JP2000046675A - Measuring method and measuring device for moment of inertia - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily and accurately measure the moment of inertia of a measured object having an indefinite shape. SOLUTION: A club head 30 is placed on the placement tray 24 of a measuring device 10 via a jig 72. Then, the placement tray 24 is rotated for winding the preset length of a string 38 around the periphery thereof. A weight 40 is thereby made to face a fall start position. Thereafter, the weight 40 is made to give a free fall. The weight 40 falling in a hollow cylinder 32 is sequentially detected with an upper sensor 42 and a lower sensor 44, and the detection signals are inputted to an arithmetic operation means. The arithmetic operation means finds a time difference Δt for the weight 40 to pass two fixed points, and the moment of inertia I3 of the club head 30 is calculated from the time difference Δt.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a measuring method and a measuring apparatus for easily measuring the moment of inertia of an object having an irregular shape such as a golf club head.

[0002]

2. Description of the Related Art For example, in a golf club head, the ball is hit at the maximum rebound position (sweet spot) on the face surface corresponding to the center of gravity, so that the speed and the launch direction of the ball are most stable. However, it is difficult to actually hit the ball at the maximum rebound position, and the actual hit position of the ball and the maximum repulsion position deviate, and the magnitude of the deviation changes the speed and launch direction of the ball, resulting in a miss shot. Is connected to As a countermeasure, it is known that the occurrence of a miss shot can be reduced by increasing the moment of inertia around the center of gravity of the club head to widen the sweet area.

That is, the moment of inertia around the center of gravity of the club head greatly affects the performance of the golf club, and it is indispensable to accurately grasp this and reflect it in the design. Is required to be performed with high accuracy.

[0004]

As an apparatus for measuring the moment of inertia of the club head, a club head is mounted on a rotary vibration shaft to which rotational vibration is given by a torsional pendulum, and the inertia is determined from the vibration cycle of the rotary vibration shaft. A method of calculating a moment by calculation is known. However, this measuring device has a disadvantage that the mechanism is complicated and the cost increases.

[0005]

SUMMARY OF THE INVENTION The present invention has been proposed in view of the above-mentioned drawbacks inherent in the prior art, and has been proposed in order to solve the problem suitably. It is an object of the present invention to provide a novel method and apparatus for measuring a moment of inertia, which can be measured accurately.

[0006]

[Means for solving the problems] To overcome the above-mentioned problems,
In order to suitably achieve the intended purpose, the method of measuring a moment of inertia according to the present invention is a method of starting to drop a weight connected via a cord to a rotatable mounting plate on which an object to be measured having an irregular shape is mounted. The placing plate is rotated through the cord by free fall from the position, the sum of the kinetic energy of the weight and the rotational energy of the placing plate including the object to be measured at this time, and the weight at the falling start position of the weight The apparatus is characterized in that the potential energy in the stationary state is substituted into the equation of the law of conservation of energy to calculate the moment of inertia of the measured object.

[0007] In order to overcome the above-mentioned problems and appropriately achieve the intended object, an apparatus for measuring the moment of inertia according to another invention of the present application is provided so as to be freely rotatable horizontally, and is provided with an object to be measured having an irregular shape. A placing plate to be placed, one end connected to the placing plate described above, and the other end connected to the weight, and a rope body for horizontally rotating the placing plate with the free fall of the weight; Detecting means for detecting a time difference of a weight passing between two points separated by a predetermined height during a fall, and calculating means for calculating the moment of inertia of the object to be measured from a value detected by the detecting means. Features.

[0008]

BEST MODE FOR CARRYING OUT THE INVENTION Next, a method and an apparatus for measuring a moment of inertia according to the present invention will be described with reference to preferred embodiments.

[0009]

FIG. 1 is a schematic perspective view of a measuring apparatus for measuring the moment of inertia according to a preferred embodiment of the present invention. In each corner of the horizontal substrate 12, an adjustment screw 16 is screwed from the upper side to the lower side, and the four adjustment screws 16 enable the horizontal substrate 12 to be mounted horizontally on an appropriate installation portion. Be composed. A level 18 is provided on the horizontal substrate 12.

The main body 14 is provided with a vertically rotatably supported support shaft 22 which is inserted from above into a receiving cylinder 20 disposed inside the main body 14, and is rotatably disposed. In addition, a mounting plate 24 having a required diameter is disposed so as to be horizontally rotated integrally. On the upper surface of the mounting plate 24, a first projection 26 corresponding to the rotation center thereof,
A pair of second protrusions 28, 28 located on both sides of the protrusion 6 are provided, and the three protrusions 26, 28, 28 position the club head 30 as an object to be measured via a jig 72 described later. It is configured to be mounted. The lower end of the support shaft 22 is formed in a sharp conical shape, and the support shaft 22 is rotatable in a state in which the tip of the support shaft 22 is brought into contact with a bearing portion formed on the inner bottom surface of the receiving cylinder 20 to minimize rotational friction. Is to be supported.

The placing plate 24 is a substantially solid cylinder, and its moment of inertia I ₁ is given by the following [Equation 1] if the weight m ₁ and the turning radius R ₁ of the placing plate 24 are clear. It is required. _{I 1 = m 1 · R 1} 2/2 ...... [Formula 1]

A hollow cylinder 32 having a predetermined length is vertically arranged at a position separated by a predetermined distance from the position where the receiving cylinder 20 is disposed on the main body 14, and the hollow cylinder 32 is open at the upper surface of the main body 14. . Immediately above the hollow cylinder 32, the main body 14 is provided.
A pulley 36 rotatably disposed on a bracket 34 erected on the upper surface of the bracket 34 rotatably faces, and one end of a thread 38 as a cord wound around the pulley 36 is positioned at an appropriate position on the outer periphery of the placing plate 24. And the other end of the thread 38 is connected to a weight 40 having a weight m _{2 that} can freely fall in the hollow cylinder 32. That is, the weight 38 is freely dropped from a predetermined drop start position H in the hollow cylinder 32 in a state where the thread 38 is wound around the outer circumference of the mounting plate 24 by a predetermined length,
The placing plate 24 is configured to rotate horizontally via the thread 38. As the yarn 38, a light and non-stretching yarn is preferably used.

As shown in FIG. 1, an upper sensor 42 and a lower sensor 44 as detecting means are arranged on the main body 14 at positions corresponding to the hollow cylinder 32 and are vertically separated by a predetermined height h. I have. The upper sensor 42 is a hollow cylinder 3
The lower sensor 44 is also composed of a pair of front and rear sensor members 44a and 44b sandwiching the hollow cylinder 32. Through holes 32a and 32b are formed in the hollow cylinder 32 at positions corresponding to the upper sensor 42 and the lower sensor 44, respectively.
The weight 4 allows the weight 40 falling freely in the hollow cylinder 32 to be detected. As shown in FIG. 2, the upper sensor 42 is disposed at a fixed point A separated from the drop start position H of the weight 40 by _a height ha below the drop start position H, and the lower sensor 44 is It is arranged from the position H to the fixed point B spaced by a height h _b downward. That is, the weight 40 that has started free fall from the drop start position H is fixed point A
The upper sensor 42 and the lower sensor 44 detect that the vehicle has passed the fixed point B. Then, the detection signals of both sensors 42 and 44 are calculated by calculation means 46 shown in FIG.
, The time difference Δt at which the weight 40 passes from the fixed point A to the fixed point B is determined based on the signal, and the moment of inertia I ₃ of the club head 30 is calculated from the time difference Δt. As the upper and lower sensors 42 and 44, transmission optical sensors are preferably used, but the type is not limited to the transmission type, and an appropriate type such as a reflection type can be adopted.

The main body 14 is provided with calculating means 46 for calculating the moment of inertia I ₃ of the club head 30 based on the time difference Δt between the fixed point A and the fixed point B when the weight 40 falls freely. A measuring device 48 is provided. The measuring device 48 includes an input means 50 and a display means 52, and inputs in advance data such as the weight m _{3 of the} club head 30 necessary for calculating the moment of inertia I _3.
0, and the display means 52 can display the calculated moment of inertia I ₃ .

Here, the kinetic energy of the weight 40 when the mounting plate 24 is rotated via the thread 38 by freely dropping the weight 40 from the drop start position H, and the club head 30 and the jig 72 are included. The sum of the rotational energies of the mounting plate 24 and the potential energy of the weight 40 in the stationary state at the drop start position H are equal according to the law of conservation of energy, and [Equation 5] to be described in detail later is established. m ₂ · G · h _b = 1/2 · m ₂ · v _b ² + ／ (I ₃ + I ₀ ) · ω ² (Equation 5)

Then, in the embodiment, from [Equation 10] (detailed later) of the time difference Δt deformed based on the above [Equation 5],
The setting is such that the moment of inertia I ₃ of the club head 30 is calculated. Δt = {√ (2 · h b) -√ (2 · h a)} / √ (m 2 · G / (m 2 + I / R 1 2)) ...... [Equation 10]

[0017]

FIG. 4 is a schematic perspective view showing a center-of-gravity aligning apparatus.
And a bracket 62 is disposed at the longitudinal center of the upper cross member 60a. A rectangular frame-shaped support 64 facing the inside of the frame-shaped main body 60 is suspended from the bracket 62 via a swing shaft 66 so as to be swingable in any of the front, rear, left and right directions. A receiving plate 68 is provided on the upper surface of the lower cross member 64a of the supporter 64, and a pair of positioning pins 70, 70 are erected on the upper surface of the receiving plate 68 so as to be separated from each other.
Then, a jig 72 attached to the club head 30 via the positioning pins 70, 70 is positioned and mounted.

At the lower end of the supporter 64, the swing shaft 6
An indicator pin 74 whose axis is aligned with and coincides with the lower end of the frame-shaped main body 60 is attached to the lower end of the indicator pin 74.
It is set to face upward from the upper surface of b. In addition, lower cross member 6
A cross-shaped mark 76 is provided on the upper surface of Ob, and the indicator pin 74 is configured to point toward the center of the mark 76 when no load is externally applied to the support 64. That is, when the club head 30 is placed on the receiving plate 68 via the jig 72, the indicator pin 74
If the center of the head 6 is oriented, it is determined that the center of gravity of the head 30 coincides with a vertical line passing through the axis of the indication pin 74 and the swing shaft 66.

[0019]

[Jig] A jig 72 for positioning and placing the club head 30 on the placing plate 24 of the measuring apparatus 10.
As shown in FIG. 5, a first hole 78 is formed in the center of the lower surface, and a pair of second holes 8 are formed with the first hole 78 interposed therebetween.
0,80 is formed. The jig 72 is positioned and mounted on the placing plate 24 by inserting the holes 78, 80, 80 into the corresponding projections 26, 28, 28, and the receiving of the center-of-gravity aligning device 54. Each of the second holes 80, 80 is configured to be positioned and mounted on the plate 68 by being inserted into the corresponding positioning pin 70, 70.

When the jig 72 is positioned and mounted on the receiving plate 68 of the center-of-gravity aligning device 54 through the second holes 80, 80, the indicator pin 74 of the supporter 64 is directed to the center of the mark 76. The jig 72 is set such that the center of gravity of the jig 72 coincides with the perpendicular. The jig 72 has holes 78, 80,
The center of gravity is set so as to coincide with the center line of rotation of the mounting plate 24 when the positioning device 24 is positioned and mounted on the mounting plate 24 of the measuring apparatus 10 via 80. That is, the center of gravity alignment device 5
4 so that the center of gravity is vertically aligned with the club head 30.
The center of gravity of the club head 30 is aligned with the rotation center line of the mounting plate 24 simply by positioning and mounting the jig 72 mounted on the mounting plate 24.

The club head 30 and the jig 72 whose centers of gravity are aligned and matched by the center of gravity aligning device 54 are attached by appropriate means (for example, an adhesive tape). Further, a plurality of screws 82 are screwed into the jig 72 in the circumferential direction so as to be separated from each other, and the ends thereof can be protruded and retracted from the upper surface side. When the jig 72 is attached to the club head 30, by adjusting the projecting dimensions of the plurality of screws 82, the jig 72 can be stably fixed to the bottom surface of the irregular club head 30, and the lower surface thereof Can be horizontal.

The jig 72 is a substantially solid cylinder like the tray 24 described above, and its moment of inertia I ₄ is determined by the jig 7.
If the weight m ₄ and the radius of gyration R ₄ are clear, they can be obtained by the following [Equation 2]. _{I 4 = m 4 · R 4} 2/2 ...... [Equation 2]

[0023]

Next, the actual measurement of the moment of inertia by the measuring device according to the embodiment will be described. When the moment of inertia is measured, the weight m ₃ of the club head 30 to be measured and other necessary data are input to the calculating means 46 via the input means 50 in advance. In addition, the inertia moment I ₁ of the placing plate 24 and the jig 72,
I ₄ is obtained by the above [Equation 1] and [Equation 2] based on the data input with respect to the placing plate 24 and the jig 72.

First, the jig 72 is fixed to the club head 30 to be measured. That is, the center of gravity alignment device 5
The club head 30 is placed on the upper surface of the jig 72 positioned and placed on the fourth receiving plate 68. At this time, the frame-shaped main body 6
Club head 3 on a perpendicular passing through the center at mark 76 of 0
If the center of gravity 0 is not located, the supporting frame 64 swings by the amount of the shift of the center of gravity with respect to the frame-shaped main body 60, and
Indicates a position deviated from the center of the mark 76. Therefore, the position of the club head 30 is adjusted with respect to the jig 72, and the position
By fixing 0, 72 with an adhesive tape or the like, the two 30 and 72 are attached in a state where the center of gravity of the jig 72 and the center of gravity of the club head 30 coincide with each other on a vertical line. As described above, by adjusting the screw 82 of the jig 72, the position of the jig 72 is adjusted to be stable and horizontal on the bottom surface of the irregular club head 30.

Next, the club head 30 to which the jig 72 is attached is mounted on the mounting plate 24 of the measuring device 10 via the jig 72. At this time, the three holes 78, 80,
By inserting 80 into the corresponding projections 26, 28, 28 of the mounting plate 24, the center of gravity of the club head 30 coincides with the rotation center line of the mounting plate 24. That is, the positioning of the club head 30 with respect to the measuring device 10 can be performed easily and in a short time, and the working efficiency is improved.

By rotating the tray 24 and winding the thread 38 around the outer circumference for a predetermined length, the weight 40 is moved to the drop starting position H.
, The weight 40 is allowed to fall freely. The weight 40 falling in the hollow cylinder 32 is sequentially detected by the upper sensor 42 and the lower sensor 44, and the detection signal is input to the calculating means 46. Then, the calculation means 46 calculates the fixed point B from the fixed point A based on the detection signals of the two sensors 42 and 44.
, The time difference Δt at which the weight 40 passes through the
, The moment of inertia I ₃ of the club head 30 is calculated by the above [Equation 10]. The calculated moment of inertia I ₃ is displayed on the display means 52.

[0027]

[Actual calculation method] Around the center of gravity of the club head 30
Moment of inertia I_ThreeThe actual calculation method of will be described.
In addition, the weight 40 that has freely dropped from the drop start position H is fixed point A
Speed when passing through_a, When passing through fixed point B
Speed v_b, Including the club head 30 and the jig 72
The angular velocity of the plate 24 was measured by ω, and the plate 24 and the jig 72 were measured.
Let the moment of inertia of the fixed system be I₀(= I₁+ I_Four). Ma
The weight acceleration is G (= 980 cm / s) ^Two).

The energy E ₁ when the weight 40 is held stationary at the drop start position H is expressed by the following equation (3) as the potential energy of the weight 40. E ₁ = m ₂ · G · h _b (Equation 3) Further, the energy E ₂ when the weight 40 that has freely fallen from the drop start position H passes the fixed point B is the kinetic energy of the weight 40 and the club head 30, Placement plate 2 including jig 72
4 is the sum of the rotational energies and is represented by [Equation 4]. E ₂ = １ ／ · m ₂ · v _b ² +1/2 (I ₃ + I ₀ ) · ω ² (Expression 4) where ω = v _b / R ₁ . Then, from the law of conservation of energy, the potential energy E ₁ of the weight 40 in the stationary state and the fixed point B
Is equal to the driving / rotational energy E ₂ in the falling state passing through, and [Equation 5] is established. E ₁ = E ₂ : m ₂ · G · h _b = １ ／ · m ₂ · v _b ² + ／ (I ₃ + I ₀ ) · ω ²式 [Formula 5]

By transforming the equation of the energy conservation law of [Equation 5] and expressing v _b , it becomes [Equation 6]. Here, the moment of inertia of the rotating system including the club head 30, the jig 72, and the placing plate 24 is represented by I (= I ₀ + I ₃ ). ^{_{1/2 · m 2 · v b 2}} +1/2 · I · v b 2 / R 1 2 = m 2 · G · h b 1/2 · v b 2 (m 2 + I / R 1 2) = m 2 G · h _b v _b = √ (2 · m ₂ · G · h _b / (m ₂ + I / R ₁ ² )) ··· [Equation 6]

Since the weight 40 is free-falling and performs a uniform acceleration motion, the acceleration α obtained from [Equation 6] is represented by [Equation 7]. α = m ₂ · G / (m ₂ + I / R ₁ ² ) (Equation 7) Note that when I = 0, α = G.

Assuming that the times at which the weight 40 passes through two fixed points A and B set on the falling line of the weight 40 are t _a and t _b , the weight 40 when passing through the fixed points A and B is velocity v _a, v _b of, [formula 8], represented by [equation 9]. _{v a = α · t a =} √ (2 · m 2 · G · h a / (m 2 + I / R 1 2)) ...... [Equation 8] _{v b = α · t b =} √ (2 · m 2 G · h _b / (m ₂ + I / R ₁ ² )) (Equation 9) Accordingly, the time difference Δ between the weight 40 passing the fixed point A and the fixed point B
t is represented by [Equation 10]. _{Δt = t b -t a = 1} / α {√ (2 · m 2 · G · h b / (m 2 + I / R 1 2)) - √ (2 · m 2 · G · h a / (m 2 ^{_{+ I / R 1 2))}} } = {√ (2 · h b) -√ (2 · h a)} / √ (m 2 · G / (m 2 + I / R 1 2)) ...... [equation 10]

That is, based on the detection results of the upper and lower sensors 42 and 44 of the measuring device 10, the above [Equation 10]
Substituting the time difference Δt for the club head 30, the jig 7
An inertia moment I of the entire rotating system including the mounting plate 2 and the mounting plate 24 is obtained. This moment of inertia I is, as described above,
I = a I ₀ + I _3, a further _{I 0 = I 1 + I 4} . The inertia moment I ₁ of the mounting plate 24 and the inertia moment I ₄ of the jig 72 are determined by inputting the mounting plate 24 and the jig 7 in advance.
Without measurement using the data relating to [Equation 1],
Since the numerical value is obtained from [Equation 2], the moment of inertia I ₃ around the center of gravity of the club head 30 is finally calculated.

[0033]

[Experimental Example] The height h _b = 24.28cm placed from falling start position H of the height h _a = 4.37cm fixed point B from the drop starting position H of the weight m ₃ = 29.9 g fixed point A of the weight 40 The relational expression between the time difference Δt and the moment of inertia I ₃ of the club head 30 when the rotation radius R ₁ of the plate 24 is set to 4.93 cm is obtained by substituting each numerical value into the above-mentioned [Equation 10]. Is represented by Δt = 0.02344 × 1.034√ (29.9 + 0.04114 (636 + I ₃ )) I ₃ = 4.181 × 10 ⁴ Δt ² -1363 (Equation 11)

Based on the above [Equation 11], the club head 30 having various inertia moments I _{3 known in} advance.
FIG. 6 shows the result of examining the relationship with the time difference Δt by actually placing the From this result, it was confirmed that the standard deviation σ of the actually measured time difference Δt was small, and the measuring apparatus 10 could measure the moment of inertia I ₃ with high accuracy. From the results of the experiments, it was confirmed that the above [Equation 11] was practical when the moment of inertia I ₃ was in the range of 2500 to 4500 gcm ² .

[0035]

[Modification] In the above-described embodiment, the weight 40 is set between the fixed points A and B.
Although There was calculated the moment of inertia I ₃ of the club head 30 from the time difference Δt to pass, by providing a means for detecting the speed v _b as it passes through the fixed point B of the weight 40, from the velocity v _b of the club head 30 it is also possible to calculate the moment of inertia I _3. That is, in the above [Equation 6], m ₂ ,
Since G, h _b and R ₁ are numerical values input as data in advance, the inertia moment I of the entire rotating system can be obtained from the detected value of the speed v _b . And finally, the moment of inertia I ₃ around the center of gravity of the club head 30
Can be calculated.

In the embodiment, the case of measuring the moment of inertia around the center of gravity of the head of the golf club has been described. However, the object to be measured is not limited to the club head, but may be the club itself. Any irregular shape can be used for measuring the moment of inertia of baseball bats, tennis rackets, and the like. Furthermore, not only the moment of inertia around the center of gravity of the measured object but also the moment of inertia around an appropriately set arbitrary position can be measured.

[0037]

As described above, according to the method and the apparatus for measuring the moment of inertia according to the present invention, the moment of inertia of an irregular-shaped object to be measured can be measured simply and accurately. Further, since the configuration of the apparatus is simple, there is an advantage that the apparatus can be provided at a low manufacturing cost.

[Brief description of the drawings]

FIG. 1 is a schematic perspective view of an apparatus for measuring a moment of inertia according to an embodiment.

FIG. 2 is an explanatory diagram illustrating a measurement principle of the measurement device according to the embodiment.

FIG. 3 is a block diagram of a measuring unit of the measuring device according to the embodiment.

FIG. 4 is a schematic perspective view of a center-of-gravity aligning apparatus according to the embodiment.

FIG. 5 is a bottom view of the jig according to the embodiment.

FIG. 6 is a table showing the relationship between the moment of inertia and the time difference, which was tested using the measuring device according to the example.

[Explanation of symbols]

 24 Placement tray 30 Club head (measured object) 38 Thread (cord) 40 Weight 42 Upper sensor (Detector) 44 Lower sensor (Detector) 46 Calculator 72 Jig

Claims (6)

[Claims] A weight (40) connected via a cable (38) to a rotatable mounting plate (24) on which an object to be measured (30) having an irregular shape is mounted.
The plate (24) is rotated via the cable body (38) by freely falling from the drop start position, and the plate containing the kinetic energy of the weight (40) and the DUT (30) at this time. The sum of the rotational energy of (24) and the potential energy of the weight (40) in the stationary state at the drop start position are substituted into the equation of the law of conservation of energy to calculate the moment of inertia of the DUT (30). A method for measuring a moment of inertia, characterized in that: 2. A jig (7) attached to the object to be measured (30) is positioned and placed on the mounting plate (24), thereby setting the jig (7).
With the center of gravity of 2) and the object to be measured (30) aligned with the center of rotation of the mounting plate (24), the kinetic energy of the weight (40) during free fall, the object to be measured (30), and the jig Placement plate containing (72)
The sum of the rotational energy of (24) and the potential energy of the weight (40) in the stationary state are substituted into the equation of the law of conservation of energy to calculate the moment of inertia around the center of gravity of the measured object (30). The method of measuring a moment of inertia according to claim 1. 3. A weight passing between two points separated by a predetermined height set on a drop line below the drop start position of the weight (40).
3. The method for measuring the moment of inertia according to claim 1, wherein the time difference of (40) is obtained, and the moment of inertia of the measured object (30) is calculated from the time difference. 4. The speed of the free fall of the weight (40) is obtained,
3. The method according to claim 1, wherein the moment of inertia of the object to be measured is calculated from the speed. 5. A mounting plate (24) which is horizontally rotatable and on which an object (30) of irregular shape is mounted, and a mounting plate (24) as described above.
One end is connected to the weight (40), and the other end is connected to the weight (40), a rope body (38) for horizontally rotating the mounting plate (24) with the free fall of the weight (40), and the weight (40) ) Detecting means (42, 44) for detecting the time difference of the weight (40) passing between two points separated by a predetermined height during the free fall, and detecting the time difference from the value detected by the detecting means (42, 44). Calculation means for calculating the moment of inertia of the measured object (30)
(46) An apparatus for measuring moment of inertia, characterized by comprising: 6. A jig (72) is attached to the DUT (30), and the DUT (30) is attached to the placing plate (24) via the jig (72).
6. The measurement of the moment of inertia according to claim 5, wherein the jig (72) and the object to be measured (30) are configured so that the center of gravity of the jig (72) and the object to be measured (30) coincide with the rotation center line of the mounting plate (24). apparatus.