JP5476025B2 - Design variable and manufacturing method of golf club shaft - Google Patents

Description

  In the present invention, when the performance of a golf club shaft is optimized using a computer, the designer can easily find the optimum solution even when there are many objective functions, thereby reducing the design time or the design cost. The present invention relates to a design method and a manufacturing method of a golf club shaft which is useful for reduction.

  In recent years, various methods for designing a golf club shaft using numerical analysis by a computer have been proposed.

  For example, in the method of Patent Document 1 below, a step of setting a plurality of types of shaft models that can be numerically analyzed by a finite element method or the like and that have different bending stiffness distributions in the length direction of the shaft, and the shaft models are preset. A step of calculating a club model motion state (for example, head speed, blow angle, etc.) depending on each shaft model by performing a swing simulation to move based on a golfer's swing pattern, and from the result of the swing simulation, And a step of searching for a distribution of bending rigidity of the golf club shaft having an optimal motion state.

  In the method of Patent Document 2 below, the shape of the mandrel of the golf shaft, the selection of the planar member, the type of the planar member, the winding position of the planar member around the mandrel, and the fiber orientation angle of the planar member are input. By doing so, it is expected that the bending and torsional rigidity of the product golf shaft is calculated, and that it is possible to easily obtain accurate information necessary for designing or manufacturing a fiber reinforced plastic golf shaft.

JP 2004-8521 A JP 2001-104522 A

  By the way, a golf club shaft made of a fiber reinforced resin has a sheet member (hereinafter, referred to as “prepreg”) in which a fiber material oriented in one direction is impregnated with an uncured resin, wound around a mandrel. It is manufactured by applying heat treatment to cure the resin. Therefore, in order to design a golf club shaft of fiber reinforced resin, at least the type of the fiber material (which affects the density, elastic modulus, Poisson's ratio, etc. of the fiber material), the fiber material with respect to the axial direction of the shaft. Many design variables such as the orientation angle of the shaft and the inner diameter of the shaft need to be considered.

  Therefore, as in the above-mentioned Patent Document 2, for example, it is examined whether it is optimized only by calculating and predicting the bending rigidity and torsional rigidity of a product golf shaft when a certain combination of design variables is used. Can not. Further, when the characteristics of the product shaft are calculated for various combinations of design variables, it takes a lot of time to review the calculation results, and there is a problem that the design time and design cost cannot be made sufficiently efficient. .

  The present invention has been devised in view of the above problems. A shaft model using a finite number of elements and design variables defined therein is set, and a plurality of objective functions of the shaft model are set using a computer. And obtain a plurality of solutions that optimize the objective function from the approximate response function that links the relationship between the design variable defined in the shaft model and the objective function, and use the data envelope analysis method from the multiple solutions Incorporating a step to obtain a Pareto solution makes it easy for designers to select solutions and finds a compromise solution from multiple optimal solutions in a short time. The main object of the present invention is to provide a golf club shaft design method capable of sufficiently increasing the cost and a manufacturing method using the same.

The invention according to claim 1 of the present invention designs a golf club shaft made of a fiber reinforced resin manufactured using a plurality of prepregs which are sheet members obtained by impregnating an uncured resin with a fiber material oriented in one direction. A method of modeling a golf club shaft using a finite number of elements to obtain a shaft model that can be numerically calculated by a computer, defining a design variable of the shaft model, Calculating a plurality of different objective functions representing the performance of the shaft model set in the step using a computer, generating an approximate response function that links the relationship between the design variable and the objective function, and the approximation Obtaining a plurality of optimal solutions for optimizing the objective function based on a response function; See containing obtaining a Pareto solutions using data envelopment analysis from a plurality of optimal solutions, and setting the respective design variables of the golf club shaft in accordance with the Pareto solutions, the design variable, the Including an orientation angle of a fiber material, and the prepreg includes two bias layers that are stacked with the same prepreg shape and different orientation angles of the fiber material. The combination of the angles of the fiber materials is selected from among the determined combinations, and continuous variables for representing the objective function are defined in descending order of the elastic modulus in the axial direction. .

According to a second aspect of the present invention, the design variable includes at least one of an inner diameter of a shaft model, a fiber type of a fiber reinforced resin , a shape of a prepreg constituting the reinforced resin , and a stacking order of the prepreg. A golf club shaft design method.

  According to a third aspect of the present invention, in the golf club shaft design method according to the first or second aspect, the objective function includes two or more selected from the strength, bending rigidity, torsional rigidity, and weight of the shaft model. It is.

  According to a fourth aspect of the present invention, a golf club shaft is manufactured by using the golf club shaft designing method according to the first aspect.

  According to the present invention, a plurality of different objective functions are calculated using a computer from a shaft model in which design variables are defined. Then, a plurality of combinations of the design variable and the objective function are calculated with different design variables, and an approximate response function that links these relations is generated, and a plurality of the objective functions are optimized based on the approximate response function. A solution is obtained. Furthermore, in the present invention, a Pareto solution is obtained from the plurality of optimal solutions obtained here by using a data envelope analysis method. A Pareto solution is a kind of compromise solution. By obtaining such a Pareto solution, a designer can find an optimal solution that suits his or her purpose in a short time. As described above, according to the present invention, for example, an optimal solution can be found efficiently and in a short time from among a plurality of combinations of design variables such as the type of fiber material and the orientation angle. Therefore, the number of trials and errors in an experiment during product development can be greatly reduced. Furthermore, the ability to optimize a golf club shaft with a high degree of freedom in design helps to efficiently customize the specifications suitable for each golfer.

It is a flowchart which shows embodiment of this invention. (A) is the whole perspective view which visualized the shaft model, (b) is the principal part enlarged view. It is a graph explaining the internal diameter of a shaft model. It is a side view explaining the three-point bending strength test of a golf club shaft. It is a side view explaining the forward type flex of a golf club shaft. It is a side view explaining the reverse type flex of a golf club shaft. It is a side view explaining the torsional rigidity of a golf club shaft. It is a graph which visualizes and illustrates an approximate response function. (A) is a block diagram explaining a data envelope analysis method, (b) is a graph explaining the example. FIG. 3 is a development view of a prepreg constituting a golf club shaft. (A), (b) is a graph which shows the relationship between a design variable and an objective function. It is a graph which shows the change rate of each objective function by optimization. It is a graph which shows the contribution rate of each objective function which occupies for a Pareto solution.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
In this embodiment, in order to design a golf club shaft made of fiber reinforced resin having excellent strength, a method for designing an optimum combination of shaft diameter, fiber reinforced resin fiber type, fiber material orientation angle, and the like in a short time. Is explained. However, the design method of the present invention is not limited to such a specific example, and it goes without saying that design variables and objective functions can be changed and implemented for various purposes.

  FIG. 1 shows an example of a processing procedure of a design method according to an embodiment of the present invention. In the golf club shaft design method of the present embodiment, first, a shaft model is set (step S1).

  FIG. 2A shows an overall view of the shaft model 2 visualized, and FIG. 2B shows an enlarged view of a main part thereof. The shaft model 2 has a long pipe shape as a whole, and is set using a finite number of elements e. Each element e defines a plurality of material properties and the like, and constitutes an analysis model (also referred to as a mesh model) in which the dynamic characteristics or static characteristics of the golf club shaft can be numerically calculated by a computer as a whole. The numerical calculation includes at least deformation calculation using a finite element method, for example.

  The length L of the shaft model 2 is desirably matched with the golf club shaft to be designed. According to custom, the length L is set to about 35 to 50 inches, for example. The length L of the shaft model 2 of this embodiment is set to 1195 mm.

  The shaft model 2 is divided into, for example, several tens to several thousand in the axial direction and several tens to several hundreds in the circumferential direction, and the element e is assigned to each divided region. In the present embodiment, each element e has the same shape, and a single thick shell element having a rectangular shape with four nodes is used.

  The thick shell element is apparently a single planar element, but a plurality of overlapping layers can be defined. For each layer, the elastic modulus, Poisson's ratio, strength anisotropy, etc. are individually defined. Such a thick shell element is preferable in that the prepreg laminated structure in the fiber reinforced resin can be efficiently expressed with a small number of nodes.

  In the shaft model 2 of the present embodiment, the axial length of one thick shell element is 1.25 mm (239 divisions in the axial direction), and the circumferential length is 10 degrees in the central angle (36 divisions in the circumferential direction). Needless to say, it can be changed as appropriate. In addition to the single thick shell element, a plurality of shell elements or solid elements may be used as the element e. These modeling can be easily performed using a computer and meshing software.

  In addition, for each element e, characteristics relating to “shape” and characteristics relating to “material” are defined in advance. The characteristics relating to the shape include, for example, the number of layers inherent in the thick shell element, the shape, the orientation angle of the fiber material, and the start position of the fiber material. The “number of layers” corresponds to the number of prepregs. In addition, the “starting position of the fiber material” is defined, for example, when the prepreg is actually a triangle shape, when the rectangular element does not necessarily match the fiber orientation region. This is to ensure.

  Further, the characteristics relating to the “material” include strength anisotropy determined by the density, Poisson's ratio, cost, thickness, elastic modulus, and fiber material orientation angle defined internally in each element e. Is included.

  Next, design variables are defined in the shaft model 2 (step S2). The design variable means a variable that is a candidate for changing the performance of the shaft model 2. That is, the performance of the shaft model 2 can be changed by changing the design variable. This process is performed automatically, for example, by predetermining an allowable range for each design variable in a computer, and arbitrarily determining a value from the range.

  The design variable may be selected from the characteristics, or may be determined as a comprehensive parameter using the characteristics. Practical preferable design variables include, for example, at least one of the inner diameter of the shaft model 2, the fiber type of the fiber reinforced resin, the orientation angle of the fiber material of each prepreg, the shape of the prepreg, and the stacking order, preferably 2 or more, more preferably Includes everything. These design variables greatly affect the characteristics of the golf club shaft.

  As described above, a fiber reinforced resin golf club shaft is manufactured by winding a sheet-shaped prepreg around a mandrel (iron core), curing the matrix resin by heat treatment, and then removing the mandrel from the core. Accordingly, the “inner diameter of the shaft model” is equivalent to determining the outer diameter of the mandrel. Further, the inner diameter of the shaft model 2 is an important factor that affects performance such as the strength, bending rigidity, and weight of the shaft.

  Further, the inner diameter of the shaft model 2 is actually a parameter continuous in the axial direction. Therefore, when the inner diameter of the shaft model 2 is defined as a design variable, for example, as shown in FIG. 3, inner diameters (for example, D1 to D5) at a plurality of axial positions are appropriately determined as discrete variables. Is done. And each section of these inner diameters can be defined as being continuous in a tapered shape.

  Further, the inner diameter of the shaft model 2 may be continuously defined from a TIP end (head end on the head side) to a BUTT end (rear end on the grip side) using a function. In order to ensure demolding of the mandrel, for example, it is effective to impose a constraint condition such that the inner diameter of the shaft model 2 is gradually decreased from the BUTT end toward the TIP end or gradually decreased.

  The fiber type of the fiber reinforced resin means a distinction such as carbon fiber, glass fiber, or resin fiber such as aramid. The fiber type affects the elastic modulus, density, Poisson's ratio, etc., respectively. Therefore, by including the fiber type of the shaft model 2 in the design variable, the performance such as the strength, bending rigidity and weight of the shaft can be changed.

  The orientation angle of the fiber material means an angle formed by the longitudinal direction of the fiber and the shaft axis direction. Depending on the orientation angle, the tensile elastic modulus and shear elastic modulus of the shaft model 2 change several times to nearly several hundred times. Therefore, it is important to include the orientation angle of the fiber material of the fiber reinforced resin in the design variable.

  Next, in this embodiment, a plurality of different objective functions representing the performance of the shaft model 2 are calculated using a computer (step S3).

  Examples of the objective function include static, for example, the strength, bending rigidity, torsional rigidity, and weight of the shaft model 2. In particular, it is desirable to include at least 2 or more, more preferably 3 or more, and still more preferably all selected from these.

  However, the objective function can include dynamic characteristics during actual swing, for example, as a dynamic function. This can include, for example, strength values based on maximum stress, maximum strain and / or various strength laws that occur on the shaft during impact. It should be noted that the objective function can also be considered by imposing constraints such as a specific range, for example, to above and / or below.

  For example, the four objective functions of the strength, bending stiffness, torsional stiffness and weight of the shaft model 2 are calculated using a finite element method or lamination theory, as will be explained below.

  In this specification, the “strength” of the shaft means the strength measured based on the SG type three-point bending strength test defined by the Product Safety Association. In this test, as shown in FIG. 4, the shaft is supported from below at two support points t1 and t2, and a load F is applied from above to below at a load point t3. The position of the load point t3 is a position that bisects the span S of the support points t1 and t2. Further, the load point t3 is measured in accordance with the measurement point.

  In the three-point bending strength test, the strength of the shaft is calculated for four points, T point, A point, B point, and C point, which are determined in advance in the section from the TIP side to the BUTT side. The T point is 90 mm from the head side of the shaft. Similarly, points A and B are located at 175 mm and 525 mm from the head side of the shaft, respectively. Furthermore, point C is set to a position of 175 mm from the end on the grip side. The span S is set to 150 mm when measuring the point T, but the span S is set to 300 mm when measuring the points A to C. The load value when the shaft is damaged is adopted as “strength” in the product standard.

  On the other hand, for the sake of convenience, the “shaft model strength” is defined as follows. For convenience, the shaft model 2 is subjected to a simulation (deformation calculation) by a finite element method of a three-point bending test with a constant load of 50 N. It is defined by the value of how much the fracture parameters of stress and strain acting on all the elements adjacent in the circumferential direction reach the prepreg fracture tolerance. That is, the destruction parameter is represented by “strength value” which is a percentage divided by the allowable value. Note that the constant load value of 50 N is smaller than the load that actually destroys the shaft. However, in the three-point bending strength test, the stress-strain relationship of the shaft is a linear relationship. Therefore, for convenience, the strength value at the time of low load may be adopted as described above.

  There are various types of destruction criteria. “Maximum stress theory” and “maximum strain theory” focusing on stress and strain in a certain direction, and “Hill”, “Hoffman”, “Tsai-Wu” expressed from multiaxial stress field states, and the like. In this specification, the “maximum stress theory” is adopted as the criterion for fracture.

  The objective functions of “bending rigidity”, “torsional rigidity”, and “weight” are calculated based on the lamination theory. That is, the bending rigidity, torsional rigidity and weight of the shaft model 2 are defined as various physical properties such as tensile elastic modulus, shear elastic modulus and Poisson's ratio of the prepreg, the orientation angle of the fiber material, the winding position, the number of windings and the shaft. It is calculated based on the material mechanics or structural mechanics from the values of the parameters relating to the shape such as the inner diameter of the model 2.

  The bending stiffness (also referred to as flex) is the hardness in the bending direction of the shaft determined from the distribution of the bending stiffness EI from the TIP side to the BUTT side of the shaft, and the forward flex or the reverse flex is known. It has been.

  As shown in FIG. 5, the forward flex has two upper and lower support points, 75 mm above the grip side end 2B of the shaft and 215 mm below the grip side end 2B. It means the amount of deflection when a load of 2.7 kgf (26.48 N) is applied at a position from 2B to 1039 mm.

  In addition, as shown in FIG. 6, the reverse flex has two upper and lower points, 12 mm above the shaft head end 2T and 152 mm below the head end 2T. This means the amount of deflection when a load of 1.3 kgf (12.75 N) is applied at a position of 932 mm from the end 2T of the lens.

  Generally, a shaft with a large bending rigidity (a shaft with a small amount of deflection) has a faster return (return) of the shaft at the time of hitting, and therefore the timing of returning the head does not match the player with a slow head speed. For this reason, head speed and flight distance are reduced. On the other hand, a shaft with a small bending rigidity (a shaft with a large amount of deflection) has a slow head return at the time of impact, and is likely to have an impact with the face facing downward. For this reason, the launch angle is reduced and the flight distance is reduced. Accordingly, there is a preferred range of bending rigidity depending on the golfer shaft target golfer to be designed.

  This bending stiffness can be calculated from the lamination theory using parameters defined for each element e of the shaft model 2. In this embodiment, the bending rigidity of the shaft model 2 is calculated by calculating the forward flex and the reverse flex from the classic lamination theory, respectively, and optimizing the sum to be a certain constant value. Defined.

  Further, as shown in FIG. 7, the “torsional rigidity” of the shaft is fixed at a position 40 mm from the end 2T on the head side of the shaft, and a torque of 13.9 N is applied to a position 865 mm from the end 2T on the head side. It is represented by the twist angle at the time (sometimes referred to as torque). A shaft having a large torsional rigidity has a large shaft weight and is difficult to swing out. On the other hand, a shaft with low torsional rigidity makes it difficult for the head to return, and therefore impacts while being twisted, resulting in poor hitting direction such as slicing. Accordingly, there is a preferred range of torsional rigidity depending on the golfer shaft target golfer to be designed. This torsional rigidity can also be calculated from the above lamination theory using the parameters defined for each element e of the shaft model 2.

  In the present embodiment, the weight of the shaft model 2 is calculated by the density of the prepreg × area × thickness. In general, it can be said that it is desirable to minimize the weight in order to improve the head speed.

  Next, an approximate response function that links the relationship between the design variable and the objective function is generated by the computer (step S4).

  Prior to the generation of the approximate response function, for example, a process of scalarizing a plurality of objective functions is performed. In order to search for a design variable of the shaft model 2 that optimizes a plurality of objective functions independent from each other, evaluation cannot be performed unless some weighting condition is given. Therefore, in the present embodiment, a plurality of objective functions are scalarized by multiplying the value of each objective function by a weighting coefficient and adding it. Thereby, an objective function to be emphasized can be determined.

A specific method for realizing the scalarization is not particularly limited. For example, linear combination (see the following formula (1) for the general formula), Chebyshev type (see the following formula (2) for the general formula), and the like. Can be adopted.
F = w ₁ · f ₁ + w ₂ · f ₂ +... + W _r · f _r (1)
F = Max {w ₁ · f ₁ , w ₂ · f ₂ ,..., W _r · f _r } (2)
However, the symbols are as follows.
F: scalar value of objective function f _i : normalized value of each objective function w _i : coefficient for each objective function

  Further, the approximate response function associates the design variables a1, a2,... An with the scalar value F of the objective function using, for example, a neural network. As an example, FIG. 8 illustrates an approximate response function including a three-dimensional curved surface that relates two weighting coefficients a1 and a2 and a scalar value F of an objective function.

  The approximate response function interpolates the analysis result (scalar value F) at the positions of the design variables a1 and a2 that are not specifically set, and enables optimization candidates to be predicted. Therefore, it is particularly important to generate such an approximate response function in order to search for an optimal solution efficiently and in a short time. The approximate response function can be realized by various methods according to the custom, and for example, a response surface method (RSM), a radial basis function (RBF) or a Kriging method is preferably used. It is done.

  Although approximation accuracy is improved in the order of RSM, RBF, and Kriging, it is a method that requires calculation cost. Since the discrete design variable “type of material” is included as in the present embodiment, the relationship between the design variable and the objective function becomes strongly nonlinear. Moreover, since the kind of material for every prepreg and the orientation angle of a fiber material are included, the number of design variables increases and calculation cost starts. For this reason, an RBF that can express a highly nonlinear function and does not have a very high calculation cost is preferable.

  The RBF is a kind of neural network and is an approximate response surface expressed by superimposing Gaussian functions. This is desirable because the input (design variable) and the output (objective function) can be expressed with high accuracy even if the relationship is very nonlinear. In addition, unlike an ordinary neural network, RBF does not require backpropagation, so that the calculation cost for generating an approximate function can be reduced.

  Next, in the present embodiment, a plurality of optimal solutions are searched by the computer from the generated approximate response function (step S5). As a method for searching for an optimal solution from the approximate response function, a genetic algorithm, a gradient method, an annealing method, or the like is employed in accordance with the custom. The plurality of optimal solutions can include, for example, the top tens to hundreds of solutions when ranked.

  Next, the computer determines whether or not the searched optimum solution is satisfactory (step S6). If it is true (Y in step S6), the process proceeds to step S7. On the other hand, if the obtained optimization cannot be satisfied (N in step S6), the design variable is changed again and step S2 and subsequent steps are repeated, and the optimization search is continued. The determination in step S6 is automatically performed by a computer based on, for example, a predetermined change rate (improvement rate) of an objective function before optimization.

  Next, a step of obtaining a Pareto solution using the data envelope analysis method from among the plurality of optimum solutions obtained in step S6 is performed by the computer (step S7).

  In the optimization calculation in step S5, a plurality of optimum solutions are derived. The designer needs to analyze each of the plurality of optimal solutions and select a truly optimal one for the designer. However, this is not an easy task as the number of solutions increases. On the other hand, if the number of outputs of the optimum solution is too narrow, the degree of freedom in design decreases.

  In the present invention, a data envelope analysis method (also referred to as Data Envelopment Analysis, hereinafter simply referred to as “DEA”) in order to streamline the analysis of the plurality of optimal solutions and reduce the burden on the designer. Is used. Thereby, it is possible to analyze the Pareto solution and its characteristics from among the plurality of optimum solutions. The designer can easily determine the design variables of the golf club shaft based on the Pareto solution (step S7).

  Data envelopment analysis is known as a method for analyzing the efficiency of an entity. That is, in DEA, a business entity is regarded as a production function that receives parameters (design variables) such as capital investment, personnel, and sales area as inputs, and outputs a plurality of parameters (objective functions) such as sales, profitability, and growth potential. This is an evaluation method based on the idea of measuring the efficiency of the conversion process.

  In the present invention, this DEA is adopted in the design of the golf club shaft. For example, as shown in FIG. 9 (a), the inner diameter of the shaft model 2, the fiber type of the fiber reinforced resin, and / or the orientation angle of the fiber material are used as design variables, and the strength, bending rigidity, torsional rigidity, and / or Alternatively, a design function that outputs an objective function such as weight is evaluated.

  FIG. 9B plots several solutions when two objective functions J1 and J2 (for example, the strength and weight of the shaft model 2) are used. In both the vertical and horizontal axes, the direction away from the origin is the target (good performance).

  When the evaluation is performed only with the objective function J1, the solution D is the best. On the other hand, when the evaluation is performed only with the objective function J2, the solution A is the best. When the evaluation is performed using the average value of the objective functions J1 and J2, the evaluation is performed at the point where each solution is projected on the straight line of J2 = J1 indicated by the broken line. In this case, the solution B is the best. Further, the evaluation line that is most advantageous for the solution E is a straight line Z passing through the origins O and E, but the solution E does not give the highest evaluation even if this straight line is used.

  In DEA, evaluation is performed by selecting an evaluation line that gives the highest evaluation. Other solutions are also evaluated using this evaluation line. Further, in DEA, a line connecting solutions with the highest evaluation, such as solutions A, B, C, and D, is obtained as a frontier line. In the frontier line, vertical lines and horizontal axes are drawn from the solutions A and D at both ends, respectively. A point on the frontier line is a Pareto solution and is evaluated as an efficiency value of 1.

  Therefore, by picking up a Pareto solution on the frontier line using a computer from the plurality of optimal solutions obtained in step S5, the designer can evaluate only the more optimal solution. Efficiency can be improved.

  Further, in DEA, the efficiency value of a solution inside the frontier line, for example, the efficiency value of the solution E is expressed by OE / OP, where P is the intersection of the straight line Z and the frontier line. Therefore, as another embodiment, it is also possible to pick up a solution having a solution on the frontier line and an efficiency value that are equal to or greater than a predetermined threshold from among a plurality of optimum solutions obtained in step S5 using a computer. In this case, the number of solutions to be evaluated by the designer increases as compared with the case of the above-described embodiment, but it is useful for improving the degree of design freedom while suppressing an excessive increase in the solutions.

  In the DEA, the case where there are two objective functions has been described as an example, but the same processing can be performed using three or more objective functions.

  Although the embodiments of the present invention have been described in detail above, the present invention is not limited to the specific embodiments described above, and various modifications can be made without departing from the paper of the present invention. Can do.

Embodiments that further embody the present invention will be described below.
In this example, the optimization was performed using the orientation angle of the eight prepregs shown in FIG. 10 (the angle shown in FIG. 10 is a value before optimization) as a design variable. The inner diameter of the shaft, the shape of the prepreg, the type and weight of the fiber material were all constant.

[Design variables (orientation angle)]
The following rules were given as the orientation angle. First, as shown in Table 1, bias layers (for example, a combination of prepreg A2 and prepreg A3 and a combination of prepregs A5 and A6) that are stacked with the same prepreg shape and different orientation angles of the fiber material are used. The combination of the bias layer angles is determined in advance, and the bias layer angle is selected from them. The combinations in Table 1 are determined in order to eliminate the anisotropy of torsional rigidity, and are arranged in order of increasing elastic modulus in the axial direction. For the layers other than the bias layer, the orientation angle of the fiber material is determined to be 0 degree or 90 degrees. In this embodiment, the bias layers are assigned consecutive numbers (in this embodiment, continuous variables of 1 to 20) in descending order of the elastic modulus in the axial direction. The angle of the bias layer, which is a design variable, is a discrete variable. As described above, by giving continuous variables to the bias layer in descending order of the elastic modulus in the axial direction, it is shown in FIG. Accordingly, an approximate response surface representing the relationship between a smooth objective function (axial elastic modulus) can be formed accordingly. As shown in FIG. 11B, this is useful for making it possible to find an optimal solution at an early stage while suppressing the approximate response surface from becoming non-linear.

[Objective function]
The strength, bending rigidity and torsional rigidity of the shaft model were used as objective functions. In addition, the strength is the stress value along the fiber orientation direction at each of the four points and the prepreg at each of the four points as the strength values of the above four points (T point, A point, B point, and C point). Interlaminar shear stress. With regard to the above stress, the maximum stress theory was used as a criterion for fracture, and the goal was to minimize it.

  In addition, the target value for “bending rigidity” is that it does not change before and after optimization. Specifically, the objective was to minimize “flexural rigidity after optimization” − “flexural rigidity before optimization”.

  Similarly, the target value for “torsional rigidity” does not change before and after optimization. Specifically, the goal was to minimize “torsional rigidity after optimization” − “torsional rigidity before optimization”.

[Optimization result]
Table 2 shows design variable values before and after optimization. Table 3 shows objective function values before and after optimization. Further, the rate of change is shown in FIG. In these symbols, T and A to C indicate the positions of the measurement points, the subscript “11” means the stress in the longitudinal direction of the fiber material, and the subscript “12” means the shear stress between the layers of the prepreg.

  As a result of optimization, it can be seen that the strength at each point is improved (stress is reduced) while the bending rigidity (EI) and torsional rigidity (TQ) are kept substantially constant (however, the interlaminar shear at the C point) Only slightly worse, but this is acceptable).

  FIG. 13 shows a graph ranked in descending order of DEA efficiency value. In FIG. 13, the breakdown in each bar graph is the “importance” of each objective function. Each is a Pareto solution of a frontier line in a multidimensional space around the objective function. Each breakdown shows the ratio of how much importance is attached to each objective function. Therefore, the characteristics of each Pareto solution can be known by looking at the breakdown. Then, the designer can select, for example, 3 or 6 having a large efficiency value at the point B where the strength tends to be the lowest from the results of the top 10 and use it as design data. Note that the DEA of this embodiment uses a super CCR model.

2 Shaft model

Claims (4)

A method of designing a golf club shaft made of a fiber reinforced resin manufactured using a plurality of prepregs which are sheet members obtained by impregnating a fiber material oriented in one direction with an uncured resin ,
Modeling a golf club shaft with a finite number of elements to obtain a shaft model that can be numerically calculated by a computer;
Defining design variables for the shaft model;
Calculating a plurality of different objective functions representing the performance of the shaft model set in the step using a computer;
Generating an approximate response function that links the relationship between the design variable and the objective function;
Obtaining a plurality of optimal solutions for optimizing the objective function based on the approximate response function;
Obtaining a Pareto solution using a data envelope analysis method from among the plurality of optimal solutions obtained above;
Viewing including the step of setting the each design variable of the golf club shaft on the basis of the Pareto solution,
The design variable includes an orientation angle of the fiber material,
The prepreg includes a bias layer composed of two sheets that have the same prepreg shape and are stacked with different fiber orientation angles,
The bias layer is selected from those in which the combination of the angles of the fiber materials is determined in advance,
The golf club shaft design method is characterized in that a continuous variable for expressing the objective function is defined in the order of increasing axial elastic modulus for the combination of the angles of the fiber materials .
The golf club shaft design method according to claim 1, wherein the design variable includes at least one of an inner diameter of a shaft model, a fiber type of a fiber reinforced resin , a shape of a prepreg constituting the reinforced resin , and a stacking order of the prepreg.
  The golf club shaft design method according to claim 1, wherein the objective function includes two or more selected from strength, bending rigidity, torsional rigidity, and weight of the shaft model.   A golf club shaft manufacturing method using the golf club shaft designing method according to claim 1.

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