JP3156027B2 - Method and apparatus for measuring moment of inertia - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is used in the technical field for measuring the moment of inertia of various objects having irregular shapes.
In particular, an axis passing through the center of gravity of the golf club head (center of gravity axis)
The present invention relates to a method of measuring a moment of inertia for measuring a moment of inertia around the device and a measuring device therefor.

[0002]

2. Description of the Related Art Considering the phenomenon of collision between objects, for example, when two objects collide, a large force interacts in a short time after the collision, and the momentum in the translational direction and the angular momentum are preserved. The state is completed. Among these, the angular momentum changes according to the moment of inertia of the collision object, and is greatly related to the motion after the collision.

[0003] In particular, it is known that the rotational motion is suppressed as the moment of inertia about the center of gravity axis of the collision object increases. This rotational movement is the same even for a collision object having an irregular shape having no axis of symmetry such as a golf club.When a club head collides with a golf ball during a shot, the effect of the shaft is extremely small and is ignored. Therefore, the moment of inertia about the center of gravity of the club head greatly affects the resilience of the golf ball.

That is, in a golf club, as shown in FIG. 8, a portion where a normal line extending from the center of gravity G toward the face F surface intersects the face F surface at a right angle (point P on the face F surface) is hit. If the collision position of the golf ball GB deviates from the maximum repulsion position P, the speed of the hit ball decreases or the launch direction changes in various ways. For example, if the collision position is above and below the face F surface, the magnitude of the back spin is affected, and if the collision position is right or left, the magnitude of the side spin is affected.

As described above, the moment of inertia of the club head GH about the center of gravity axis is deeply related to the performance of the golf club. The greater the moment of inertia, the more the degree of change in the orientation of the face F of the head GH at the time of a collision. As a result, the direction of launching the golf ball GB becomes better, and the sweet area becomes wider. Therefore, knowing the moment of inertia about the center of gravity axis is an important condition for manufacturing a golf club.

Next, the relationship between the moment of inertia about the center of gravity axis and the hit ball will be described in detail with reference to FIGS.

FIG. 8 is a plan view of a golf club head viewed from above, FIG. 9 is a side view of the club head viewed from the toe side, and FIG. 10 is a front view of the club head viewed from the face side.

[0008] Here, a description will be given of a popular wood club as a reference example. In this wood club, the face F side of the club head GH is formed substantially flat, the toe T side at the tip is curved, and a shaft is connected to the heel H side. The center of gravity G of this club head GH
Is regarded as substantially the center of the face F, but the moment of inertia about the center of gravity axis M passing through the center of gravity G can be grasped in two axial directions in the orthogonal coordinates.

That is, as described above, the center of gravity G is defined on the XY coordinates, where the X axis is the direction of the hitting ball of the golf ball GB, the Y axis is the horizontal direction of the face F surface, and the Z axis is the vertical direction of the club head GH. Can be regarded as the maximum repulsion position of the golf ball GB, and the moment of inertia is the inertia moment Iz about the center of gravity in the Z-axis direction. (In the direction of arrow YY in FIG. 8) and a moment of inertia Iy around the center of gravity in the Y-axis direction (in the direction of arrow ZZ in FIG. 9).

Of these, the moment of inertia Iz has a strong influence on the impact deviated from the maximum repulsion position P in the left-right direction as the Y-axis, and is related to the launch speed of the golf ball GB, the left-right launch angle, the side spin, and the like. ing. In addition, the moment of inertia Iy strongly affects the impact of displacement from the maximum repulsion position P in the vertical direction which is the Z axis, and is related not only to the launch speed of the golf ball GB, but also to the vertical launch angle, back spin, and the like. .

Therefore, accurately grasping the moment of inertia about the center of gravity of the club head GH greatly affects the performance of the golf club and is an indispensable condition for the design. It is desired to perform with accuracy.

Therefore, a measuring instrument 2 as shown in FIG. 19 is employed as a device for measuring the moment of inertia of an object having an irregular shape such as the club head GH. The measuring device 2 measures the vibration period of the rotary vibration shaft 8 by a torsional pendulum. A cylindrical portion 7 is vertically provided above the instrument body 6, and an operation portion 9 and a display portion 2 a are provided on the front surface. Is provided.

The cylindrical portion 7 has an opening 7a at an upper portion and an elongated hole 7b at a lower portion, and a rotatable vibration shaft 8 extending vertically is rotatably housed. The rotary vibration shaft 8 has a screw portion 8a formed at an upper end thereof. The screw portion 8a protrudes from the opening 7a of the upper part 7 of the cylinder to fix a calibration body (not shown) or a workpiece to be measured. Screw holes.

On the other hand, an elastic lever 8b extending in the horizontal direction is provided below the rotary vibration shaft 8, and the tip of the lever 8b projects outward from the long hole 7b of the upper part 7 of the cylinder. And perform the operation at the time of measurement. When the lever 8b is pulled away from the stopped state by being drawn to the right end side of the long hole 7b, it is repelled by elasticity and moves to the left end side of the long hole 7b, and is rotated with respect to the rotary vibration shaft 8 by a torsional pendulum. Vibration is given. The vibration period at this time is calculated by a measuring device (not shown), and data in units of seconds corresponding to the mass of the measured object is given to the control unit.

The control section starts or ends the measurement in response to a signal from an operation section 9 comprising an on / off switch, a setting switch, a reset switch, and the like, and displays a signal from a measuring instrument at the time of measurement. It is sent to the unit 2a side.
The display unit 2a digitally displays the measured value of the vibration period in seconds. When the vibration period is measured in this way, the moment of inertia is determined according to a predetermined calculation formula.

Next, a conventional measuring method using this measuring instrument will be described. 1. The position of the center of gravity of the club head GH is measured by static balance or the like, and the center of gravity G is determined. 2. Using the calibrator (the moment of inertia is I ₀ ), a calibration value C for calibrating the vibration period to the moment of inertia is determined by the following equation.

C = I ₀ / (Tc ² −T ₀ ² ) where, Tc: the vibration period of the torsional pendulum when the calibration body is set, T ₀ : the vibration period of the calibration body itself. The combined center of gravity axis M of the club head GH and the axis of the rotational oscillation axis 8, obtaining the oscillation period T _2, including fixtures of the club head GH. 4. Request oscillation period T ₁ of the only fastener. 5. The moment of inertia I around the center of gravity of the club head GH alone is determined by the following equation.

[0018] ^{_{I = C (T 2 2 -T}} 1 2)

In this way, the center of gravity M of the club head GH is aligned with the rotational vibration axis 8 of the torsion pendulum, and the vibration cycle around the center of gravity of the club head GH is measured, and the moment of inertia is known in advance. By converting with the calibration body,
The moment of inertia around the center of gravity axis is derived.

[0020]

However, in the case of the above-mentioned conventional measuring method and measuring apparatus, there is a limit to the measuring accuracy, so that the inertia around the center of gravity of the irregularly shaped collision object such as the club head GH is particularly large. There was a problem that it was difficult to accurately grasp the moment.

That is, in order to specify the position of the center of gravity of an irregularly shaped object that does not have a clear symmetrical glaze, measurement by static balance is generally performed by examining the center of gravity immediately below the rotating spindle that supports the object to be measured. Has been adopted. Despite high accuracy being required for specifying the center of gravity by this static balance, there is a certain limit in the measurement accuracy.

Further, it is not easy to make the center of gravity axis coincide with the rotational vibration axis for measuring the vibration period, which requires considerable skill and takes a long time.
As described above, the position of the center of gravity is measured first, and then the center of gravity must be aligned with the rotational vibration axis. This is a two-stage process, and the measurement operation is extremely complicated.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems, and a method and apparatus for measuring a moment of inertia capable of accurately measuring the moment of inertia around the center of gravity of an irregular-shaped object by a simple operation. The task is to provide

[0024]

In order to achieve the above object, a method of measuring the moment of inertia according to the present invention is directed to a method of measuring a center of gravity which is set at an arbitrary distance from a center of gravity passing through the center of gravity of an object having an irregular shape. The moment of inertia around each of the three axes parallel to is measured, and the coordinates of the movement of the center of gravity are calculated based on the coordinate values of the three axes based on the geometrical positional relationship between the three axes and the center of gravity axis represented by XY coordinates. The value is determined, and the center of gravity axis and the 3
The distance between each axis and the axis is calculated, and the distance between each axis, the moment of inertia around the three axes, and the mass of the object to be measured are substituted into the parallel axis theorem relating to the moment of inertia to be established for each of the three axes. A moment of inertia about the center of gravity axis of the object to be measured is derived from an equation of moment of inertia.

Further, the apparatus for measuring the moment of inertia according to the present invention is a measuring device for measuring the moment of inertia of a non-uniform object to be measured around a center of gravity axis by the rotational vibration of a rotary vibration shaft, and a holding device for holding the object to be measured. the ingredients movably supported on the axis of the rotary oscillation axis, wherein a measurement axis setting means for setting an arbitrary position parallel measuring axis to the central axis through the center of gravity of the object, the object to be measured Between the center of gravity axis passing through the center of gravity
Around each of three axes parallel to this center of gravity set at intervals
The moment of inertia of
Based on the geometrical positional relationship between the three axes and the center of gravity,
To obtain the coordinate value of the center of gravity axis,
The distance between each axis between the axis and the three axes is calculated, and the distance between each axis is calculated.
Separation, the moment of inertia about the three axes and the
Substituting mass into the parallel axis theorem for moment of inertia
From the equation of the moment of inertia established for each of the three axes,
It is characterized in that a moment of inertia about the center of gravity axis of the measured object is derived .

In the apparatus for measuring the moment of inertia around the center of gravity of the object to be measured, the holder is provided with a deviated plane parallel to the axial direction of the rotational vibration axis, and the deviated plane is provided on the flat surface of the holder.
It is preferable that an object to be measured that rotates along the axis is rotatably held.

In the apparatus for measuring moment of inertia about the center of gravity of the object to be measured, it is preferable that the distance between a plurality of measurement axes parallel to the center of gravity of the object to be measured is set in a range of several mm to several tens mm. It is.

Further, in a method of measuring a moment of inertia according to another embodiment of the present invention, a measurement axis is arbitrarily set on an object to be measured having an irregular shape, and this measurement axis is made to coincide with the rotational vibration axis of a rotational vibration measuring instrument. in the state, the inertia moment I ₀ measurement axis of the measured object measured by the rotational vibration of the rotational oscillation axis, said fulcrum provided on the base plate for placing the object to be measured X-Y
As a base point of coordinates, the first weighing device is arranged at a distance Lx in the X-axis direction from the fulcrum, and the inter-axis distance measurement is arranged at a distance Ly in the Y-axis direction, and the second weighing device is arranged. By means, the weight of the object to be measured is measured by aligning the measurement axis on the fulcrum while holding the base plate horizontally, the weight of the object to be measured m, the measurement value m1 of the first weighing device, the distance The distance lx from the measurement axis in the X-axis direction is calculated from a calculation formula that satisfies the equilibrium condition in Lx, and the weight m of the measured object, the measurement value m2 of the second weight measuring device, and the distance L
The distance ly from the measurement axis in the Y-axis direction is calculated from a calculation formula satisfying the equilibrium condition in y, and the distance lx and the distance l are calculated.
Substituting y into the three-square theorem as two sides sandwiching a right angle,
Calculating the center distance l between the center of gravity axis passing through the center of gravity of the measuring axis and the measurement object as the hypotenuse, the center distance l, the measurement axis of the moment of inertia I ₀ and the object to be measured of the object to be measured Substituting the weight m into the parallel axis theorem for the moment of inertia,
It is characterized in that a moment of inertia I around the center of gravity of the object to be measured is derived.

The method of measuring the moment of inertia is performed by measuring the weight of the object at three points by means of an inter-axis distance measuring means in which a third weight measuring device is arranged at the fulcrum position of the base plate. Based on m2, m3, the weight m of the measured object, the distance Lx, and the distance Ly, the distances lx and Y from the measurement axis in the X-axis direction are calculated by a calculation formula that satisfies the respective equilibrium conditions in the X-axis and Y-axis directions. The distances ly in the axial direction are respectively obtained, and the distances lx and ly are substituted into the three-square theorem as two sides sandwiching a right angle, and the distance between the measurement axis serving as the hypotenuse and the center of gravity passing through the center of gravity of the measured object is determined. calculating the center distance l, the distance between the axes l, the center of gravity axis by substituting the weight m of the measuring axis of the moment of inertia I ₀ and the object to be measured of the object to be measured parallel axis theorem about moment of inertia Deriving the moment of inertia I of This is suitable because it is not necessary to separately measure m.

Furthermore, the measuring method of moment of inertia according to another embodiment of the present application, by arbitrarily setting the measuring axis to be measured of irregular shape, the moment of inertia I ₀ measurement axis of the object to be measured Measure and align the measurement axis with the axis of a flexible shaft provided with a strain detector for detecting a bending moment, and in a state where the object to be measured is placed on the upper portion of the flexible shaft. Measure the bending moment of the shaft with a strain detector,
From the measured value M and the weight m of the measured object, the moment
Based on the equilibrium condition, calculates the center distance l between the center of gravity axis of the measuring shaft and the object to be measured, the center distance l, the moment of inertia of the weight m of the measuring axis of the moment of inertia I ₀ and the object to be measured By substituting into the parallel axis theorem with respect to the moment of inertia I about the center of gravity axis of the object to be measured.

Further, in the apparatus for measuring the moment of inertia according to another embodiment of the present invention, the rotational moment for measuring the moment of inertia about the center of gravity of the object of irregular shape held by the holding means by the rotational vibration of the rotational vibration axis. A support is provided on a vibration measuring instrument and a base plate on which the holding means is mounted.
-A first weighing device arranged at an arbitrary distance in the X-axis direction as a base point of the Y coordinate, a second weighing device arranged at an arbitrary distance in the Y-axis direction, and around the support portion. Ri Do and a center distance measuring means with the placed third gravimetric measuring instrument, the measurement value m obtained by measuring the weight of the object to be measured at three points
1, m2, m3, weight m of the measured object, distance Lx, distance L
y, the respective equilibrium conditions in the X-axis direction and the Y-axis direction are satisfied.
The distance l from the measurement axis in the X-axis direction is calculated by the following equation.
The distance ly in the x and Y axis directions is obtained, and the distance
Theorem of three squares with lx and distance ly as two sides sandwiching a right angle
And the weight of the measurement axis, which is the hypotenuse, and the object to be measured.
Calculate the distance l between the center of gravity and the axis passing through the center, and calculate the distance between the axes.
l, the moment of inertia I ₀ around the measurement axis and the weight of the DUT
Substituting the quantity m into the parallel axis theorem for the moment of inertia
To calculate the moment of inertia I of the object to be measured about the center of gravity axis.
It is characterized by putting out .

Further, a device for measuring the moment of inertia according to still another embodiment of the present invention comprises a rotational vibration measuring device for measuring an inertial moment of a non-uniform object to be measured around a center of gravity axis by rotational vibration of a rotational vibration shaft. A bending detector for detecting bending strain of the flexible shaft body, and bending the shaft body based on bending strain of the shaft body when the shaft body is erected vertically and an object to be measured is placed on an upper end thereof; consists of a bending strain measuring means for measuring a moment, the arbitrarily set the measuring axis to be measured, the moment of inertia I ₀ of the measurement axis is measured, the distortion detection to detect a bending moment to the measuring axis The bending moment of the shaft is measured with a strain detector while the object to be measured is placed on the upper part of the flexible shaft. wherein the measured value M and a weight m of the object to be measured, Mo Based on the balance condition of the
The distance l between the measurement axis and the center of gravity of the object to be measured is calculated, and the distance l between the axes and the moment of inertia I around the measurement axis are calculated.
_By substituting ₀ and the weight m of the measured object into the parallel axis theorem relating to the moment of inertia, a moment of inertia I about the center of gravity axis of the measured object is derived.

[0033]

According to the method of measuring the moment of inertia according to the above embodiment of the present invention, the mass of a known irregularly shaped object to be measured, the inertia moment of the object to be measured around three axes measured in advance, and XY By substituting the inter-axis distance of each axis with respect to the center of gravity axis of the measured object in coordinates into the parallel axis theorem regarding the moment of inertia, the moment of inertia around the center of gravity axis is derived from the equation of the moment of inertia established for each of the three axes. I do. In this way, the moment of inertia of an object having an irregular shape can be obtained by a single measurement operation and calculation.

Further, according to the apparatus for measuring the moment of inertia according to the above embodiment of the present invention, the holder is moved on the axis of the rotational vibration axis by the measuring axis setting means, and a plurality of parallel to the center of gravity axis of the object is measured. Set the measurement axis arbitrarily. Then, the moment of inertia around the axis of each measurement axis is measured by a measuring instrument, and a predetermined operation is performed from the measured value to determine the moment of inertia of the object to be measured having an irregular shape.

Furthermore, according to the measuring method of moment of inertia according to the another embodiment of the present application, first, measured using a rotational vibration meter the moment of inertia I ₀ around the measurement axis set in the measurement of the irregular shape . Next, the measurement axis of the measured object is made coincident with the fulcrum of the base plate, and the weight of the measured object is measured at a plurality of locations to obtain measured values m ₁ and m ₂ . Next, the first moment around the fulcrum where each equilibrium condition is satisfied is obtained based on the well-known distances Lx and Ly from the fulcrum to each weighing device, the weight m of the object to be measured, and the measured values m ₁ and m _2. The first moment about the fulcrum is obtained in the X-axis and Y-axis directions by the formulas. Further, the distances lx and ly from the measurement axis in the X-axis and Y-axis directions are substituted into the theorem of three squares, and the distance l between the measurement axis and the center of gravity passing through the center of gravity of the measured object is calculated. By substituting the inter-axis distance l, the moment of inertia I ₀ of the object to be measured about the measurement axis and the weight m of the object to be measured into the parallel axis theorem relating to the moment of inertia,
A moment of inertia I about the center of gravity of the object to be measured is derived. In this way, the moment of inertia of an object to be measured having an irregular shape can be obtained by a simple measuring technique and calculation.

Further, according to the method of measuring the moment of inertia according to the another embodiment of the present invention, the measurement axis is arbitrarily set on the object having an irregular shape, and the moment of inertia about the measurement axis of the object is measured. Measure I ₀ . Next, the measurement axis is aligned with the axis of a flexible shaft provided with a strain detector for detecting a bending moment, and the object to be measured is placed on the upper portion of the flexible shaft. Then, the bending moment of the shaft body is measured by the strain detector. Next, based on the measured value M and the weight m of the measured object, an inter-axis distance 1 between the measurement axis and the center of gravity of the measured object is calculated based on the cantilever balance theory.
Then, the distance l between the axes, the moment of inertia I ₀ of the DUT around the measurement axis and the weight m of the DUT are substituted into the parallel axis theorem relating to the moment of inertia, and the inertia of the DUT around the center of gravity axis is obtained. The moment I can be determined.

Further, according to the apparatus for measuring the moment of inertia according to the another embodiment of the present invention, the object to be measured having an irregular shape is held by the holding means, and the measuring axis is arbitrarily set. Is measured by a rotational vibration measuring instrument. Further, a holding means for holding the object to be measured is placed on a base plate of the inter-axis distance measuring means, and a first portion is provided with a supporting portion as a fulcrum.
And the second and third weighing devices keep the base plate horizontal or add a third weighing value instead of the supporting portion.
The weight of the object to be measured is measured by a weighing device with the base plate kept horizontal. Then, by substituting these measured values into a predetermined calculation formula and performing an operation, the moment of inertia of the measured object around the center of gravity axis can be obtained.

Further, according to the apparatus for measuring the moment of inertia according to the above-mentioned still another embodiment of the present invention, the moment of inertia of an object to be measured having an irregular shape is measured by a rotational vibration measuring instrument by the rotational vibration of a rotational vibration shaft. Next, the bending strain of the flexible shaft is detected by a strain detector. Next, the bending moment of the shaft is measured from the bending strain of the shaft when the shaft is placed upright and the object to be measured is mounted on the upper end by bending strain measuring means. Then, by substituting these measured values into a predetermined calculation formula and performing an operation, the moment of inertia of the measured object around the center of gravity axis can be obtained.

[0039]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Some embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a side view showing a moment of inertia measuring device used for carrying out a method of measuring a moment of inertia according to an embodiment of the present invention, and FIG. 2 is a front view of this measuring device.

The apparatus 1 for measuring the moment of inertia measures a club head of a golf club having an irregular shape, and a measuring axis setting tool 3 and a holding tool 4 are attached to a conventionally known measuring instrument 2 as shown in FIG. It is provided with.

The measuring instrument 2 includes a measurement setting tool 3
The connector 5 is provided as an accessory for holding the connector 5. The connector 5 is disc-shaped, that is on the back side and the protrusion 5a which is formed a screw hole is projected, so that screwing the protruding portion 5a to the screw portion 8a of the rotary oscillation axis 8 Has become.

As shown in FIGS. 3 and 4, the measuring axis setting tool 3 is composed of a substantially hexagonal mounting plate 11 and a triangular auxiliary plate 12, and is spaced apart so that the connector 5 can be inserted. And are integrated by three support members 13.

The mounting plate 11 is provided with a screw hole near one edge thereof, and a screw body 14 having a thumb screw 14b is inserted into the screw hole. The auxiliary plate 12 has three round holes a, b, and c having a diameter larger than the diameter of the screw portion 8a of the rotary vibration shaft 8. In addition, these round holes a,
b and c are moving positions when selectively setting a measurement axis parallel to the center of gravity axis of the measured object.

The holder 4 is formed by connecting a flat vertical plate 16 to a rectangular sliding plate 15 in a direction perpendicular to the rectangular slide plate 15 so that an object to be measured is held on one side surface 16a of the vertical plate 16. Has become. The sliding plate 15 is formed with a long hole 15a extending in the longitudinal direction, and the vertical plate 16 is marked with a mark S for aligning the approximate center of the object to be measured with the center of one side surface of the vertical plate 16. (Fig. 2).

The holding member 4 inserts the screw body 14 from the screw hole side of the mounting plate 11 toward the elongated hole 15a of the sliding plate 15, and screws the thumb screw 14b into the screw portion 14a of the screw body 14. By being inserted, it is slidably mounted on the mounting plate 11 of the measuring axis setting tool 3.

In this way, when the measuring axis setting tool 3 with the holding tool 4 integrated is attached to the upper end of the rotary vibration shaft 8 via the connector 5, the moment of inertia around the center of gravity of the object to be measured is properly measured. can do.

However, it should be possible to measure with high accuracy without theoretically aligning the center of gravity M of the object to be measured, which is unknown in theory, with the axis of the rotary vibration axis 8 in theory.
If they are extremely separated from each other, the rotational vibration shaft 8 is eccentric and an error occurs in the measured value. Therefore, in this example, in order to achieve high measurement accuracy, the axis between the circular holes a, b, and c is particularly used. The distance is set in the range of 10 mm to 50 mm.

The mounting plate 11 is formed in a hexagonal shape in order to prevent a decrease in the measurement accuracy due to the eccentricity of the shaft. Of the measurement accuracy may be prevented.

When measuring the moment of inertia of the club head GH, first, the projecting portion of the connector 5 is inserted into one of the round holes a, b, and c provided in the auxiliary plate 12 of the measuring axis setting tool 3. 5a, and the screw portion 8 of the rotary vibration shaft 8
The support plate 11 is supported by being screwed into a so that the mounting plate 11 is perpendicular to the axial direction of the rotary vibration shaft 8.

Next, the face side of the club head GH is held in contact with the vertical plate 16 of the holder 4. As the holding method, the club head GH may be bonded with a double-sided tape, or may be held by suction using a vacuum device or the like.
The center of the club head GH is made to coincide with the mark S described in. Thus, the center of gravity M substantially coincides with the axis J of the rotational vibration shaft 8 shown in FIG.
The side and the heel H side are kept substantially horizontal while being separated from the mounting plate 11.

Next, the operation unit 9 and the lever 8 of the measuring instrument 2
b, and the three round holes a, b, and c are sequentially moved by the attachment / detachment work of the connector 5 so that the first through third measurement axes A, parallel to the center of gravity axis M of the club head GH.
The moments of inertia around the axes B and C are measured.

Since the coordinate values (unit: mm) of the measurement axes A, B, and C in the XY coordinates are arbitrarily set in advance as shown in FIG. 5, for example, the first axis A (1 .05,
1.70), second axis B (1.98, 0.0), third axis C
(0.0, 0.0). FIG. 5 shows the geometric relationship between the rotational vibration axis 8 and the center of gravity axis M. From this, the distances r ₁ , r ₂ , r ₃ between the axes in the XY coordinates are shown.
You can know.

When the vibration period around each axis is measured as described above, the moment of inertia is obtained according to the following equation. This formula is calculated by the mass m (g) of the club head GH,
The measured value of the moment of inertia (gcm ² ) and each measurement axis A,
By substituting the inter-axis distance r (cm) in the XY coordinates of B and C into the parallel axis theorem (Steiner's theorem) regarding the moment of inertia, the moment of inertia around the center of gravity axis is calculated from the equations established for each of the three axes. It is to be calculated.

Here, the coordinates (x ₁ ,
y ₁ ), the coordinates (x ₂ , 0) of the second measurement axis B, the coordinates (0, 0) of the third measurement axis C, and the moments of inertia I ₁ , I around the axes of the measurement axes A, B, C. ₂ , I ₃ and the mass (m) of the measured object are known quantities, and the coordinates (x ₀ , y ₀ ) of the centroid axis M and the moment of inertia I around the centroid axis, which are unknown quantities, are derived from these values. . First, from the geometric relationship between the center of gravity axis M and the three axes A, B, and C,

X₀ ²+ Y₀ ²= R₃ ² ... (1) (x₀-X₂)²+ Y₀ ²= R₂ ² ... (2) (x₁-X₀)²+ (Y₁-Y₀)²= R₁ ² ... (3) Expression (1) is replaced by y₀Is transformed.y ₀ ² = R ₃ ² -X ₀ ² (4) The equation (4) is substituted into (2). -2x₂x₀+ X₂ ²+
r₃ ²-R₂ ²= 0, the coordinates (x₀,
y₀) Are represented as follows. x₀= X₂/ 2 + (r₃ ²-R₂ ²) / (2x₂) ・ ・ ・ (5)Here, the definition of the center of gravity of the moment of inertia and the parallel axis between each axis
From the theory (Steiner's theorem) I₁= I + mr₁ ² ... (6) I₂= I + mr₂ ² ... (6) 'I₃= I + mr₃ ² .. (6) ″ Expressions (6) ′ and (6) ″ are transformed to r₂And r₃Relate to
In the formula, r₂ ²= I₂/ M-I / m (7) r₃ ²= I₃/ M−I / m (8) By substituting equations (7) and (8) into equation (5), x₀= X₂/ 2 + (I₃-I₂) / (2x₂m) (9) Further, when Expressions (7) and (8) are substituted into Expression (5) ′,Next, the coordinates (x₁, Y₁) And the second measuring axis
B coordinates (x₂, 0)₁Is the equation (3)
(X₁-X₀)²+ (Y₁-Y₀)²= R₁ ²As table
Substituting this into equation (6) gives:₁= I + m (x₁-X₀)²+ M (y₁-Y₀)²  = I + m (x₁-X₀)²+ My₁ ²  -2my₁y₀+ My₀ ² ... (11) y in equation (10)₀Into this equation (11),₁= I + m (x₁-X₀)²+ My₁ ²  Transforming this equation,-Mx₀ ²+ I₃-I₁｝ / (2my₁This equation is squared on both sides and rearranged for I.

[0056]

As a result, a moment of inertia I around the center of gravity axis can be obtained. In the golf club, a portion where the normal extending from the center of gravity M toward the face F surface intersects the face F surface at a right angle (FIG. 8 and FIG. Point P on face F of No. 9
) Can be grasped as the maximum rebound position of the hit ball.

Thus, the club head GH with excellent performance
Can be designed and provided. That is, a golf club having a large moment of inertia, a small degree of change in the direction of the face F of the head GH at the time of collision with the golf ball GB, an improved direction of launching the golf ball GB, and a wide sweet area is designed and provided. can do.

FIG. 6 is a front view of a holder showing another embodiment of the moment of inertia measuring device. This moment of inertia measuring apparatus rotatably holds the face F side of the club head GH on the vertical plate 16 of the holder 4 according to the above embodiment, and is otherwise the same as the above embodiment.

The holder 4 has a flat support plate 17 smaller than the vertical plate 16, and holds the club head GH on one side surface of the support plate 17 by bonding or suction. On the other side of the support plate 17, a threaded body 18 having a threaded portion 18a at its tip protrudes.

When the screw body 18 is inserted into a screw insertion hole formed in the center of the vertical plate 16, a screw portion 18a projects from the vertical plate 16, and the wing nut 18 is inserted into the screw portion 18a.
b into the support plate 1 with respect to the vertical plate 16.
7 can be rotatably held in a state of being arranged in parallel.

The holder 4 is rotated by 360 degrees as indicated by the imaginary line while holding the club head GH on the support plate 17, so that a plurality of rotation axes having an angle difference of 30 degrees are formed. Once set, the moment of inertia can be measured as described above.

As a result, as shown in FIG. 7, when the measured values at every 30 degrees are superimposed on the face F of the club head GH to obtain a characteristic diagram, the moment of inertia with the center on the face F as a base axis is obtained. You can know.

In this characteristic diagram, a plurality of points E indicate measured values of the moment of inertia. By connecting these points E with a curve K, the distribution of the moment of inertia can be grasped . When the points L1 and L2, which are the outermost peripheral portions of the characteristic curve K, are connected by a straight line, the principal axis of inertia L can be known, and
The principal axis of inertia L is understood to have an inclination of 5.2 degrees against the center line l extending in the longitudinal direction of the club head GH through the center of the face F.

The characteristic curve K and the main inertia axis L are as follows:
Together with the maximum repulsion position P, this becomes important basic data for designing the club head GH.

FIG. 11 is a side view showing an apparatus for measuring the moment of inertia used for implementing the method for measuring the moment of inertia according to another embodiment of the present invention, and FIG. 12 is a plan view of this measuring apparatus.

The measuring apparatus 100 of the moment of inertia is also
The club head GH of a golf club having an indefinite shape is measured, and a conventionally known rotational vibration measuring device 2 (FIG. 19)
) And an inter-axis distance measuring device 110. The rotational vibration measuring device 2 is provided with a measuring axis setting tool 103 and a holder 104, and the inter-axis distance measuring instrument 110 has a base plate 111, a measuring tool 112, Is provided.

As shown in FIGS. 11 and 12, the measuring axis setting tool 103 comprises a substantially hexagonal mounting plate 103a and a rectangular auxiliary plate 103b. It is integrated by the book support member 103c. The mounting plate 103a has a substantially hexagonal shape in order to prevent a decrease in measurement accuracy due to eccentricity of the shaft. However, the mounting plate 103a is not limited to such a polygonal shape but may be formed in a circular shape.
It is also possible to prevent the measurement accuracy from being lowered due to the shaft deviation.

The auxiliary plate 103b has an insertion hole 103d formed substantially at the center thereof, through which a support shaft 114 of a measuring tool 112 described later can be inserted without a protrusion of the connector being loose. The connector is an accessory for holding the measuring axis setting tool 103 on the rotating vibration shaft 8 of the rotating vibration measuring instrument 2, and although not shown, is formed on a protruding portion thereof. Screw hole 8a of rotary vibration shaft 8
And screwed into it.

The holding tool 104 is provided with a short horizontal plate 10.
A flat vertical plate 104b is continuously provided in the direction perpendicular to the vertical plate 4a, and an object to be measured is held in close contact with one side surface 104c of the vertical plate 104b. This vertical plate 10
4B, a mark S is written (not shown) so that the approximate center of the measured object coincides with the center of the one side surface 104c.

The holder 104 is provided with the mounting plate 103a described above.
And fixed by the fixing member 104d. The fixing member 104d is a square member, and has a holder 1 on one side.
04, and the lower portion of the rotary vibration measuring instrument 2
After the positioning is adjusted so that the axis of the object coincides with the approximate center of the object to be measured, it is bonded to the upper surface of the mounting plate 103a.

When the measurement axis setting tool 103 integrated with the holder 104 is attached to the upper end of the rotary vibration shaft 8 by a connector, the measurement axis of the club head GH, which is the object to be measured, is set. The moment of inertia about the measurement axis can be measured by the rotational vibration measuring device 2.

The inter-axis distance measuring device 110 is mounted on the instrument body 1.
15, load cells 121 to 123 are provided.
1. It is configured to include a measurement tool 112. The instrument body 115 has a measurement hole 116 having a circular opening 116a on the upper surface 115a, an operation unit 117 and a display unit 118 arranged on the 115b, and a control unit built in the body. ing.

The operation unit 117 includes an on / off switch 11
7a, changeover switch 117b, reset button 117c
And a zero adjustment button 117d, etc., each of which is connected to the control unit. ON / OFF switch 117a
Sends a measurement start signal or an end signal to the control unit. The changeover switch 117b is connected to the first through third switches .
The load cells 121 to 123 are selectively switched, and a load measurement signal from each measuring device is transmitted to the control unit.

The reset button 117c is connected to the display unit 118
Outputs a signal that clears the measurement value displayed in and enters the measurement start state. Further, the zero adjustment button 117d sends a command signal for setting the numerical display on the display unit 118 to zero in a state where the object to be measured is not placed at the start of the measurement. 117e, 1
17f is a display lamp for displaying the operation state.

The display section 118 displays the measured value of the load. The display unit 118 receives the signal from the control unit and digitally displays the current value.

The control section controls the operation of the entire distance measuring device 110. The control section starts or ends the measurement based on an operation signal from the operation section. At the time of the measurement, a reset button 117c and a zero adjustment button 117d are used. The display of the display unit 118 is changed in accordance with the signal of (1). Further, in response to signals from the load cells 121 to 123 selected by the changeover switch 117b, control is performed to display the current value on the display unit 118.

The base plate 111 is, as shown in FIG.
The measurement axis setting tool 103 is formed in a substantially triangular shape.
The object to be measured is measured in a state where is placed. That is, the base plate 111 has the shaft hole 111a serving as a support portion formed in the right-angled corner. This shaft hole 111a is
When a measuring tool 112 having a support shaft 114 described later is inserted, it becomes one fulcrum for supporting the base plate 111, and XY coordinates are set on the base plate 111 based on this fulcrum (see FIG. 14). ).

The measuring tool 112 serves as an auxiliary tool for weight measurement together with the base plate 111, and has a structure in which a support shaft 114 is detachably attached to a base 113 as shown in FIG. The pedestal 113 has a disk shape, and has a concave portion 113a at the center of the upper surface.
The lower end 114a of the fourth member 4 is fitted.

The support shaft 114 is fitted into the opening 116a so that the upper surface of the pedestal 113 and the upper surface 115a of the instrument body 115 are flush with each other.
When the measurement axis setting tool 103 is attached via the
Is the length of the upper end 114b of the support shaft 114 reaches the lower surface. Thus, a small interval SG is provided between the third load cell 123 and the upper end 114b as a fulcrum, and a two-point measurement method using only the two load cells 121 and 122 becomes possible.

First to third load cells 121 to 123
The upper part of the instrument body 1 so that the load can be evenly received.
15 is provided so as to protrude from the upper surface 115a. As shown in FIG. 12 and FIG. 14, when the XY coordinates are set on the base plate 111, the load cells 121 to 123 are separated from each other by a distance of Lx in the X-axis direction.
1 and the second load cell 122 is arranged at a distance of Ly in the Y-axis direction.

Further, the third load cell 123 has a through hole 123a formed in the center thereof. The through hole 123a is aligned with the shaft hole 111a of the base plate 111, and is arranged above the measuring tool 103. The insertion makes the operation of the third load cell 123 impossible. In addition, by removing the support shaft 114 from the pedestal 113 and applying a load to the third load cell 123, three points of weight can be measured. The first to third load cells 121
To 123 are connected to the control unit via lead wires, so that the loads applied to the load cells 121 to 123 are converted into electric signals and sent to the control unit.

Next, a method of measuring the moment of inertia by this measuring device will be described. Incidentally, for the measurement is the mass of the club head GH in advance measured, as a rotational oscillation period T ₁ of the measurement axis setting device 103 has already been measured.

First, an inertia moment I ₀ about the measurement axis of the club head GH is measured by a rotational vibration measuring device. Here, when the connector is inserted into the screw portion of the rotary vibration shaft 8 and the auxiliary plate 103b is fixed, the measurement axis setting tool 103 is mounted on the rotary vibration measuring device 2. With this, the club head GH
From the measurement axes it is set, measured by a predetermined operation of the oscillation period T ₂ of the club head GH comprising measuring axis setting tool 103.

When the vibration period T ₂ of the club head GH is obtained, the moment of inertia I around the measurement axis of the club head GH is determined from the previously measured vibration period T _{1 of} only the measurement axis setting tool 103 and the known calibration value C. _{0 is obtained} by the following equation. ^{_{I 0 = C (T 2 2}} -T 1 2)

Next, the mass of the club head GH is measured by the two-point measuring method (the load cells 121, 1
22 to determine the center-to-axis distance, and then perform a predetermined calculation to derive the moment of inertia I about the center of gravity of the club head GH.

In this two-point measuring method, the measuring axis setting tool 103 is removed from the rotational vibration measuring instrument 2 and attached to the inter-axis distance measuring instrument 110. Here, the instrument body 115
The auxiliary plate 10 is attached to the support shaft 114a projecting from the upper surface 115a of the
3b, the measuring axis setting tool 103 is placed on the base plate 111. Then, the upper end 114b of the support shaft 114a serves as a fulcrum, and the measurement axis setting tool 103 is horizontally held on the first and second load cells 121 and 122 via the base plate 111.

As a result, the first and second load cells 12
Since 1,122 receives the load, one of the measured values is displayed on the display unit 118. Since the measured value is the weight including the base plate 111 and the measurement axis setting tool 103, the display is set to 0 by operating the zero adjustment button 117d.

Next, the club head GH having a mass m is mounted on the vertical plate 116 of the holder 104. Then, since the load of the club head GH is applied to the first and second load cells 121 and 122, the measured value of the club head GH is changed to the first value.
It is displayed on the display window 118a. At this time, when the changeover switch 117b is operated, the current values of the first load cell 121 and the second load cell 122 are sequentially displayed.

Subsequently, the distance l between the center of gravity axis J of the club head GH and the measurement axis is calculated based on the known data including the measured load. Here, the weight of the club head GH is m,
The distance from the fulcrum to the first load cell 121 is Lx, the distance from the fulcrum to the second load cell 122 is Ly,
When the weight measurement value of the first load cell is m ₁ and the weight measurement value of the second load cell is m ₂ , a calculation formula that satisfies the equilibrium conditions in the X-axis direction and the Y-axis direction with the measurement axis as a fulcrum, ie, a fulcrum The unknown distances lx and ly in FIG. 14 can be calculated by the equation for calculating the first moment around.

Now, the first moment about the fulcrum in the X-axis direction is Lx · m ₁ = lx · m, and the first moment about the fulcrum in the Y-axis direction is Ly · m ₂ = ly.
M, the distance lx = m ₁ / m · Lx, the distance ly
= M ₂ / m · Ly. Then, by substituting the distance lx and the distance ly into a three-square theorem having two sides sandwiching a right angle, the distance between the measurement axis, which is the hypotenuse, and the center of gravity axis J passing through the center of gravity of the club head GH is obtained. The distance l between the axes can be obtained by the following equation.

[0092]

Next, the center distance l is obtained, from the moment of inertia I ₀ measurement axis of the club head GH, calculates a central axis J moment of inertia around I. That is, I
₀ is the moment of inertia about the measurement axis of the club head GH, not the moment of inertia about the center of gravity axis J. Therefore, the moment of inertia I about the center of gravity axis J is derived based on the parallel axis theorem (Steiner's theorem). is there.

Here, the moment of inertia in the parallel axis theorem is I ₀ = I + ml ² , where I ₀ is the moment of inertia around the measurement axis, m is the weight of the club head GH, and l is the distance between the axes. , The moment of inertia I around the center of gravity axis J can be obtained by the following equation.

I = I ₀ -ml ²

Next, a method of measuring the moment of inertia according to another embodiment of the present invention will be described. The basic principle of this measuring method is the same as that of the above-described two-point measuring method.
As shown in FIG. 15, a three-point measurement method in which a load is applied to the third load cell 223 and measurement is performed by removing the support shaft 114 from the shaft 13.

Here, the measured weight of the third load cell 223 is m ₁ , the measured weight of the first load cell 221 is m ₂ ,
When the weight measurement value of the second load cell 222 is _{m 3,}
The moment of inertia I around the center of gravity of the club head GH can be calculated according to the known data used in the two-point measurement method.

That is, since the measured value of the weight of the club head GH is m = m ₁ + m ₂ + m ₃ , one point around the fulcrum that satisfies the equilibrium conditions in the X-axis direction and the Y-axis direction with the center of the third load cell 223 as the fulcrum. By formulating an equation for calculating the next moment, the unknown distances lx and ly shown in FIG. 16 can be calculated.

Distance lx on the X-axis side = m ₁ / (m ₁ + m ₂ +
m ₃ ) · Lx , and the distance ly on the Y-axis side ly = m ₂ / (m ₁
+ M ₂ + m ₃ ) · Ly , the distances lx and ly
By substituting into the theorem of three squares, the center distance l between the club head GH and the center of gravity axis J passing through the center of gravity can be obtained by the following equation.

[0100]

When the distance 1 is obtained in this manner, the club head GH is calculated according to the same calculation procedure as the two-point measuring method.
Can be derived from the moment of inertia I ₀ around the measurement axis on the basis of the parallel axis theorem.

Next, still another embodiment of the present invention will be described with reference to FIGS. The apparatus for measuring the moment of inertia according to this embodiment includes a bending strain detector 319 in the inter-axis measuring device 110 of the above embodiment, and a tool main body 315.
And a load measuring device 324 built therein.

The load measuring device 324 is arranged on the bottom side of the measuring hole 316 of the instrument main body 315, and measures the weight of the object placed on the bending strain detector 319. The output of the load measuring device 324 is given to the control unit, and the measured value is displayed on the display unit 318.

The bending strain detector 319 is connected to the shaft 32.
0 is provided with a strain sensor 320, and the bending moment is measured from the bending strain of the shaft body 320. The shaft body 320 has flexibility, but has an outer diameter that does not contact the opening 316a of the measurement hole 316 or the inner wall even if the shaft body 320 is flexed and deformed. The shaft 320 has a lower end 320a mounted on the load measuring device 324 and an upper end 320b.
A mounting table 320c is integrally attached to the, and the measurement axis setting tool 303 is mounted on the mounting table 320c. 320d is an auxiliary plate 303b of the measurement axis setting tool 303.
Is a support shaft inserted through.

As a strain sensor (not shown), a conventionally known strain gauge, transducer, or the like is used, which is mounted on the peripheral surface of the shaft 320. The output of the strain sensor is also provided to the control unit, and the measured value is displayed on the display unit 318.
Is displayed.

Next, a method of measuring the moment of inertia by this measuring device will be described. However, at the time of the measurement, the rotational vibration period T ₁ of the measurement axis setting tool 303 is already measured and the moment of inertia I ₀ measurement axis of the club head GH also to already calculated.

First, the bending strain detector 319 is set on the load measuring device 324, and the measuring axis setting tool 303 is mounted thereon so that the measuring axis of the club head GH coincides with the axis of the shaft body 320. Let it. Further, zero display is performed on the display unit 318 in the same manner as in the two-point and three-point measurement methods.

Next, the club head GH is mounted on the mounting table 320c.
Is placed, the weight is measured by the load measuring device 324, and the bending moment associated with the bending strain of the shaft body 320 is measured by the strain sensor. Then, based on the measured value and the weight m of the club head GH, the center distance l between the measurement axis and the center of gravity axis J of the club head GH is calculated based on the cantilever suspension theory.

Here, since it is known that the bending moment M = m · l, the center distance l = M / m. When the distance l between the axes is obtained, similarly to the above embodiment, the moment of inertia I around the measurement axis of the club head GH is obtained.
By substituting ₀ and weight m into the parallel axis theorem, the moment of inertia I can be derived very easily.

As described above, according to each of the above-described embodiments, the moment of inertia I of the club head GH about the center of gravity axis J can be easily known, and the golf club has a strong effect on off-center shot performance. The moment of inertia I can be grasped.

Thus, the golf club head GH having excellent performance can be designed and provided. That is, it is possible to design and provide a golf club having a large moment of inertia, a good launching direction of the golf ball GB, and a wide sweet area.

In each of the above embodiments, the case of measuring the moment of inertia of the club head GH of the iron club has been described. However, the measurement of a wood club, a putter, and the like is also performed by the above measuring method using the above measuring apparatus. Of course, it can be easily performed.

[0113]

As described above, according to the method of measuring the moment of inertia of the above-described configuration according to the present invention, the moment of inertia of an object having an indefinite shape can be obtained by a single measurement operation and calculation. The work of accurately measuring the center of gravity of an indefinite-shaped object and the work of matching the axis passing through the center of gravity with the rotational vibration axis that measures the vibration cycle are not required as in the past. It's easy. In addition, since there is almost no error in measuring the position of the center of gravity and the error occurring when the axes are aligned, there is an effect that the moment of inertia can be measured with high accuracy. Further, according to the moment of inertia measuring device having the above-described configuration according to the present invention, the weight of the object to be measured is measured at a plurality of locations, and the moment of inertia around each of the plurality of measurement axes is obtained. Since an unknown moment of inertia around the center of gravity axis can be obtained, there is an effect that the moment of inertia around the center of gravity of an irregular shape can be easily measured.

[Brief description of the drawings]

FIG. 1 is a side view showing an apparatus for measuring a moment of inertia according to an embodiment of the present invention.

FIG. 2 is a front view showing a state where an object to be measured is held in the measuring apparatus for moment of inertia.

FIG. 3 is a plan view of a measurement axis setting unit included in the moment of inertia measurement device.

FIG. 4 is a bottom view of a measurement axis setting unit included in the moment of inertia measurement device.

FIG. 5 is an explanatory diagram showing a geometric arrangement of a center of gravity axis and a measurement axis of an object to be measured by XY coordinates.

FIG. 6 is a front view showing a measurement axis setting unit according to another embodiment of the present invention.

FIG. 7 is an explanatory diagram of a distribution and characteristics of a moment of inertia of an object to be measured.

FIG. 8 is a plan view of the golf club for describing a phenomenon of collision of the golf club.

FIG. 9 is a side view of the toe side of the golf club.

FIG. 10 is a front view of the face side of the golf club.

FIG. 11 is a side view showing an apparatus for measuring a moment of inertia according to another embodiment of the present invention.

FIG. 12 is a plan view showing a state where an object to be measured is held in the moment of inertia measuring device according to the embodiment.

FIG. 13 is a layout view of a base plate and a weight measuring device which constitute the moment of inertia measuring device according to the embodiment.

FIG. 14 is an explanatory diagram showing the geometric arrangement of the center of gravity axis and the measurement axis of the object to be measured by XY coordinates.

FIG. 15 is a layout view of a base plate and a weight measuring device which constitute a moment of inertia measuring device according to still another embodiment of the present invention.

FIG. 16 is an explanatory diagram illustrating the geometric arrangement of the center of gravity axis and the measurement axis of the object to be measured according to the same example in XY coordinates.

FIG. 17 is a side view showing an apparatus for measuring a moment of inertia according to still another embodiment of the present invention.

FIG. 18 is a plan view showing a state where an object to be measured is held in the moment of inertia measuring device according to the embodiment.

FIG. 19 is a perspective view showing a rotational vibration measuring device of a moment of inertia.

FIG. In another embodiment of the present invention, the moment of inertia
It is a partial enlarged sectional view of FIG. 11 which is a side view showing a measuring device.
is there.

[Explanation of symbols]

2
Rotational vibration meter 3,103
Measurement axis setting means 4, 104, 304
Holder 8
Rotational vibration axis 10,110
Interaxial distance measuring means 11, 111, 211
Base plate 121,122,123,221,222,223
Weight measuring device 319
Strain detector

──────────────────────────────────────────────────続 き Continued on the front page (58) Fields surveyed (Int. Cl. ⁷ , DB name) G01M 1/00-1/12 A63B 53/00

Claims (9)

(57) [Claims] 1. An object having an indeterminate shape, which is set at an arbitrary distance from a center of gravity passing through the center of gravity of an object to be measured and is parallel to the center of gravity.
A moment of inertia around each axis is measured, and a coordinate value of the center of gravity axis is obtained based on a coordinate value of the three axes based on a geometrical positional relationship between the three axes represented by XY coordinates and the center of gravity axis. Calculate the distance between each axis of the center of gravity axis and the three axes, and substitute the distance between each axis, the moment of inertia around the three axes, and the mass of the DUT into the parallel axis theorem relating to the moment of inertia. A method of measuring the moment of inertia, which derives the moment of inertia about the center of gravity axis of the object to be measured from the equation of the moment of inertia established for each of the three axes. 2. A measuring instrument for measuring the moment of inertia of an object to be measured having an irregular shape around a center of gravity axis by a rotational vibration of a rotational vibration axis, and a holder for holding the object to be measured on an axis of the rotational vibration axis. Movably supported, comprising a measurement axis setting means for setting a measurement axis parallel to a center of gravity axis passing through the center of gravity of the object to be measured at an arbitrary position, from a center of gravity axis passing through the center of gravity of the object to be measured.
Three axes parallel to this center of gravity axis set at arbitrary intervals
The moment of inertia around each axis is measured and expressed in XY coordinates.
From the geometrical positional relationship between the three axes and the center of gravity
While obtaining the coordinate value of the center of gravity axis based on the standard value,
The distance between each axis of the center of gravity axis and the three axes is calculated.
The distance between axes, the moment of inertia around the three axes, and the measured
Replace the mass of the constant with the parallel axis theorem for the moment of inertia.
Equation of moment of inertia for each of the three axes
Derive the moment of inertia about the center of gravity axis of the DUT from
For measuring the moment of inertia about the center of gravity of the object to be measured . 3. The holder has a depressed plane parallel to the axial direction of the rotary vibration axis, and the flat surface of the holder is provided on the deflected side.
3. An apparatus for measuring a moment of inertia according to claim 2, wherein the object to be measured rotating along the axis is rotatably held. 4. The apparatus for measuring moment of inertia according to claim 2, wherein the distance between the axes of a plurality of measurement axes parallel to the center of gravity axis of the object to be measured is set in a range from several mm to several tens mm. 5. A measurement axis is set arbitrarily on an object to be measured having an indefinite shape, and the measurement axis is set by the rotational vibration of the rotational vibration axis in a state where the measurement axis coincides with the rotational vibration axis of the rotational vibration measuring instrument. A first inertial moment I ₀ is measured, and a fulcrum provided on the base plate on which the object to be measured is placed is set as a base point of XY coordinates, and a distance Lx is placed in the X-axis direction from the fulcrum to perform the first weight measurement. A distance measuring means in which a second weight measuring device is disposed at a distance Ly in the Y-axis direction while the measuring device is disposed, the measuring axis is aligned with the fulcrum while holding the base plate horizontally, and The weight of the measured object is measured, and the distance lx from the measurement axis in the X-axis direction is calculated from a calculation formula that satisfies the equilibrium condition for the weight m of the measured object, the measured value m1 of the first weighing device, and the distance Lx. And the weight m of the object to be measured and measurement by the second weighing device m2, a distance ly from the measurement axis in the Y-axis direction is calculated from a calculation formula that satisfies the equilibrium condition for the distance Ly, and the distance lx and the distance ly are substituted into the three-square theorem as two sides sandwiching a right angle. Te to calculate the center distance l between the center of gravity axis passing through the center of gravity of the measuring axis and the measurement object as the hypotenuse, the weight m of the center distance l, the measurement axis of the moment of inertia I ₀ and the object to be measured A method of measuring the moment of inertia, which derives the moment of inertia I about the center of gravity of the measured object by substituting into the theorem of the parallel axis regarding the moment of inertia. 6. A measurement value m1, m2, m3 obtained by measuring the weight of an object to be measured at three points by an inter-axis distance measuring means having a third weight measuring device arranged at a fulcrum position of a base plate. Based on the weight m of the object, the distance Lx, and the distance Ly, the X-axis direction and Y
The distance lx from the measurement axis in the X-axis direction and the distance ly in the Y-axis direction are respectively obtained from the calculation formulas satisfying the respective equilibrium conditions in the axial direction, and the distances lx and ly are defined as three sides of a right angle. Substituting into the theorem, calculates the distance l between the measurement axis serving as the hypotenuse and the center of gravity axis passing through the center of gravity of the measured object,
Substituting the inter-axis distance l, the moment of inertia around the measurement axis I _0, and the weight m of the device under test into the parallel axis theorem relating to the moment of inertia, derives the moment of inertia I around the center of gravity of the device under test. 5. The method for measuring the moment of inertia according to 5. 7. arbitrarily set the measuring axis to be measured of irregular shape, the moment of inertia I ₀ of the measurement axis is measured, provided the distortion detector for detecting a bending moment to the measuring axis variable The bending moment of the shaft is measured by a strain detector in a state where the object to be measured is placed on the upper part of the flexible shaft by aligning the axis of the flexible shaft with the measured value M. From the weight m of the measured object, the distance l between the measurement axis and the center of gravity axis of the measured object based on the moment balance condition l
The distance l between the axes, the moment of inertia I ₀ around the measurement axis and the weight m of the object to be measured are substituted into the parallel axis theorem relating to the moment of inertia, and the moment of inertia I around the center of gravity of the object to be measured is calculated. Is a method of measuring the moment of inertia. 8. A rotary vibration measuring instrument for measuring the moment of inertia of the irregular-shaped object to be measured held by the holding means around the center of gravity axis by rotational vibration of a rotary vibration axis, and a base plate on which the holding means is mounted. A first weight measuring device disposed at an arbitrary distance in the X-axis direction with the support portion as a base point of the XY coordinates, and a second weight measuring device disposed at an arbitrary distance in the Y-axis direction; A weight measuring device and an inter-axis distance measuring means provided with a third weight measuring device disposed around the supporting portion.
In addition, the measured values m1,
m2, m3, weight m of the measured object, distance Lx, distance Ly
Satisfies each equilibrium condition in X-axis direction and Y-axis direction
From the calculation formula, the distance lx from the measurement axis in the X-axis direction and
And the distance ly in the Y-axis direction are obtained, and the distance lx is obtained.
And the distance ly as two sides sandwiching a right angle,
And the center of gravity of the measuring axis and the object to be measured
The distance l between the center of gravity and the passing center axis is calculated.
Moment of inertia I ₀ around the measurement axis and weight m of the measured object
Into the parallel axis theorem for the moment of inertia,
Deriving the moment of inertia I about the center of gravity of the measured object
A device for measuring the moment of inertia of the measured object around the center of gravity . 9. A rotational vibration measuring device for measuring the moment of inertia of the object to be measured having an irregular shape around the center of gravity axis by rotational vibration of a rotational vibration shaft, and a distortion detector for detecting bending distortion of a flexible shaft body. Comprises bending strain measuring means for measuring the bending moment of the shaft body from the bending strain of the shaft body when the workpiece is placed on the upper end with the shaft body standing upright,
Wherein by arbitrarily setting the measuring axis in the object to be measured, the moment of inertia I ₀ of the measurement axis is measured, the axis of the measuring shaft and bending flexibility shaft body provided with a distortion detector for detecting a moment And the bending moment of the shaft is measured by a strain detector while the object to be measured is placed on the upper part of the flexible shaft, and the measured value M and the weight m of the object to be measured are measured. From the above, the inter-axis distance l between the measurement axis and the center of gravity of the object to be measured is calculated on the basis of the moment balance condition , and this inter-axis distance l, the moment of inertia around the measurement axis I ₀ and the object to be measured are calculated. The inertia moment I about the center of gravity axis of the object to be measured is derived by substituting the weight m of the object into the parallel axis theorem relating to the moment of inertia.