GOLF CLUB SHAFT SIMULATION METHOD
A computer-aided golf club shaft swing simulation method, includes: dividing a model of a shaft into a plurality of model areas continuously along its length from a proximal end to a distal end thereof; inputting values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia into the plurality of model areas or their joint portions; and analyzing a behavior of the shaft when the shaft is swung according to a given swing pattern.
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This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2007-220919, filed Aug. 28, 2007, the entire contents of which are incorporated herein by reference.
BACKGROUND OF THE INVENTIONThe present invention relates to a computer-aided golf club shaft simulation method and more particularly to a simulation method for analyzing the behavior of a golf club shaft when it is swung.
Conventionally, in studying the behavior of a golf club shaft when it is swung, it is common practice that a plurality of strain gauges are attached to the shaft, so that the amount of strain of the shaft is measured by these strain gauges (refer to, for example, JP-A-2003-205053 and JP-A-2003-284802).
With the methods of JP-A-2003-205053 and JP-A-2003-284802, however, since lead wires are connected respectively to the plurality of strain gauges attached to the shaft, the golf club gets heavy, and this makes it difficult for a golfer to swing the golf club. Because of this, it is difficult for the golfer to make identical swings, and hence, it has been difficult to measure the amount of strain of the shaft through repetition of identical swings.
In addition to them, JP-A-2002-331060 proposes a golf club swing simulation method as the method for analyzing the behavior of a golf club. In this method, a golfer's swinging behavior is measured using a true golf club, so as to obtain coordinate time history data of a grip of the golf club when the golf club is swung by the golfer, time history data of the inclination angle of the grip, time history data of the rotational angle of the grip round the shaft's axis which is a geometrical center axis of the shaft, and a swinging motion is given to a golf club model based on the three time history data, so as to analyze the behavior of the golf club through simulation in consideration of twisting of the golf club model (See claim 1 of JP-2002-331060).
With the method of JP-A-2002-331060, however, since many data such as the properties of shaft materials, shaft's volume and shaft's diameter are inputted into the computer, the simulation takes time.
SUMMARY OF THE INVENTIONThe invention has been made in view of the situations and an object thereof is to provide a golf club shaft simulation method which can perform a simple and accurate simulating calculation by inputting fewer parameters into a computer.
The invention provides a computer-aided golf club shaft swing simulation method, including: dividing a model of a shaft into a plurality of model areas continuously along its length from a proximal end to a distal end thereof; inputting values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia into the plurality of model areas or their joint portions; and analyzing a behavior of the shaft when the shaft is swung according to a given swing pattern.
In this embodiment, since Young's modulus, modulus of elasticity in shear and geometrical moment of inertia which are associated with bending rigidity and torsional rigidity of the shaft are selected as parameters to be inputted into the computer, a simple and accurate simulation can be implemented by inputting the few parameters. In addition, since there are few parameters to be inputted into the computer, the parameters can easily be changes so verify a change in the behavior of the shaft on the spot, so that the results of the simulation can of help to the design of a golf club quickly.
Hereinafter, the embodiment will be described in greater detail. In this embodiment, the shaft is divided into the plurality of model areas continuously along its length from the proximal end to the distal end thereof, and values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia are inputted into the plurality of model areas or their joint portions. As this occurs, it is appropriate that the shaft is divided into 5 to 20 model areas along its length from the proximal end to the distal end thereof. In addition, assuming that an area of the shaft which lies 5 to 20 cm away from the proximal end is a first model area, the shaft can then be divided into a plurality of model areas of the same length along the length from a distal end of the first model area to the distal end of the shaft.
In the embodiment, the Young's modulus, modulus of elasticity in shear and geometrical moment of inertia are inputted into the plurality of model areas. Values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia can be obtained as below.
[Young's Modulus, Geometrical Moment of Inertia]An EI value is such as to constitute a pilot value for bending rigidity, and an EI value can be obtained by performing a three-point bending test. Values of Young's modulus (E) and geometrical moment of inertia (I) can be obtained from this EI value. Specifically, a shaft is horizontally supported by a pair of supporting tools which are spaced a certain distance (L) apart from each other, a load (P) is exerted vertically on a central position between both the supporting pints (the supporting tools), and an amount of strain (σ) at the central position is obtained.
EI=(L3/48)·(P/σ)(kg·mm2×106)
- L: Distance between both the supporting tools (mm) . . . 300 mm
- P: Load exerted vertically on the shaft (Kg) . . . 20 Kg
- σ=Amount of strain when the load is exerted (mm)
A geometrical moment of inertia can be obtained by a computational expression from the cross section of the shaft.
I=π×(d4−d14)/64
- d: Outside diameter of the shaft
- d1: Inside diameter of the shaft
A Young's modulus (E) can be obtained from the result of the above computational expression.
E=(L3/48)·(P/σ)(kg·mm2×106)/I
Firstly, to obtain a modulus of elasticity in shear, a torque is obtained in each portion. Namely, a certain portion of the shaft is fixed in such a manner as to permit no rotation, a constant rotating force is exerted on a location which is spaced apart from the fixed portion of the shaft in a certain direction, that is, in a direction towards the distal end or a direction towards the proximal end of the shaft, and an angle through which the location to which the rotating force was exerted rotates is measured. In this embodiment, the shaft is fixed in the fixed position by a chuck, a rotating force (1 ft·1 bt: 138.25 kgf·mm: 1.35 N·m) is then exerted on a location which is spaced 100 mm apart from the fixed position, and an angle through which the rotating force exerted location has rotated is measured.
T=G·Ip(x)·dθ/dx
- T: Torque (torsional moment)
- G: Modulus of elasticity in shear
- IP(x): Polar moment of inertia of area
- dθ/dx: rotational angle per unit
A polar moment of inertia of area can be obtained from the section of the shaft by a computational expression.
Ip(x)==π×(d4−d14)/32
- d: Outside diameter of the shaft
- d1: Inside diameter of the shaft
Consequently, a modulus of elasticity in shear can be obtained from the following expression.
G=T/(Ip(x)·dθ/dx
In this embodiment, club head weight, gravity center distance and gravity center depth can be added to factors that are inputted for simulation, whereby a load can be reproduced that would be exerted on a shaft of a true golf club when the true golf club is swung. In addition, a simulation can be implemented for enabling a shaft design matched to the characteristics of a club head.
In the embodiment, by adding club head weight, gravity center distance, gravity center depth and gravity center height to factors that are inputted for simulation, a dynamic loft and face angle at the time of impact, which will be described later, can be outputted, whereby the conditions of the head at the time of impact can be estimated.
Hereinafter, while an embodiment of the invention will be described by reference to the drawings, the invention is not limited to the following embodiment. As is shown in
- STD: Standard shaft
- TipDown: Shaft with low Young's modulus at the distal end
- TipUp: Shaft with high Young's modulus at the distal end
- ButtDown: Shaft with low Young's modulus at the proximal end
- ButtUp: Shaft with high Young's modulus at the proximal end
In addition, as is shown in
In this case, as is shown in
The behaviors of the shafts were analyzed when the five kinds of shafts were swung in the four types of swing patterns. In this case, the shafts 10 were swung while inclined 50° relative to a horizontal plane. In addition, the head speed at the distal end portion of the shaft was set to be 45 m/s with the angular speed of the proximal portion of the shaft maintained constant and when assuming that the shafts would not flex. As output parameters, a difference in speed between the distal end and proximal end of the shaft, dynamic loft and face angle were outputted.
The results of analysis of speed difference of the respective shafts between the distal end and proximal end are shown in
The results of analysis of dynamic lofts were shown in
The results of analysis of face angles are shown in
The following become obvious from the results of the simulations described above. With some of the output parameters, the tendency is not changed, while with others, the tendency is changed by the relationship between swing pattern and shaft rigidity distribution, and consequently, the importance of bending rigidity and torsional rigidity that are possessed by the portions of the shaft are made clear by the simulation method of the embodiment, whereby the design of a shaft having target properties or the design of a shaft matching a specific swing pattern is enabled. Thus, the simulation method of the embodiment can be of help to the design of golf clubs.
As described with reference to the embodiment, there is provided a golf club shaft simulation method which can perform a simple and accurate simulating calculation by inputting fewer parameters into a computer.
In the embodiment, by setting the mechanical factors (bending rigidity, torsional rigidity) of the shaft in the respective model areas aligned in the longitudinal direction, the flexure and torsion of the shaft in swing are studied on the computer, whereby it becomes possible to know how the flexure and torsion of the shaft change depending upon different swing patterns. In addition, by adding the data of a head which is attached to the shaft, information at the time of impact can be obtained. By giving shaft data in each portion, the respective factors can be made to approach their optimal values from the size of the head or the like by this simulation method, thereby making it possible to implement a shaft design in a short period of time.
Claims
1. A computer-aided golf club shaft swing simulation method, comprising:
- dividing a model of a shaft into a plurality of model areas continuously along its length from a proximal end to a distal end thereof;
- inputting values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia into the plurality of model areas or their joint portions; and
- analyzing a behavior of the shaft when the shaft is swung according to a given swing pattern.
2. The computer-aided golf club shaft swing simulation method as claimed in claim 1,
- wherein the model of the shaft is divided into 5 to 20 model areas along its length from the proximal end to the distal end thereof.
3. The computer-aided golf club shaft swing simulation method as claimed in claim 1,
- wherein assuming that an area of the shaft which lies 5 to 20 cm away from the proximal end is a first model area, the model of the shaft is divided into a plurality of model areas of the same length along the length from a distal end of the first model area to the distal end of the shaft.
4. The computer-aided golf club shaft swing simulation method as claimed in claims 1,
- wherein club head weight, gravity center distance and gravity center depth are added to factors to be inputted for simulation.
Type: Application
Filed: Jun 25, 2008
Publication Date: Mar 5, 2009
Applicant: BRIDGESTONE SPORTS CO., LTD (Tokyo)
Inventor: Fumiaki SATO (Chichibu-shi)
Application Number: 12/145,624
International Classification: A63B 57/00 (20060101);