2.6 mm nor more than 5.0 mm; and an area of said central reinforcing rib is set to not less than 10 mm²nor more than 1000 mm².

12. The golf club head according to claim 9, wherein a thickness of said central reinforcing rib is set to not less than 2.6 mm nor more than 5.0 mm; and an area of said central reinforcing rib is set to not less than 10 mm²nor more than 1000 mm².

13. The golf club head according to claim 10, wherein a thickness of said central reinforcing rib is set to not less than 2.6 mm nor more than 5.0 mm; and an area of said central reinforcing rib is set to not less than 10 mm²nor more than 1000 mm².

14. The golf club head according to claim 5, wherein a portion where said adjacent belt-shaped reinforcing ribs intersect with each other is rounded; and a ratio (θ/R) of an intersection angle θ (degree) formed between said adjacent belt-shaped reinforcing ribs to a radius of curvature R (mm) of said rounded portion is set to not less than three nor more than 50.

15. The golf club head according to claim 6, wherein a portion where said adjacent belt-shaped reinforcing ribs intersect with each other is rounded; and a ratio (θ/R) of an intersection angle θ (degree) formed between said adjacent belt-shaped reinforcing ribs to a radius of curvature R (mm) of said rounded portion is set to not less than three nor more than 50.

16. The golf club head according to claim 7, wherein a portion where said adjacent belt-shaped reinforcing ribs intersect with each other is rounded; and a ratio (θ/R) of an intersection angle θ (degree) formed between said adjacent belt-shaped reinforcing ribs to a radius of curvature R (mm) of said rounded portion is set to not less than three nor more than 50.

17. The golf club head according to claim 8, wherein a portion where said adjacent belt-shaped reinforcing ribs intersect with each other is rounded; and a ratio (θ/R) of an intersection angle θ (degree) formed between said adjacent belt-shaped reinforcing ribs to a radius of curvature R (mm) of said rounded portion is set to not less than three nor more than 50.

18. The golf club head according to claim 11, wherein a portion where said adjacent belt-shaped reinforcing ribs intersect with each other is rounded; and a ratio (θ/R) of an intersection angle θ (degree) formed between said adjacent belt-shaped reinforcing ribs to a radius of curvature R (mm) of said rounded portion is set to not less than three nor more than 50.