JP4996449B2 - Golf ball design method and manufacturing method thereof - Google Patents

Description

  The present invention relates to a golf ball design method useful for efficiently designing a golf ball capable of exhibiting an optimal motion state using numerical analysis by a computer, and a manufacturing method thereof.

  A golf ball usually has a multilayer structure in which a plurality of layers of different materials are concentrically arranged. In order to optimize the various motion states of the golf ball, different materials are employed for each layer based on their position and / or function. In order to develop a golf ball capable of exhibiting an optimal motion state, it is necessary to assign a variety of materials to each of the above-described layers and make a number of trial golf balls to evaluate the performance. However, since the number of combinations of materials is enormous, the development of a golf ball requires a great deal of time and effort.

  Therefore, in recent years, various methods for designing a golf ball that can exhibit an optimal motion state using a numerical analysis method using a computer have been proposed (for example, see Patent Documents 1 to 7 below). In these methods, a plurality of types of golf ball models that can be numerically analyzed by a finite element method or the like are set, a ball hitting simulation is performed using the golf ball model, and the results of the simulation (for example, the initial launch velocity and the backspin amount) From the above, it is proposed to select the material distribution of the golf ball with the optimal motion state.

JP 2005-40233 A JP 2005-103127 A JP 2005-21191 A JP-A-2005-319304 JP-A-2005-324023 JP 2006-31430 A JP 2006-87451 A

  By the way, in the above-described design method, in order to find a golf ball capable of exhibiting an optimal motion state, a large number of golf ball models in which different design variables (material characteristics such as elastic modulus) are assigned to each layer are set. Is done. However, in the conventional method, the number of design variables becomes equal to the number of layers of the golf ball model. For example, when the number of layers of the golf ball model is increased for detailed analysis, the number of design variables is accordingly increased. There has been a problem that the search for the optimum solution takes a very long time.

  In the conventional method, design variables of each layer are not associated at all. For this reason, the value of the design variable obtained by optimizing the motion state may vary greatly between adjacent layers, and actual design or manufacture may be difficult.

The present invention has been devised in view of the above circumstances. In the golf ball model layer, the material property distribution from the innermost layer to the outermost layer is regarded as one function (basic function). The golf ball model layer is based on setting a plurality of types of golf ball models based on a plurality of functions obtained by sequentially linearly combining one or more basis functions consisting of continuous functions by changing weighting coefficients. Regardless of the number, it is possible to reduce the number of design variables, and to suppress a large difference in material properties between layers of the golf ball model, and to use a golf ball design method that can be actually designed or manufactured. The main object of the present invention is to provide a golf ball manufacturing method.

The invention described in claim 1 of the present invention is a method for designing a golf ball having a multilayer structure in which a plurality of layers made of different materials are concentrically arranged, and can be numerically analyzed and launched by a golf club. The golf ball is modeled using a plurality of elements in which the characteristics of the material of the golf ball that affect the motion state of the golf ball are defined, and the characteristics of the material from the innermost layer to the outermost layer in the layer A model setting step for setting a plurality of types of golf ball models having different distributions, a simulation step for calculating the motion state of each golf ball model based on preset conditions, and the plurality of types of golf ball models with movement state and a searching step of searching the optimum, the model setting step, as the following equation (1) The basic function X ₀ representing the preset distribution of properties of the material, based on one or more basis functions consisting of a continuous function by changing the weighting factors to a plurality of functions X _S obtained by linear combination, said A plurality of types of golf ball models are set.
_{X S = X 0 + a 1} · X 1 + a 2 · X 2 + ... + a n · X n ... (1)
Here, X ₀ is a basic function, a ₁ , a ₂ ,..., _An are weighting coefficients, X ₁ , X ₂ ,... X _n are basis functions consisting of continuous functions. The layer number is used as an explanatory variable.

According to a second aspect of the present invention, in the golf ball according to the first aspect, the number n of the basis functions linearly coupled to the basic function is smaller than the number of layers distinguishable by the characteristics of the material of the golf ball model. This is the design method.

According to a third aspect of the present invention, the basis function includes a linear function group including a constant function and a linear function, a sine function group including a plurality of sine functions having different periods, and a cosine function including a plurality of cosine functions having different periods. 3. The golf ball design method according to claim 1, comprising a total of two or more continuous functions selected from at least two groups.

According to a fourth aspect of the present invention, in the golf ball design according to any one of the first to third aspects, the characteristics of the material include at least one of an elastic modulus, a Poisson's ratio, a density, a shear elastic modulus, or a damping constant. Is the method.

According to a fifth aspect of the present invention, a golf ball is manufactured based on a distribution of characteristics of the material of an optimum golf ball model obtained by the golf ball design method according to any one of the first to fourth aspects. It is a manufacturing method of the golf ball characterized by including a step.

In the first aspect of the present invention, the model setting step may be performed by changing the weighting coefficient to a basic function that represents the distribution of material characteristics that affect the motion state of the golf ball when it is launched by a golf club. Based on a plurality of functions obtained by sequentially linearly combining basis functions consisting of continuous functions, a plurality of types of golf ball models having different material property distributions are set. Therefore, in the invention according to claim 1, the design variable of the golf ball model is equal to the number of the weighting factors, in other words, the number of basis functions linearly coupled to the basic function. Therefore, for example, even if the number of layers of the golf ball model is increased in order to perform detailed analysis, the number of design variables can be made smaller than the number of layers. Therefore, the search time for the optimum solution can be shortened, and the design efficiency can be improved. In addition, for example, when the types of continuous functions to be linearly combined and / or the weighting coefficient are restricted within a certain range, it is possible to prevent the material property values between adjacent layers of the golf ball model from greatly differing.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
In the golf ball designing method of the present embodiment, a golf ball that optimizes the motion state when hit by a golf club, in particular, a solid type golf ball having a multilayer structure in which a plurality of layers of different materials are concentrically arranged. Designed. FIG. 1 shows an example of the procedure of such a design method.

  As shown in FIG. 1, in the design method of the present embodiment, first, a golf ball model is set (step S1). An example of a specific process for setting the golf ball model is shown in FIG. In the present embodiment, first, a process of modeling a golf ball using a finite number of elements is performed (step S11).

  In FIG. 3, an example of the golf ball model 2 is visualized as a cross-sectional view. In the golf ball model 2, for example, a golf ball to be analyzed (whether or not actually exists) is divided using a plurality of elements e capable of numerical analysis. In other words, the golf ball model 2 is an aggregate of a finite number of small elements e. The possibility of numerical analysis means that the model can be deformed by a numerical analysis method such as a finite element method, a finite volume method, a difference method, or a boundary element method. Therefore, for each element e, the coordinate value of the node, the element shape, the physical property value of the material represented by the element, and the like are appropriately defined. Such an entity of the golf ball model 2 is numerical data that can be handled by a computer device (not shown).

  The element e is preferably a three-dimensional solid element, for example. The golf ball model 2 of the present embodiment is modeled with 11 layered objects. Specifically, the spherical core portion 2a that forms the innermost layer and the 10 cores that are sequentially stacked concentrically on the outer side. It consists of layer portions 2b to 2k. It goes without saying that the number of layers (the number of materials) can be appropriately changed according to the golf ball to be analyzed or designed, but is set to two or more layers, more preferably three or more layers in accordance with the conventional practice. Is desirable.

Each element e defines at least a material characteristic that affects the motion state of the golf ball when it is launched by a golf club. Here, examples of the motion state of the golf ball include a flight distance, a launch angle, a backspin amount, or a launch initial speed. In addition, the golf ball model 2 of the present embodiment is set as an elastic body model in which all elements e are defined as elastic bodies. For this reason, it is desirable that the characteristics of the material affecting the motion state include at least one of elastic modulus, Poisson's ratio, density, shear elastic modulus, or damping constant. The flight distance is obtained by ballistic calculation using a launch angle, a backspin amount, and a launch initial speed obtained by a hit simulation described later.

  Further, the total number (total number of elements) of the elements e constituting the golf ball model 2 is not particularly limited. However, if the number is too small, for example, it may be difficult to analyze the deformation of the ball in detail. If the amount is too large, the deformation calculation of the golf ball model 2 may take a long time. From such a viewpoint, the total number of elements e constituting the golf ball model 2 is preferably 100 or more, more preferably 1000 or more, and preferably 1000000 or less, more preferably 100000 or less. .

  In the golf ball model 2 of the present embodiment, each of the layers 2b to 2k excluding the core 2a is formed in a spherical shell shape by connecting hexahedral solid elements in the spherical direction. The core portion 2a of the present embodiment includes a cube portion 2a1 formed into a cube by superimposing a plurality of regular hexahedron solid elements, and each element surface of the outer surface of the cube portion 2a1, in order to easily represent a spherical shape. And a plurality of hexahedral solid element shells 2a2 that extend in the radial direction and constitute a spherical outer surface as a whole. The golf ball model 2 can be modeled by various methods as long as it can reproduce a spherical shape. For example, the golf ball model 2 of the above embodiment is configured using all solid elements, but may include a shell element, for example.

Next, in the present embodiment, a basic function X ₀ representing the distribution of the material characteristics of the basic golf ball model 2 is set (step S12). The properties of the material, but include various ones as described above, the properties of the materials represented by the basic function X _0, optimize the motion state of a golf ball model the values by which variously changed What to do is selected. In the present embodiment, the elastic modulus is adopted as a characteristic of the material representing this distribution. Such a distribution of elastic modulus is determined by various methods. For example, the distribution of elastic modulus of an existing golf ball may be assigned to each layer 2a to 2k of the golf ball model 2 or may be set to a constant value.

  FIG. 4 shows a basic function X0 representing the elastic modulus distribution of the basic golf ball model 2. In FIG. 4, the elastic modulus is set on the vertical axis, and the layer numbers assigned in order from the innermost layer (core portion 2 a) to the outermost layer (layer 2 k) of the golf ball model 2 are set on the horizontal axis. The basic function X0 of the present embodiment is defined as a function indicating a distribution in which the elastic moduli of all the layers 2a to 2k are 300 MPa, as shown in FIG.

Then, as in the illustrative formula (1), the basic function X _0, the weighting coefficients a _1, a 2, 1 or more to change the _... a _n, basis functions X and more preferably comprising a plurality of continuous functions _1, X 2, and _... X _n, successively, by a linear combination (linear combinations), the process of obtaining a plurality of functions X _S representing the distribution of the different elastic modulus and the basic function X ₀ is performed (step S13).
_{X S = X 0 + a 1} · X 1 + a 2 · X 2 + ... + a n · X n ... (1)

Thus, the basic function _{X 0,} the weighting coefficients _{a 1,} a 2, ... basis function _{X 1,} X 2 which changed _{a n,} by ... sequentially linear combination of _{X n,} characteristic of the material (elastic modulus distribution) can make a plurality of different functions X _S different. In order to achieve various functions X _S, basis functions X _1, X 2, the _... X _n, may any continuous function may be used, for example constant function, a linear function, quadratic function, cubic function, exponential function One or more, more preferably a plurality of functions selected from continuous functions such as a logarithmic function and a trigonometric function are used.

The selected basis function is multiplied by a weighting coefficient. Thereby, functions Xs representing various elastic modulus distributions can be obtained. For example, when three basis functions X ₁ , X _2, and X ₃ are linearly combined with the basic function X ₀ , the equation (1) is expressed as follows.
X _S = X ₀ + a ₁ · X ₁ + a ₂ · X ₂ + a ₃ · X ₃
As is clear from the above equation, the newly set function Xs indicating the distribution of material properties is represented by three variables (a ₁ · X ₁ ), (a ₂ · X ₂ ), and (a ₃ · X _3). ) Alone, the distribution of the elastic modulus of each layer of the golf ball model 2 can be specified. Therefore, in the design method of the present invention, the number of basis functions X ₁ , X ₂ ... Linearly coupled to the basic function X ₀ is equal to the number of design variables of the golf ball model 2.

Also in the conventional design method, a material characteristic (for example, elastic modulus) is assigned to each element. However, the properties of these materials are not related at all between adjacent elements (interlayers) in the ball radial direction. Therefore, in the conventional design method, the number of layers constituting the golf ball model 2 is the number of design variables of the golf ball model 2 (for example, the number of layers constituting the golf ball model 2 is 11). In that case, the number of design variables is 11.) As described above, the design variable targets are completely different between the design method of the present embodiment and the conventional design method. Therefore, in the design method of this embodiment, the number of design variables can be freely determined separately from the number of layers of the golf ball model 2.

In the design method of the present embodiment, the number of basis functions linearly coupled to the basic function X ₀ is the number of layers constituting the golf ball model 2 (here, “number of layers” refers to the characteristics of the material). It means the number of layers that can be distinguished by being different). Therefore, the elastic modulus distribution of the golf ball model 2 having 11 layers can be defined with fewer design variables than the conventional one (only three design variables in the above example). In addition, the golf ball model 2 having a small number of design variables can greatly reduce the computational load of the computer, and the calculation time required for the optimum solution search process described later can be shortened. Therefore, the design method of this embodiment can greatly improve the design efficiency.

In particular but not limited, in the function X _S represented by the formula (1), the basis function X ₁ is a linear combination to the basic function X _0, X 2 _... number is too small, the golf ball model Therefore, there is a risk that the optimal solution for sufficiently improving the motion state of the golf ball model cannot be obtained. From this point of view, when obtaining the function X _s , the number of basis functions linearly coupled to the basic function X ₀ is preferably 6 or more, more preferably 10 or more, and still more preferably 14 or more. desirable. On the other hand, if the number of the basis functions is too large, the design variables of the golf ball model 2 increase as in the conventional case, and the calculation time until finding the optimum solution may be long. From this point of view, the number of the basis functions is desirably smaller than the number of layers constituting the golf ball model 2, but is preferably 30 or less, more preferably 25 or less, and still more preferably 20 Less than the number is desirable.

By the above processing, the basic function _{X 0,} the weighting coefficients _{a 1,} a 2, ... basis function _{X 1,} X 2 which changed _{a n,} ... by sequentially linear combination of _{X n,} and the basic function _{X 0} can obtain a number of different functions X _S showing the distribution of different modulus.

  Here, in order to obtain a function Xs having a smoother change in elastic modulus, the basis function is a total of 2 each selected from at least two groups of a linear function group A, a sine function group B, and a cosine function group C. It is desirable to use the above function.

FIG. 5 shows an example of the linear function group A, and the group A can include, for example, a constant function A-1 and a linear function A-2. The constant function A-1 is a function having a constant elastic modulus in each layer of the golf ball model 2 and being continuous. If such a constant function A-1 linear combination to the basic function X ₀ as a basis function X _1, can be moved parallel to the bottom or top the basic function X _0. The amount and direction of the movement can be adjusted by changing the value and sign of the weighting coefficient to be multiplied.

The linear function A-2 is a function in which the elastic modulus increases in proportion to the position from the innermost layer of the golf ball model 2. If linear combination to the basic function X ₀ the linear function A-2 as a basis function X _2, it is possible to change the entire inclination basic function X _0. The direction and angle of the inclination can be adjusted by the value and sign of the weighting coefficient multiplied by it. The linear function A-2 of this embodiment has an elastic modulus of zero at an intermediate position of the number of layers of the golf ball model 2 (in this example, the sixth layer). Thus, the primary function A-2 can be rotated a basic function X ₀ the intermediate position of the number of layers as a fulcrum.

  FIG. 6 shows an example of the sine function group B. The group B includes, for example, a plurality of sine functions (sin functions) having different periods. Specifically, four sine functions having a period of 1/2 or more and 2 or less times the horizontal axis length L from the layer number 1 to 11 of the golf ball model 2 of the horizontal axis are desirable. Specifically, a basic sine function B-1 having a period twice as long as the length L, a double sine function B-2 having a period equal to the length L, and a period of 2/3 of the length L. And a quadruple sine function B-4 having a period of ½ of the length L.

  FIG. 7 shows an example of the cosine function group C. The group C includes a plurality of cosine functions (cos functions) having different periods, for example. Specifically, examples of four cosine functions having a period of 1/2 or more and 2 or less times the horizontal axis length L from the layer number 1 to 11 of the golf ball model 2 of the horizontal axis are shown. Specifically, a basic cosine function C-1 having a period twice as long as the length L, a double cosine function C-2 having a period equal to the length L, and a period that is 2/3 of the length L. And a quadratic cosine function C-4 having a half period of the length L.

If these sine and cosine functions is used as a basis function may smoothly or decrease to increase the elastic modulus of the basic function X ₀ at the peak position of the waveform. In addition, it is desirable that substantially all continuous functions can be expressed by appropriately overlapping trigonometric functions (sine function and cosine function). Further, as in the present embodiment, when each period of the sine function and cosine function is set to ½ or more of the length L, the peak of the waveform of the sine function or cosine function is only five at the maximum. not exist. Therefore, such a basis function, the modulus of elasticity of the basic function X ₀ is also desirable because it prevented from being deformed in a waveform as repeated frequently moved up and down a number of peaks.

It is particularly preferable that two or more functions selected from at least two groups of the linear function group A, the sine function group B, and the cosine function group C are used. That is, at least two groups are selected from the three groups A to C (for example, A and B), and at least one function (for example, a constant function A-1 and a basic sine function B-1) is selected from each of the selected groups. ) Is preferred. This may alter the various aspects of the distribution of the represented modulus basic function X _0. It is particularly preferable that at least one function is selected from each of the three groups. As a result, various elastic modulus distributions can be obtained. Needless to say, when the functions _XS are sequentially obtained, the number of basis functions to be combined may be constant or may be changed.

  The selection of the basis function and the setting of the weighting coefficient value are not particularly limited, and may be performed randomly, for example, or may be performed according to some predetermined algorithm (for example, a genetic algorithm). May be.

Next, it is determined whether not the number of types is enough of functions X _S representing the distribution of the set elasticity modulus (step S14), and if the result is true (Y), the process returns to step S2 of FIG. On the other hand, if the result is false (N) in step S14, the value of the basis function and / or the weighting coefficient is changed (step S15), and the process of step S13 is performed until the result of step S14 becomes true (Y). Is repeated. In this way, the function X _S is obtained which represents the distribution of the elastic modulus of the necessary and sufficient golf ball models in the design of the golf ball. These functions _XS are sequentially stored in a storage device of a computer (not shown).

Figure 8 shows an example of a 299 amino function X _S showing the distribution of the elastic modulus of the resulting golf ball model 2 by steps S11 through S15 in the is shown with the basic function X _0. In this embodiment, the resulting function X _S is narrowed by the constraint that only some in the upper and the scope of the lower limits of a predetermined elastic modulus is employed, the function X _S are available that do not meet this It is deleted without being done. Thereby, it can suppress that the function which shows distribution of the elasticity modulus of the ball which is difficult to manufacture is generated. As a criterion for such a constraint condition, for example, the minimum value (lower limit) of the function X _S representing the newly set elastic modulus distribution is 50% or more of the minimum value of the basic function X ₀ , and the function X the maximum value of _S (upper limit) include be 150% or less of the maximum value of the basic function _{X 0.}

  Next, in the present embodiment, various conditions are set (step S2), and based on the conditions, an impact simulation step for calculating the motion state of each golf ball model 2 is performed, and the motion state is output from the result. (Step S3). That is, a hitting simulation is performed using the large number of golf ball models 2 obtained in step S1, and the respective motion states are calculated.

  As shown in FIG. 9, the hitting simulation is executed, for example, by causing the golf ball model 2 to collide with the fixed flat plate model 3 and performing deformation calculation of the golf ball model 2 in time series. The flat plate model 3 imitates a golf club head and, like the golf ball model 2, is composed of a finite number of elements. In order to simplify the calculation, the flat plate model 3 of the present embodiment is defined by a rigid element 3a that does not deform. However, an elastic characteristic or the like based on an actual club head material may be defined.

  Further, various conditions (physical property values) are defined in the golf ball model 2 in the hit simulation. Since the golf ball model 2 of the present embodiment is an elastic body model, a mass density, a Poisson's ratio, and the like are set for each element e. In the present embodiment, these values are defined as the same value in all layers in order to examine the influence of the elastic modulus mainly. Further, for the impact simulation, the collision speed (corresponding to the head speed), the collision angle (corresponding to the loft angle) between the golf ball model 2 and the flat plate model 3 and the friction coefficient between the golf ball model 2 and the flat model 3 Etc. are set.

  In the hit simulation, deformation calculation of the golf ball model 2 is performed. In the deformation calculation, a mass matrix, a stiffness matrix, and a damping matrix for each element are created based on the shape and material characteristics of each element, and a matrix for the entire system is created by combining these matrices. . Then, equations of motion are created by applying the various conditions described above, and for example, these are sequentially calculated and stored by the computer device in increments of minute time increments Δt. Thereby, the deformation behavior of the golf ball model 2 colliding with the flat model 3 is obtained in time series as numerical data indicating the coordinate values of the nodes of each element.

  Further, the flight distance of a golf ball when hit with a golf club is substantially determined by the three motion states of the backspin amount, launch angle, and launch initial speed. Therefore, a golf ball having excellent motion characteristics (flight characteristics) can be designed by determining the motion state as an objective function and finding the elastic modulus distribution of each layer of the golf ball model 2 in which the objective functions are all optimal. Therefore, in the hitting simulation of the present embodiment, the results regarding the three movement states together with the flight distance are output for each golf ball model 2 and stored in the computer device. However, the exercise state is not limited to the above three indicators.

Next, in the design method of the present embodiment, a process for scalarizing the motion state is performed (step S4). In order to search for a distribution of elastic modulus of each layer of the golf ball model 2 that optimizes a plurality of independent motion states (objective functions), the distribution of the optimal elastic modulus is determined unless some weighting condition is given. It becomes difficult. Therefore, in the present embodiment, a plurality of motion states are scalarized by multiplying the weighting coefficient by the value of each motion state and adding it. Thereby, the exercise state that should be emphasized can be determined. A specific method for realizing the scalarization is not particularly limited. For example, linear combination (see the following formula (2) for the general formula), Chebyshev type (see the following formula (3) for the general formula), etc. Can be adopted.
F = w ₁ · f ₁ + w ₂ · f ₂ +... + W _r · f _r (2)
F = Max {w ₁ · f ₁ , w ₂ · f ₂ ,..., W _r · f _r } (3)
However, the symbols are as follows.
F: scalar value of motion state f _i : normalized value of each motion state w _i : coefficient for each motion state

  Next, in the present embodiment, an approximate response function is generated (step S5), and an optimal solution for the motion state is searched using it (step S6).

Approximation response functions is a function that relates with the weighting coefficients of basis functions a _1, a 2 _... a _n is a design variable, between a scalar value F of the motion state is the objective function, for example, a neural network . FIG. 10 shows, as an example, an approximate response function including a three-dimensional curved surface that relates two weighting coefficients a ₁ and a ₂ and a scalar value F of a motion state.

  Generating an approximate response function is not a requirement of the present invention. However, the approximate response function interpolates the analysis result (scalar value F) at the position of the weighting coefficient that has not been set, and enables quick prediction of optimization candidates. Therefore, it is desirable to generate such an approximate response function in order to search for an optimal solution efficiently and in a short time. Further, in the design method of the present embodiment, the number of design variables can be reduced as compared with the prior art, and therefore it is desirable in that the approximate response function can be generated in a short time. Therefore, the design efficiency is further improved. The approximate response function can be realized by various methods according to the custom, but for example, a response surface method (RSM), a radial basis function (RBF) or a Kriging method is preferable. Used for. In addition, as a method for searching for an optimal solution from an approximate response function, a genetic algorithm, a gradient method, an annealing method, or the like is employed in accordance with a customary practice.

Next, it is determined whether or not the searched optimal solution (motion state) is satisfactory (step S7), and if it is true (Y in step S7), each layer of the golf ball model 2 that provides the optimal solution is determined. The elastic modulus distribution (function) is output as visible information to a monitor or printer (step S8). On the other hand, if the obtained optimal solution cannot be satisfied (N in step S7), step S1 and subsequent steps are repeated again, and the search for optimization is continued. Determination in step S7, for example, prior to optimization (the result of the reference function X ₀₎ and the rate of change of the motion state compared (improvement rate), can be easily performed in comparison with a predetermined threshold value.

The distribution of elastic modulus of each layer of the golf ball model 2 of the present embodiment designed according to the above procedure is based on the basis functions X ₁ and X consisting of continuous functions by changing the weighting coefficient to the preset basic function X _{0. 2 ...} sequentially because they are set on the basis of a plurality of functions X _S obtained by linearly combining the change in elastic modulus is relatively smooth ones. Therefore, there is an advantage that it is possible to design a ball having an elastic modulus distribution that is easy to manufacture and an optimized motion state. Furthermore, when the number of basis functions serving as design variables is set to be smaller than the number of layers of the golf ball model, the number of design variables is significantly reduced as compared to the conventional case. Therefore, the time for searching for the optimum solution can be shortened, and the design efficiency can be greatly improved.

  Needless to say, a golf ball in which the elastic modulus of each layer is determined can be easily made by adjusting the blending of each layer in accordance with the custom.

  Although the embodiments of the present invention have been described above, the present invention is not limited to the specific embodiments described above, and can be implemented with various modifications. For example, although the golf ball model 2 has been shown to be an elastic body model in which all elements are made of an elastic body, it is not limited to such a model. For example, the golf ball model 2 may be set as a rigid model in which elements are composed of only rigid bodies, an elasto-plastic model in which elements are composed of elasto-plastic elements, or a super-elastic body model in which elements are composed of super-elastic bodies.

In the case of the rigid body model, the mass density can be defined for each element of the golf ball model 2 as a characteristic of a material having a different distribution in each layer. In the case of an elastoplastic model, it is possible to define each layer by changing the characteristics of at least one material of mass density, shear elastic modulus, yield stress, plastic hardening coefficient after yielding, and bulk elastic modulus. Furthermore, in the case of a superelastic body model,

  In order to confirm the effect of the present invention, the golf ball was optimally designed according to the present invention. The golf ball model is composed of 4257 solid elements and has 11 layers as shown in FIG. Moreover, the mass density and Poisson's ratio of each element were made constant, and only the elastic modulus of each element was changed. Table 1 shows the distances from the center of the golf ball model to each layer.

  As shown in FIG. 4, the basic function is that each layer has an elastic modulus of 300 MPa. In addition, as the motion state (objective function) to be optimized, the back spin amount, launch angle, and launch initial speed were selected.

  Next, in order to optimize the above three motion states, a plurality of types of golf ball models having different elastic modulus distributions are created by linearly combining various basis functions with the basic function, and a hitting simulation is performed on these models. It was. In addition to the linear function group, the basis function includes at least two groups: a sine function group consisting of a sine function whose period is ½ or more and twice or less the length of the golf ball model, and a cosine function group consisting of a cosine function. A total of 10 functions, each selected from: Further, a constraint condition was given so that the minimum value of the elastic modulus was 10 MPa or more.

For the impact simulation, a computer having an Intel Itanium (registered trademark) 1.6 GHz processor is used, and an engineering analysis application software using the finite element method (LS developed and improved by Livermore Software Technology, USA). -DYNA) was calculated for about 10 hours. The following conditions were set for the collision conditions, assuming a driver's hitting.
Collision speed: 34m / s
Collision angle: 13 degrees Friction coefficient between golf ball model and flat plate model: 0.16
Needless to say, by changing each of the above values, a hitting simulation of an iron, a wedge, or a putter can be performed.

Next, after the hit simulation, the motion state was scalarized, the approximate response function was generated, and the optimum solution was searched. A computer having an Intel Pentiume 4 (registered trademark) 3.8 GHz processor was used for these processes, and an optimal solution could be found in about 5 hours. In addition, the following formula was adopted as the scalarization function of the motion state.
F = 2.0 · f ₁ + 1.0 · f ₂ + 1.0 · f ₃
f ₁ : Normalized value of backspin amount f ₂ : Normalized value of launch angle f ₃ : Normalized value of launch initial speed

  The distribution of the elastic modulus of each layer of the golf ball model that optimizes the three motion states of the golf ball model is as shown in FIG. As is clear from these figures, in the distribution of the elastic modulus of the golf ball model obtained by this example, there is no so-called “elasticity jump” in which the elastic modulus changes greatly between adjacent elements, And since all the peaks are suppressed few, it is desirable at the point which can manufacture comparatively easily. Further, Table 3 shows the above-described three motion states based on the impact simulation before and after the optimization, and the flight distance obtained by the ballistic calculation using them.

  FIG. 12 shows a graph with the vertical axis representing sensitivity and the horizontal axis representing basis functions. The sensitivity is obtained by quantifying the degree of influence on each objective function when the weighting coefficient applied to the basis function is changed. The greater the sensitivity, the greater the importance of the objective function. From FIG. 12, it can be seen that in the impact simulation of this embodiment, the sensitivity of the constant function, the basic sine function, and the basic cosine function is high.

  For comparison, FIG. 13 shows an optimization result when the elastic modulus of each layer of the golf ball model is directly defined as a design variable without using the basic function and the basis function. In this method, the number of design variables is 11, and it takes about 30 hours to find the optimum solution. It can also be seen that the distribution of elastic modulus of the golf ball model that brings about optimization has many peaks and jumps in elastic modulus between layers.

Further, golf balls according to the elastic modulus distribution shown in FIG. 11 were made as prototypes, and they were hit with five golfers to measure the flight distance. The results are average values at the time of hitting 10 balls, respectively, and are shown as an index with the value before optimization being 100. The larger the value, the better. Note that the golf club used was a wood-type club with a loft angle of 12 degrees in order to ensure consistency in conditions between the hit simulation and the actual hit test, and the head speed is about 40 m / s for golfers. Was chosen.
Table 3 shows the test results.

  As a result of the test, it was confirmed that the optimized golf ball showed favorable results such as an increase in flight distance and a reduction in the backspin amount as compared with before optimization.

It is a flowchart which shows an example of the procedure of the design method of the golf ball of this embodiment. It is a flowchart which shows an example of the setting procedure of a golf ball model. It is sectional drawing which visualizes and shows a golf ball model. It is a graph which shows the basic function of a golf ball model. It is a graph which shows the function which belongs to a linear function group among basis functions. It is a graph which shows the function which belongs to a sine function group among basis functions. It is a graph which shows the function which belongs to a cosine function group among basis functions. It is a graph which shows the function which linearly combined the basic function and the basic function with the basic function. It is a diagram which shows a hit simulation. It is a graph which visualizes and illustrates an approximate response function. It is a graph which shows distribution of the elastic modulus which optimizes the motion state of a golf ball model. It is a graph which shows the relationship between each basis function and the sensitivity to each performance of the golf ball model. It is a graph which shows distribution of the elastic modulus which optimizes the motion state of the golf ball model obtained by the conventional method.

Explanation of symbols

2 golf ball model e element X ₀ basic function X ₁ , X ₂ ... basis function A linear function group B sine function group C cosine function group

Claims (5)

A method for designing a golf ball having a multilayer structure in which a plurality of layers of different materials are concentrically arranged,
The golf ball is modeled using a plurality of elements that define the characteristics of the material of the golf ball that can be numerically analyzed and that affect the motion state of the golf ball when it is launched by a golf club. A model setting step for setting a plurality of types of golf ball models having different distributions of properties of the material from the inner layer to the outermost layer;
A simulation step for calculating the motion state of each golf ball model based on preset conditions;
A search step for searching for an optimal motion state from the plurality of types of golf ball models,
In the model setting step, as shown in the following formula (1), one or more basis functions composed of continuous functions are linearly combined with a basic function X ₀ representing the distribution of the characteristic of the material set in advance by changing the weighting coefficient. the golf ball design method based on the plurality of functions X _S obtained, wherein the plurality of types of the golf ball model is set by.
_{X S = X 0 + a 1} · X 1 + a 2 · X 2 + ... + a n · X n ... (1)
(Where X ₀ is a basic function, a ₁ , a ₂ ,... _An are weighting coefficients, X ₁ , X ₂ ,... X _n are basis functions made up of continuous functions. Also, the layer number is an explanatory variable.) 2. The golf ball designing method according to claim 1, wherein the number n of the basis functions linearly coupled to the basic function is less than the number of layers that can be distinguished by characteristics of the material of the golf ball model. The basis functions are selected from at least two groups of a linear function group composed of a constant function and a linear function, a sine function group composed of a plurality of sine functions with different periods, and a cosine function group composed of a plurality of cosine functions with different periods. The golf ball design method according to claim 1, comprising a total of two or more continuous functions. The golf ball design method according to claim 1, wherein the material characteristics include at least one of an elastic modulus, a Poisson's ratio, a density, a shear elastic modulus, and a damping constant. A golf ball comprising a step of manufacturing a golf ball based on a distribution of characteristics of the material of an optimal golf ball model obtained by the golf ball design method according to claim 1. Ball manufacturing method.

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