Abstract:
By bringing a golf ball into collision with a collisional plate and measuring a coefficient of dynamic friction at this collision, contact force at the time of collision between an actual golf club and the golf ball is analyzed and spin rate of the golf ball is estimated. This invention provides a method for measuring a coefficient of dynamic friction between a golf ball and a collisional plate when the golf ball collides with the collisional plate disposed aslant at a predetermined angle with respect to a flying direction of the golf ball. The method includes concurrently obtaining a time function Fn(t) of contact force in the direction perpendicular to the collisional plate, and a time function Ft(t) of contact force in the direction parallel with the collisional plate; and determining as a coefficient of dynamic friction, a maximum value of a time function M(t) of ratio between Fn(t) and Ft(t) represented by M(t)=Ft(t)/Fn(t).

Description:
This nonprovisional application is based on Japanese Patent Application No. 2005-167111 filed with the Japan Patent Office on Jun. 7, 2005, the entire contents of which are hereby incorporated by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a method of measuring a coefficient of dynamic friction between a golf ball and a collisional plate when the golf ball collides with the collisional plate. Analysis of such measurement allows for prediction of a coefficient of dynamic friction at the time of hitting of a golf ball by an actual golf club and can facilitate adjustment of a spin rate of the golf ball. 
   2. Description of the Background Art 
   Spin rate of a golf ball is an important characteristic that controls flying distance performance and controllability. A golf ball having high spin rate is able to rapidly stop on the green due to back spin, and is controllable such that its flying path is a draw or a fade by applying side spin to a golf ball. For this reason, golf balls of high spin rate are favored by professional golfers and low-handicapped golfers. 
   Contrarily, golf balls having low spin rate are inferior in controllability due to their small back spin, however, they are superior in that they can achieve large flying distances. Therefore, they are frequently used by high-handicapped golfers. 
   Conventionally, spin rate is adjusted by making adjustments on various factors such as rigidity of the entire golf ball, its distribution, degree of rigidity of outermost layer, thickness of outermost layer, distribution of specific gravity of the entire golf ball and the like. For example, U.S. Publication No. 2002/0019268A1 proposes a multilayered golf ball which realizes a larger launch angle and a smaller back spin compared with conventional golf balls. 
   Meanwhile, in view of golf clubs, depth, width, size, shape, arranging interval of grooves, punch marks or the like formed in a face plane of a club head, as well as surface roughness of the face plane are adjusted. In one known approach, for example, surface roughness or the like of a face plane is changed depending on the club number so that the lower the number of club head, or the relatively smaller the loft angle, the smaller friction coefficient the face plane has, and that the higher the number of club head, the larger friction coefficient the face plane has (see Japanese Patent Laying-Open No. 2004-000675). 
   SUMMARY OF THE INVENTION 
   As described above, a friction coefficient that contributes to a spin rate of a golf ball depends on the combination of a type of golf ball and a surface structure of a golf club head. And, estimation of friction coefficients of a golf club head against different golf balls would facilitate designing of spin rate. The present invention provides a method of readily designing spin rate of a golf ball, wherein a collisional plate which is mounted in a detachable manner is created as a model of a golf club head, and a coefficient of dynamic friction is measured by bringing a golf ball into collision with the collisional plate, and then based on the measurement, a contact force and a coefficient of dynamic friction at the time of collision between an actual golf club head and the golf ball are estimated. 
   The present invention provides a method for measuring a coefficient of dynamic friction between a golf ball and a collisional plate when the golf ball collides with the collisional plate disposed aslant at a predetermined angle with respect to a flying direction of the golf ball. The method includes concurrently obtaining a time function Fn(t) of contact force in the direction perpendicular to the collisional plate, and a time function Ft(t) of contact force in the direction parallel with the collisional plate; and determining as a coefficient of dynamic friction, a maximum value of a time function M(t) of ratio between Fn(t) and Ft(t) represented by M(t)=Ft(t)/Fn(t). 
   The collisional plate is adjustable at an angle (α) range of 10 degrees to 90 degrees with respect to the flying direction of the golf ball. Preferably, the collisional plate is mounted in a detachable manner. Further, the collisional plate may be attached with a pressure sensor. 
   In the measuring method of the present invention, the golf ball may be emitted vertically upward via an air gun system to collide with the collisional plate. 
   In the measuring method of the present invention, an initial velocity of the golf ball before collision with the collisional plate, and an angle of collisional plate may be controlled by a control box. 
   In the measuring method of the present invention, the collisional plate may include a substrate, a pressure sensor, a superficial plate, and a main bolt for integrally fixing them. 
   In the measuring method of the present invention, the substrate may be made of steel. 
   In the measuring method of the present invention, the superficial plate may include a main body and a covering plate, and a coefficient of dynamic friction may be measured while arbitrarily designing and varying a material, a planner shape and a surface structure of the covering plate. 
   In the measuring method of the present invention, the main body of the superficial plate may be made of stainless steel. 
   In the measuring method of the present invention, the covering plate of the superficial plate may be made of a titanium alloy containing 6% by mass of aluminum and 4% by mass of vanadium. 
   The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic view of a measuring method used in the present invention. 
       FIG. 2  is an enlarged partial section view of a collisional plate used in  FIG. 1 . 
       FIG. 3  is a graph showing Ft(t), Fn(t) and M(t). 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The measuring method of the present invention uses a detachably mounted collisional plate, and hence is a very close model for hit of an actual golf club. It can analyze collision phenomena such as contact force and a friction phenomenon at the time of collision between an actual golf club and a golf ball by measuring a coefficient of dynamic friction. 
   (Method of Measuring Coefficient of Dynamic Friction) 
   A method of measuring a coefficient of dynamic friction between a golf ball and a collisional plate in the present invention will be explained below with reference to a measuring apparatus of  FIGS. 1 and 2 . 
   In  FIG. 1 , a golf ball  2  is emitted upward perpendicularly in the vertical direction from an emitter  1  of an air gun system. Golf ball  2  is emitted at an initial velocity in the range of about 20 to 50 m/second, for example. The initial velocity of golf ball  2  is calculated by measuring a distance and a blocking time difference between a first sensor S 1  and a second sensor S 2 . 
   Golf ball  2  thus emitted is brought into collision with a collisional plate  3  set in advance at a predetermined angle (α) in the emitting direction of golf ball (flying direction). These initial velocity of golf ball and angle (α) of collisional plate are controlled in a control box  4 . 
   Golf ball  2  after collision is reflected in the left downward direction as shown in  FIG. 1 . Fn(t) which is time-series data of force along the direction perpendicular to the collisional plate and Ft(t) which is time-series data of force along the direction parallel with the collisional plate at the time of collision are measured by a pressure sensor  22  which is attached to collisional plate  3 . 
   In  FIG. 3 , a point PO represents a position where pressure sensor  22  starts sensing force, and generally corresponds to the point at which collisional plate  3  and golf ball  2  come into collision with each other. Fn(t) which is a contact force of perpendicular direction gradually increases from point PO, peaks at a point P 4 , comes down therefrom to reach zero at a point P 3 . Point P 3  represents a point where pressure sensor  22  no longer senses force, and generally corresponds to the point where golf ball  2  leaves collisional plate  3 . 
   On the other hand, a value of Ft(t) which is contact force in the direction parallel with the collisional plate (i.e., shear strength) increases with time from point P 0 , peaks at P 1 , then gradually decreases to zero at point P 2  after which it takes a negative value. Since the golf ball leaves pressure sensor  22  at point P 3 , the curve of Ft(t) sensed at pressure sensor  22  takes zero at point P 3 . An area S 1  of the region where Ft(t) takes positive values within the area surrounded by the curve of Ft(t) and the time axis represents impulse where shear strength is positive. On the other hand, an area S 2  of the region where Ft(t) takes negative values within the area surrounded by the curve of Ft(t) and the time axis represents impulse where shear strength is negative. Impulse S 1  acts in such a direction that promotes back spin, and impulse S 2  acts in such a direction that restrains back spin. Here, impulse S 1  takes a larger value than impulse S 2 , and a value obtained by subtracting impulse S 2  from impulse S 1  contributes to back spin of a golf ball. 
   A coefficient of dynamic friction can be derived by calculating a maximum value of M(t) which is obtainable by Ft(t)/Fn(t). 
   (Concurrent Measuring Method of Spin Rate of Golf Ball) 
   In the measuring apparatus of  FIG. 1 , spin rate, speed, and launch angle of a golf ball that collides with the collisional plate are measured. This may be used as identification data for determining correlation between calculated value of M(t) and spin rate. 
   In  FIG. 1 , golf ball  2  that is reflected by the collisional plate is measured for spin rate, speed and flying angle of golf ball  2  during fly by a stroboscopic device Kb and a camera device Ka disposed laterally of the flying trajectory. Stroboscopic device Kb is connected to a stroboscopic power  5 , and camera device Ka is connected to a camera power  6  via a capacitor box  8 . Spin rate, speed, and flying angle may be analyzed by using a spin analyzing device  7 . Further, by comparing these analysis results with results of measured coefficient of dynamic friction, it is possible to evaluate correlation between coefficient of dynamic friction and spin rage, as well as influences of coefficient of dynamic friction on the initial velocity and flying angle of a golf ball. 
   (Structure of Collisional Plate) 
   In  FIG. 2 , collisional plate  3  has a substrate  21 , pressures sensor  22 , a superficial plate  23  and a main bolt  25  for integrally fixing these elements. 
   Substrate  21  may be formed of any material without particular limitation insofar as it has a predetermined strength and rigidity, but preferably formed of steel. Substrate  21  is 5.0 to 20.0 mm thick. A model number of main bolt  25  is, for example, M 10  according to Japanese Industrial Standards (JIS). 
   Pressure sensor  22  may be implemented by a variety of products such as 3-component force sensor (model 9067) manufactured by Kistler Instrument Corp., for example. This sensor is able to measure force components in a parallel direction, a Y direction and a perpendicular direction. Although not illustrated, measurement of pressure is conducted with a charge amplifier (model 5011B of Kistler Instrument Corp.) connected to pressure sensor  22 . Pressure sensor  22  is formed in its center with a through-hole  24  through which main bolt  25  is inserted to integrally fix pressure sensor  22  with substrate  21 . 
   Superficial plate  23  is made up of a main body  23   a  and a covering plate  23   b . The covering plate is attached to the main body in a detachable manner. By appropriately changing the material, the planner shape and the surface structure of covering plate, it is possible to create approximate models of various golf club heads and to measure coefficients of dynamic friction thereof. Main body  23   a  and covering plate  23   b  may be mounted in any way without special limitation, for example, via a bolt. 
   Main body  23   a  of superficial plate  23  may be formed of any materials without limitation, but typically of stainless steel (SUS-630). The thickness of main body  23   a  is typically in the range of 10 to 20 mm. Also, main body  23   a  may have a planner shape which is substantially the same with that of pressure sensor  22 , such as a square 40-60 mm on a side. Into main body  23   a , a distal end of main bolt  25  is screwed. As a result, pressure sensor  22  is sandwiched and fixedly positioned between substrate  21  and main body  23   a.    
   As to covering plate  23   b , various materials, planner shapes and surface structures may be adopted, however, a titanium alloy (6-4Ti) containing 6 wt % of aluminum and 4 wt % of vanadium is typically used in view of evaluation of model of club head. Thickness of covering plate  23   b  may be arbitrarily changed, for example, within the range of 1.0 to 5.0 mm. The planner shape of covering plate  23   b  is substantially the same with that of main body  23   a , such as a square 40-60 mm on a side, for example. Also, covering plate  23   b  has a surface roughness which may be arbitrarily adjusted, for example in the range of 2 to 20 μm in terms of 10-point average roughness Rz. 
   Collisional plate  3  may be positioned at any angle (α) with respect to the flying direction (launching direction) of golf ball. In the present invention, the angle (α) is typically adjusted in the range of 10° to 90°. This angle corresponds to a loft angle of golf club and may be efficiently used for designing different numbers of club heads. 
   EXAMPLES 
   A coefficient of dynamic friction of a golf ball was measured using a measuring apparatus having a general structure shown in  FIG. 1  and having the following specification. 
   1. Specification of Measuring Apparatus 
   (A) Emitter: air gun system 
   (B) Collisional plate 
   Substrate 
   
       
       
         
           Steel 
           Thickness: 5.35 mm
 
Main body
 
         
       
     
  
   Superficial plate
         Size: 56 mm×56 mm×15 mm   Stainless steel (SUS-630)       

   Covering plate
         Size: 56 mm×56 mm×2.5 mm   Titanium alloy: 6-4Ti (6 wt % Al, 4 wt % V)   Average roughness: 13.6 μm±2.0 μm       

   Angle of inclination (α)
         22 degrees (with respect to flying direction of golf ball)       

   (C) Pressure sensor 
   3-component force sensor (model 9067), product of Kistler Instrument Corp. 
   Charge amplifier 
   Model 5011B, product of Kistler Instrument Corp. 
   (D) Capture of contact force into PC 
   A pulse counter board PCI-6101 (manufactured by INTERFACE CORPORATION) was used. With a 16-bit PCI pulse counter board with 4 channels, measurement suited for a specific application may be realized in four counter modes. The maximum input frequency is 1 MHz. 
   2. Measuring Procedure 
   Measurement of coefficient of dynamic friction was conducted in the following manner. 
   (a) Set angle (a) of collisional plate at 22 degrees with respect to flying direction of golf ball (vertical direction). 
   (b) Adjust air pressure of emitter  1 . 
   (c) Emit golf ball from emitter. 
   (d) Measure initial velocity of golf ball from preset distance between sensor  1  and sensor  2  and blocking time difference of golf ball therebetween. 
   (e) Measure contact force Fn(t) and contact force Ft(t), and calculate maximum value of Ft(t)/Fn(t). 
   (f) Measure spin rate of golf ball with stroboscopic device and camera device. 
   3. Result of Measurement 
   Results obtained with the above apparatus and measuring procedure are shown in  FIG. 3 . From  FIG. 3 , a value of M(t) is calculated as Ft(t)/Fn(t), and a maximum value is 0.21. Since Ft and Fn tend to generate noises in initial and terminal periods where contact force rises up, a maximum value of M(t) is calculated while trimming an early stage of the initial period and a late stage of the terminal period. 
   The present invention provides a method capable of adjusting a contact force between a golf ball and a golf club, and a spin rate of the golf ball when the golf ball is hit by the golf club. The present invention allows for evaluation of spin rate at the time of hitting with a golf club by measuring a coefficient of dynamic friction between a golf ball and a collisional plate in an apparatus employing a club model with the collisional plate. 
   Although the present invention has been described and illustrated in detail, it is clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of the present invention being limited only by the terms of the appended claims.