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This is to certify that the

thesis entitled

Design and Implementation of a Transducer
to Measure the Cross-sectional Dimensions
of Bearing Raceways

presented by

Kristin Beth Zimmerman

has been accepted towards fulfillment
of the requirements for

Masters Mechanics

 

 

degree in

Aflm

/Major professor

 

Au ust 2, 1990
Date 3

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

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‘ Mlchlgan State
Unlverslty l

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

DATE DUE DATE DUE DATE DUE

l__l_____

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fiF—j

MSU I. An Affirmative Action/Equal Opportunity Institution
' chS-o:

 

 

 

DESIGN AND IMPLEMENTATION OF A TRANSDUCER TO
MEASURE THE CROSS-SECTIONAL DIMENSIONS
OF BEARING RACEWAYS

By

Kristin Beth Zimmerman

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Metallurgy, Mechanics, and Material Science

1990

ABSTRACT
DESIGN AND IMPLEMENTATION OF TRANSDUCER TO

MEASURE THE CROSS-SECTIONAL DIMENSIONS
OF BEARING RACEWAYS

By

Kristin Beth Zimmerman

The cross-sectional dimensions of a 45" biangular roller
bearing race cavity is measured to determine the proper
roller size. Measurement is conducted by using a resistance
strain gage based transducer. The transducer indicates the
cross-sectional dimensions of the raceway, and this
analog/digital information is fed into a computer program
that generates the dimensions for a properly fitting roller
for the bearing. The transducer uses the deflection of four
cantilever beams to detect the cross-sectional dimensions of
the bearing cavity. This transducer is capable of measuring

dimensions on the order of one micro-inch or less.

This thesis is dedicated to my parents.

ACKNOWLEDGEMENTS

I would like to thank Kaydon Corporation for offering this very
intrigueing research project and I owe my utmost gratitude and

respect to my advisor, Dr. Gary Cloud, for his time, patience,

and faith in me during this endeavor.

ii

TABLE OF CONTENTS

1. LIST OF TABLES ........................................ v1

2. LIST OF FIGURES ...................................... vii

3. INTRODUCTION

1. THE PHYSICAL MEASUREMENT PROBLEM ..................... 1
II. METHODS EVALUATED FOR DISPLACEMENT MEASUREMENT ....... 3
A. Optical Methods .................................. 4

B. Eddy Current Probe ............................... 6

C. Load Cell ........................................ 7

D. Electrical Resistance Strain Gages ............... 7

E. Measurement Techniques Used In Industry .......... 8

III. SUMMARY .............................................. ll

4. DESIGN AND RESULTS

iii

I. FINAL DESIGN ........................................ 12

II. EXPERIMENTAL SETUP .................................. 12
III. TRANSDUCER CONSTRUCTION ............................. 17
IV. THEORETICAL STRAIN CALCULATION ...................... 20
V. CALIBRATION PROCEDURE ............................... 24
VI. COMPUTER PROGRAM - PHYSICAL SETUP ................... 30
VII. COMPUTER CALIBRATION SUBROUTINE ..................... 32
VIII. EXPERIMENTAL PROCEDURE .............................. 34
IX. SUMMARY ............................................. 43

5. DISCUSSION AND CONCLUSIONS

I. Experimental Results ................................ 44

II. Further Study/Recommendations ....................... 46

6. APPENDICES

APPENDIX A

iv

7.

I. HISTORICAL BACKGROUND ON ELECTRICAL RSG'S ........... 48

A. Definition of Strain/How it Relates to

Displacement .................................... 48

B. Properties of RSG's ............................. 50

C. Types of Strain Gages ........................... 53

II. PERFORMANCE CHARACTERISTICS OF ELECTRICAL RSG'S ..... 54
APPENDIX B

COMPUTER CODE - ATARI BASIC ..................... 57

BIBLIOGRAPHY .......................................... 63

LIST OF TABLES

2.1 Comparison of sensitivity, load, and displacement...23
2.2 Sensitivity Calibration ............................. 28

2.3 Data from sample run ................................ 42

vi

CHAPTER 1

FIGURE

CHAPTER 2

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

LIST OF FIGURES

Schematic of optical measuring devices ..... 5

Preliminary designs after which the final

design was modeled ........................ l3
Transducer final design ................... l4
Schematic showing experimental setup ...... 15

Placement of 1000 ohm RSG's on the two
sets of cantilever beams .................. l8

Wheatstone bridge circuit with compensating

wire hook-up scheme ....................... l9
Cantilever beam model ..................... 20
Micrometer/Calibration apparatus .......... 25
Calibration curve ......................... 29

vii

FIGURE 2.9:

FIGURE 2.10:

FIGURE 2.11:

FIGURE 2.12:

APPENDICES:

FIGURE A.1:

FIGURE A.2:

Y deflection shown for preloaded
max

cantilever beams .......................... 35
Transducer placement along centerline of
bearing raceway cavity .................... 37
Design showing the flexibility and
adaptibality of the transducer's

measuring pads ........................... 139

Plot showing data from sample test ........ 42

Strain measurement over a short line segment

of length 10: (a) before deformation; (b)

after deformation [5] ..................... 49
Apparent strain as a function of temperature
for an advance alloy temperature compensated
strain gage mounted on a specimen having a
matching temperature coefficient of

expansion [5] ............................. 56

viii

CHAPTER 1

INTRODUCTION

I. THE PHYSICAL MEASUREMENT PROBLEM

During the evolution.of'roller and ball bearings, the
necessity for accurately measuring the cross-sectional
dimensions of bearing raceways to determine the proper
roller/ball size has arisen. Many techniques to solve this
problem have been developed in the past, but they were only
able to measure, with 1/1000" precision, the raceway of
bearings less than approximately 24 inches in diameter.
Measuring larger bearings with l/1000" precision has not yet

been possible.

The manufacturing process for most large—diameter bearings
is very labor/time intensive because of the precision
required for close running tolerances between rolling
elements and their matching inner and outer rings.
Therefore, a method needs to be established to cut assembly
time by at least a factor of two. This trial and error
assembly-time problem can be solved by developing a
measurement tool that indicates, exactly, the correct cross-

sectional dimensions of the bearing race cavity. This

dimensional measurement can then be used to determine the

proper roller/ball size.

To begin, the project's design criteria must be established,
and a measurement tool must then be designed to meet these

criteria.

The design criteria for the measurement device were governed

by the necessity for it to:

1. be a differential method of measurement;

2. be unaffected by the presence of the clearance groove

machined into the raceway;

3. indicate small axial and radial misalignments between

the two rings taken as a pair;

4. be user-friendly for appropriate use on the "shop floor"

and require minimum time on any given set of rings;

5. yield a continuous record of measurement and indicate
any deviations from raceway cross-section to give a

first approximation to actual cross-section;

6. accommodate different raceway configurations, for
example: (i) biangular roller, (ii) 4 point contact,

(iii) angular contact thrust;

7. achieve the proper balance between sensitivity and

range;

8. indicate on a read-out device, such as a computer, the

proper roller and/or ball size for the particular

bearing measured;

9. be cost effective.

These nine design criteria have been taken into account, and

the solution lies in maintaining the aforementioned criteria

in a measurement tool design.

Section II compares four potentially feasible techniques for

measuring dimensional quantities.

II. METHODS EVALUATED FOR DISPLACEMENT MEASUREMENT

Experimentalists are always challenged to find simple but

accurate techniques for dimensional measurement. Such

techniques include optical and mechanical methods as well as

resistance strain gage devices.

Some potentially suitable methods, such as optical,
mechanical, and electrical measurement devices are described
below; and they are evaluated against a few measurement

techniques used in industry.

A. Optical Methods

For this particular problem, the optical methods
considered were fiber optics and CCD (charged coupled
device) arrays. In this application, the fiber optic
measures dimensions by indicating the change in the fiber's
radii as it traverses the surface being measured, while a
CCD image sensor array measures displacement by indicating
the variation in optical mismatch along a planar grid
pattern [1]. Schematics of two such devices are shown in
Fig. (1.1). Both of these methods are capable of measuring
with considerable accuracy and sensitivity, but they have
drawbacks in reproducibility of data. Many inconsistencies
are incurred during the location of a datum or reference
position for data collection. Therefore, both the fiber

optic and CCD array fail items 1, 2 and 6 of the design

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criteria. An optical method might work for this type of
measurement problem, but with these drawbacks, attention was

diverted to other methods.

B. Eddy Current Probe

The eddy current probe is another measuring device option.
This probe emits a magnetic field which, when placed a
runninal distance from the target, induces a current flow on
the surface and within the target. Because this induced
current creates a circular pattern, it is called an eddy
current. It is this current that contains information about
the contour of the target's surface and distance variations
from the probe's reference position [2] . This device is
unaffected by lubricants in the bearing raceway, but one
drawback is that it is not easily adapted to analyzing
different (ie. rounded or arched), raceway configurations.
The eddy probe is capable of exibiting sufficient
sensitivity and range for accurate measurement, but again,
it would only be able to analyze the biangular race
configuration. Therefore, the eddy probe fails items 2 and

6 of the design criteria.

C. Load Cell

Currently, a module housing a load cell is being created.
The load cell is a force measuring device [3]. Each contact
surface (in this case, the walls of the race cavity)
creates different forces within the load cell; and any
variances in force are recorded as displacement. A
reference is established and successive readings are taken
and compared differentially to that reference as the probe
traverses the bearing raceway. This device has the
potential of satisfying all but item 9 of the design
criteria. Manufactured load cells cost approximately
$400.00 each, and.two would be needed for each transduceru
Preliminary tests of a load cell device in the bearing
cavity revealed sensitivities in a range from (0.30 to 0.35
mv/inch displacement). This approach was not pursued
further as it seemed inferior to and much more expensive

than the RSG transducer.

D. Electrical Resistance Strain Gages (RSG'S)

An electrical resistance strain gage (RSG), in elementary

terms, is a device containing a foil grid (resistor). When

the surface that the strain gage is bonded to deforms,

then a change in resistance is recorded. This is the basic
idea behind the resistance strain gage. As to application,
RSG's are frequently used to measure strain, and
displacement, and are incorporated as sensors in transducers
designed to measure such quantities as load, torque,

pressure, and acceleration.

An RSG device, when properly designed, should satisfy all of
the design criteria so attention was concentrated on this
approach. Since an RSG transducer was designed to evaluate
the bearing measurement problem, it is essential to describe
how an RSG transducer works and why it was used. An in-
depth description on the historical background of RSG's is
contained in the Appendix A, along with an illustrative
procedure on the definition of strain and how it relates to

displacement.

E. Measurement Techniques Used in Industry

Among the reasons to create a means of accurately measuring
bearing raceways is that both the inner and outer bearing
rings need to match one another in tolerance so as to glide
smoothly across the rollers or balls separating them.

Currently, very accurate methods are being used to evaluate

bearings that are less than 24 inches in diameter, but the
problem lies in the eccentricities and out-of—roundness of
larger bearings. Listed below are various methods used by

industry to evaluate the measurement of large bearings [4].

Dimensional Measurement
1. Bendix Auto - DC Measuring Machine
- diametral internal clearance
2. Bendix Cordax
- deviation from true position or shape
3. Bendix Proficorder
4. Bendix Indicorder
5. Rank Tallycentric
- deviation from true circle
6. Rank Precision Vertical Slide (with rotary
surface plate)
- deviation from squareness and cylindricity
7. Federal Comparator
- 2-point size calibration, 32/1 scale (for
master ring diameter calibration)
8. Rank Tallysurf
- deviation from true radius (transverse
surface finish)
9. Bendix Wavometer

- raceway waviness (dynamic)

10

Note that even though these evaluation methods are used,
there still exists a trial and error phase during the
insertion of rollers/balls into the bearing raceway. This
phase is very time consuming, since the procedure requires
that the rolling elements and spacers (188 rollers and
approx. 188 spacers in a 45" bearing) be inserted, one-by-
one, through the bearing's loading plug until the bearing
race is fully loaded. After the bearing is loaded, it is

tested using the following criteria [4]:

Testing Criteria

1. The ring's diametral preload is recorded and
the tolerance between mating rings is checked

to match (+ 0.0001-0.0005 inches).

2. The breakaway torque, which is the force
required to rotate the inner ring while the
outer ring remains stationary, is measured.
This measurement must yield 20-100 ft-lbs when
checked at 6 equally spaced locations on the
inner race, again, while the outer race is
stationary. If this measurement is out-of-

range, then an adjustment must be made by

11

changing either the roller size or spacer size.

3. If neither requirement is met, then the

bearing must be either re-machined or scrapped.

The testing procedure, listed above for the 45" biangular
roller bearing suggests that this process is extremely time
intensive. Therefore, finding a means of expediting the

"process" is critical.

III. SUMMARY

The purpose of this study is to determine whether or not
a measurement tool can be designed to measure, with more
precision than l/lOOO", the cross-sectional dimensions of a
bearing race cavity. This measurement is critical in
determining the proper roller/ball size to use in each

bearing assembly.

Now the discussion leads to the development of an actual
displacement transducer design. Other methods were
evaluated, and each had their own strengths, but the
transducer satisfied more of the design criteria and
'became the chosen approach to solving this unique

measurement problem.

12

CHAPTER 2

DESIGN AND RESULTS

I. FINAL DESIGN

The stages leading to the final design evolved from
consideration of several potential models, some of which are
featured in Fig. (2.1). Also, a large number of the design
criteria previously mentioned in Chapter 1 were taken into
considerathnn Specifically, the transducer is designed
with four cantilever beams (containing 2 resistance strain
gages each) mounted onto a cube, Fig. (2.2), and the

resistance strain gages respond to the deflection of the

beams.

The following section outlines the experimental measurement
setup and measurement scheme, while the remainder of the

chapter discribes each component of the scheme.

II. EXPERIMENTAL SETUP

The experimental setup is shown, schematically, in Fig.

(2.3). The transducer, which is located inside the bearing,

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generates a measured value of distance across each diagonal
flat of the raceway cavity. This dimension is sent directly
to two strain conditioners/indicators via 16 lead wires from
the RSG'S. The final output is a digital display of the
deflection in each individual set of beams. This digital
output is then fed into an A-D converter and is assimilated
by a computer program which reduces the data via software
written in Atari Basic (Appendix B). An Atari Computer was
chosen because a useful data acquisition program had already
been prepared and was readily available for a feasibility
study. Also, the Atari system can handle data character
strings of great length (48K less committed memory) quickly

and efficiently.

The computer program is written to read the values from the
strain gages on the tranducer, calculate the cross-sectional
dimensions of the race, plot the average dimensions, and
finally, indicate the correct roller and/or ball size for
each bearing configuration. This procedure of implementing
the transducer to accumulate valuable cross-sectional
dimensions is a very simple procedure that will expedite

assembly time for each bearing.

17

III. TRANSDUCER CONSTRUCTION

Critical elements of the transducer design, including the
placement and wire hookup of each RSG, are outlined in this
sectixni. The procedure in assembling the RSG transducer is
quite methodical and begins by applying eight RSG'S to each
set of cantilever beams, Fig. (2.4). Two lead wires
(approx. 30 gage) are soldered to each gage and then woven
through the cube's clearance hole enroute to two strain
indicators/conditioners. Eight wires (wires 1-8) represent
Channel #1, while the remaining eight wires (wires 9-16)
hook into channel #2. Each channel has its respective
indicator. The indicators were set-up in a Wheatstone
bridge circuit configuration with four active gages to
alleviate temperature drift in the circuit. The gages
themselves were compensated, but the circuit also had to be

compensated to minimize errors. See Fig. (2.5).

With the transducer design complete, the next step was to
verify the target of 10-20 micro-strain sensitivity with a

theoretical calculation.

The next section illustrates a sample theoretical

calculation.

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wire hook-up scheme.

20

IV. THEORETICAL STRAIN CALCULATION

Verification of the target sensitivity begins with the

calculation of strain (based on beam theory) and by the

equation:

6 - My/EI
(2.1)
where: I - moment of inertia (bh3/12)
y - distance from centroid (0.5 * a)
M - moment arm (force * distance)
E - Young's Modulus (28 x 10E6 psi)

stainless steel

The cantilever beam parameters are found in the Fig.(2.6)

below:

 

21

Values for a, b, h, and L are:

b - 0.10 inch
a,h - 0.020 inch

L - 0.225 inch

To calculate I and y let:

I - bh3/12 - (0.10)(0.02)3/12 - 6.67 x 10E-8 in4

y = 0.5 (0.02) - 0.01 in

Now that each component is calculated, strain can be

determined as:

e = My/EI - Force [(0,225) (0.01)]/[(6.67 x lOE-8)
*(28 x10E6)]

- 1205 p strain * Force

(2.2)

The calculation for displacement can now be determined.

22

Let displacement Y - -FL3/ 3EI
max

(2.3)

where: F - load (pounds)

L - lever arm
In this sample calculation let F - 0.008299 pounds, so:

Ymax - -(0.008299) (0.225)/3(EI) - 17 p inch

This calculation demonstrates that the amount of maximum

deflection (Ymax) at the end of one cantilever beam equals

17 micro-inch at a load of 0.0083 lbs. This deflection
'value falls into the strain range of 10-20 micro-strain and
verifies that by using RSG's in a cantilever beam
configuration ample sensitivity is achieved. Table (2.1)
shows hOW'the 10-20 micro-strain sensitivity might be
achieved.by'inserting particular values of force (column 1,

Table (2.1)) into equation (2.3).

Theoretically, the sensitivity was proven to fall in a
range from 10-20 micro-strain. It now remains essential to
calibrate and verify, experimentally, that the RSG

transducer achieves a calibrated sensitivity comparable to

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24

the theoretical sensitivity. The next section describes

this calibration procedure.

V. CALIBRATION PROCEDURE

To determine, experimentally, the sensitivity of the RSG

transducer, a calibration scheme was established by
inserting the transducer into an X-Y micrometer apparatus
that separately induced compressive loads onto each set of
cantilever beams, Fig. (2.7). As each set of beams was
deflected along both the X and Y axes, the displacement in
the beams was recorded in terms of a voltage difference
across each set of RSG hookup wires. Therefore, two
corresponding values of voltage and displacment were
recorded. These two corresponding values establish points
on a calibration curve, and the slope of the curve indicates

the sensitivity of the system.

The preceding calibration also includes calibrating each
channel. The calibration constant to convert'duaudcro-
strain or milli-voltage readings to readings of displacement
was simply adjusted on each indicator by rotating the span
dial. Utilization of the calibration constants will be

outlined further in section IV.

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The transducer was now calibrated for differential
measurement, but it still remained necessary to develop a
means for obtaining the absolute calibration measurement of
the bearing cavity. This can be done in any number of ways.
The most effective approach is to machine at least two
different biangular cavity configurations with dimensions

varying slightly above and below the known range of the
machined cavity size. For example, the bearing cavity is
nominally machined with a cross-sectional dimension of
(0.625 +/- 0.0002) inches; it is necessary to machine two
other cavity configurations with dimensions of (0.625 +
0.0002 and 0.625 - 0.0002) inches, respectively. An Optical
Comparator or Jo-Blocks can be used to verify the two
dimensions. Note that the precision of Jo-Blocks is on the
order of one micro-inch, while the Optical Comparator can

achieve only 0.0001" precision.

Now plot the two cavity configurations. This results in a
calibration curve evaluating displacement and voltage. The
slope of the calibration curve is then used as the zero
reference calibration constant. This zero reference is used
in determining the absolute bearing cavity dimension. Note
that the transducer must remain linear within this

calibration range. A sample case is illustrated in

27

Table (2.2) and Fig (2.8). The sensitivity of the system is
found to be 6.1 mv/0.0001" displacement for channel #1 and
2.5 mv/0.0001" displacement for channel #2. The difference
between these two sensitivity values is caused by the
dissimilar placement of each RSG on the top and bottom sides

of the cantilever beams.

This calibration technique establishes the absolute size of

the bearing cavity. Now the deflection values recorded off’
the transducer's two sets of cantilever beams, as the
transducer traverses the race cavity, can be subtracted from
the absolute cross-section of the cavity. As a check, this
calibration test should be done both before and after the

actual measurement has taken place.

A computer subroutine was written to handle the calibration.
measurements for absolute dimensions, as well as to compare
the incoming measurements from the transducer. An average
of the two sets of measurements is calculated, separated
from the absolute cavity size, and this determines the
correct roller/ball size to be used. Iflxflnmtely, a roller
size with a clearance fit throughout the circumference of

the bearing is sought.

28

CALIEZATION ME

Reference Mperature : 72 F
Excitation Voltage : 5 volts dc
RSG ID : SK-O9-060CD-10C
gage factor . : 2.11+/- 0.3% at 24 degrees C
Ohms per use : 1000 =/- 0.3% at 24 c
Transducer sensitivity :
channel #1

6.1 mv per 0.0001 inch disp.
channel #2
Range

2.5 mv per 0.0001 inch disp.

0-0.004 indies displ.

mm 2.2: Sensitivity Calibration

29

CHANNEL III SENSIIIVITY = 6.1 nv/OIIOOI INCH DISPLACEMENT
CHANNEL Ila SENSITIVITY = 2.5 I'IV/IIIIIIIII INCH DISPLACEMENI

SENSITIVITY/CALIBRATION CURVE

 

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0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0(x10-3).
DISPLACEMENT (INCHES)

llllIIIIIIIIIIIIIIIIIlllIllllIllllIllllIlIllIIIllIIlllIlIlIIlIllIllIlIllllIllIIIIIIIIIIIIIIIIIIIIII

 

 

 

 

 

 

 

FIGURE 2.8: Calibration Curve

30

The following section outlines the physical setup of the
computer program and describes the communication process

between the transducer and the computer.

VI. COMPUTER PROGRAM PHYSICAL SETUP

The computer program is listed in Appendix B, but an

explanation of the physical set-up is pertinent.

The strain indicators displayed displacement in each set of
beams, via channels #1 and #2, therefore an interface was
necessary to relay this information to the computer. This
communication was achieved by hooking two cables (positive
and negative) into each indicator's voltage output jack and
connecting them to a Starbuck A/D converter [7]. Two
channels were evaluated, so two separate channels were used
on the A/D converter. The voltage was checked during the
calibration.process and was offset by a factor of 1 (volt)
to insure a.positive voltage reading for all displacements.

The Starbuck A/D converter required positive voltage inputs.

Next, a single hook-up was made from the A/D converter to an
R8232 interface (port 1). This hook-up enabled

communication between computer, A/D converter, plotter, and

31

printer. Only one communication port was used, and the two
channels remained as separate strings of information; so a
comparison between the two sets of beams could be made
throughout the investigation. As the voltage information
was read into the computer it became necessary to convert
this number to a tangible displacement and ultimately into
the actual cross-sectional dimension of the bearing raceway.
(UniS‘was done using the calibration factors and can be seen

in the program as, "indicated voltage input converted to:"

1. indicated displacement
2. indicated diagonal channel size
3. actual diagonal channel size
* 4. correct roller/ball size to use in the

bearing.

The analog input of voltage to the converter is computer
keyboard activated, and up to 100 data points along the
bearing circumference can be analyzed in a single run. As a
recommendation for further study, it would be advantageous
to create a randomized continuous sampling of points along

360 degrees of the bearing.

32

VII. COMPUTER CALIBRATION SUBROUTINE

'To expand on the computer's contribution to the calibration

calculation, an example procedure follows:

Step 1 - record dimensions and voltages for each
calibration cavity. Disks 1,2 refer to
calibration cavity disks of a particular
size, while voltages 1,2 refer to the
corresponding voltages created by inserting

the transducer into both disk 1 and 2; i.e.

disk 1

0.624" [001]

disk 2 - 0.626" [002]

voltage 1 0.392 volts [CV1]

voltage 2 0.267 volts [CV2]

Step 2 - calculate the slope of the voltage vs

displacement curve; i.e.

CV2 - CV1

51°pe ' 002 - 001

- 62.5 v/inch

33

Step 3 - insert the transducer into the bearing and take

a voltage reading; i.e.

average voltage [AV] - 0.331 v

Step 4 - calculate the interpolation increment; i.e.

increment [INC] - AV - CV2 - 0.064

Step 5 - calculate the absolute dimension of the cavity;

i.e.

absolute dimension [AD] - disk2 - (inc/slope) = 0.624976"

This procedure is incorporated into the computer program

listed in Appendix B.

Section VIII describes the experimental procedure and

illustrates how the design criteria is satisfied by the RSG

transducer.

34

VIII . EXPERIMENTAL PROCEDURE

Before the transducer is inserted into the bearing, the
geometry of the bearing cavity must be established. This is
done by inserting three balls, via the loading plug hole,
into the gap between the bearing's mating rings. Each ball
is then positioned every 120 degrees to allow the inner ring
to rotate freely with respect to the outer ring. At this
stage, the bearing cavity is ready to receive the

transducer.

The transducer is inserted, via the loading plug hole, into
the bearing. After insertion, the transducer traverses the
bearing raceway, via rotating the inner race manually with

respect to the outer race, and measures the cross-sectional
variation within the dimensions of the cavity by indicating
deflection in each set of cantilever beams. It is worth
noting again that the cantilever beams located on the
transducer were preloaded by the walls of the race cavity to
ensure measuring contact at all times. An illustration of
the preload configuration is found in Fig. (2.9). The
sixteen wires from the transducer's RSG'S were then fed
through the clearance gap at the top of the race cavity and

were hooked into their respective channel indicators.

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36

As the transducer accumulated dimensional readings along the
bearing's circumference, there was an indication that some
sagging or misalignment was occurring between‘dnanwting
rings. This sagging was probably the result of the outer
ring being stationary, while the inner ring was suspended by
the three balls located 120 degrees apart. Again,
implementing the three balls was essential to the rotation
of the inner ring with respect to the outer ring.
Transducer readings were taken at locations near each of the
three balls, as well as at varying distances between each
ball” It became apparent that the balls alleviated most of

the sag between rings.

A complete description of how the transducer satisfies the

design criteria follows.

The transducer is:

A. Unaffected by the clearance groove in the raceway. In
fact, the clearance groove, which is located in the
center of both the inner and outer ring, is used as a
guide for the transducer's positioning (compression) pin
as it traverses the circumference of the raceway,

Fig. (2.10).

37

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38

Able to measure relative out-of—roundness for the rings
as well as radial and axial misalignment between the two
rings. In preliminary readings from the transducer, it
became apparent that if a reading was taken directly
next to one of the three balls, located every 120
degrees, then misalignment between rings virtually
cancelled. This must mean that the 5/8" + 0.001 size
and tolerance on each ball is sufficient to take up most
of the slack or gap (misalignment) existing in the
bearing race cavity. Misalignment/out-of-roundness was

apparent at arbitrary distances from each of the raceway

balls.

Able to accommodate different raceway configurations (i)
biangular roller, (ii) 4 point contact, and (iii)
angular contact thrust. This feature is built into the
transducer design and is located at the end of each of
the cantilever beams, Fig. (2.11). Each beam

achieves a preloaded (raceway flat) contact, at the
extreme ends of the beams. Kel-F (a common
flourocarbon) was selected as the material used at the
contact surface because of its very low friction

factor. Kel-F insured an easy, gliding, measuring

surface between the bearing race and the transducer.

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40

The shape or configuration of these pads can be changed
to accommodate the different raceway configurations and
dimensions; therefore, a common transducer "module" can
be created for each "nominal" raceway diameter. For
example, if 1" diameter balls are used in a particular
raceway, then a transducer can be used with a l" radial

pad configuration.

D. Able to achieve a proper balance between sensitivity and
range. Qualitatively, the sensitivity must allow the
detection of small dimensional changes within the
comparatively large cross-sectional dimension of the
bearing race cavity. Preliminary calculations of
sensitivity revealed a proper balance of sensitivity
and range by achieving a range of 10-20 micro-strain for

beam deflections of 1/1000".

A sample test was conducted to verify the experimental
procedure, see Table (2.3), and a plot was generated from
the data; this is shown in Fig. (2.12). Note the location
of the loading plug along each curve. At this location

there appears to be a relaxation in both sets of beams which
indicates that this location could possibly be used as a

reference for initial calibration of the transducer.

41

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43

IX . SUMMARY

The critical elements of the RSG tranducer design, along
with a sample run verifying the transducer's validity, were
outlined in the preceding sections. Theoretical
calculations revealed that the transducer design could
maintain the desired sensitivity (at least lmv/0.000l"
displacement), while the experimental procedure verified
that sensitivities as high as 6.1 mv/0.0001" displacement
could be achieved by a single set of measuring cantilever

beams .

The computer program, though written in Atari Basic, proved
very expedient in assimilating the strings of voltage
information inputed by the A/D converter. It is worth
noting that Atari Basic is similar to other versions of
Basic; therefore if desired, it can be easily converted to

suit the user's needs.

The following chapter contains concluding remarks, as well

as recommendations for further research.

44

CHAPTER 3

DISCUSSION AND CONCLUSIONS

I. Experimental Results

At the current level of development the means of accurately
measuring raceway cavities in large bearings is inadequate.
This creates the need to supply industry with a measurement
tool which alleviates this problem. The measurement tools
described in this study, primarily the electrical resistance
strain gage, offer a means of quickly and accurately solving
the time-consuming problem of trial and error assembly of

large bearings.

In the preliminary stages of the study it became apparent
that an RSG transducer could feasibly be designed to
maintain accuracy, sensitivity, and range while ultimately
collecting tangible data about the cross-sectional area of
the bearing raceway. Theoretical calculations were made
before and during the calibration process and comparisons
with experimental results remained within a "feasible"
working range of 10-20 micro-strain per 1/1000"

displacement.

45

In the final stages of the measurement analysis, during the
process where the transducer was traversing the bearing
cavity and the computer was actively gathering data, a
sample test:was actuated to trace approximately 300 degrees
of the bearing's circumference. Ten data points were taken
on each of the two independent channels. The results are
listed in Table (2.3) and Fig. (2.12). As stated in the
calibration procedure, the actual bearing cavity size was
determined and used as a reference to compare differentially
with each set of deflections from the cantilever beams.
The nominal machined cross-sectional size of the raceway was
0.625 +/- 0.0005 inches while the experimental average
cross-section was generated to be 0.624976 inches. The
roller size machined for the 5/8" race cavity was 0.594 x
0.625 dia.+/— 0.00020 inches. This roller is therefore
compatible with this set of bearing rings, as long as the
race cavity diameter does not become less than 0.624976".
The testing criteria found in chapter 1, relating
breakaway torque and preload requirements, will still have
to be checked to verify the roller selection determined by

the transducer.

46

II . FURTHER STUDY/RECOMMENDATIONS

This research began as a feasibility study to determine if a
device could be developed to accurately measure the cross-
sectional dimensions of raceway cavities in large bearings.
This open-ended endeavor led to many creative ideas which
led to designing the RSG transducer. This tranducer has
been shown to satisfy the established design and testing
criteria, but at this time it is still in the prototype
stage. Further recommendations therefore are focused on
developing this prototype to a final manufacturable design.
Ideas should also be focused on developing the software into
a more universally compatible form, i.e. convert Atari Basic

into BasicA or Quick Basic.

Another area which was not pursued was comparative modes of
data collection. The existing physical setup evaluates,
both statistically and statically, ten groups of ten data
points around the bearing circumference, and the
communication between the transducer and computer is
keyboard-initiated. It would be more advantageous to record
the data continuously while traversing the bearing. This
‘modification can be easily implemented.into the existing

computer program.

47

This study remains as an investigation of a unique
measurement problem, but the preceeding pages have supported
the fact that the RSG transducer is a feasible and creative
means to a positive solution of accurately measuring raceway

cavities in large bearings.

APPENDICES

A - HISTORICAL BACKGROUND ON RSG’S

B - COMPUTER CODE

48

APPENDIX A

I. HISTORICAL BACKGROUND ON ELECTRICAL RSG'S

A. Definition of Strain and How it Relates to Displacement

In elementary terms, strain is a change in length of a line
segment divided by its original length. The concept of
strain is also thought of in terms of deformation and
displacement of a certain specimen surface; in this case a

cantilever beam.

The general relationship for in-plane strain is given

by:

exx - (lX - lo)/lo - Au/Ax

(A.l)

where Au lx - 10 is the deformation in the x direction
over the length of the line segment 10 - Ax, see Fig. (A.l).

Strain measured in this manner is an average because of the

limitation incurred by the paramenter 10 (the gage length).

49

 

 

 

(a)

 

 

 

 

 

 

FIGURE.A.1: Strain measurement over a short line segment of
length 10: (a) before deformation; (b) after

deformation [5].

50

To curcumvent this error, great effort has been focused on

reducing the gage length 10’ but two factors complicate
matters. Mechanical difficulties are encountered when 10 is

reduced because the gage, inevitably, has a finite size
limitation, and the strain being measured is a very small
quantity. Suppose, for example, that strain or displacement
measurements are to be made with an accuracy of i l p in/in
over a gage length of 0.1 inch. The strain gage must then
measure the corresponding displacement to an accuracy of i l
x lOE-6 x 0.1 - i l x lOE—7 inches or one txn11nillionth of
an inch. This size and accuracy limitation remains a

problem [5].

B. Properties of Resistance Strain Gages

Historically, the development of strain gages is based on
mechanical, optical, electrical, acoustical, and pneumatic
principles. No single gage system has all the properties
required for an optimum gage, but some of the optimum
characteristics used to judge the adequacy of a strain gage

system are listed below [5].

l. The calibration constant for the gage should be stable

and should not vary with time or temperature.

10.

51

The gage should be able to measure strains with an
accuracy of i l p in/in over a strain range of 10%.

The gage size i.e., the gage length 10 and width wo,

should be small so that the strain at a point is
adequately approximated.

The response of the gage, largely controlled by its
inertia, should be sufficient to permit the recording
of dynamic strains.

The gage system should promote on-location or remote
read-out.

The output from the gage during the read-out period
should be independent of temperature and other
environmental parameters.

The gage and the associated auxiliary equipment should
be economically feasible.

The gage system should not involve overcomplex instal-
lation and operational techniques.

The gage should exhibit a linear response to strain.
The gage should be suitable for use as the sensing
element in other transducer systems where the unknown
quantity, such as displacement, is measured in terms of

strain.

52

Proper consideration was placed on all of the aforementioned
criteria before developing the displacement transducer in

this study.

In addition to the criteria listed above, it is also worth
noting that in selecting a gage for a given application,

gage length 10 is one of the most important considerations

[5]. The second most important characteristic is gage
sensitivity. Sensitivity is the smallest value of strain
that can be read on the scale associated with the strain
gage. The term sensitivity should not be mistaken for
accuracy or precision, since very large values of
magnification can be built into a gage to increase its
sensitivity; but friction, wear, and deflection introduce
large errors which limit the accuracy.[5] The choice of a
gage is dependent upon the degree of sensitivity required,
and a very high sensitivity does not necessarily increase

the complexity of the measuring method.

The third basic characteristic of a strain gage is its
range. Range represents the maximum strain which can be

recorded without resetting or replacing the strain gage.

53

The range and sensitivity are interelated since very
sensitive gages respond to small strains with appreciable
indicator deflections and range is usually limited to the
full-scale deflection of the indicator. To obtain
reasonable performance between sensitivity and range it is

often necessary to make a compromise between the two [5].

C. Types of Strain Gages

The major focus of strain gages is to determine the motion

between two points a distance 10 apart. The principles

employed in strain gage construction classify the gages into
the following four groups [5]:

1. Mechanical

2. Optical

3. Electrical

4. Acoustical

The electrical foil strain gage system or transducer was
chosen as a measuring device because of its size

adaptability and superior sensitivity and range.

The preceding section outlined the background of RSG'S and

how they can be used to measure displacements. The

54

following section details the performance characteristics
that support implementing the electrical resistance strain

gage as the measurement tool.

II. PERFORMANCE CHARATERISTICS OF ELECTRICAL RESISTANCE

STRAIN GAGES

An electrical resistance strain gage (RSG) is simply a
resistor mounted on a flexible carrier that is bonded to a
component part, and it exibits the ability to accurately
monitor the changes in resistance that<xnmespond to
particular deformations in the component part. The gage
resistance for the 1000 ohm RSG's used in this study is
accurate to approximately i 0.3%, and the gage factor, which
is simply based on a lot number calibration, is certified as

2.11 i 1.0%.

Though these factors are important, strain accuracy is still
directly proportional to how uniformly the gages are applied

to each specimen.

When a testing procedure is undertaken using RSG'S, and the
specimen is subjected to variances in temperature, then

attention must be focused on whether or not the changes in

55

resistance are resulting from strain or temperature; see
Fig.(A.2). When the ambient temperature changes, four
effects that occur are:

1. Changes in the strain sensitivity 8 in the alloys grid

A
2. Gage grid either elongates or contracts (Al/l a aAT)
3. Carrier either elongates or contracts (Al/l - fiAT)
4. Resistance of the gage changes; due to the influence
of the temperature coefficient of resistivity in the

gage material (AR/R - 7AT)

Note that the gage reacts to temperaturelmufllixxthe same
way as it reacts to mechanical strain due to an applied
load, and it is impossible to distinguish between the two.
If the gage alloy and the carrier have the same thermal

coefficients of expansion, then the term (AR/R)AT vanishes.

The gage may still register a change in resistance or strain
in the material, but this becomes an apparent strain which

actually does not exist in the specimen [6].

Today gages can be purchased that are already temperature
compensated, but it is still necessary to compensate the
electrical circuit; this can be done with four active gages

in a Wheatstone Bridge Circuit, refer to Fig. (2.5).

56

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FIGURE Am2: Apparent strain as a function of temperature

for an advance alloy temperature compensated
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matching temperature coefficient of expansion

[5]-

APPENDIX B

COMPUTER CODE

S7

1 ? "THIS MAM IS DESIGNED TO GENERATE EXACT DIMENSIONS
OF THE RESPECTIVE BEARING RACEWAY":
? "THE CDRRECI‘ ROLLER/BAIL SIZE WILL ALSO BE INDICEX‘I'ED"

? II n
? I! ll
DIM

$(10) .NN$(10) .B$(100) .C$(100) .D$(100) .E$(10) .V1(10.100) .V2(
0.100).BRB$(1).FPC$(1).FPR$(1).ACI$(1)

7 com 1448

8 com 1501

9 0010 1504

10 com 1523

11 ? "THE PDIIDWING ARE INIEEAcrIVE QUESTIONS, PLEASE
ANSWER"

12 0010 3000

13 ? "HmmmGEaJPsomesmchomIS?MAxxs
10":me N$:N=VAL(N$) :NN$=STR$ (N*10) :? N

18 NN=10*N:? NN

21 PDKE 82,0

25 CLOSE #1

28 ? n n

29 OPEN #1,13,0,"Rl:"

31 ? "31"

32 x10 36,#1,10,0,"R1:"

35 x10 38,#1,64,93,"R1:"

37 x10 40,#1,0,0,"R1:"

42 PRINI‘ #1,cm$(27) ;"01";an$(13);

45 B$=" ":INPU'I‘ #1,B$:? "45",B$

48 ? "EMEDIATE ANALOG INPUT '10 BEGIN"

49 ? II n

51 com 108

52 REM

108 ? "THE INDICATED VOLTAGE IS:":? ""

109 ? "CHANNEL #1, W, "emu. #2";

110 DIM KZ$(3)

111 FOR I=1 '10 NN

112 INPUT KZ$

114 PRINT #1,"IA1";Gm$(13);

116 INPUI‘ #1,8$:V1(I,1)=I:V1(I,2)=((VAL(8$(4)))/51)
117 PRINT v1 (1,2),"",

118 PRINI' #1,"IA2";C}R$(13);

120 INPUT #1,D$:V2(I,1)=I:V2(I,2)=((VAL(D$(4)))/51):PRmr
V2(I,2)

121 NEXT I

122 ?llfl

123 ? "THE INDICATED DISPLACEMENT 15:"

124 ? III!

125 ? "CHANNEL #1", W, "GIANNEL #2";

HZO‘bUN

127
129
131
135
141
143

148 .

150
151
152
153
154
156
158
162
168

58

DIM KBZ$(3)
FDR I=1 10 NN
INPUT KBZ$
V1(I,2)=(V1(I,2)*392.31):PRD1'I‘ v1(I,2) ,m',
V2(I,2)=(V2(I,2)*392.31) :PRINI' v2(I,2)
NEXT I
7 "fl
? "THE AMOUNT OF DEHEchw IN EACH SET OF BEAMS IS:"
? fl"
3 "0mm, #1", II", "mm #2";
"fl .
DIM KZS$(3)
FOR I=1 '10 NN
INPUT KZS$
V1(I,2)=(((V1(I,2)-100)/1000)/61000) :PRIN'I' v1(I,2) , "",
V2(I,2)=(((V2(I,2)-100)/1000)/61000) :PRINI‘ v2(I,2)
I

170 NEXT

171
172
173
174
176

? "":? "WHAT IS “THE ABSOIIJTE DIMENSION OF THE CAVITY?"
? "THE ACTUAL DIASDNAL CHANNEL SIZE 18:"

7 ll"

? "QIANNEL #1","","C1~IANNEL #2";

DIM I<AZ$(3), Tor(10,10), TAV(10), ‘IV(10), AD(10)

177 ‘IUI'=O

178
180
184
190
211
216
230
231
233
234
235
236
237
238
240

FOR I=1 '10 NN

INHJT ICAZS

V1(I.2)=((V1(I.2)'(AD)*('1))=PRINT V1(I.2) ."".
V2(I.2)=((V2(I.2)‘(AD)*("1))=PRINT V2(I.2)

?II"
? "I!

TV-‘-(((V1(I.2))+(V2(I.2)))/2)
‘IUI‘='IUI‘ + TV

? II n

PRINT "THIS IS THE CDRRECT ELDER/BAIL SIZE FOR THE

RESPECTIVE BEARING: (DIMENSIONS ARE IN INCHES) "

245
300
350
354
375

6010 300
CLOSE #1:?

? ll"
? ll"

? "RAW DATA IS STOREDAS Two SIRINGSA$(I) AND Z$(I) OF

LENGIHION: YCIJCANPRINTIT'IODISCORPAPER"

380
381
385

? ll"
? "ll

?"Y(IJCAN'IHENPIOI‘ORIRINI"IODISCORIRINTER;'IHE

VARIABLES ARE V1(L,I) AND V2(L,I) WITH DIM N x 10"

 

59

499 INPUT BS

500 ?:? "DO YOU WANI‘ A SCREEN PLOT? (Y,N)":B$=" ":INPUT
B$:IF B$="Y" THEN GOSUB 515

502 ? "DO YOU WANT A PAPER PLOT? (Y,N)":INPUI‘ B$:IF B$="Y"
THEN 1200

503 ? "SAVE VOLTS OR RAW DATA TO DISC? (Y,N)":INPUT 13$le
B$="Y" THEN 505

504 G010 508

505 ? "SAVE VOLTS (V1), (V2) OR DIGITAL DATA STRINGS (A),(Z)
TO DISC—WHICJ-I?(V,A)"

506 INPUT B$:IF B$="V1" THEN GOSUB 1400

507 IF B$="A" THEN GOSUB 1600

508 ? "STARI'mmTANDPLOTm'mESO\7ERWITHSAMEDATA?
(Y,N)":INPUT B$:IF B$="Y" TEEN 499

509 ? "START ALL. OVER? (Y,N)":INHJ'I' B$:IF B$ = "Y" THEN
GRAPHICS O:END

510 IF B$<>"Y" THEN GRAPHICS 0:END

515 I=1:J=1:X=9:C=1

520 GRAPHICS 7:OOLOR 1

522 GOTO 1100

528 GOTO 698

529 GOTO 502

698 REM "PLOT OF CHANNEL #1"

700 OOIOR c

702 INPUT 1<zszx=19

703 PLOT x,TAV + 35

705 FOR I = 1 TO NN

718 Y = ((TAV + 35)-((((AD)-(V1(I,2))))*10000000))

73o x=x + (10)

731 DRAWLO X,Y

740 NEXT I

750 REM "PLOT OF CHANNEL #2"

755 OOIOR c

756 INPUT KBZ$:X=19

757 PLOT x,TAV + 35

758 FOR I=1 TO NN

759 Y = ((TAV + 35)-((((AD)-(VZ(I,2))))*10000000))

760 x=x + (10)

761 DRAWTO X,Y

762 NEXT I

800 ? "x SCALE (NUMBER OF POINTS)=";NN$:? "Y SCALE
(DISPLACEMENT) =" ;TAV: ?" DONE--";

802 ? "HIT RETURN TO GET GiOICES":mPLIT BS

899 RETURN

900 ? "STOP"

1100 ? ""

1110 PLOT 9,70:DRAWIO 9,1

1115 PLOT 8,70:DRAWTO 11,70

1120 PLOT 8,1:DRAWIO 11,1

1135
1140
1141
1142
1143
1144_
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1190
1191
1200
1201
1202
1203
1204
1205
1210
1220
1225
1230
1240
1250
1252
1255
1260
1265
1270
1280
1284
1285
1287
1290
1295
1399
1400
1448
1449
1450
1451

60

PUJP
PIOT
FEET
PUD?
PTOT
PUJP
PTDT
FTOT
PDOT
PIOT
PLOT
PUIP
PIUI'
PDOT
PUJP
PDUT
PLOT
PLOT
GflflO 698

GOTO 503

REM : PLOT WINE FOR 1020 PIOI'I‘EIR

Gtflo 503

TRAP 40000:TRAP 1204

GOIO 1205

? "PRINTER 0m":GOIO 502

CILEE2#1;CIOSE #2

OPEN #2,8,0,"P:"

? #2;"ll

c=1:? #2;"C"; C-l

? #2; "MSG, 0*x1,80,5"

? #2; "Mso, -950*x0 , 95 , 10"

z=INT (900/(12*N)) +1:IF N>20 THEN z=4
Q=N:IFQ>C*20 THEN Q=C*20

Ito

? #2; "C";C-1

Y=80*’IUI‘((C-1)*20 +1,1)

? #2; "M";50 + Y1; ",";‘I‘

POR L=(C-1)*20 +1 TO Q:POR I=1 TO 10

Y = 80*‘IUI' (L,I)

? #2;"D";50 + Y;",";T

T = T + 2:? T,

NEXT IzNEXI‘ L

c = C + 1:IF ((C-1) *20)-N<0 TEEN 1252
CTDSE #2:RETURN

GOIO 1599

? "WHRI'TYPE OF BEARING IS BEING ANALYZED?"

? "I!

? "CHOOSE THE BEARING TYPE"

? "ll

9,35:DRAWTO 159,35
59,31:DRAWIO 59,39
7,45:DRAWIO 11,45
7,55:DRAWTO 11,55
7,65:DRAWTO 11,65
7,25:DRAWIO 11,25
7,15:DRAWTO 11,15
7,5:DRAWIO 11,5
19,34:DRAWIO 19,36
29,34:DRAWID 29,36
39,34:DRAWTO 39,36
49,34:DRAWTO 49,36
59,34:DRAWIO 59,36
69,34:DRAWTO 69,36
79,34:13RAWIO 79,36
89,34:DRAWTO 89,36
99,34:DRAWTO 99,36
109,34:DRAWLO 109,36

61

1452 ? "HIE = BIANGULAR ELIER BEARING"

1453 ? "FPC = 4 POINT MCI BEARING"

1454 ? "FPR = 4 POINT RADIAL (DNI'ACI' BEARING"
1455 ? "ACI' = ANGUIAR CDNI‘ACI‘ THHJST BEARING"
1456 ? ""

1457 ? ""

1497 INPUT C5

1499 IF C$ = "BIB" THEN ? "'IHE AWESIS OF A BIANGUIAR
ROLLER BEARDIG FOLILMS"

1500 GOIO 8

1501 ? ""

1502 IF GS = "FPC" THEN ? "THE ANALYSIS OF A 4 POINT CDN'I'ACI‘
BEARING 170110178"

1503 G010 9

1504 ? ""

1520 IF C$ = "I'M?" THEN ? "THE ANALXSIS OF A 4 POINT RADIAL
CDN'IACI' BEARING FOLICNS"

1522 GCIO 10

1523 ? ""

1530 IF GS = "ACI‘" THEN ? "THE ANALYSIS OF AN ANGHAR
CDN'I‘ACI‘ ‘IHHJST BEARING FOLILWS"

1532 0010 12

1599 RETURN

1600 ? "NOT AVAILABLE"; GOIO 1799

1799 RETURN

1800 ? "NOI' AVAIABIE"; 6010 2099

2099 RETURN
2200 "******************************************H

2300 "******************************************N
2400 " CALIBRATION W"

2450 "******************************************fl
2455 fl******************************************"

2500 "n

2600 ? ""

3000 DIMCV1(10),cv2(10),CD1(10),CD2(10),DR1(10),DR2(10),
SIP(10) .AV(10) .INC(10) .AV2(10) .SLP$(1) .AD$(1) .AV$(1)
3005 ? ""

3006 ? ""

3007 ? "THE GALIBRATION OONSEANTS FUR ABSOLUTE DIMENSIONS OF
THE BEARING RACEWAY CAVITY.ARE.AS FOLDOWS:"

3008 ? ""

3009 ? ""

3010 ? "WHAT ARE THE DIMESIONS OF THE Two CALIBRATON
CAVTTIES?":INPUT DKI:? DK1:? "DISK #1 = 0.6248"

3011 ? ""

3012 ? ""

3015 INPUT DK2: ? DK2: ? "DISK #2 = 0.6252"

3016 ? ""

3017 ? ""

0" 0‘) 0‘) 0‘) 0‘) 0‘)

62

3020 ? "WHAT Is THE WLTAGE AND DISPLACEMENT ASSOCIATED WITH
BOTH OF’THE CALIBRATION CAVTTTES?"

3021 REM

3022 ? ""

3023 ? "VOLTAGE FROM DISK #1=":INPUT CV1:? cm

3024 REM ..

3025 ? "VOLTAGE PROM DISK #2=":INPUT CV2: ? CV2

3026 REM

3027 ? ""

3030 ? "DISPLACEMENT PROM DISK #1=":INPUT (131:? C131

3031 ? ""

3032 ? "DISPLACEMENT PRLIM DISK #2=":INPUI' c132: ? C02

3033 I."

3037 REM

3038 ? ""

3040 ? "me THE SLOPE OF THE CALIBRATTON CURVE TO
DETERMINE TEE ZERO REFERENCE CAIIBRATON CONSTANT"

3041 ? I".

3042 ? ""

3045 ? " SLOPE = SENSITIVITY, WHICH EQUALS ..."

3047 INPUT SLP$:SLP = (((CVl-CV2)/(CDl-CDZ)/10)):? SLP$:?
"(NV/0.0001 INC}! DISPLACEMENT)"

3048 ? ""

3049 ? ""

3050? "DITERPOLATEBETWEENTMETWOVOLTAGEVALUESTOPIND
'IHE VOLTAGE VALUE FOR ABSOLUTE 0.625 +/- 0.0002 INCHES"
3051 ? ""

3053 ? "INPUT THE ABSOLUTE mm READING TRIM THE
VOLTMETER:"INPUT Av: ?.AV

'0

3054 ? "N

3055 ? "ABSOLUTE VOLTAGE = AV = (CV1 + (INC*(CV2-CV1)))"
3056 ? ""

3057 ? "OOMPUTE 'IHE INCREMENT (INC) FOR THE EQUATION (AV) :"
3058 ? ""

3059 INC = CV1-AV:? INC

3060 ? ""

3075 ? "THE ABSOLUTE DISPLACEMENT = (AD) AND IS COMPUTED
USING THE FOLLOWING EQUATION:"

3076 ? ""

3078 ? "AD=(DK1+(INC* (DK2-DK1) ) ) "

3079 ? ""

3080 AD = (DK2-(INC*(DK2-D1c1))):? AD

3081 ? ""

3082 ? ""

3090 ? "PLUGTMECALIIJLATEDVALUEEORTHE ZEROREFERENCE
DISPLACEMENT (AD) INTO THE EQUATION EOR ACTUAL DIMANSION"
3091 ? ""

3100 GOTO 13

BIBIIGERAHiY

63

BIBIICIERABIY

EB and G Retioon, "Ima e Sem' Products", 910 Benicia
Ave., Sunnyvale, CA 94086, 1987.

Kaman Measuring Systems, 'Measurement Solutions
Handbook", PO Box 7463, Colorado Springs, (1) 80933,
vol. 2, 1987.

Ehtran Devices Inc” "Low Profile load Cells", Errtran
Bulletin flo-200 Series, 10 Washington Ave. , Fairfield,
NJ 07006, 1986.

"Perfonnanoe Brochure", Kaydon Corporation, Muskegon,
MI, 1988.

mimental Stresé Analfiis, Dally, J .W. and Riley,
W.F., MoGraw Hill, 2’nd edition, 1978, diapter 6, pp.
153-199.

Ibid, chapter 8, pp. 212-266, chapter 10, pp. 318-333.

"Starbuck 8232 Data m'sition and Control m,
mtions Manna ", Starbuck Data Company, PO Box 24,
Newton, MA 02162, 1983.

MICHIGAN STATE UNIV.
ll‘WWWWII"WllHlmlmll
3129300904