Method and apparatus for measuring dynamic imbalance of sphere

A sphere is supported in a floating condition by a pneumatic bearing so as to be rotated by compressed air sprayed from a nozzle. The sphere has a single point magnetized on its surface, and is placed on its rotating axis. If the sphere has a dynamic imbalance, the single point is subjected to pressesion around its inertia axis, the locus and displacement velocity of which are measured by the Hall elements arranged in an arc line around the pneumatic bearing, thereby obtaining the dynamic imbalance of the share.

FIELD OF THE INVENTION 
This invention relates to a measurement method and measurement device for 
measuring the dynamic imbalance of a sphere, and can be used, for example, 
in measuring the dynamic imbalance of spheres manufactured from magnetic 
material such as balls in a ball bearing. 
DESCRIPTION OF THE RELATED ART 
In order to be able to use a ball bearing for supporting a spindle that 
rotates at high speed so that there is no uneven wear on the balls, 
spheres whose dynamic imbalance is small must be used for the bearing 
balls. Of course, it is best if it does not exist at all. Moreover, in 
order to manufacture this kind of ball bearing, the dynamic imbalance of 
the spheres, such as bearing balls, must be measured, so that only the 
spheres with small dynamic imbalance are produced. 
A measurement device for measuring the dynamic imbalance of spheres that 
are used for this kind of purpose has been previously disclosed in 
Japanese Patent First Publication KOKAI S62-297740. FIG. 4 shows an 
example of this formerly known device for measuring the dynamic imbalance 
of spheres. This measurement device comprises a pneumatic bearing 3. The 
top portion of this pneumatic bearing 3 is open and its surface 1 has a 
spherical concave shape, and the inner surface of this spherical, concave 
surface 1 supports a sphere 2 so that it is capable of rotating freely. 
Moreover, at the top of this pneumatic bearing 3 there is a nozzle 4 which 
is capable of freely spraying compressed air. When performing measurement, 
compressed air is sprayed from this nozzle 4 onto the sphere 2 supported 
by the pneumatic bearing 3 so that it rotates. Furthermore, magnetic 
pick-up coils 5a, 5b and 5c are located so that if a straight line is to 
project from them, respectively, they would all cross orthogonally at the 
center of the aforementioned sphere 2 (located on the x, y, and z axes), 
and the detectors of these magnetic pick-up coils 5a, 5b and 5c are 
located near the outer surface of the sphere 2. 
When measuring the dynamic imbalance of the aforementioned sphere 2, a 
magnetic spot is attached to the sphere 2 before placing it into the 
aforementioned spherical, concave surface 1. Then compressed air is 
supplied from a air-supply conduit 6, so that the sphere 2 floats and it 
is sprayed with compressed air from the aforementioned nozzle 4. As a 
result, the sphere 2 rotates around a specified axis of rotation, and if 
there is any dynamic imbalance of the sphere 2, then precession occurs in 
this sphere 2. The locus and displacement velocity of this precession is 
detected by the change in density of magnetic flux using the 
aforementioned pick-up coils 5a, 5b and 5c. If the locus and displacement 
velocity of the precession is found from the measured values of the 
magnetic pick-up coils 5a, 5b and 5c, it is then possible to find the 
amount of dynamic imbalance .DELTA.I, that is, difference in moment of 
inertia of the sphere 2, from equation (1) below. 
EQU .DELTA.I=.OMEGA..multidot.(I/.omega.).multidot.cos .beta. (1) 
In equation (1) above, .omega. is the angular velocity of gyration of the 
axis of rotation at a certain instant, and found from the measured values 
of the magnetic pick-up coils 5a, 5b and 5c. Also, I is the moment of 
inertia of the sphere 2, and found from actually measuring the sphere 2, 
specifically its mass and diameter. Moreover, .omega. is the angular 
velocity of the sphere 2, and found from the measured values of the 
magnetic pick-up coils 5a, 5b and 5c. Furthermore, .beta. is the angle 
between the principal axis of inertia and the axis of rotation, and found 
from the measured values of the magnetic pick-up coils 5a, 5b, and 5c. 
In the former device for measuring the dynamic imbalance of a sphere 
constructed as described above, there are the following problems (1) and 
(2). 
(1) To detect the precession using the three magnetic pick-up coils 5a, 5b 
and 5c, it is necessary to distribute a magnetic flux all the way around 
the surface of the sphere 2, however in the method of using a magnetic 
spot it is difficult to evenly distribute the magnetic flux around the 
entire sphere 2. Therefore, it is easy for errors to occur when measuring 
the density of the magnetic flux, and it is easy for errors to occur in 
the measurement results of the dynamic imbalance that are based on the 
results of the measurement of the density of the magnetic flux. 
(2) When measuring the precession from the change in density of the 
magnetic flux, it is very difficult to precisely measure minute changes in 
density of the magnetic flux using the three magnetic pick-up coils, so 
that the measurement precision is poor. 
SUMMARY OF THE INVENTION 
An object of this invention is to provide a method of measurement and the 
device for measuring dynamic imbalance which solves the aforementioned 
problems (1) and (2). 
Another object of this invention is to provide a method of measuring 
dynamic imbalance of a sphere made of magnetic material wherein a first 
point on the sphere is magnetized, the sphere is freely rotatably 
supported, the sphere is rotated with the point placed on the axis of 
rotation causing precession due to the dynamic imbalance of the sphere, 
the locus and displacement velocity of the point due to the precession are 
measured, and the dynamic imbalance of the sphere is calculated based on 
the measurement results. 
Now, if a second point is magnetized at the opposite pole of the sphere 
from the first point so that the angle between the second point and the 
first point is not 180 degrees, it is also possible to calculate the 
rotational velocity of the sphere by observing the displacement of this 
second point. 
Moreover, another feature of the invention is to provide a method of 
measuring dynamic imbalance of a sphere made of non-magnetic material, 
wherein a magnetic material such as magnetic paint, magnetic spot, 
magnetic foil, magnetic film are attached at one point or several 
locations for magnetization on the surface of the sphere, the sphere is 
freely rotatably supported, the sphere is rotated with the point placed on 
the axis of rotation causing precession due to the dynamic imbalance of 
the sphere, the locus and displacement velocity of the point due to 
precession are measured, and the dynamic imbalance of the sphere is 
calculated based on the measurement results. 
Furthermore, another object of the present invention is to provide a 
measurement device for measuring the dynamic imbalance of a sphere made of 
magnetic material comprising a pneumatic bearing where the upper portion 
is open and has a spherical concave surface in which the sphere having a 
magnetized point on its surface can be supported so that it rotates 
freely, several magnetic detector elements that are located in an arc 
shape around the upper open portion of the pneumatic bearing, a nozzle 
that sprays pressurized air on a portion of the sphere supported in the 
pneumatic bearing, so that the sphere rotates, and an electrical circuit 
for obtaining the measurement values necessary for calculating the dynamic 
imbalance of the sphere based on the output signals of the several 
magnetic detector elements. 
Another object of the present invention is to provide a retaining ring 
which is attached to the upper edge around the upper open portion of a 
pneumatic bearing, where the upper portion is open and has a spherical 
concave surface in which a sphere having a magnetized point on its surface 
can be supported so that it rotates freely, such that magnetic detector 
elements comprising Hall elements are arranged in a semi-arc line at equal 
intervals around the inner peripheral surface of the retaining ring, and 
that a nozzle faces to the sphere above the Hall element at the 
circumferentially central position and sprays pressurized air on a portion 
of the sphere supported in the pneumatic bearing.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIGS. 1 thru 3 show an embodiment of the measurement device for measuring 
the dynamic imbalance of a sphere of this invention. There is a seat 
member 8 that is fastened to the top surface of a base 7 so as to mount a 
pneumatic bearing 11 therein. 
A cylindrical case 9 with a bottom is fastened to the top surface of the 
seat member 8. The pneumatic bearing 11 is constructed from this case 9 
and a porous material 10 that is fitted on the inside of the case 9. 
An upwardly open spherical, concave surface 12 is formed on the top surface 
of this porous material 10. The inner radius of this spherical, concave 
surface 12 is a little larger than the outer radius of the sphere 2 that 
is to be measured. 
Also, an air-supply hole 14 is formed on the bottom plate 13 of the case 9 
and the inside of the seat member 8, and the upstream end of the conduit 
for this air-supply hole 14 is connected to an air supply device 15 such 
as a compressor. Compressed air is fed to the inside of the case 9 from 
this air supply device 15 through the air-supply hole 14, and blown out 
from the inner surface of the spherical, concave surface 12 causing the 
sphere 2 to float so that it rotates freely. Thus, the sphere 2 is 
supported. 
There is a circular retaining ring 16 on the top surface of the case 9 that 
makes up this kind of pneumatic bearing. Also, disposed around half of the 
inner peripheral surface of this retaining ring 16 are the Hall elements 
17, 17a and 17b that are used as the magnetic detector elements. In the 
embodiment shown in the figure, the nineteen Hall elements 17, 17a and 17b 
are arranged at equal intervals to be separated by center angle pitch of 
10 degrees, forming a semi-circular arc line. The maximum inscribing 
circle of these Hall elements 17, 17a and 17b arranged in this kind of 
semi-circular arc has a diameter a little larger than the outside diameter 
of the sphere 2. Accordingly, these Hall elements 17, 17a and 17b are 
faced to the outer surface of the sphere 2 through a very small gap, 
respectively. 
Moreover, the detection signals from these Hall elements 17, 17a and 17b 
are input to a voltmeter 19 and adding circuit 20 through separate lines 
18. The total value from this adding circuit 20 is displayed on the 
display 21. The voltmeter 19 and adding circuit 20 make up the electrical 
circuit used for obtaining the measured values that are necessary for 
calculating the dynamic imbalance of the sphere 2 based on the output 
signals from the Hall elements 17, 17a, and 17b. 
Furthermore, in a part of the retaining ring 16, there is a nozzle 22 (FIG. 
2) that is located above the Hall element 17a at their circumferentially 
central position, and used for blowing compressed air. The opening of this 
nozzle 22 is faced toward the top of the sphere 2. There is a valve 24 
located along the air-supply pipe 23 that supplies compressed air to the 
nozzle 22, and by opening this valve 24, compressed air is blown onto the 
top of the sphere 2 from the nozzle 22. By blowing compressed air onto the 
sphere 2 that is supported in the spherical, concave surface 12 of this 
pneumatic bearing 11, the sphere 2 starts to rotate so that its axis of 
rotation is parallel to the line .alpha. that connects the pair of Hall 
elements 17b and 17b located on both ends in the circumferential direction 
of the multiple Hall elements 17, 17a, and 17b. 
To measure the dynamic imbalance of the sphere 2 made of magnetic material 
using the measurement device constructed as described above, a first point 
25 is magnetized on the surface of the sphere 2 (for example at the North 
pole). The size of this magnetized point should be as small as possible so 
long as it is able to maintain adequate magnetic strength. Also, a second 
point 26 that is separate from this first point 25 is magnetized on the 
opposite pole from the first point 25 (for example the South pole) so that 
the angle between the second point 26 and the first point 25 (the angle of 
the straight lines connecting both points through the center of the sphere 
2) is not 180 degrees. 
The bottom half of the sphere 2 is placed into the spherical, concave 
surface 12 so that the first point 25 is located on the axis of rotation. 
Compressed air is fed to the case 9 through the air-supply hole 14, so 
that the sphere 2 floats. In this state, the valve 24 is opened, so that 
the compressed air is blown from the nozzle 22, and the sphere 2 begins to 
rotate. 
If the sphere 2 has absolutely no dynamic imbalance, then the sphere 2 will 
just rotate around the axis of rotation and there will be no other motion. 
However on the other hand, if the sphere 2 does have some dynamic 
imbalance, precession will occur with respect to the extent of dynamic 
imbalance. Specifically, the axis of rotation caused by the compressed air 
blown from the nozzle 22 does not move, however precession of the sphere 2 
does occur. As a result of this precession, the point 25 moves away from 
the axis of rotation, and turns around the principal axis of inertia to 
return again to the axis of rotation. 
The locus and displacement velocity of the point 25 that is based on this 
kind of precession can be found from the change in the output signal from 
the Hall elements 17, 17a and 17b. In other words, when the point 25 turns 
around the principal axis of inertia, the point 25 moves away from the 
Hall element 17b on the end in the circumferential direction and 
approaches one of the other Hall elements 17. The locus can then be found 
from which of the Hall elements 17 the point 25 came close to, and the 
displacement velocity can be found from the time that it takes to go from 
the closest Hall element 17 to the next closest Hall element 17 due to the 
precession. That is, it is possible to find the time difference between 
one Hall element and a different Hall element to which the point 25 comes 
closest. 
If the locus and the displacement velocity are found in this way, by using 
the device described above, the amount of dynamic imbalance, .DELTA.I, of 
the sphere 2 can be found from equation (1) below. 
EQU .DELTA.I=.OMEGA..multidot.(I/.omega.).multidot.cos .beta. (1) 
In equation (1), .omega. is the angular velocity of gyration of the axis of 
rotation and can be found from the time it takes for the point 25 to go 
from the closest Hall element to the next closest Hall element as 
mentioned above. Also, the moment of inertia, I, of the sphere 2 can be 
found from actual measurement values of the mass and radius of the sphere 
2. Moreover, .OMEGA. is the angular velocity of the sphere 2 around the 
axis of rotation and can be detected from the output signals from the Hall 
elements generated by the rotation of the point 25. 
However, if the point 25 is facing the Hall element 17b on the end in the 
circumferential direction, in other words if the point 25 is located on 
the axis of rotation, the output signals from the Hall elements generated 
by the rotation of the sphere 2 will not be a pulse wave, and the angular 
velocity, .omega., cannot be found by just observing the output signals 
from the Hall elements generated by the first point 25. Therefore it can 
be found from the pulse-wave output signals from the Hall elements 17, 17a 
that are generated by the passing of the second point 26. Furthermore the 
angle, .beta., between the principal axis of inertia and the axis of 
rotation can be found from the locus which is based on the measurement 
values obtained from the Hall elements 17, 17a. 
By making the angle between the first point 25 and the second point 26 
something other than 180 degrees, if it is impossible to measure the 
precession when the first point 25 is lined up with the principal axis of 
inertia, the second point 26 can be used to measure the precession, and 
the angular velocity, .omega., can be found from the first point 25. 
If an extremely light magnetic coating or magnetic spot of known mass is 
attached at one point or several locations to the surface of a sphere made 
of non-magnetic material and then magnetized, and if the sphere is rotated 
so that the magnetized points are located at the axis of rotation, it is 
possible to calculate the imbalance that occurs due to attaching this 
magnetic coating or magnetic spots, from the attached mass and the angle 
.beta. between the principal axis of inertia and the axis of rotation, and 
from this it is possible to accurately find the amount of imbalance of the 
sphere itself. 
In the embodiment shown in the figure, the nineteen Hall elements 17, 17a 
and 17b are arranged at equal intervals so that the center angle pitch is 
10 degrees, however if the number of the Hall elements is increased, it is 
possible to improve the accuracy of detection. 
Moreover, even with the nineteen Hall elements, if the sensitivity of all 
of the Hall elements 17, 17a and 17b is the same, it is possible to 
improve the accuracy of detection by comparing the strength of the 
detection signals of adjacent Hall elements 17, 17a and 17b when the point 
25 passes between the adjacent Hall elements 17, 17a, and 17b, and thereby 
determining the position of the point 25. 
In either case, with the method of measurement and the measurement device 
for measuring the dynamic imbalance of a sphere of this invention, when 
the sphere 2 made of magnetic material is magnetized itself, there is no 
change in the dynamic imbalance of the sphere 2 due to being magnetized. 
Moreover, the locus and displacement velocity of the precession of the 
sphere 2 are obtained by observing the single point 25 which is 
magnetized, so that the measuring steps are precisely carried out without 
being affected by the distribution of the magnetic flux density. In other 
words, the locus and displacement velocity of the precession are obtained 
by observing the passing of the magnetized point or single point 25, so 
that the precision in detecting is improved when compared to the method of 
measuring the continuously changing magnetic flux density. 
In the method of measurement and measurement device of this invention for 
measuring the dynamic imbalance of a sphere constructed as described 
above, the locus and displacement velocity of the precession of the sphere 
is found by observing the point that is magnetized on the surface of the 
sphere without being affected by the distribution of the magnetic flux 
density, thus the imbalance can be performed accurately. In other words, 
the locus and displacement velocity of the precession is found by 
observing the travel of the magnetized point, and this improves accuracy 
of detection when compared with the method of measuring the continuously 
changing density of the magnetic flux. 
Accordingly the measurement method and measurement device for measuring the 
dynamic imbalance of a sphere of this invention makes it possible to 
accurately measure the dynamic imbalance of a sphere. As a result, this 
invention can make a contribution to the development of high-performance, 
high-speed rotating devices, where for example, ball bearings that 
normally rotate even at high speeds are realized.