The mounted, preloaded contact angle of the structural bearings in the assembled design mechanical assembly was measured. A modification of the Turns method is presented, based upon the clarity and definition of moving parts achieved with X-ray technique and cinematic display. Contact angle is estimated by counting the number of bearings passing a given point as a function of number of turns of the shaft. Ball and pitch diameter variations are discussed. Ball train and shaft angle uncertainties are also discussed

Fowler, P. H.

Manders, F.

English

NASA Technical Reports Server

ESTIMATION OF BEARING CONTACT ANGLE 
IN-SITU BY X-RAY KINEMATOGRAPHY 
by Peter H. Fowler* & Frank Manders** 
The DSCS II Satellite consists of an earth-pointing platform carrying 
the transponder and antenna farm, mounted on a spinning section providing 
power and command. Attitude control and pointing are performed entirely in 
the spinning section. The whole satellite weighs about 650 kg. 
The two sections are joined by the "despin mechanical assembly" (DMA), 
consisting of drive motors, slip rings, and a pair of ball bearings on which 
the spinning section revolves, all enclosed in a load bearing case (Fig. 1). 
The system is required to maintain precise earth pointing for at least five 
years at 60 rpm. 
The need arose to measure the bearing contact angles in assembled units 
which had completed acceptance test. The usual bench methods of estimating 
contact angle are not applicable to a bearing assembled in an opaque case, 
and in any case the contact angle as assembled includes the effects of 
preload and assembly tolerance. Dismantling a flight-accepted unit is both 
costly and introduces program risk. 
The usual methods of measuring bearing contact angle are the Turns 
method and by measuring internal clearance. 
The Turns method is the most popular since it is fairly accurate, 
requires simple tooling and it can be performed in a relatively short time. 
This method provides free bearing, preloaded contact angle data. Three 
marks are located on the outer ring, inner ring and ball cage. These 
marks are initially aligned. The outer ring or inner ring is rotated a 
predetermined number of revolutions with the other ring restrained from 
rotation. The number of ball cage rotations is measured (whole number plus 
the fraction). The contact angle is then calculated by using the following 
equation: 
B = arc cos 
2NE i(l- T) 
i 
or 
2N 
B = arc cos ;(l+ N; ) 
where B is bearing contact angle 
E is bearing pitch diameter 
d is bearing ball diameter 
NE is number of ball cage revolutions 
Ni is number of inner ring revolutions 
No is number of outer ring revolutions 
*Peter H. Fowler, TRW Space and Technology Group, Redondo Beach, CA 90278 
**Frank Manders, Ball Aerospace Systems Division, Boulder, CO 80306 
189 
https://ntrs.nasa.gov/search.jsp?R=19820015482 2020-03-21T16:27:46+00:00Z
Figure 1. DMA Cutaway View 
190 
The internal clearance measurement determines the free bearing, unloaded 
contact angle. This method is generally used in small bearing production 
lines since it requires the least amount of time. The outer ring is held, 
while the inner ring is moved to its extreme radial positions. This 
motion (C) is measured and the contact angle is calculated by the following 
equation: 
B = arc cos (l-$y 1 
here C is the total diametral measurement (called radial clearance) 
B is the total curvature constant = f. + fi - 1 
f, is the ratio of outer race radius to ball diameter 
fi is the ratio of inner race radius to ball diameter. 
If, during installation on the shaft and in the housing, the bearing 
interfaces are slip fits and the bearing preload is equal to the gaged load 
of the free bearing measurement, the installed bearing contact angle will 
be as measured by either method. If, however, the bearing is installed 
with either or both of its interfaces press-fit and/or the preload is 
different from the gaged load, the mounted, preloaded contact angle is 
different from any free bearing measurement. 
To complicate the situation, in most cases the bearings are not visible 
after installation in a device. Analysis can be performed to approximate 
the mounted preloaded contact angle, but this may result in errors of 
several degrees. 
Our problem was to attempt to measure the mounted, preloaded contact 
angle of the structural bearings in the already assembly DMA. 
Initially, it occurred to us that the contact angle could be measured 
by counter-rotating the inner and outer races at such a speed that the ball 
train is stationary, hoping to determine this point by x-ray observation. 
The free bearing, preloaded contact angle can then be calculated from: 
B = arc cos i 
(Ri - !o) 
(Ri + Ro)' 
where Ri is the speed of the inner ring 
R. is the speed of the outer ring. 
This method is not normally used because the individual speeds or the 
speed ratio must be known to a high degree of accuracy (on the order of 50 
parts per million) for reasonable (20.250 ) accuracy. 
We proposed to construct a rather complicated device to counter-rotate 
the DMA shaft and housing and use this method to calculate the required 
contact angle. 
191 
We located an x-ray facility with a manipulator capable of mounting a 
DMA and with kinematic display capability. The facility is owned by Test 
Equipment Distributors, in Detroit. Not being familiar with the state of 
the art of this type of equipment, we were surprised at the clarity and 
definition with which moving parts could be seen. Figure 2 is a print of 
one frame of a video tape of the DMA in motion. The ball positions can 
clearly be determined with accuracy, even though, of course, the phenolic 
retainer position cannot be seen. A less complicated modification of the 
Turns method appeared practical. 
Contact angle can be estimated by counting the number of balls 
passing a given point as a function of number of turns of the shaft. The 
Turns method is then modified as follows: 
The angular distance between the leading edge of one ball and the 
leading edge of the following ball ($) is: 
G = y (degrees), 2 (radians) 
where n is the number of bearing balls. 
The total angle for ball train motion depends upon the number of balls 
observed passing a stationary point or: 
where N = the number of balls observed passing a stationary point. 
The contact angle equation then becomes: 
B = arc cos g d (l - ';;" ) 
i 
where Oi = the shaft angle rotation in degrees. 
Using this technique and estimating the bearing individual errors 
(d, E, OE' Oi) the test accuracy can easily be determined. 
For the purpose of illustration, let us use one of the DMA bearings 
as an example. The basic bearing parameters are: 
d = 0.5 inch1 
E = 5.14 inches 
B = 15 degrees 
n = 23 balls 
Ball Diameter Variation 
The selection of ball diameter is one of the primary methods of setting 
free-bearing gaged preload. Ball diameter variation for bearing of the 
approximate size as the example can vary by +O.OOl inch. The total varia- 
tion within a single bearing, however, is 0.00001 inch. In our example, 
we have measured the basic ball size and therefore have knowledge to 10 
microinches. 
lBearing dimensions and tolerances are given in inches, since the design 
and specifications were pre-SI and an arbitrary translation reduces clarity. 
192 
BALLS 
Figure 2. Bearing Appearance on Video Monitor 
193 
Pitch Diameter Variation 
Pitch diameter variation is the most difficult dimensional parameter 
to determine, since it is made up of several other dimensions which are not 
normally known by an aerospace applications engineer. For bearings of this 
size and quality, the range is LO.001 to H.005 inch. For our bearing, 
the lower figure was used in the error analysis. 
Ball Train Uncertainty 
If we assume knowledge of the ball in the raceway to &O.Ol inch,- the 
resulting error in ball train angle is about LO.2 degree. 
Shaft Angle Uncertainty 
The interface fixture design will dictate the accuracy of shaft angle. 
If an optical encoder is used, the shaft angle error will be a small part 
of one degree. For our test, assume a reasonable potentiometer with a 
readout error of about +0.25 degree. 
Figure 3 shows the contact angle total error for the four parameters 
using our example bearing, counting 100 balls. This figure shows for equal 
uncertainty the ball position error is the more critical angular parameter 
and the ball diameter variation is the more critical dimensional error. 
Figure 4 shows the total contact angle error as a function of the .ball 
count and contact angle, for the expected parameters for the example bearing. 
As can be easily seen, the contact angle accuracy improves with an 
increase in ball count and as the contact angle increases. 
If we count 300 balls, the calculated contact angle will be accurate 
to approximately +0.2 degree. If we increase the count to 700, the er- 
ror will decrease-to about +O.l degree. We are thus able to estimate 
the assembled bearing contaFt angle with excellent accuracy. 
The measurement is made by mounting the assembly shaft on a rotating 
table, as shown in Figure 5. The x-ray source and imaging system are 
arranged to view the bearing at a convenient angle so that the balls 
can be tracked individually; Note that ideally the x-ray axis should be 
tilted rather than the device axis, as having the weight off-center alters 
the net preload and side-loads the bearings. 
A ball position is marked on the viewing screen, and the shaft rotated 
slowly some preset number of times. The number of balls is counted, including 
the fraction. Alternately the shaft may be rotated until some preset 
number of balls has passed, and the total shaft angle read off. In 
principle the counting could be automated, but for an occasional measurement 
on a high-value device this is not worthwhile. 
Using a modern image multiplier, the total x-ray dose is very small, 
insignificant compared with the energies and integrated fluxes of a life in 
orbit. Radiation damage to lubricant and other parts is thus not a factor 
in the measurement. 
The DMA has a beryllium housing and shaft, with stainless steel balls 
and races. The x-ray source for clear viewing of the ball positions is 
about 1 mA at 50 kV. A sharp focus x-ray source and imaging system is 
capable of showing ball position when the ball is as little as 2% of the 
total x-ray density. Thus, the measurement could be made as easily if the 
case and shaft were also stainless steel. 
194 
1.0 
0 
1.0 
0 
BALL POSITION ERROR 
SHAFT ANGLE READOUT ERROR 
BEARING PARAMETERS 
(BASIS FOR ERROR 
ANALYSIS): 
5J I I I I 0.1 0.2 0.3 0.4 
ANGULAR UNCERTAINTY-DEGREES 
d = 0.5 IN. 
E = 5.14 IN. 
P= 15 DEG 
i.i 
= 23 BALLS 
= lOOBALLS 
- I 
-i 
BALL DIAMETER ERROR 
.a 
/ 
0 \ 
0 
PITCH DIAMETER ERROR 
DIMENSIONAL UNCERTAINTY - INCHES 
Figure 3. Effect of Measurement Uncertainty on Contact Angle Calculations 
195 
r 
BE
AR
IN
G
 
PA
R
AM
ET
ER
S:
 
d 
= 
0.
5 
IN
. 
‘8
E 
= 
0.
2 
D
EG
 
E 
= 
5.
14
 
IN
. 
ee
L 
= 
0.
25
 
D
EG
 
t) 
= 
23
 B
AL
LS
 
cd
 
= 
O
.o
oo
O
l 
IN
. 
‘E
 
= 
0.
00
1 
IN
. 
01
 
I 
I 
I 
I 
I 
I 
I 
I 
I 
J 
0 
10
0 
20
0 
30
0 
40
0 
50
0 
60
0 
70
0 
80
0 
90
0 
10
00
 
N
U
M
BE
R
 
O
F 
BA
LL
S 
O
BS
ER
VE
D
 
- 
N
 
Fi
gu
re
 4
. 
Ef
fe
ct
s 
of
 B
al
l C
ou
nt
 o
n 
C
on
ta
ct
 A
ng
le
 C
al
cu
la
tio
ns
 
- I 
IM
AG
E 
M
U
LT
IP
LI
ER
 
TV
 
C
AM
ER
A 
7 
TE
ST
 
AR
TI
C
LE
 
7 
R
O
TA
TO
R
 
W
IT
H
 
PO
SI
TI
O
N
 
R
EA
D
O
U
T 
SU
PP
O
R
T 
TO
 
PR
EV
EN
T 
R
O
TA
TI
O
N
 
O
F 
H
O
U
SI
N
G
 
Fi
gu
re
 5
. 
M
ea
su
re
m
en
t S
ys
te
m
 
I 
X-
R
AY
 
SH
IE
LD
ED
 
R
O
O
M
 SH
AF
T 
PO
SI
TI
O
N
 
TV
 
M
O
N
IT
O
R
 
IN
D
IC
AT
O
R
 
For the DMA, and other comparable-value equipment, it is good practice 
to make a simultaneous video tape of the monitor as this provides a record 
of the correctness of the ball count. Since the DMA has a large wire 
bundle coming out of each end and other connections with opportunity for 
interference, it is also wise to lock the case with tape or similar easily 
broken connection. If something hangs up, the case will then pull free and 
only the measurement is lost. 
We suggest that the method described is useful in confirming 
capability of assembled units, and facilitates in-situ adjustment of 
preload to obtain a defined contact angle. 
198 
Peter II. Fowler 
TEW Space and Technology Group 
1 Space Park 
Eedondo Beach, California 90278 
Mr. Fowler was educated in England,. emigrating to the United States in 1957. 
He is currently System Engineering Subproject Manager for the Defense Communi- 
cation Satellite Phase II. Previous responsibility at TRW includes Assistant 
Project Manager for the Viking Lander biology and meteorology experiments. 
Prior to joining TEW in 1967, he worked on test equlpment design, communica- 
tion system design, and launch vehicle reliability. He holds patents on a 
temperature-compensated accelerometer and a pneumatic shock machine. In addi- 
tion, Mr. Fowler has written papers on wideband shaker design, system pathol- 
ogy, and orbital experience with TWTA reliability. 
Co-author of this paper is Mr. Frank Manders who is affiliated with Ball Aero- 
space Systems, Boulder, Colorado. 
199. 


Estimation of bearing contact angle in-situ by X-ray kinematography

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server