Abstract:
An apparatus for determining the torsional stiffness of a shaft comprises a rigid frame having a collet for securing one end of the shaft to be measured the rigid frame. A second collet secures the opposite end of the shaft to an inertial weight, which is supported for rotation by a separate bearing so that the inertial weight introduces no axial load in the shaft being measured. The inertial weight has mounted to it a biaxial accelerometer, optical gate or other electronic means for measuring the torsional frequency of the shaft/weight combination. When the inertial weight is displaced from the initial static position and released, the inertial weight oscillates about its center of mass under the urging of the torsional stiffness of the shaft. A computer is programmed with the mass moment of inertia of the inertial weight and therefore is able to solve the differential equation of motion for the torsional spring constant of the shaft based on the frequency of oscillation.

Description:
BACKGROUND 
     This invention relates to an apparatus for measuring physical properties of golf club shafts, specifically to an apparatus for measuring the torsional stiffness (torsional spring constant) of a golf club shaft. 
     In the field of designing, modifying and fitting golf clubs, it is advantageous to know the physical properties of the golf club shaft as well as the physical properties of the golf club head. It is common in the industry to rate clubs based on the flexural stiffness designated typically by the terms: Extra Stiff (XS); Stiff (S); Firm (F); Regular (R); Average (A); and Ladies&#39; (L). The flexural stiffness is important, of course, because it determines the maximum bending as well as the first bending mode frequency of the shaft and, therefore, by selecting the appropriate shaft stiffness, the club can be optimized for the swing speed of the particular golfer. The torsional stiffness of the golf club shaft is of equal importance because it determines the maximum windup of the club head relative to the shaft and the torsional frequency at which the club head oscillates about the axis of the golf club shaft during the swing. For optimum performance, in addition to matching the flexural stiffness of the shaft to the player&#39;s swing speed, the torsional stiffness of the shaft should also be matched to the club head swing weight and the player&#39;s swing speed. 
     Prior art methods for determining the torsional stiffness of a golf club shaft comprise fixing one end of the shaft in a collet or chuck then applying a predetermined torque (one to five foot pounds is a standard) to the opposite end of the shaft. The total angular deflection of the shaft is then read. In order to obtain sufficient resolution, a relatively high torque, must be used, therefore, in order to ensure the shaft does not move in the fixture under the high torque, a relatively high clamping force must be used. This results in many of the exotic composite shafts being crushed by the clamping force exerted by the collet on the end of the shaft. In order to avoid crushing the composite shafts, many manufacturers have resorted to using a lower torque on composite shafts and high torque on steel shafts, with the result that there is now no longer a consistent scale to compare the flexural stiffness of composite shafts to steel shafts or indeed in many cases clubs of the same type from manufacturer to manufacturer. Accordingly, what is needed is an apparatus for measuring the torsional stiffness of a golf club shaft that has sufficient resolution to measure small differences in the torsional stiffness of steel shafts without requiring high torque (and high clamping forces) that can damage composite shafts. 
     SUMMARY OF THE INVENTION 
     The present invention satisfies the foregoing need by providing an apparatus and method for determining torsional stiffness of a shaft by measuring the torsional frequency at which the shaft oscillates when coupled to a torsional weight having a known mass moment of inertia. In a preferred embodiment of an apparatus for determining the torsional stiffness of a golf club shaft incorporating features of the present invention, a collet is provided for securing one end of a shaft to the rigid frame of the apparatus. A second collet secures the opposite end of the shaft to an inertial weight. The inertial weight has mounted to it a conventional biaxial accelerometer. When the inertial weight is displaced from the initial static position and released, the inertial weight oscillates about its center of mass under the urging of the torsional stiffness of the golf club shaft. The accelerometer provides a signal indicative of the amplitude and frequency of oscillation of the inertial mass which is fed into a computer. The computer is programmed with the mass moment of inertia of the inertial weight and therefore is able to solve the differential equation of motion for the torsional spring constant of the golf club shaft based on the frequency of oscillation. The torsional spring constant can be displayed directly in Newton meters per radian (or any other engineering unit) or can be converted into units directly comparable to the prior art measurement systems by multiplying the spring constant by the appropriate load (e.g. five foot pounds). 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     The present invention will be better understood from a reading of the following detailed description, taken in conjunction with the accompanying drawing figures in which like references designate like elements and on which: 
     FIG. 1 is a side elevation view of an apparatus for measuring torsional stiffness of a golf club shaft according to the prior art; 
     FIG. 2 is a partial schematic side elevation view of an apparatus for measuring torsional stiffness of a golf club shaft incorporating features of the present invention; 
     FIG. 3 is an alternative embodiment of an apparatus for measuring torsional stiffness incorporating a shaft encoder or photo gate for determining the frequency of oscillation of the inertial mass; and 
     FIG. 4 is an alternative embodiment of an apparatus for measuring torsional stiffness of a golf club shaft in which the axis of the shaft is oriented vertically. 
    
    
     DETAILED DESCRIPTION 
     The drawing figures are intended to illustrate the general manner of construction and are not necessarily to scale. In the description and in the claims, the terms left, right, front and back and the like are used for descriptive purposes. However, it is understood that the embodiment of the invention described herein may be capable of operation in other orientations than are shown and the terms so used are for the purpose of describing relative positions and are interchangeable under appropriate circumstances. 
     As discussed hereinbefore, the prior art method for determining the torsional stiffness of a golf club shaft comprises exerting a known torque on a sample shaft and measuring the resulting angular deflection of the shaft. An apparatus for carrying out the aforementioned measurement is shown in FIG.  1 . To carry out the measurement, the shaft  10  is placed with a first end  12  in a collet  14  supported by a tailstock  16  mounted to the frame  18  of the apparatus  20 . The second end  22  of shaft  10  is secured between movable jaws  24  of a chuck  26 . Chuck  26  is freely rotatable about an arm  28  mounted to the end of frame  18  opposite that of tailstock  16 . A weight “W” is suspended from chuck  26  so as to provide a known torque on chuck  26  about its axis. The resulting angular deflection of chuck  26  is determined with reference to the movement of a calibrated scale  30  against a point of reference  32 . 
     In order for accurate determinations of torsional stiffness to be made, it is obviously imperative that shaft  10  be clamped tightly between collet  14  and jaws  24  so that no slippage occurs. As discussed hereinbefore, in order to provide sufficient resolution to determine small differences in torsional stiffness between relatively stiff shafts, such as steel shafts, a relatively large amount of torque must be applied to shaft  10 . However, where a large torque is applied and it is necessary to ensure that no slippage occurs between the shaft  10  and collet  14  or shaft  10  and chuck  26 , relatively large clamping forces must be applied to shaft  10 . This may result in undesirable damage or even destruction of the shaft itself. If a lesser torque is used, resolution suffers and if different torques are used for steel shafts versus the more flexible composite shafts, inconsistent measurement standards will result. Moreover, due to the static nature of the prior art measurement method, measurement precision suffers as a result of hysteresis caused by static to dynamic friction transition (“stiction”) of the rotating chuck. Finally, the prior art method provides only one data point from which to determine the torsional spring constant of the shaft. For steel shafts which exhibit a linear spring constant (at least up to the elastic limit) a single data point is adequate. However, many composite shafts do not exhibit a linear torsional spring constant and, therefore, a single data point may provide a misleading indication of the effective torsional stiffness of the club when in use. 
     FIG. 2 is a partial schematic side elevation view of an apparatus incorporating features of the present invention. The apparatus comprises a frame  40  the first end  42  of which has a track  44  on which is mounted a tailstock  46 . At the second end  48  of frame  40  is a support arm  50  on which is mounted a chuck  52 . Chuck  52  is supported on support arm  50  by bearing  54 , which permits chuck  52  to rotate freely about an axis of rotation  56  passing through the center of mass  58  of chuck  52 . Chuck  52  has movable jaws  60  which are adapted to grip shaft  10  such that the longitudinal axis of shaft  10  is substantially co-linear with axis of rotation  56 . By “substantially” co-linear, what is meant herein is that the shaft is co-linear within reasonable manufacturing tolerances or at least sufficiently co-linear that the resulting eccentricity does not result in more than a five to ten percent inaccuracy in the measured torsional stiffness. 
     Tailstock  46  further comprises a collet  62  having a longitudinal aperture  64  adapted to receive and clamp first end  12  of shaft  10 . The longitudinal axis  66  of aperture  64  is substantially co-linear with axis of rotation  56  such that when shaft  10  is clamped between collet  62  and movable jaws  60 , it is constrained to move in substantially pure torsion as chuck  52  rotates about axis of rotation  56 . In order to permit apparatus  38  to accommodate shafts of different length, tailstock  46  is movable toward and away from chuck  52  on track  44  and is selectively secured to track  44  by clamp  68 . Preferably track  44  comprises a conventional dove-tail bed similar to the tailstock bed found on a conventional lathe. An accelerometer  70  such as a biaxial accelerometer chip such as VTI Hamlin SCA600 is mounted to chuck  52  such that the axis of sensitivity is oriented in the tangential plane relative to axis of rotation  56 . Preferably accelerometer  70  is mounted at the top or bottom of chuck  52  when the shaft  10  is in the neutral position so as to minimize any offset caused by the earth&#39;s gravitational field. The analog output of accelerometer  70  may be fed into an analog to digital converter  72  such as a model PCB482A17 signal conditioner prior to conversion into digital data which can be read by a conventional digital computer  74  for processing. Results may be displayed on a conventional screen  76  in response to operator inputs through keyboard  78 . 
     As is well known, for a torsional spring such as a shaft displaced angularly about its axis, the torsional spring constant can be expressed by the equation 
     
       
         T=−Kƒ  (1) 
       
     
     When “K” is the torsional spring constant in units of torque per radian; “T” is the torque applied to the shaft and θ is the displacement of the shaft in radians. Since the force exerted by the shaft resisting the torque is in the opposite direction as the torque, the sign of “K” is negative. 
     For a torsional system comprising a torsional mass such as a large disk supported by a torsional spring, in which the mass of the spring is small enough relative to the mass of the disk that the mass of the spring can be ignored, then according to Newton&#39;s Law: 
     
       
         T=I{umlaut over (θ)}  (2) 
       
     
     Where “T” is torque e is angular acceleration and “I” is the mass moment of inertia of the inertial mass. Combining equations 1 and 2 yields: 
     
       
         I {umlaut over (θ)}=−K θ 
       
     
     
       
         {umlaut over (θ)}+(K/I) θ= 0   
       
     
     
       
         {umlaut over (θ)}+Ω 2 θ= 0   
       
     
     
       
         {umlaut over (θ+)}ω 2 θ= 0   (3)  
       
     
     
       
         Where ω={square root over (K/I)}  (4) 
       
     
     Where ω is the circular frequency of the torsional system. 
     Since the units of ω are radians per second and the output of the accelerometer is most conveniently expressed in terms of cycles per second (Hertz), equation 4 may be expressed as: 
      2πF={square root over (K/I)} 
     
       
         4π 2 F 2 =K/I 
       
     
     
       
         K=I(4π 2 )F 2   (5) 
       
     
     Where “F” is frequency in Hertz (i.e. cycles/second). 
     As can be determined from equation 5, if the moment of inertia is known, the spring constant “K” of shaft  10  can be determined directly from the measured frequency of oscillation. Although it would be possible to calculate the mass moment of inertia of chuck  52  based on its density and geometry, in practice apparatus  38  is calibrated by clamping a shaft having a known torsional spring constant in apparatus  38  and measuring the frequency of oscillation of the known shaft. With the spring constant “K” of the calibration shaft and frequency “F” known from the measurement, the mass moment of inertia “I” of chuck  52  can be determined from equation 5. Once the mass moment of inertia “I” of chuck  52  is known, shafts having unknown torsional stiffness can be analyzed based on the mass moment of inertia determined using the calibrated shaft. As noted in the foregoing, for maximum accuracy, the moment of inertia “I” of the inertial mass (chuck  52 ) must be large relative to the mass of the shaft being tested  10 . Accordingly, in the embodiment of FIG. 2, chuck  52  is typically made of steel two or more inches thick and six or more inches in diameter. 
     FIG. 3 depicts an alternative embodiment of an apparatus for measuring torsional stiffness  80  in which, a photo gate  82  comprising an emitter  84  and a detector  86  are used to measure the period of oscillation of chuck  52  in lieu of accelerometer  70 . A peg  88  extending from chuck  52  breaks the beam of light passing from emitter  84  to detector  86  each time chuck  52  passes the neutral position. Accordingly, the frequency of oscillation can be determined based on the number of times the beam of light is broken by the passage of peg  88 . Alternatively, a conventional shaft encoder  90  may be used to measure the period of oscillation of chuck  52 . 
     FIG. 4 is yet another alternative embodiment of an apparatus for measuring torsional stiffness of a shaft  94  in which shaft  10  is suspended such that the longitudinal axis of shaft  10  is oriented in the vertical direction relative to the earth&#39;s gravitational field. In the embodiment of FIG. 4, chuck  52  is supported for rotation by a conventional thrust bearing  96  supported by frame  98 , however, chuck  52  may be suspended by shaft  10  itself, thereby eliminating the possibility of friction from bearing  96  affecting the measurements. As with the embodiment of FIG. 2, accelerometer  70  is mounted such that the axis of sensitivity is oriented in the tangential (circumferential) direction relative to chuck  52 . Since the tangential direction is orthogonal to the earth&#39;s gravitational field, the circumferential position of accelerometer  70  on chuck  52  is irrelevant in the embodiment of FIG.  4 . 
     Once the torsional spring constant is obtained from any of the foregoing apparatus, it can be expressed in conventional engineering units such as Newton meters per radian, foot pounds per radian, etc. or can be converted into the pure angular expressions used commonly in the art by multiplying the spring constant by the appropriate torque such as five foot pounds, one foot pound, etc. 
     Although certain preferred embodiments and methods have been disclosed herein, it will be apparent from the foregoing disclosure to those skilled in the art that variations and modifications of such embodiments and methods may be made without departing from the spirit and scope of the invention. For example, although a collet and chuck are disclosed as preferred methods of securing shaft  10  in the apparatus, any conventional means of holding a shaft such as a set screw, or a keyed adapter (where test specimens can be bonded with an end fitting) may be used to secure the shaft in the apparatus in accordance with the present invention. Similarly, although a digital computer is shown, any means of determining the frequency of oscillation and solving equation 5 is considered within the scope of the present invention. Accordingly, it is intended that the invention shall be limited only to the extent required by the appended claims and the rules and principles of applicable law.