Constant torque ball bearing

A ball structure for stabilizing bearing torque in high speed, preloaded, angular contact load supporting ball bearings operating on elastohydrodynamic lubricant films. Angular momentum developed about a ball spin axis that is not parallel to the bearing rotation axis results in a continuous creep of the ball about the momentum axis, thereby allowing a long term preload and torque variation. The improved ball set is shaped so that each ball has a mass inertia about its desired spin axis that is greater than about all other axes, so as to develop a restoring moment tending to maintain rotation about a fixed axis in each ball. The ball cage is configured to maintain ball alignment during run-up and run-down of the bearing.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to the art of antifriction bearings 
and more particularly to the art of ball bearings. More specifically, the 
invention relates to preloaded, angular contact ball bearings for 
precision instruments such as the spin bearings of gyroscopic instruments, 
and to a ball and cage structure for stabilizing bearing torque and 
preload. 
2. Description of the Prior Art 
The accuracy and stability of a gyroscope, that is, its ability to maintain 
its spin axis fixed in inertial space, is dependent, among other factors, 
on the characteristics of the ball bearings which support the spinning 
rotor. It has been observed that spin ball bearings utilized in Reaction 
Wheel Assemblies (RWA's) and instrument gyros exhibit low level long term 
torque periodicity (on the order of 2 to 60 minutes). This torque 
variation is evidenced in very small but undesirable periodic wheel speed 
changes in the case of RWA's (resulting in spacecraft position changes) 
and drift variations in the case of gyros. The magnitude of these 
variations is very small, on the order of 5 percent or less of the mean 
torque at speeds to 6 KRPM. 
While is is desired that all of the balls of a ball bearing set be 
identical in size and all perfectly spherical, it is recognized in the art 
that such perfection is normally unattainable. Also, those skilled in the 
art recognize that conventional ball cage designs leave much to be desired 
in terms of stability and mechanical as well as audible noise. Given these 
practical limitations, even the most carefully manufactured ball bearings 
will not provide ultimate antifriction support, particularly of the 
precision required for supporting a gyroscope rotor, since the slightest 
imperfection in the rotor shaft support bearings can result in a long term 
drift of the gyro. The foregoing variations in torque have been found to 
be due to gyroscopic precession of the individual balls of the ball set, 
resulting in variations in the ball diameter presented to the points of 
angular contact with the ball races and an associated variation in 
preload. There have been no known previous attempts to stabilize ball 
bearing torque by preventing ball precession. It is probable that the 
existence of this torque periodicity as well as the reason for it is not 
commonly known. For these reasons it is doubtful that prior related art 
exists. 
It has been discovered by the present inventor that a major source of these 
variations has been traced to small preload variations and changing 
differential ball spin velocities caused by shifts of the balls' spin axes 
as the balls precess. This invention solves the problem of torque 
periodicity by preventing ball precession by combinations of mass inertia 
configuration control of the balls and mechanicl capture of the balls. 
SUMMARY OF THE INVENTION 
The constant torque ball bearing assembly of the present invention 
comprises an outer bearing ring having an outer bearing race and an inner 
bearing ring having an inner bearing race. The rings are spaced apart and 
concentrically disposed on a bearing axis. A plurality of balls are spaced 
apart and in essentially free rolling contact between the races. A spin 
axis is developed in each ball orthogonal to the points of contact with 
the inner and outer races at each ball. The balls are configured to 
provide a mass inertia about their respective spin axes that is greater 
than that about any other of their axes, and in operation results in 
inertial moments that resist any tendancy of the balls to deviate from the 
desired spin axis. 
In a further embodiment, the ball bearing is of the preloaded angular 
contact type having outer and inner bearing rings having corresponding 
races and concentric with respect to a common bearing axis. A plurality of 
balls in rolling contact with the races are preloaded along the bearing 
axis so that the line of contact between the balls and the races lies at 
an angle with respect to a plane normal to the bearing axis. In operation 
the balls are subjected to a gyroscopic moment which if of significant 
magnitude tends to precess the balls about an axis normal to both the line 
of contact of the ball and raceways and the rotation axis of the balls. 
The balls are configured to provide a non-uniform mass inertia 
distribution so that the potential precession induces a restoring inertial 
movement to stabilize the ball position and resultant bearing torque.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 illustrates graphically, and somewhat simplified, the torque 
characteristics of a typical conventional precision preloaded, angular 
contact elastohydrodynamic (EHD) lubricant supported spin bearing for a 
gyroscope of the type disclosed in the present assignee's U.S. Pat. Nos. 
3,529,477 or 3,677,097 and embodying a conventional free floating ball 
cage. The gyro rotor may be spun at speeds of say 6,000 to 24,000 R.P.M. 
The short term variation in torque or hash is due primarily to dynamic 
interaction between the individual balls and their separating cage. Such 
dynamics result from somewhat spasmodic ball-cage contact, cage-race ring 
contact, etc. These short term variations in load torque may be eliminated 
or substantially eliminated by incorporating in the bearing the unique 
dynamically stabilized ball cage disclosed in the present inventor's U.S. 
Pat. No. 3,918,778 also assigned to the present assignee. However, 
substantial elimination of this most evident torque variation by 
introducing the dynamically stabilized ball cage made evident a subtle and 
very long term periodic torque variation as illustrated graphically by the 
sinusoidal variation in the aforesaid FIG. 1. It is to the practical 
elimination of this long term variation in torque, attributed to 
precession of the balls and resultant shift in their spin axes, that the 
present invention is directed. 
The invention may best be understood by analyzing the forces and moments 
acting on the ball complement. Referring now to FIG. 2, a conventional 
ball bearing assembly comprises relatively radially spaced concentric 
inner race ring 10 and outer race ring 11, illustrated in phantom, having 
raceways 12 and 13 respectively, between and in which are spaced by means 
of a ball separator (usually referred to as ball retainer or cage as will 
be discussed below, but not shown in FIG. 2 for clarity), a plurality of 
balls, sometimes referred to as the ball complement or ball set, only one 
of which is shown in FIG. 2. Each ball 14, ideally identical to each other 
in the complement and almost perfectly spherical, supports the load (not 
shown), herein assumed to be a shaft supported by the inner race ring 10 
and on which is suspended a gyroscope rotor, for example for high speed 
spinning about a bearing spin axis x--x. It will also be assumed and 
understood that the shaft is supported by at least another, preferably 
identical, ball bearing assembly (not shown) spaced laterally along the 
spin axis x--x. It will further be assumed that each ball bearing assembly 
is carefully lubricated such that during normal operation each ball of the 
assembly supports the rotor shaft load on an elastohydrodynamic (EHD) 
lubricant film so that the ball is essentially free to rotate (slip) about 
all of its axes as it supports the load. Although only recently coming 
into general use, the principles of EHD films are discussed in a book by 
Tedric A. Harris entitled "Rolling Bearing Analysis" and published by John 
Wiley and Sons, New York, 1966. 
The ball 14 is axially preloaded between the inner and outer races 12, 13 
so that it contacts the ball races along axis v--v at an angle .beta. 
relative to the radial axis y--y. The diametrically opposed preload forces 
therefore may be represented by the force arrows F.sub.BALL along axis 
v--v at the inner and outer contact points 15 and 16, respectively. It 
will be understood that at high bearing speeds an elastohydrodynamic film 
separates the ball 14 from the races 12 and 13 so that there is no actual 
metallic contact at these points. During operation, the ball 14 is 
restrained by the races 12, 13 to follow the ball path 17, as illustrated, 
at the angular velocity of the ball set, .omega.BALL SET, dependent on the 
angular velocity of the inner race, .omega.INNER RACE, about axis x--x. If 
the ball bearing were not of the preloaded, angular contact type (i.e., 
.beta.=0) the angular velocity of each of the balls would be about an axis 
x'--x' parallel with the angular velocity vector of the ball set about 
axis x--x and no gyroscopic moments would be produced. However, since the 
effective diametrically opposed contact points 15, 16 and disposed are at 
the angle .beta. relative to the radial axis y--y, the ball tends to spin 
about an axis z--z orthogonal to an axis defined by contact points 15, 16 
and disposed at an angle with respect to axis x'--x' and therefore 
develops momentum about the axis z--z that is not parallel to the ball's 
mass center spin axis x'--x'. It is assumed, in this description, that 
both radial and axial centrifugal forces are negligible to simplify the 
discussion. In practice the radial centrifugal force is not zero and will 
modify the effective ball spin axis z--z slightly. The basic concept, 
however, is not changed. 
Since each of the balls has mass and is spinning about a spin axis, it is 
in effect a small gyroscope and possesses the inherent characteristics of 
a gyroscope, including precession. Thus, in spinning about the axis z--z 
which is not parallel with the axis x'--x', the illustrated gyroscopic 
moment M.sub.G along ball axis u--u normal to the ball's spin axis z--z is 
developed. This moment may result in a precession or creep of the ball 14 
about its axis u--u, illustrated by a broken arrow, if the EHD lubricant 
film is adequate. The magnitude of this gyrosopic moment, M.sub.G, may be 
expressed approximately by 
EQU M.sub.G =0.05.rho.(d.sub.B).sup.5 .omega..sub.BALL SET sin 
.beta.(.omega..sub.BALL -.omega..sub.BALL SET cos .beta.) (1) 
where 
d.sub.B =Ball Diameter 
.rho.=Ball Material Density 
.omega..sub.BALL SET =Angular velocity of the ball set about axis x--x 
.omega..sub.BALL =Angular velocity of the ball about axis z--z. 
If the ball is free to creep due to a sufficient EHD lubricant film and 
gyroscopic moment, the ball will continuously present different diameters 
between its effective contact points 15 and 16 with the bearing races. As 
discussed above, the ball 14, like all of the balls of the ball set, is 
not perfectly spherical, and variations in preload and torque inherently 
result. Also, since the angle .beta. is normally relatively small, the 
gyroscopic moment is small and the resulting creep and periodicity is 
relatively slow so that the torque variation is likewise long term. For 
one particular spin bearing, the torque variation period was well over an 
hour, which produced a corresponding long term drift of the gyro in which 
it was incorporated. 
In accordance with the teachings of the present invention this long term 
preload and torque variation is substantially eliminated by so configuring 
each ball of the ball set that the gyroscopic precession of the ball is 
opposed and rendered ineffective. This is accomplished by configuring each 
ball so that it will inherently spin about the axis z--z, that is, by 
configuring the ball such that its mass inertia about any nonspin axis is 
less that its mass inertia about its normal desired spin axis (z--z). 
One embodiment of the present invention by which this inherent alignment 
will occur is illustrated in FIG. 3. As illustrated, each ball is 
configured so that its mass inertia about its axis z--z is greater than 
about any other of its axes, this configuration being achieved, for 
example by grinding diametrically opposed planar surface 18, 19 on each of 
the balls; i.e., by equally truncating opposed surfaces on a given 
diameter thereof. The thickness t determines the ball's moment of inertia 
about the axes z--z and v--v, that about axis z--z being greater. A 
restoring moment opposing the creep will be developed about axis u--u 
which increases as the ball precesses about that axis. When this restoring 
moment is equal to the gyroscopic moment, the precession will cease and 
the balls will spin with the axis of symmetry slightly misaligned from the 
ball spin axis z--z and stabilized whereby only one annular surface of 
each ball will present itself to the contact points 15 and 16 of the 
races, resulting in essentially zero variation in load torque. 
When the bearing of the present invention is not operating during the time 
it is being brought up to a speed at which the EHD film is formed, means 
may be provided to prevent the ball's annular contact surface from 
becoming greatly misaligned with the raceways. This may be accomplished as 
illustrated in FIG. 3 by providing a low speed limit stop 20 on the ball 
retaining cage 21. This stop is configured to present a surface 22 which 
is parallel with the surface of the ball flat 19 and close enough at 
speeds lower than operational to prevent the ball from presenting a 
nonspherical surface to the raceway contact points 15 and 16 and yet far 
enough away as to allow for gyroscopic precession and the attendant 
advance of the ball flat 19 while maintaining the flat ball surface nearly 
normal to the ball spin axis z--z. As shown in FIG. 7, the ball retaining 
cage rotates about an axis x--x and is provided with a plurality of 
circular apertures for receiving and retaining the balls. The surface 22 
is comprised of a radially extended ridge which acts in cooperation with a 
single planar surface 19 for controlling the relative angular position of 
the ball for rotation. It should be noted, here, that the ball flat 19 
will rotate with respect to the cage flat 22 after the ball has precessed 
to an axis of equilibrium even though the gyrosocpic moment, M.sub.G, is 
essentially constant. 
Other ball configrations for accomplishing the above purposes may also be 
clear from the above concepts. One such alternative configuration is 
illustrated in FIG. 4 in cross section wherein the mass inertia of the 
ball 30 about the spin axis z--z is made larger than that about axis v--v 
by drilling a hole 32 of the required size through a diameter of the ball. 
FIG. 5 shows the means by which the ball illustrated in FIG. 4 may be 
constrained to maintain the hole 32 nearly aligned with the desired spin 
axis z--z during operation of the bearing at speeds below the design 
speed. An extension flange 34 on cage 21 mounts a retaining pin 36 which 
provides the required restraint of the ball 30 in hole 32 with the same 
design guidelines as discussed previously. 
As shown in FIG. 6, another alternative would be to construct the ball with 
a high mass outer annular rim portion 44 and a low mass inner portion 40. 
A relatively low mass steel or other insert 40 is pressed into a 
cylindrical hole 52 bored in a relatively high mass ball 44 and secured by 
weldments 46 and 48. The ball may then be finish ground and lapped to size 
such as is used in conventional (solid) ball fabrication. These latter 
configurations may eliminate the need for the cage stop and retaining pin 
structures of the ball cage. 
Using a ball of type 52100 chrome alloy bearing steel with a 0.1875 nominal 
diameter, having a linear dimension of 0.0938 inches across flats at a 
skew angle relative to the ball's spin axis of 45.degree. the peak 
restoring torque would be about 7.times.10.sup.-4 in-lb. Increasing the 
flat dimension to 0.125 inches provides about 4.5.times.10.sup.-4 in-lb of 
torque. These data were calculated with a modified type 101H bearing 
operating at 3000 rev/min inner ring speed. 
For the drilled ball of FIG. 4 using a 0.1875 diameter ball of 51200 alloy, 
a bore 0f 0.032 diameter provide useful results in the type 101H bearing. 
Note that a useful configuration may also be obtained by varying the depth 
of the bore, as well as the bore diameter. 
The ball structure of FIG. 3 may be fabricated by first capturing the ball 
group on a magnetic plate which contains a set of holes smaller then the 
ball diameter in which the balls may be nested and grinding a flat on the 
exposed surface of each ball. A second operation would involve rotating 
the balls 180 degrees on the magnetic plate (but without the nesting 
holes) and grinding the second set of flats. The holes in the balls of 
FIG. 4 can be provided by a spark discharge, or similar process, wherein 
an electrode shaped like a cylindrical rod of a diameter slightly smaller 
than the desired hole size is attached to an oscillating arbor and the 
ball is nested in a suitable chuck. A voltage potential is developed 
between the electrode and the ball, with the ball submerged in a suitable 
coolant fluid, and the hole is developed by bringing the electrode into, 
and out of, mechanical and electrical contact with the ball such that the 
arcing developed when the contact is broken gradually removes material 
from the ball. This is an established process known by the trade as "spark 
discharge" machining. 
While the invention has been described in its preferred embodiments, it is 
to be understood that the words which have been used are words of 
description rather than limitation and that changes may be made within the 
purview of the appended claims without departing from the true scope and 
spirit of the invention in its broader aspects.