U.S. patent application number 10/425885 was filed with the patent office on 2003-10-23 for rolling bearing.
This patent application is currently assigned to NSK Ltd.. Invention is credited to Miyagawa, Takayuki, Momono, Tatsunobu, Muto, Yasushi, Noda, Banda.
Application Number | 20030198415 10/425885 |
Document ID | / |
Family ID | 26509582 |
Filed Date | 2003-10-23 |
United States Patent
Application |
20030198415 |
Kind Code |
A1 |
Miyagawa, Takayuki ; et
al. |
October 23, 2003 |
Rolling bearing
Abstract
The frequencies generated based on the undulations existing on
the inner and outer ring raceways 8, 10 and on the rolling surface
of the balls 11, 11 are out of coincidence with the rotational
frequency itself of the rotation member supported by the rolling
bearing, and with a frequency component which is a multiple of the
rotational frequency, or kinds of frequencies generated due to the
undulations are out of coincidence with each other in the natural
frequency domain of a rotation system which is a rotation
supporting portion having the rolling bearing incorporated therein,
whereby without using a special grease, the self-excited frequency
of the rolling bodies hardly grows to abnormal vibration, and a
rolling bearing having sufficient durability and causing no
abnormal vibration and noise even if used at low temperature is
realized.
Inventors: |
Miyagawa, Takayuki;
(Fujisawa-shi, JP) ; Noda, Banda; (Fujisawa-shi,
JP) ; Muto, Yasushi; (Fujisawa-shi, JP) ;
Momono, Tatsunobu; (Fujisawa-shi, JP) |
Correspondence
Address: |
CROWELL & MORING LLP
INTELLECTUAL PROPERTY GROUP
P.O. BOX 14300
WASHINGTON
DC
20044-4300
US
|
Assignee: |
NSK Ltd.
Shinagawa-ku
JP
|
Family ID: |
26509582 |
Appl. No.: |
10/425885 |
Filed: |
April 30, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
10425885 |
Apr 30, 2003 |
|
|
|
09674850 |
Feb 22, 2001 |
|
|
|
Current U.S.
Class: |
384/450 |
Current CPC
Class: |
F16C 27/066 20130101;
F16C 19/06 20130101; F16C 19/527 20130101; F16C 2326/06
20130101 |
Class at
Publication: |
384/450 |
International
Class: |
F16C 019/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 9, 1999 |
JP |
H11-196169 |
Jul 4, 2000 |
JP |
2000-201821 |
Claims
What is claimed is:
1. A rolling bearing comprising a first race having a first
raceway, a second race having a second raceway, and Z rolling
bodies having a rolling surface and rollably disposed between the
first raceway and the second raceway, wherein, when assumed that n
is a positive integer, and that vibration is generated at
frequencies due to the circumferential undulations of (nZ) waves
and (nZ+1) waves existing on the surface of the first and second
raceways, and the undulation of (2n) waves existing on the rolling
surface of the respective rolling bodies, the frequencies are out
of coincidence with the rotational frequency itself of the rotation
member supported by the rolling bearing, and with a frequency
component which is a multiple of the rotational frequency.
2. A rolling bearing comprising a first race having a first
raceway, a second race having a second raceway, and Z rolling
bodies having a rolling surface and rollably disposed between the
first raceway and the second raceway, wherein, when assumed that n
is a positive integer, and that vibration is generated at kinds of
frequencies due to the circumferential undulations of (nZ) waves
and (nZ.+-.1) waves existing on the surface of the first and second
raceways, and the undulation of (2n) waves existing on the rolling
surface of the respective rolling bodies, the kinds of frequencies
are out of coincidence with each other in the natural frequency
domain of a rotation system which is a rotation supporting portion
having the rolling bearing incorporated therein.
3. A rolling bearing comprising a first race having a first
raceway, a second race having a second raceway, and Z rolling
bodies having a rolling surface and rollably disposed between the
first raceway and the second raceway, wherein, when assumed that n
is a positive integer, and that vibration is generated at
frequencies due to the circumferential undulations of (nZ) waves
and (nZ+1) waves existing on the surface of the first and second
raceways, and the undulation of (2n) waves existing on the rolling
surface of the respective rolling bodies, the frequencies are out
of coincidence with the rotational frequency itself of the rotation
member supported by the rolling bearing, and with a frequency
component which is a multiple of the rotational frequency, and
kinds of frequencies generated due to the undulations are out of
coincidence with each other in the natural frequency domain of a
rotation system which is a rotation supporting portion having the
rolling bearing incorporated therein.
4. The rolling bearing of one of claims 1 to 3, wherein the
frequencies or frequency components to be compared with each other
have differences at least 1% of the frequencies or frequency
components.
Description
TECHNICAL FIELD
[0001] A rolling bearing according to this invention is
incorporated into a rotation supporting section which is installed
outdoors and may be driven at low temperatures, such as for
example, a propeller shaft of a vehicle, or a rotation shaft of an
electric motor, to thereby prevent the occurrence of harmful
vibration or noise even at low temperatures.
BACKGROUND ART
[0002] In order to dampingly support for example, a middle portion
of a propeller shaft of a vehicle under a floor of the vehicle, a
rotation supporting unit 1 as shown in FIG. 1 is used. This
rotation supporting unit 1 supports a rolling bearing 3 via a
buffer material 4 and a housing 5, on the inner diameter side of a
support bracket 2. Of these, the buffer material 4 is formed from a
material having a large internal loss, such as rubber, so as to be
freely displaceable in the radial direction (vertical direction in
FIG. 1) and in the axial direction (lateral direction in FIG. 1).
The housing 5 is formed by fitting and combining elements 6a, 6b
respectively formed in a cylindrical shape, for fittingly
supporting an outer ring 7 of the rolling bearing 3 on the
inside.
[0003] The rolling bearing 3, being a deep groove ball bearing,
comprises an inner ring 9 having an inner ring raceway 8 on an
outer peripheral surface thereof, an outer ring 7 having an outer
ring raceway 10 on an inner peripheral surface thereof, and a
plurality of rolling bodies (balls) 11, 11 arranged rollably
between the inner ring raceway 8 and the outer ring raceway 10. The
rolling bodies 11, 11 are rollably held by a retainer (not shown),
respectively. Also, grease is filled into a space 12 existing
between the outer peripheral surface of the inner ring 9 and the
inner peripheral surface of the outer ring 7, in which the rolling
bodies 11, 11 are arranged, and openings on the opposite ends of
this space 12 are respectively sealed by ring-shaped seal rings 13,
13. Such a rolling bearing 3 constitutes the rotation supporting
unit 1 described above, in such a manner that the outer ring 7 is
supported under the floor of the vehicle via the housing 5 and the
buffer material 4, and the inner ring 9 on the outside is fittingly
secured to the middle portion of the propeller shaft 14.
[0004] The rotation supporting unit 1 for a propeller shaft
described above, or a rotation supporting apparatus incorporated in
an electric motor installed outside, is used in a low temperature
environment in the winter season. In the case of the rotation
supporting unit 1 used under such a low temperature environment and
lubricated by grease, when the temperature in the portion of the
rolling bearing 3 is still low just after startup, abnormal
vibration often occurs, and it is known that when the vibration is
conspicuous, offensive noise to the ear occurs due to this abnormal
vibration. In particular, it is known that under an environment of
-10.degree. C. or less, the offensive noise occurs
conspicuously.
[0005] The mechanism in which such a noise occurs was elucidated in
a paper "Research Regarding Abnormal Vibration of Ball Bearings"
described in Nihon Machinery Society Paper, Vol. 63, No. 616
(Chapter C), pp 250.about.256, issued in December 1997. According
to this paper, the above described mechanism is such that
self-excited vibration of the rolling body becomes a cause of the
above described abnormal vibration.
[0006] For example, if a rotation supporting unit 1 for supporting
the middle portion of a propeller shaft 14 as shown in FIG. 1 is
considered, when an axial force is applied to the rolling bearing 3
due for example to a change in the operating conditions, external
disturbances, or friction in a joint portion disposed at the end of
the propeller shaft, axial slippage occurs in each abutting portion
between the rolling surface of the respective rolling bodies 11, 11
and the inner ring race 8 and the outer ring race 10. This
generates a shear rate in the oil film of the grease intervening in
each abutting portion. When this shear rate exceeds a certain
value, the shear stress decreases, and the grease acts as a
negative resistance. That is to say, there is a relationship
expressed by an equation of equilibrium in the lubricant film:
dp/dx=d.tau./dy, between the pressure p of the oil film in the
grease and the shear stress .tau. of the oil film. As is obvious
from this relation, as the shear stress .tau. of the oil film
decreases, the pressure p of the oil film also decreases, to
generate the self-excited vibration of the respective rolling
bodies 11, 11 whose rolling surface abuts against the oil film. It
is made clear in the paper "Simulation Regarding Nonlinear
Vibration of Ball Bearings" described in Nihon Machinery Society
Lecture Paper, No. 985-2, pp 269, issued in October 1998, that the
frequency of such self-excited vibration becomes a multiple of the
rotational frequency.
[0007] When the self-excited vibration occurs in the respective
rolling bodies 11, 11 with the above described mechanism, the film
thickness of the grease existing in the inner ring raceway 8, the
outer ring raceway 10 and the rolling surface portion of the
respective rolling bodies 11, 11 becomes uneven over the
circumference, depending on the traveling tracks based on the
rotation movement and revolution movement of the respective rolling
bodies 11, 11. In other words, an undulation (bank of grease) is
formed by the grease on the surface portion of the inner ring
raceway 8 and the outer ring raceway 10 and on the rolling surface
portion of the respective rolling bodies 11, 11, respectively. The
banks of grease formed in this manner cause radial and axial
vibrations, in the same manner as undulations originally existing
on the inner ring raceway 8, the outer ring raceway 10 or the
rolling surface of the respective rolling bodies 11, 11.
[0008] If the frequency of the self-excited vibration of the
rolling bodies coincides with the vibration frequency resulting
from the banks of grease, vibration is promoted . Moreover, if the
frequency of the self-excited vibration of the rolling bodies and
the vibration frequency resulting from the banks coincide with the
vibration frequency resulting from undulations originally existing
(not the banks of grease, but originally existing) on the inner
ring raceway 8, the outer ring raceway 10 or the rolling surface of
the respective rolling bodies 11, 11, vibration is further promoted
to become large. Vibration which has grown in such a manner
resonates with a member circumjacent to the rolling bearing 3,
thereby resulting in offensive noise to the ear.
[0009] Abnormal vibration and noise described above occurs in the
first place, based on the self-excited vibration of the rolling
bodies and this self-excited vibration grows due to the banks of
grease. Accordingly, in order to eliminate the above described
banks of grease or to reduce the strength thereof so that the
self-excited vibration does not grow to an abnormal vibration,
grease having a low viscosity may be used. However, even with such
a measure, it is difficult to obtain a sufficient effect at
extremely low temperatures, as low as -10.degree. C. Moreover, if
grease having such a low viscosity that abnormal vibration does not
occur even at such an extremely low temperature is used, the grease
tends to leak through the above described respective seal rings 13,
13. Furthermore, grease having a low viscosity has a weak oil film
holding power at the rolling contact portion, and in many cases, it
is not always satisfactory from the standpoint of lubricating
ability. As a result, when grease having a low viscosity is used,
it becomes difficult to favorably maintain the lubricating
condition of the rolling bearing 3 for a long period of time.
[0010] The present invention addresses the above situation, and
realizes a rolling bearing which hinders growth of the self-excited
vibration of the rolling bodies to an abnormal vibration, without
using a special grease, and which has sufficient durability, and
which does not generate abnormal vibration or noise, even if it is
used at low temperatures.
DISCLOSURE OF THE INVENTION
[0011] All the rolling bearings of the present invention comprise a
first race having a first raceway, a second race having a second
raceway, and Z rolling bodies rollably disposed between the first
raceway and the second raceway, as with the aforesaid conventional
rolling bearing.
[0012] In particular, in the rolling bearing of the present
invention, when assumed that n is a positive integer, the
frequencies of the vibration generated due to the circumferential
undulations of (nZ) waves and (nZ.+-.1) waves existing on the
surface of the first and second raceways, and the undulation of
(2n) waves existing on the rolling surface of the respective
rolling bodies, are controlled by the relation with the frequencies
in other parts.
[0013] At first, in the case of the rolling bearing according to
claim 1, the frequencies of the vibration generated due to the
above described undulations does not coincide with either the
rotational frequency itself of the rotation member supported by the
rolling bearing, or a frequency component which is a multiple of
the rotational frequency.
[0014] Also, in the case of the rolling bearing according to claim
2, a plurality of kinds of vibration frequencies generated due to
the above described undulations do not coincide with each other, in
the natural frequency domain of a rotation system which is a
rotation supporting portion constituted by incorporating the
rolling bearing.
[0015] In the case of the rolling bearing of the present invention
constructed as described above, banks of grease are formed due to
the self-excited vibration of the rolling bodies, but this
vibration is not susceptible to growth even if vibration occurs due
to the banks of grease. As a result, harmful abnormal vibration and
offensive noise to the ear are unlikely to occur. The reason for
this will be described below.
[0016] At first, a description is given of the reason why the
vibration frequencies controlled by the relation with the
frequencies in other parts, are limited to one due to the
undulations of (nZ) waves and (nZ.+-.1) waves existing on the
raceway surface, and the undulation of (2n) waves existing on the
rolling surface of the respective rolling bodies. Here, it is well
known, as described for example in Japanese Unexamined Patent
Publication No. Toku Kai Hei 8-247153 or the like, that the
undulations existing on the raceway surface and the rolling surface
exist in a plurality of kinds in number, even when seen on the same
surface.
[0017] It is also well known, as described in Japanese Unexamined
Patent Publication No. Toku Kai Hei 8-247153, that if it is assumed
that the number of the rolling bodies is Z, and n is a positive
integer, then with regard to the undulations existing on the
surface of the first and second raceways, the circumferential
undulations of (nZ) waves and (nZ.+-.1) waves cause larger
vibration compared to the undulations of other numbers of waves.
Moreover, with regard to undulations existing on the rolling
surface of the respective rolling bodies, the undulation of the
(2n) waves cause large vibration. This is because since the
undulation of the (2n) waves is formed such that peaks and valleys
in the undulation exist in the diametrically opposite positions of
the rolling surface, variations in the diameter of the rolling
surface due to the rotation of the rolling bodies, in other words,
variations in the gap between the first and second raceways
described above, which put the rolling surface therebetween,
increase. Therefore, the undulations regarding the controlled
vibration frequency are respectively limited to the (nZ) waves and
the (nZ .+-.1) waves with regard to the raceway surface and the
(2n) waves with regard to the rolling surface.
[0018] On the assumption described above, the reason why with the
rolling bearing of the present invention, harmful abnormal
vibration or offensive noise to the ear is unlikely to occur will
be described. At first, in the case of the invention according to
claim 1, the vibration frequencies due to the undulations of the
number of waves which tend to result in large vibration as
described above, do not coincide with either the rotational
frequency itself of the rotation member supported by the rolling
bearing, or the frequency components which are a multiple of the
rotational frequency, including a case of substantially coinciding
therewith (to the extent of resonating, for example approaching
within an error of 1 to 2%). As a result, even if banks of grease
are formed due to the self-excited vibration of the rolling body,
and vibration occurs due to the banks, the vibration due to the
banks is not promoted by vibration due to the undulations existing
on the surface of the first and second raceways and on the rolling
surface, and hence the vibration does not grow.
[0019] That is to say, when the rolling bearing is used in a state
that, for example, the inner ring, being the first race, rotates at
fr (Hz), self-excited vibration occurs in the rolling bodies at a
frequency of f.omega.=n.multidot.f.sub.r, and based on this
self-excited vibration, banks of grease having a shape
corresponding to the frequency of f.omega.=n.multidot.fr are formed
on the inner ring raceway, being the first raceway, and the outer
ring raceway, being the second raceway, and the rolling surface
portion of the respective rolling bodies. On the contrary, if the
vibration frequencies due to undulations existing on the surfaces
of the first and second raceways and undulations existing on the
rolling surface, shown in Table 1, deviate from the above described
frequency, f.omega.=n.multidot.f.sub.r (for example, by 1 to 2% or
more, as described above), the undulations and the shape of the
banks do not coincide with each other, thereby enabling prevention
of growth of vibration due to the banks. Here, the degree of
deviation in the frequencies so as not to cause resonance of the
two vibrations more or less differs depending on various conditions
such as the bearing size, but deviation of at least 1% is
necessary. Moreover, if the deviation in the frequencies increases
to 2% or more, resonance will not occur in almost all cases.
1 TABLE 1 Radial Vibration Axial Vibration No. of Vibration No. of
Vibration waves in frequency waves in frequency undulation
generated undulation generated Inner ring nZ .+-. 1 nZf.sub.i .+-.
f nZ nZf.sub.i Outer ring nZ .+-. 1 nZf.sub.c nZ nZf.sub.c Rolling
2n 2nf.sub.b .+-. f.sub.c 2n 2nf.sub.b body
[0020] Wherein n: positive integer, Z: number of rolling bodies,
f.sub.r: rotational speed of the inner ring (Hz), f.sub.c:
rotational speed of a retainer {=revolving speed of the rolling
bodies (Hz)}, f.sub.i=f.sub.r-f.sub.c (Hz), f.sub.b: rotating
frequency of the rolling bodies (Hz).
[0021] If the frequencies of the vibration due to undulations
determined by the expression described in the above Table 1 are
deviated from the frequency of f.omega.=n.multidot.f.sub.r
described above, banks of grease formed corresponding to the
frequency of f.omega. are crushed between each rolling surface and
the surface of the first and second raceways and collapse, as the
respective rolling bodies carry out the rotation movement and the
revolution movement. That is to say, if the above described both
frequencies coincide with each other, banks of grease once formed
further grow due to the vibration based on the undulations, and the
vibration itself also grows, thereby resulting in the above
described abnormal vibration and noise. On the contrary, if the
above described both frequencies do not coincide with each other,
the track of the respective rolling bodies which generates
vibration due to the undulations does not coincide with the shape
of the banks of grease. Hence, the respective rolling bodies crush
this bank, to thereby prevent the vibration generated due to the
self-excited vibration of the rolling bodies from growing. Rather,
the bank of grease collapses to thereby absorb the energy of
vibration due to the undulations, and hence alleviate the vibration
due to the undulations.
[0022] Moreover, according to claim 2, even in the case where a
plurality of kinds of vibration frequencies generated due to the
undulations existing on the surfaces of the first and second
raceways and the rolling surface of the respective rolling bodies
are made so as not to coincide with each other, in the natural
frequency domain of the rotation member supported by the rolling
bearing, the growth of the vibration can be suppressed, to thereby
prevent the occurrence of the above described abnormal vibration
and noise. That is to say, vibrations of different frequencies
generated due to the undulations on the above described surfaces do
not promote the growth each other, and vibration of at least any of
the frequencies makes the banks of grease collapse, to thereby
prevent the occurrence of the above described abnormal vibration
and noise.
BRIEF DESCRIPTION OF DRAWINGS
[0023] FIG. 1 is a cross sectional view showing one example of a
rotation supporting portion incorporating a rolling bearing, being
an object of the present invention.
[0024] FIG. 2 is a Campbell chart representing vibration generated
when a conventional rolling bearing is used.
[0025] FIG. 3 is a Campbell chart representing vibration generated
when a rolling bearing in a first embodiment of the present
invention is used.
[0026] FIG. 4 is a Campbell chart representing vibration generated
when a rolling bearing in a second embodiment of the present
invention is used.
[0027] Respective reference symbols denote the followings: 1:
rotation supporting apparatus; 2: support bracket; 3: rolling
bearing; 4: buffer material; 5: housing; 6a, 6b: elements; 7: outer
ring; 8: inner ring raceway; 9: inner ring; 10: outer ring raceway;
11: rolling body (ball); 12: space; 13: seal ring; 14: propeller
shaft; 15: acceleration sensor; 16: amplifier; 17: computer.
BEST MORE FOR CARRYING OUT THE INVENTION
[0028] In a procedure for designing a rolling bearing satisfying
the requirement of the present invention, a description will be
made of a case where a radial ball bearing in which the rolling
bodies are balls, and where in use the outer ring, being the first
race, is kept stationary and the inner ring, being the second race,
is rotated, is used for supporting the rotation of a propeller
shaft 14 as shown in FIG. 1.
[0029] The axial vibration frequency nZf.sub.c (Hz) of the outer
ring, the axial vibration frequency mZf.sub.i (Hz) of the inner
ring, and the axial vibration frequency 2kf.sub.b (Hz) of the
balls, resulting from the undulations of the bearing parts, which
are nZ with regard to the inner ring and the outer ring, and 2n
with regard to the rolling bodies described in the above Table 1,
are respectively represented by the following Expressions (1) to
(3): 1 Z f c = ( 1 2 ) n f r { 1 - ( D a d m ) cos } Z ( 1 ) mZf i
= ( 1 2 ) mf r ( 1 + ( D a d m ) cos } Z ( 2 ) 2 kf b = kf r { 1 -
( D a d m ) 2 cos 2 } d m D a ( 3 )
[0030] Here, in these expressions (1) to (3), n, m and k are
optional positive integers. In the above described Table 1, all are
denoted by n. However, in order to distinguish the source of axial
vibration generated in the radial ball bearing, consideration is
given by dividing these into three kinds of positive integers.
Moreover, d.sub.m (mm) denotes a diameter of a pitch circle of a
plurality of balls constituting the radial ball bearing, and a
denotes a contact angle between these balls and the respective
races. Other symbols have the same meaning as described in the
Table 1.
[0031] In order to realize a radial ball bearing corresponding to
claim 1, this is constructed such that the axial vibration
frequency generated in each constituent part of the radial ball
bearing, as shown by Expressions (1) to (3), does not coincide with
the frequency jf.sub.r (j is an optional positive integer)
proportional to the rotational frequency f.sub.r of the inner ring,
being a rotation member, that is, nZf.sub.c.noteq.jf.sub.r,
mZf.sub.i.noteq.jf.sub.r, 2kf.sub.b.noteq.jf.sub.r (first design
condition). This first design condition corresponding to claim 1 is
a condition in which even if a bank of grease is formed due to
resonance, this does not promote noise and vibration.
[0032] Moreover, in order to realize a radial ball bearing
corresponding to claim 2, this is constructed such that vibration
frequencies of the constituent members of the radial ball bearing
represented by the above Expressions (1) to (3) do not coincide
with each other, that is, nZf.sub.c.noteq.mZf.sub.i,
nZf.sub.i.noteq.2kf.sub.b, mZf.sub.i.noteq.2kf.sub.b, in the
natural frequency domain of a rotation system given by external
conditions (conditions other than those for the constituent parts
of the radial ball bearing) (second design condition).
[0033] The design procedure to realize these first and second
design conditions will be described below. Since it is easy to
design such that the frequency of the vibration generated due to
the undulation of the (2n) waves existing on the rolling surface of
each ball does not coincide with other frequencies, the following
description is about the design procedure for constructing such
that the axial vibration frequency due to undulations of the nZ
component existing on each raceway surface (outer ring raceway and
inner ring raceway) does not coincide with other frequencies.
Moreover, since the radial vibration frequency due to the
undulations of the nZ.+-.1 components existing on the raceway
surface can be obtained in a similar manner to for the axial
vibration frequency due to the undulations of the nZ component
existing on this raceway surface, the description thereof is
omitted.
[0034] It is assumed that in order to satisfy the condition of
nZf.sub.r.noteq.mZf.sub.i so as to realize the radial ball bearing
corresponding to claim 2, these frequencies nZf.sub.c and mZf.sub.i
need only be different by .+-.2% or more. To realize this, it is
necessary to satisfy the following Expressions (4) and (5):
nf.sub.c/mf.sub.i.gtoreq.1.02 (4)
.sub.nf.sub.c/mf.sub.i.ltoreq.0.98 (5).
[0035] If the aforesaid expressions (1) and (2) are substituted in
these expression (4) and (5) and rearranged, the following
expression (6) can be obtained. Here, since a radial pre-load is
applied on the radial ball bearing, it is assumed that
.alpha..apprxeq.0. 2 nf c mf i = ( d m - D a ) n ( d m + D a ) m =
( D i D e ) ( n m ) ( 6 )
[0036] In this expression (6), D.sub.i denotes a groove diameter of
the inner ring (diameter of the bottom portion of the inner ring
raceway) and D.sub.e denotes a groove diameter of the outer ring
(diameter of the bottom portion of the outer ring raceway). Also, m
and n are optional positive integers, as described above.
[0037] If a value obtained from the above Expression (6) is
deviated from the range of from 0.98 to 1.02 (if the difference
between nf.sub.c and mf.sub.i is at least .+-.2%), banks formed by
the grease on the inner ring raceway and the outer ring raceway are
not retained. In other words, a condition in that even if a bank of
grease is formed, this is crushed by the rolling surface of the
ball and does not grow, can be obtained.
[0038] The operation to obtain such a condition is performed by
shifting the above described two frequencies nZf.sub.c and
mZf.sub.i, based on a rolling bearing 3 (radial ball bearing) that
is used in the middle portion of the propeller shaft 14 or the like
and has caused vibration and noise problems. More specifically,
this is performed according to the procedure of (1) to (8)
described below. Here, the calculation shown in this procedure is
automatically executed by a computer in which a predetermined
program is installed.
[0039] (1) The number Z of rolling bodies of the rolling bearing 3
that has caused vibration and noise problems described above
(nf.sub.c/mf.sub.i.apprxeq.1), and the groove diameter D.sub.i of
the inner ring and the groove diameter D.sub.e of the outer ring
are designated as the initial values.
[0040] (2) These groove diameter D.sub.i of the inner ring and
groove diameter D.sub.e of the outer ring are then changed by
.+-.1.about.2%. At this time, preferably each groove diameter
D.sub.i and D.sub.e is changed such as by .+-.1%, .+-.2%, . . .
sequentially, in performing the following calculation.
[0041] The rotational frequency fr of the inner ring (for example,
32 Hz) is obtained from a representative value of the actual number
of revolutions of the inner ring (for example, 1920 min.sup.-1
(r.p.m.)). Also, the pitch circle diameter d.sub.m of the rolling
bodies is obtained from the above described each groove diameter
D.sub.i and D.sub.e
(d.sub.m=D.sub.i+D.sub.e)/2=D.sub.i+D.sub.a=D.sub.e-D.sub.a).
[0042] (3) By designating 1 as an initial value, n and m are
incremented by +1 sequentially, to obtain the axial vibration
frequency nZf.sub.i (Hz) of the outer ring and the axial vibration
frequency mZf.sub.i (Hz) of the inner ring, resulting from the
waves in undulation existing in the outer ring raceway and the
inner ring raceway, from the above described Expressions (1) and
(2).
[0043] (4) By designating 1 as an initial value, j is incremented
by +1 sequentially, to obtain the frequency jf.sub.r proportional
to the rotational frequency f.sub.r of the inner ring fr.
[0044] (5) As the first designing condition described above, it is
judged if the values of
.vertline.nZf.sub.c-jf.sub.r.vertline./nZf.sub.c, and
.vertline.mZf.sub.i-jf.sub.r.vertline./mZf.sub.i are at least
1.about.2%.
[0045] (6) If these respective values are not at least 1.about.2%
(if the judgment result in the above step (5) is No), the groove
diameter D.sub.i of the inner ring and the groove diameter D.sub.e
of the outer ring are changed as shown in the above step (2), and
the operation up to the above step (5) is repeatedly performed
until the respective values become at least 1.about.2% (until the
judgment result in the above step (5) become Yes). When these
respective values become at least 1.about.2%, the procedure
proceeds to the next step (7).
[0046] (7) The calculation in the above described expression (6) is
carried out by using the axial vibration frequencies nZf.sub.c of
the outer ring and mZf.sub.i of the inner ring obtained by step
(3). This calculation is performed with respect to all values of n
and m that can be practically considered.
[0047] (8) Based on the calculation result in the above step (7),
it is judged if the second design conditions described above,
namely (nZf.sub.c/mZf.sub.i).gtoreq.1.02 and
(nZf.sub.c/mZf.sub.i).ltoreq.0.98, are satisfied. If both these
conditions are not satisfied, the groove diameter D.sub.i of the
inner ring and the groove diameter D.sub.e of the outer ring are
changed as shown in the above step (2), and the operation up to the
above step (7) is repeatedly performed until both conditions are
satisfied.
[0048] (9) If both conditions are satisfied (the judgment result in
the above step (8) becomes Yes), the groove diameter D.sub.i of the
inner ring and the groove diameter D.sub.e of the outer ring at
that time are designated as the appropriate values.
[0049] In the above described calculation, the deviation between
frequencies to be compared is made at least .+-.2%. However, the
deviation need only be different so as not to cause resonance, and
the size of the deviation required is not limited to at least
.+-.2%. Accordingly, in the above step (2), when the groove
diameter D.sub.i of the inner ring diameter and the groove diameter
D.sub.e of the outer ring are to be changed, they need only be
changed taking into consideration the degree so as not to cause
resonances, and they may be changed by a degree outside the range
of +1.about.2%.
[0050] The next Table 2 shows an example of calculation results for
the design conditions and the vibration frequencies of the radial
ball bearing such as with the above described steps (1) to (9). In
this Table 2, there is described as an example a case where the
value (order) of n in the vibration frequency nZf.sub.c regarding
the undulation of the outer ring raceway is designated as 7, and
the value of m in the vibration frequency mZf.sub.i regarding the
undulation of the inner ring raceway is designated as 5. In this
Table 2, there is shown a calculation result of the Expression (6)
described above, in the case where the groove diameter D.sub.i of
the inner ring and the groove diameter D.sub.e of the outer ring
are changed under this condition.
2 TABLE 2 D.sub.i/D.sub.e = (D.sub.i/D.sub.e) (d.sub.m -
D.sub.a/(d.sub.m + D.sub.a) n/m (n/m) Comparative 0.713 7/5 = 1.4
0.998 .apprxeq. 0% product Present invention 1 0.73 7/5 = 1.4 1.022
.apprxeq. 2.2% Present invention 2 0.722 7/5 = 1.4 1.010 .apprxeq.
1.0%
[0051] Among the three calculation examples shown based on the
result exemplified in this Table 2, the result of the conventional
product is nZf.sub.c.apprxeq.mZf.sub.i. That is to say, 1026 Hz of
the frequency component of the vibration resulting from undulation
on the outer ring raceway and 1027 Hz of the frequency component of
the vibration resulting from undulation on the inner ring raceway,
become almost the same. On the contrary, the result in the present
invention is such that these do not coincide with each other. For
example, in the case of the present invention product 1, 1109 Hz
with respect to 1135 Hz, and in the case of the present invention
product 2, 1022 Hz with respect to 1033 Hz. This means that in the
case of the conventional product, banks of grease are retained for
a long time and lead to vibration and noise of the radial ball
bearing, but in the case of the present invention products 1 and 2,
banks of grease disappear, and are unlikely to cause the above
described vibration and noise.
[0052] Moreover, with regard to resonance in the natural frequency
domain of the rotation system, with the conventional product, this
is conspicuous such as at 32 f.sub.r and 64 f.sub.r as shown in
FIG. 2 described below, but on the contrary, with the present
invention products 1 and 2, vibration becomes small.
[0053] In the above description of the calculation procedure for
the designs for realizing the rolling bearing of the present
invention, the description is concerned with the case where the
initial values of n, m and j are designated as 1, and these values
are incremented by +1 from the initial value. However, the
vibration level (amplitude) of the frequency components nZf.sub.c,
mZf.sub.i, and jf.sub.r of the above described respective
vibrations decreases as the order increases (as the value of n, m
and j becomes large). Therefore, from the viewpoint of decreasing
the vibration and noise, it is not necessary to limitlessly
increase the value of each natural number n, m and j. For example,
it is preferable to limit the upper limit of these natural numbers
n, m and j to about 100, respectively, in view of reduction of the
calculation time, while exerting a practically effective reduction
effect on vibration and noise.
EXAMPLES
[0054] Results of experiments carried out to confirm the effect of
the present invention will now be described. The experiments were
carried out by using a deep-groove type ball bearing having an
inner diameter of 30 mm, an outer diameter of 55 mm and a width of
13 mm, corresponding to model number 6006, and rotating the
rotation shaft with the inner ring externally fitted thereto. The
natural frequency of a rotation system, serving as a rotation
supporting portion constituted by this rotation shaft, the ball
bearing, and a housing supporting this ball bearing was determined
by detecting the acceleration generated by impulse excitation using
a hammer, with an acceleration sensor 15 as shown in FIG. 1,
transmitting this detection value to a computer 17 via an amplifier
16, and processing the detection value by means of FFT (Fast
Fourier Transform) with the computer. The natural frequency of the
rotation system used in the experiments was approximately 850 Hz,
and an area of .+-.250 Hz centering on the natural frequency, that
is, the area of from 600 to 1100 Hz becomes the natural frequency
domain where the amplitude increases due to the resonance.
[0055] In the experiments, with respect to three kinds of samples,
that is, a conventional product outside the technical range of the
present invention, a first embodiment belonging to the present
invention and satisfying the conditions of claims 1 and 2, and a
second embodiment belonging to the present invention and satisfying
only the condition of claim 2, as shown in the following Table. 3,
obtained by changing the diameter of the rolling bodies, the number
of rolling bodies and the pitch circle diameter of the rolling
bodies, without changing the inner and outer diameters and the
width of the ball bearing, the relation between the axial vibration
frequency with respect to the rotational speed and the level (size)
of the generated vibration were obtained, while rotating the
respective inner rings. The Table 3 shows a case where the
rotational frequency f.sub.r of the inner ring is 32 Hz (=1920
min.sup.-1 in rotational speed).
3 TABLE 3 Ball Ball No. of Vibration diameter number PCD waves in
frequency (mm) (pieces.) (mm) Order undulation (Hz) Conventional
7.144 11 42.7 Inner 5 355 1027 product ring 10 110 2054 Outer 7 77
1026 ring 14 154 2052 First 6.747 12 43.4 Inner 3 36 665.6
embodiment ring 4 48 887.4 5 60 1109 Outer 4 48 648.6 ring 5 60
810.8 6 72 972.9 7 84 1135 Second 6.747 11 41.8 Inner 3 33 613
embodiment ring 4 44 817 5 55 1022 Outer 5 55 737 ring 6 66 885 7
77 1033 8 88 1180
[0056] Results of experiments are shown in FIG. 2 to FIG. 4. Of
these figures, FIG. 2 is a Campbell chart showing the experiment
result regarding the ball bearing described as a conventional
product, FIG. 3 is a Campbell chart showing the experiment result
regarding the ball bearing described as the first embodiment, and
FIG. 4 is a Campbell chart showing the experiment result regarding
the ball bearing described as the second embodiment, respectively,
in the above Table 3. In these Campbell charts described as FIGS. 2
to 4, the ordinate denotes the frequency and the rotation order,
and the abscissa denotes the number of revolutions, respectively.
Also, a circle existing on the same order (on a straight line
upward slanting to the right, representing nf.sub.b or the like)
denotes a vibration level with respect to the rotation, and the
amplitude of the vibration spectrum in that portion is expressed by
the size (diameter) of the circle. Moreover, the component parallel
to the abscissa at the center of each circle (ordinate component)
denotes the natural frequency.
[0057] As is obvious (from the fact that the size of the circle in
FIGS. 3 and 4 are smaller than that of the circle in FIG. 2), when
FIGS. 2 to 4 which are the Campbell charts showing the results of
the experiments are compared, in the case of the rolling bearing of
the present invention, vibration generated can be kept low compared
to with the conventional product.
[0058] Respective samples are given consideration below.
[0059] At first, in the case of the conventional product described
in the upper part of Table 3, since the 32nd order component
(32f.sub.r=1024 Hz) of the rotational frequency coincides with the
frequency of the vibration based on the fifth order of the
undulation component of the inner ring (5Z.multidot.f.sub.i=1027
Hz) and the frequency of the vibration based on the seventh order
of the undulation component of the outer ring
(7Z.multidot.f.sub.c=1026 Hz) in the aforesaid natural frequency
domain, a large vibration occurs. Moreover, since the 64th order
component (64f.sub.r=2048 Hz) of the rotational frequency coincides
with the frequency of the vibration based on the tenth order of the
undulation component of the inner ring (10Z.multidot.f.sub.i=2054
Hz) and the frequency of the vibration due to the 14th order of the
undulation component of the outer ring (14Z.multidot.f.sub.c=2052
Hz), a large vibration occurs.
[0060] Next, in the case of the first embodiment described in the
middle part of Table. 3, as is obvious from FIG. 3 in which the
straight line of 5Z.multidot.f.sub.i and the straight line of
7Z.multidot.f.sub.c are deviated from each other, with regard to
the frequency of the vibration based on the fifth order of the
undulation component of the inner ring (5Z.multidot.f.sub.i=1109
Hz) and the frequency of the vibration based on the seventh order
of the undulation component of the outer ring
(7Z.multidot.f.sub.c=1135 Hz), which are relatively close, these do
not coincide with each other. Hence, as is obvious from the small
circles present on the straight lines of 5Z.multidot.f.sub.i and
7Z.multidot.f.sub.c the generated vibration is small. Moreover,
these straight lines of 5Z.multidot.f.sub.i and 7Z.multidot.f.sub.c
exist between the straight lines of 32f.sub.r and 36f.sub.r, but do
not coincide with any of the straight lines of (33.about.35)
f.sub.r existing between these two straight lines. As a result, the
generated vibration can be made sufficiently small.
[0061] Moreover, in the case of the second embodiment described in
the lower part of Table. 3, the frequency of the vibration based on
the fifth order of the undulation component of the inner ring
(5Z.multidot.f.sub.i=1022 Hz) coincides with the 32nd order
frequency (32 f.sub.r=1024 Hz) of the rotational speed. That is to
say, this does not satisfy the conditions of claim 1. However, this
still satisfies the conditions of claim 2, such that the vibration
frequency components due to undulations existing on the surfaces of
the outer ring and inner ring raceways and on the rolling surfaces
of the rolling bodies do not coincide with each other in the
aforesaid natural frequency domain (600.about.1100 Hz).
[0062] In the case of the second embodiment, though the vibration
becomes slightly larger than in the case of the first embodiment,
the generated vibration is considerably smaller compared to the
case of the conventional product described above. Moreover,
according to experiments of the present inventor, even in the case
of the second embodiment, if the atmospheric temperature is equal
to or higher than -20.degree. C., harmful vibration and noise does
not occur.
[0063] As is obvious from Table 1 above, for example, with regard
to the axial vibration, if the rotational frequency of the rotation
member and the frequency due to undulations of each constituent
member of the rolling bearing do not coincide at any of the
rotational frequencies, then even if this rotational frequency
changes (even if the rotational speed of the rotation member
changes), this rotational frequency does not coincide with the
frequency due to undulations described above. That is to say,
nZf.sub.i, nZf.sub.c, 2nf.sub.b representing the axial vibration
frequency due to the undulations, and nf.sub.r representing the
rotational frequency, as described above in Table 1, with respect
to each constituent member of the rolling member, are respectively
expressed by a straight line passing through an origin point (a
point of vibration frequency=0, and number of revolutions=0) on the
Campbell charts in FIG. 2 to FIG. 4. Therefore, if these do not
coincide with each other at any rotational frequency, these do not
coincide at other rotational frequencies. Also, with regard to
radial vibration, even though vibration frequencies generated with
regard to the inner ring and the rolling bodies are respectively in
two kinds, the straight line representing the vibration frequency
passes through the origin point on the Campbell chart. Hence, also
in the case of the radial vibration, this is the same as in the
case of the axial vibration in that if these do not coincide with
each other at any rotational frequency, these do not coincide at
other rotational frequencies.
[0064] Since there is little possibility of a situation where only
the conditions of claim 1 are satisfied and the conditions of claim
2 are not satisfied, any experiment for such a case was not
performed. However, as is obvious from the above description, it is
believed that even a structure satisfying only the conditions of
claim 1 can practically reduce vibration sufficiently. Needless to
say, the most preferable structure is the one described in claim 3,
wherein both conditions of claims 1 and 2 are satisfied as with the
first embodiment. Moreover, the above description has been made for
the case of a deep groove type ball bearing, being a radial ball
bearing, and for the case of axial vibration. However, the present
invention can be similarly applied to radial vibration, by using
the vibration frequency generated in the radial direction, instead
of the vibration frequency generated-in the axial direction. Also,
the same idea can be applied not only to a radial ball bearing but
also to a thrust ball bearing or a radial or thrust roller
bearing.
INDUSTRIAL APPLICABILITY
[0065] The rolling bearing of the present invention is constructed
and operates as described above, and hence the occurrence of
vibration and noise at the time of low temperatures can be
effectively prevented, without using grease having a low
particularly viscosity. As a result, a rolling bearing having
excellent durability can be realized without causing an
uncomfortable sensation.
* * * * *