DEVELOPMENT OF AN INSTRUMENT TO MEASURE
FRICTION OF TEXTILE FIBERS
A THESIS
Presented to
The Faculty of the Graduate Division
by
Thomas Eugene McBride
In Partial Fulfillment
of the Requirements for the Degree
Master of Science in Textile Engineering
Georgia Institute of Technology
August, 1965
In presenting the dissertation as a partiaJL fulfillment of
the requirements for an advanced degree from the Georgia
Institute of Technology, I agree that the Lihrary of the
Institution shall make it availahle for inspection and
circulation in accordance with its regulations governing
materials of this type. I agree that permission to copy
from, or to publish fl-om, this dissertation may he granted
hy the professor under whose direction it was written, or,
in his absence, by the Dean of the Graduate Division when
such copying or publication is solely for scholarly purposes
arid does not involve potential financial gain. It is understood that any copjring from, or publication of, this dissertation which involves potential financial gain will not
be allowed without written permission.
/ {]
DEVELOPMENT OF AN INSTRUMENT TO MEASURE
FRICTION OF TEXTILE FIBERS
Approved;
Chairman
fl
Dsze approved by ChaIrman\2'3''Gi
ii
ACKNOWLEDGEMENTS
At the conclusion of this past year of graduate study, the
author finds himself indebted to the Callaway Foundation and the Agriculture Department for their financial aid, and to Dr. James L.
Taylor for his support and assistance in securing these grants.
The author is grateful to Professor J.W. McCarty for the Mettier
balance used in the testing program, to Professor R.K. Flege for his
assistance in selecting a topic for study, and to Mr. Tom Buckley for
the preparation of the illustrations. Especial thanks are extended to
Mr. B.R. Livesay for the use of his facilities, his ideas, and his unselfish support and assistance. The author also is grateful for the
help and suggestions offered by Mr. Lester Dozier and Mr. L.K. Jordan,
and to Dr. William L. Hyden, Mr. Richard B. Belser and Mr. John Brown
for their service on the reading committee.
Special thanks go to his
advisor. Dr. Hyden, for his support and enthusiasm, which he offered so
graciously.
Finally, the author wishes to express his appreciation to his
wife, Mary Jo, and his parents for their encouragement and support
during the year.
iii
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
ii
LIST OF TABLES
iv
LIST OF ILLUSTRATIONS
SUMMARY
V
vii
Chapter
I.
INTRODUCTION
1
Statement of the Problem
Organization and Approach
Literature Survey
II.
DESIGN AND CONSTRUCTION OF APPARATUS
15
Design of Fundamental Principle
Mechanical Equipment
Electrical Servo-System
Alternate Method for Measuring Fiber Friction
III.
EXPERIMENTAL WORK
24
Selection and Preparation of the Test Specimens
Measurements of Fiber Friction and Data Analysis
IV.
V.
DISCUSSION
32
CONCLUSIONS AND RECOMMENDATIONS
35
Conclusions
Recommendations
APPENDIX
39
BIBLIOGRAPHY
57
IV
LIST OF TABLES
Table
Page
Computed Average Friction Coefficients for Three
Staple Lengths of Cotton Fibers
40
2.
Analysis of Variance Calculations
41
3,
Coefficient of Friction of Ten Samples of De-Waxed
Cotton Fibers
42
Coefficient of Friction of Ten Samples of Staple
Nylon on Nylon
,
42
Static Frictional Force Developed Between Single
Fiber and Parcel of Parallel Fibers
.
43
1.
4,
5.
LIST OF ILLUSTRATIONS
Figure
1„
Page
Method Used by Chakrabarti to Measure Friction Between
Jute Fibers . ,
,
8
Principle of the Measurement of Static Fiber Friction
by du Bois
8
Apparatus for Measurement of Fiber-to-Fiber Friction
Developed by Bowden and Tabor
14
4.
Apparatus for Measurement of Fiber Friction
44
5.
Balance Arm and Fiber Assembly
45
6.
Balance Arm Support and Counterbalance Mechanism
7.
Fiber Mount Assembly
46
8.
Galvanometric Principle
47
9.
Silicon Dual-Element Photovoltaic Null Indicator
2.
3.
....
....
46
47
10.
Two-Stage D.C. Amplifier
48
11.
D.C. Power Supply
49
12.
Attachment for Measuring Slip of Single Fiber in
13.
14.
15.
16.
17.
Parcel of Parallel Fibers
50
Frictional Force Between Two 3/4 Inch Cotton Fibers
as a Function of Fiber Displacement
51
Frictional Force Between Two 1 Inch Cotton Fibers as a
Function of Fiber Displacement
52
Frictional Force Between Two 1-1/4 Inch Cotton
Fibers as a Function of Fiber Displacement
53
Frictional Force Between Two De-Waxed, 1 Inch Cotton
Fibers as a Function of Fiber Displacement
54
Frictional Force Between Two Nylon Staple Fibers
as a Function of Fiber Displacement
55
VI
LIST OF ILLUSTRATIONS (Continued)
Figure
18.
Page
Confidence Intervals for Coefficient of Friction of
Cotton as a Function of Staple Length
56
VI1
SUMMARY
In recent years, textile scientists have begun to delve into the
rationale of cotton fiber behavior during processing operations in an
attempt to improve quality of textile goods by improving processing and
handling techniques. Of major importance are the surface characteristics of cotton and its role in the frictional behavior of the fiber.
The purpose of this investigation was to evaluate previous
methods of measuring the frictional behavior displayed by the surface
of cotton fibers and to construct an instrument which offered superior
accuracy and flexibility.
Previous instruments displayed varied appli-
cation and potential but, as a whole, were not completely suitable.
Many possessed no control of a normal force between single fibers, and,
consequently, calculation of a frictional coefficient was impossible.
From the various instruments found, those using the torque principle
presented superior data and it was decided to employ this principle in
the development of the new instrument.
A galvanometric principle had been investigated for the past
year and had been used to measure extremely small torques very accurately.
An apparatus was constructed which provided translation of one
fiber slowly across a second fiber, the latter of which was mounted on
the needle of a small D'Arsonval galvanometer.
The force of friction
developed between surfaces of the two fibers normally would cause deflections of the needle. However, an arrangement for feeding deflection information to a servo mechanism caused currents to flow through
Vlll
the galvanometer coil and apply sufficient restoring force to keep the
needle in the balance position. The current variations in the galvanometer coil furnished a voltage to an XY plotter which was proportional
to the force of friction between the two fibers. The normal force acting between the fibers was established by measurement, and the coefficient of friction was determined from the expression:
Frictional Force
Weight
Frictional measurements were made for nylon, de-waxed cotton,
and for 35 samples each of 3/4, 1, and 1-1/4 inch cotton fibers. The
value for the coefficient of friction was found to be 0.40, and this
value correlated well with data published by Harris in his Handbook of
Textile Fibers and Bowden and Tabor in their book Friction and Lubrication of Solids. Statistical tests indicated no significant difference
between the frictional coefficients obtained for the three fiber
lengths at the 5 per cent level.
The principal instrument described furnished a rapid and accurate method of obtaining frictional information concerning fibers; however, further refinement is needed.
A wide range of values was obtained
in the data, probably resulting from the variation in applied normal
forces which varied as much as 10 per cent.
Further study is being
conducted to correct this problem as well as other minor inaccuracies.
A second apparatus was developed to increase the scope of the
investigation by permitting the measurement of fiber friction as a
single fiber is separated from a parcel of parallel fibers. Thus, an
IX
Instrument has been developed which, with the aid of an attachment,
measures fiber to fiber friction with flexibility and fair accuracy
and offers the potential for obtaining still more superior results.
CHAPTER I
INTRODUCTION
Statement of the Problem
In textile processing operations, inter-fiber friction is a factor of primary importance.
Inter-fiber friction can greatly influence
the operation of many drafting assemblies, guides, rolls, and critical
tensioning devices with which fibers being processed come into contact.
The major importance of the role of fiber friction has been brought
into sharp focus in the last decade because textile machinery is running at higher speeds, and for many textile constructions, more delicate and accurate operations are required.
Furthermore, the introduction of synthetics into the trade has
brought with it not only new opportunities but also new problems which
are related directly to the frictional properties in the yam.
For
example, the abrasiveness of some of the new fibers has instigated much
research with roll coverings to prevent excessive wear.
The importance of fiber friction can be readily illustrated by
a specific example.
If the friction is too low, the yarn strength will
decline and consequently, the dimensional stability of the fabric will
be greatly reduced.
In this instance, high friction is desirable.
However, there are numerous occasions when high friction is a nuisance.
For example, in the weaving operation, bobbins wound under too high
tension can cause streaks in the fabric, a result of unnecessarily induced friction on the tightly wrapped bobbins. Thus, the importance
and necessity of a more precise determination of inter-fiber friction
becomes quite evident.
As the surface characteristics of any material almost completely
determine its frictional behavior, it is desirable to mention briefly
two characteristics of the cotton fiber which are of particular importance.
Cotton is well known for its kinky profile and its spiraled,
twisted appearance.
These characteristics, known as crimp and convolu-
tions, probably have a considerable effect on the frictional behavior
of cotton fibers.
The obvious importance of the surface of cotton fibers on its
frictional behavior has been brought into sharp focus with the initiation of programs for investigation of fiber-to-fiber friction, and
much effort is being expended in an attempt to correlate friction with
these surface characteristics. Of course, the ultimate objective of
these programs is to make possible better control of the fibers during
processing as well as to produce higher quality yarns and fabrics.
Necessary to attain this objective is the development of an instrument
featuring rapid and accurate determination of the friction between single fibers.
Organization and Approach
The first phase of this investigation was a thorough, systematic
search of the literature to determine the methods previously employed
to measure inter-fiber friction, the type of instruments successfully
used, and how the results have been analyzed and evaluated.
Next, at-
tention was turned to the development of instruments which would give
dependable and precise measurements of fiber to fiber friction.
The writer's motive for the development of a second instrument
was twofold.
The first instrument was designed to achieve superior ac-
curacy and control while presenting potential of previously unachieved
flexibility for the measurement of various types and kinds of fibers.
This instrument, fundamental in construction and principle, was designed to broaden the scope of the research on fiber friction as experienced in textile operations. It makes possible the measurement of
frictional forces acting on a single fiber while it is being extracted
from a parcel of fibers, much like the situation encountered in the
drafting operation.
After construction of these instruments, measurements were made
on more than 125 fibers, both natural and man-made. A prime objective
was to develop relationships in the frictional force of "standard" cotton fibers as related to surface and shape characteristics, fiber
length, and maturity.
The "standard" cotton is that cotton defined by
T.R. Boys in his thesis.^
Since Boys had correlated fiber length with
crimp and convolutions, the writer was able to correlate frictional behavior with crimp and convolutions by calculating coefficients of friction for various staple lengths.
By including synthetic materials in the testing program, it was
possible to correlate test results with data given by others and thereby to evaluate the usefulness and authenticity of the instrument.
Literature Survey
T.E. Stanton defined friction in 1923 as
the resisting force which is called into existence at the common
boundary of the two substances in contact when under the action
of some external agency, one of the substances slides or tends to
slide over the surface of the other. The direction of the friction and its magnitude is equal to the component in the direction
of motion of the external force tending to oppose sliding.'^
The influence of friction on various textile processes was well illustrated by W.L. Ball's paradox: "up to the front mule roller, cotton
must be slippery; afterwards it must be sticky."^
Two classical laws of friction, upon which the frictional study
of materials is based, state that the frictional force is independent
of the area of contact between the two surfaces, and is proportional
to the normal force between them.'* For example, the ratio between the
frictional force and load is constant. This ratio is known as the coefficient of friction.
These laws were stated by Amontons in 1699 and
verified by Coulomb in 1781. Aristotle and da Vinci had, long before,
discussed these principles in their writings but had not stated them
clearly.
With these laws as a basis, many other facets of fiber friction
have been investigated.
One of the earliest studies of fiber friction
was conducted by Monge in 1790 in which he discovered the directional
effect of friction in wool fibers. Although experimental work pertaining to friction of fibrous materials existed in the eighteenth century, it was not until the early twentieth century that frictional
forces and their effects became of great interest in textile research.
The initial objective of each experimenter concerning himself with
these studies was the measurement of the forces within fabrics and
yarns, and recently, between fibers. Thus, various instruments and apparatuses were developed for this purpose.
From an examination of these investigations, it was found that
they could be classified nicely into three categories. These three
classifications are: (1) the fiber twist method, (2) the torque principle, and (3) the stick-slip technique. A characteristic of interest is
that of the numerous instruments employed, almost all yielded a relative measure of friction based on some standard rather than an absolute
value of the coefficient of friction. The few instruments which did
make calculation of the coefficient of friction possible were designed
for continuous filament fibers or yarns.
A few experimenters have made use of the fiber twist method.
B.G. Hood^ devised such an instrument. His instrument embodied a principle of suspending the fibers vertically from a pair of arms capable
of exhibiting up and down motion alternating 180° out of phase. Preanalyzed weights were secured to the lower ends of the fibers and twist
inserted, which resulted in fiber to fiber contact. The arms then alternately moved and the twist was increased until slippage in the fibers
ceased.
The number of turns of twist at the instant slippage ceased
was adopted as a standard unit of measure of the friction.
Another more intricate and perhaps accurate apparatus was developed by Lindberg and Gralen.^
It performed the same function as the
Hood instrument, except an intricate torsional balance measurement system was employed.
There were several instruments involving the stick-slip principle, the most popular of the three methods. One of the earliest of
these developments was that of A. Adderley
in which he applied a nor-
mal force to two glass plates, covered with cotton fibers, between
which was placed a single fiber. To the lower end of this fiber was
attached a float suspended by water in a larger tube. By slowly dripping the water from the tube, until the first slip was noticed, he was
able to, by weighing that amount of water drawn off, determine the
force applied to the fiber necessary to cause slippage.
Adderley used
the data to correlate half convolutions per centimeter for many varieties of cotton to the force required to cause the slip.
A device developed by Tennessee Eastman Company^ to measure vibrations caused by alternate sticks and slips of yarn as it passed over
rolls and guides during processing, consisted of drawing the yarn over
a short length of music wire at constant speed and tension. The resulting vibration of the wire was picked up by a flat stylus in contact
with the wire. The stylus transmitted a force to a piezo-electric crystal pick-up and the mechanical motion was converted to an electrical
impulse.
The impulses were amplified and recorded by an oscillograph.
In Mercer's experiments, as discussed by Bartlett,^ a single
fiber was mounted in a bow and carried at a linear speed of between
0.01 and 0.10 centimeters per second while pressed against a cylindrical piece of ram's horn.
The horn was mounted on a piece of clock
spring, and the deflection of the spring was recorded using a movingfilm camera.
There has been concern as to the effect of finishes which cause
uneven fluctuations to develop or which do not minimize these vibrations in the various drafting assemblies. An instrximent was developed
and discussed by Bartlett^^ for the measurement of internal friction in
cotton roving. This device also employed a Statham Gage. A piece of
roving was drafted by means of a small timing motor which rotated at
one-third revolution per minute. A pulley was attached which effectuated a drafting rate of two inches per minute.
By fixing the oppo-
site end of the roving to a rod which contacted the gage, the roving
was slowly drawn and the force on the rod, and consequently the gage,
was recorded.
Bartlett stated that the study of frictional behavior
within roving or any other fiber assembly necessitated the consideration of other contributing factors. Some of these are: (1) staple
length, (2) fiber stiffness, (3) luster, (4) and the twist in the assembly.
He found that it was possible to minimize the stick-slip ef-
fect using a short staple length; whereas, the stick-slip effect became
very pronounced as the staple lengths increased.
Chakrabarti^^ described a method of measuring friction of jute
fibers.
A triangular arrangement of jute-covered plates, AB, BC, DE,
(Figure 1) were used and a horizontal force was applied at the center
of gravity, G, of the plate DE, constituting the hypotenuse of the triangle.
The force was applied with a silk thread, T, attached to the
plate and passing over a smooth glass rod, R.
On the opposite end was
attached a small bucket to which a uniform amount of water could be
added and increase the force on the plate. The weight of water collected thus became a measure of the frictional force acting.
An apparatus was developed by du Bois^ to study principles of
static fiber friction in which he used a modification of the Cambridge
Textile Extensometer, Figure 2. The method was developed primarily for
testing friction between fringes of fabric samples. It was accomplished
using two independently supported tables, T^ and T-, and three fabric
fringes, f,, f^, f^.
The fringes were secured by mounting brackets.
SLIDING JUTE COVERED PLATE DE
GLASS ROD R
BASE PLATE AB
Figure 1. Method Used by Chakrabarti to Measure
Friction Between Jute Fibers.
/WV^Ao=Tf
Figure 2. Principle of the Measurement of Static
Fiber Friction by du Bois.
k- and k^, on one table, while the interior fringe was fixed to a
Lting bracket, k„, on the other table. A set of contact points, c,
mount
and c^, were used to make impending motion possible. When a weight was
placed on the three fringes, one contact was closed and displacement of
one table was obtained and an attached spring was elongated.
This mo-
tion continued until the other contact was closed and an independent motor imparted motion to the other table and consequently the other
fringes. Motion continued and the spring was further extended until
the force exerted by the spring equaled the force of static friction between the three fringes of fibers and slippage occurred.
By utilizing
the spring displacement and spring constant, it was possible to calculate the force required to cause slippage.
Frishman^^ experimented with friction of wool fibers over a woolfelt covered roll.
He used small tabs sufficiently weighted to main-
tain the fiber in an untwisted or unkinked collocation. At one end of
the fiber was attached a tiny chain which slowly increased the force until slippage occurred.
Analysis of the data showed that the coefficient
of friction could be calculated from the experimentally determined
equation.
y
=
0.733 log^Q (T/TQ) ,
where T_ is the constant weight on one end and T the constant weight
plus weight of chain at the instant slippage occurs.
Two similar methods, one by Guthrie and Oliver^^ and the other
by Howell^^, employed an apparatus which was capable of imparting
10
motion to a horizontally mounted fiber in either of four perpendicular
directions.
The fiber was placed in contact with a freely hanging ver-
tical fiber weighted at the free lower end.
By moving the horizontal
fiber into the plane of the vertical fiber and perpendicular to it, a
normal force was induced.
The horizontal fiber was then moved in a di-
rection perpendicular to the plane of the vertical fiber, causing a
series of alternate sticks and slips as a result of the frictional
forces acting between them.
King^^ developed an instrument for measuring friction of wool
against a cylinder using a pair of mirrors and reflected light. He attached one end of the fiber to a mirror on the end of a small leaf
spring, passed it around a cylinder and fastened the other end to a
similar mirror arrangement.
By slowly rotating the cylinder, the fric-
tional forces between the fiber and cylinder caused a deflection of the
mirrors and thus a deflection of the light beam, reflected by the mirrors, from a source back onto a screen. The forces of friction involved were calculated from a measure of the displacement of the focused light beam and other known parameters.
Mercer and Makinson^^ used the principles of Bowden and Leben^^
in their study on friction of metals, and adapted them to be used for
fine fibers. A horizontal fiber mounted in a bow was carried at the
end of a balance arm on a moveable platform.
The fiber was pressed
slightly against a surface (usually polished horn) mounted on a clock
spring containing a small mirror on the side. By slowly moving the
horizontal fiber over the horn, the clock spring, and consequently the
mirror, was deflected.
A light beam was then reflected by the mirror
11
and the sticks and slips were recorded on photographic film by a camera.
A precise method of measurement of pending forces within an untwisted sliver, as is the case in the drawing process particularly, was
developed by Postle and Ingham^^.
They found from experimental re-
sults that the force required to withdraw a single fiber from within a
group of parallel fibers was dependent upon both the external force on
the set of fibers and their dimensions. The fundamental principle of
the apparatus consisted of a channel with rectangular cross section,
one inch long. One of the four sides, namely the top, was a well fitting lid.
A single fiber was inserted into a parcel of fibers and a
pressure of known magnitude applied to the lid. The fiber was withdrawn using a torsion-head assembly consisting of a pivoted rod fixed
to a coiled spring at its pivot point. The other end of the spring
was attached to a pinion gear which meshed with a worm gear. On the
end of the worm gear shaft was a simple dial used as a gage or zeroing
device.
The torsion-head was calibrated prior to the testing for the
purpose of obtaining a reference position. A clip fixed to one end of
the rod was then attached to the fiber and the dial rotated.
As a re-
sult, a force was applied to the arm by the coiled spring and the fiber
was withdrawn from the bundle. The pre-calibrated dial made possible a
direct reading of the force necessary to cause slippage.
A few references are discussed under this group which did not use
the stick-slip technique as such, but which were included under this
classification because of the close resemblance of basic principles.
Bartlett, Smith, and Thompson^" developed another instrument known as
a slow-speed y a m tester, where the yarn was drawn through the device
12
at a speed of one inch per minute utilizing a synchronous motor. A
Statham Strain Gage was employed to measure the individual forces.
The frictional force was applied by a series of staggered cylinders
which caused a deflection of about ten degrees at each cylinder. The
force was transmitted through an aluminum lever, mounted at the bottom
in roller bearings, and was measured by the strain gage.
Fort and Olsen^^ devised a slow speed apparatus for testing friction of a continuous yarn. A constant speed motor was used to pull
yarn at 0.01 centimeters per second over a roll and pulley arrangement
covered with the test yarn.
A floating pulley mounted on a Statham
Strain Gage was used to measure the force required to preserve continuous motion.
Instruments within the final classification, the torsion principle, in general required more delicate and involved mechanisms and, as
a result, offered potential for extremely accurate, precise results.
In many cases, more accurate and reproducible results are obtained if fiber assemblies are used rather than a single fiber. The
reason is evident since the resulting data is an average and individual
fiber irregularities are kept at a minimum.
Bowden and Tabor developed
an instrument as discussed by Chakravarty^^ which utilizes this principle.
face.
They used a rotating disc to provide a continuously moving surSuspended from a small torsion wire was a yoke assembly support-
ing two fiber pads which rested on the surface of the rotating disc.
The friction between the fibers and disc caused a torsional displacement of the wire which was used as a measure of the frictional force.
A very successful attempt was made by Guthrie and Oliver^^ on
13
the measurement of friction by the torsion method. Figure 3. They suspended a small metal tube from a torsion wire perpendicular to it. A
mirror was mounted in the center of the tube perpendicular to it, and a
fiber was mounted at one end. Another fiber was mounted on the end of
a long rod which could be given rotational motion about a vertical axis
near one end.
The two fibers were mounted horizontally and at ninety
degrees to each other. As the arm was rotated, the friction between the
fibers caused a torsional displacement of the wire. This displacement,
a rotational effect, was recorded by means of a beam of light reflected
from a source, by the mirror, onto a screen.
The linear shift of the
light on the screen was thus a measure of the frictional force imposed
on the torsional system.
Many of these aforementioned instruments were of limited value
because of questionable reproducibility.
In a majority of cases, par-
ticularly among those measuring friction within staple fibers, the only
results achieved were relative to a predetermined standard value and
thus gave relative and not absolute results. A flexible apparatus,
capable of producing accurate data for varied classes of materials,
appeared to be a desirable and necessary development to accomplish the
purpose of this work.
14
Figure 3. Apparatus for Measurement of Fiber-to-Fiber
Friction Developed by Bowden and Tabor.
15
CHAPTER II
DESIGN AND CONSTRUCTION OF APPARATUS
Design of Fundamental Principle
A thorough search of the literature disclosed only a small number of relatively flexible instruments which made possible the measurement of the coefficient of friction for single fiber-to-fiber surfaces.
Each of these had certain disadvantages with respect to accuracy or
time consumed in testing.
It was the desire of those concerned with
this investigation to develop an instrument which, initially, was sufficiently delicate to deal with very small fibers, secondly, was capable of measuring forces accurately of only a few milligrams in magnitude, and thirdly, contained some method of determining the normal
force between two single fibers. From these data it was possible to
determine the coefficient of friction of the specific fiber pair from
the equation,
y
=
F/N ,
where y is the coefficient of friction, F the force of friction, and N
the normal force applied. Also, it was objectionable to produce any
data based on standard or previously determined measures, but, rather,
to obtain values of frictional and normal forces per se.
The design of the instrument was then approached with these goals
in mind.
The investigation of past principles of measuring small forces
16
disclosed that a likely method might be to measure forces induced on a
galvanometer needle by a fiber being slowly pulled across a second fiber mounted on the needle by employing an electric current to restore
the galvanometer to the null position. The current required is proportional to the frictional force exerted between the fibers. Hence, this
proposed method gave promise of satisfying the objective of accuracy in
measuring exceedingly small forces. It was also possible to display
the data on a recorder, plotting the displacement of the fiber being
moved against the force exerted on the needle resulting from the friction between the two fibers. A diagram of the assembled, experimental
instrument constructed as discussed below is shown in Figures 4 and 5.
Mechanical Equipment
Consideration of several methods of mounting a fiber and imparting a slow, constant, linear motion to it, led to mounting the fiber on
the end of a long rod which acted as a balance arm. The rod was pivoted
in sapphire bearings about a point approximately ten inches from the
mounted fiber.
A counterbalance was used on the opposite end o£ the
rod for positioning and adjusting the load.
By rotating the arm and
consequently the fiber, an approximately linear motion was imparted to
the fiber.
Use of the lengthy arm was mandatory to prevent any significant
arc being traversed by the fiber in its short movement. The maximum
traverse of a fiber was limited to less than three-fourths inch.
Therefore, if the fiber was moved the full three-'fourths inch from
start of the run to termination, and using the ten inch balance arm
17
from pivot to fiber, the maximum deviation from a linear path attainable was less than one thirty second of an inch. This was considered
negligible.
A problem developed, resulting from the long arm, was that of
obtaining a sufficiently slow traverse of the fiber. The balance arm
was mounted in a stainless steel holder. Figure 6, which was itself affixed to the top of a rotating shaft. Exceptionally slow rotation was
obtained by gearing down a synchronous motor which rotated at a constant 1/37.5 revolution per minute. The reduction ratio used was two
to one which produced a final rotation of the shaft and balance arm of
1/75 revolution per minute.
Therefore, the linear displacement of the
fiber was approximately three-fourths inches per minute, a speed slow
enough to make practical the study of the stick-slip effect by photographic methods.
Since it was desired to establish normal forces as low as five to
ten milligrams, it was essential that the balance arm be pivoted in
nearly frictionless bearings. For this purpose, sapphire bearings,
similar to those in watches, were used and set in the ends of threaded,
knurled studs in the arm support. Figure 6.
The bearings were set in
the threaded studs to facilitate adjustment of the pressure of the pivot
pin in the arm and free or restrict oscillation of the arm as desired.
The balance arm was fabricated from K-Monel tubing which exhibited properties of high strength, light weight, and was not influenced by stray magnetic fields.
In both ends of the tube, short stain-
less steel plugs were press-fitted and threaded.
The plug on the rear
of the arm was for mounting the micrometer screw sleeve, shown in
18
Figure 6.
A line was scribed on the arm and the circumference of the
micrometer screw was divided into twenty-five equal segments. The micrometer screw was made of brass and served as a counterbalance for
controlling the normal force between the fibers. Normal forces were
applied at the fiber end of the balance arm by adjustment of the micrometer screw and calibrated at each of the twenty-five divisions on
the sleeve. The calibration was performed by using a Mettler balance
on which readings could be made to the nearest one-tenth milligram.
It
was found that one-twenty fifth turn of the micrometer, one division,
produced an incremental change in the normal force of approximately
three milligrams.
The fiber mount, Figure 7, consisted of two small clamps mounted
in a groove of the holder.
Consequently, they could be adjusted for
various length fibers. Each clamp contained a pair of soft rubber pads
between which the fibers were secured under tension. The holder was
then attached to the end of the arm with a cap-screw which could be
tightened or loosened as desired, thus fixing or freeing the holder.
The motor and drive, the balance arm, and the fiber holder were
mounted as a unit on a two-way milling vise which made possible motion
of the arm and fiber assembly both parallel and perpendicular to the
axis of the balance arm.
Therefore, the fiber could be placed at any
desired position on the second fiber mounted on the galvanometer
needle.
Electrical Servo-System
An automatic, self-balancing servo-system is employed for detecting and recording the minute forces encountered in this investigation.
19
The fiber of interest is drawn across a second fiber mounted on the indicating needle attached to the coil of a D'Arsonval galvanometer movement.
A current is generated and passed through the galvanometer coil
to supply a balancing counterforce.
The sensing mechanism consists of
a system employing a beam of light reflected from the galvanometer mirror to a dual photo-diode which detects the slightest shift of the
light beam.
The signal from the photo-diode is fed into a high gain,
servo-amplifier. The output of the amplifier is fed into the galvanometer coil so that the needle is not significantly displaced by an applied frictional force from the null position. The counter-force
thereby generated is directly proportional to the galvanometer current
and is displayed on a recorder as a function of the ordinate displacement.
The instrument was designed using a galvanometric principle for
measuring accurately the small forces encountered.
This principle had
been used during the past year by Mr. B.R. Livesay, Research Physicist
at Georgia Tech, for measuring small torques exerted on materials by
magnetic fields. Upon his recommendation, the galvanometer selected
for this particular purpose was a D'Arsonval type, Honeywell No.
726281-3.
The galvanometer consists of a coil located in a magnetic field
and can be best described with reference to a simplified diagram.
Figure 8 shows a single coil suspended in a uniform magnetic field with
its plane parallel to the lines of induction.
As a current flows in
the wire, equal and opposite forces are generated on the coil, and a
torque is developed.
The moment imparted to the coil is dependent on
20
the magnetic flux density, B, the current, I, the number of turns of
wire cutting the induction lines of the magnetic field, N, and the area
of the coil, A. With B, N, and
M
=
BINA
A constant, we can conclude that the torque M is directly proportional
to the current in a given coil with permanent magnets.
The conducting coil is supported at top and bottom by a small
gold ribbon which permits rotation, although somewhat limited, about
its vertical axis.
Attached to the top of this coil is a needle which
passes over a scale designed to give its relative position with respect to some zero point.
The particular galvanometer used in this investigation has a
small reflecting mirror attached to the bottom of the coil.
The mir-
ror is used to reflect a light beam back onto a small silicon dualelement photovoltaic null indicator (LS 221 - Texas Instruments Incorporated) . The null indicator is a silicon diffused-junction photovoltaic cell, mounted in a dielectric case, and employs silicon monoxide coated surfaces to minimize reflection losses. The light source
used is a No. 85 grain of wheat lamp containing a tungsten filament and
operated at three volts.
The dual diode. Figure 9, consists of two light sensitive elements.
The tungsten lamp was positioned so that with the beam focused
on the null position, the differential amplifier delivers a zero output current. A torque applied to the galvanometer causes the beam to
21
shift more to one side of the diode, and a larger EMF is generated by
this side. An EMF from each side of the diode is fed to the amplifier
which returns a correcting current to the galvanometer coil, restoring
it to the balance position.
The servo-amplifier, Figure 10, employed to receive the differential EMF and produce a correcting current to re-zero the coil is a
D.C. amplifier consisting of two, resistance coupled, Burr-Brown Model
No. 1509 operational amplifiers. The first stage is wired for differential input and single ended output operation with a closed loop gain
3
of 1 X 10 . The output voltage is impressed across a 1000 ohm coupling
potentiometer into the second stage.
The second stage amplifier is wired for both single ended input
and output operation, and the gain reduced to 300 for purposes of stability.
The output voltage is developed across a resistance network
consisting of a 1000 ohm resistor in parallel with a series combination
composed of a 25,000 ohm potentiometer and the 300 ohm galvanometer
coil.
Both stages possess 100,000 ohm zeroing potentiometers for the
purpose of compensating for any amplifier offset voltages.
In addition,
phase compensating networks were employed.
In general, should the light beam be shifted off the zero position, such as is the case when friction between the fibers causes a deflection of the galvanometer needle and coil, unequal currents are
emitted from the sides of the diode causing a differential input to be
sent into the amplifier. As this occurs, the differential current is
amplified tremendously and an output current, the restoring current, is
22
produced.
The negative feedback thus causes the coil to return to the
zero position.
The amplified signal is fed into a Moseley Autograf, Model 135,
designed to plot cartesian coordinate graphs from D.C. electrical information and functions of time as well.^^
An electrostatic holddown sys-
tem is employed to secure the 8 1/2" x 11" graph paper.
The control
unit consists of sixteen calibrated voltage ranges, from a minimum of
0.5 millivolts per inch to 50.0 volts per inch. Optimum pen sensitivity occurred at an input voltage of 50 millivolts per inch although
the stability of the pen was a problem throughout the investigation.
The force exerted by inter-fiber friction on the galvanometer needle
was plotted on the Y axis of the recorder while distance traveled by
the fiber was plotted on the X axis.
A five second per inch chart speed
was used, making possible the coordination of time and fiber position.
The recorder offers an accuracy of better than 0.2 per cent of full
scale, resetability better than 0.1 per cent, and a time sweep accuracy of 5 per cent full scale.
The power supplied to the system is produced by two full wave
diode (IN-4383) bridged rectifier units wired to produce plus and minus fifteen volts with respect to ground.
The transformers employed
are of the filament type with a 115 volt primary and 9.2 volt secondary
rating.
Two transformers, with their secondaries in series are used
in each rectifier unit to yield a secondary voltage of 18.A volts.
The primaries are wired in parallel for use with normal 110-120 volt
supply.
By employing the components listed in Figure 11, a ripple
voltage of 0.1 per cent is observed.
23
Alternate Method of Measuring Fiber Friction
A second apparatus, Figure 12, was designed to measure frictional
forces of a nature somewhat similar to those encountered in textile
processing operations.
It is desirable to determine the static force
required to cause an initial slip of a single fiber to occur while enclosed in a parallel parcel of fibers. The apparatus consists of two
2
rubber pads (1 cm ) on which are cemented a parallel group of cotton
fibers.
A single fiber is then attached, using sealing wax, to the
galvanometer needle, placed in the center of the two fiber covered pads,
and a small pressure applied.
The pad holder is slowly moved away
causing the needle to deflect until a slip occurs. It is possible to
read the value of the force required to cause slippage directly from
the chart scribed by the recorder, and the magnitude is taken as the
force of static friction.
24
CHAPTER III
EXPERIMENTAL WORK
Selection and Preparation of the Test Specimens
Brief History of Specimen
A major portion of the work done in this study concerned the investigation of cotton fibers. The cotton used was the same cotton previously defined as "standard" cotton by T.R. Boys which was grown near
Experiment, Georgia, during the 1962 and 1964 growing seasons."^^
The Empire WR cotton was grown on a one acre tract of land which
had been broadcast with 700 pounds of 4-12-12 fertilizer and 250 pounds
of ammonium nitrate. The growth of the cotton was carefully observed
and directed by personnel of the agriculture station at Experiment and
Mr. Boys and was hand-picked.
The careful observation and handling of
this sample insured its suitability for use as a standard while providing a history of its growth process. Since this study was concerned
with single fiber-to-fiber friction, the condition of the mass or overall bale (cleaner and less damaged than machine-picked) was irrelevant
in this particular study.
Classification of Sample Groups Tested
The cotton samples were grouped into three general length divisions, namely, short, medium, and long, using the Suter-Web fiber sorter,
For purposes of this investigation, measurement and comparison of friction of various staple lengths, it was decided to use only three particular staple lengths. These lengths were 3/4, 1, and 1-1/4 inches.
25
Because of certain variables within the operation of the instrument at
this early stage of development, it was evident that accuracy was somewhat limited.
Therefore, there was no reason at this time to attempt
any smaller division of fiber lengths for purposes of friction measurements .
The fibers were carefully placed on a piece of black velvet, both
to secure the fiber and provide a dark background, and each fiber was
measured to the nearest one-eighth inch using a stereo-microscope.
Those fibers not within prescribed limits were discarded.
To prevent
additional error in the data obtained, it is necessary to observe each
end of the selected fibers to prevent usage of broken fibers. This
was done and all inferior fibers were discarded.
The selected fibers were stored in loose containers at the testing location for at least twenty-four hours prior to their use in the
program.
Since each fiber tested was mounted, immediately tested, and
discarded, variation in data resulting from inconsistent values of
fiber tension was minimized.
Therefore, a controlled atmosphere was
not necessary to prevent deterioration of this pre-applied tension.
Ten samples of nylon 66 were tested to use for comparative purposes to prove the accuracy and capability of the instrument. No
special preparation of these samples was necessary.
As a result of the
elastic properties and larger diameter, consequently higher total
strength, these nylon samples were easier to handle than the delicate
cotton fibers.
Fiber Mounting Technique
Inasmuch as both tension and normal force have such a pronounced
26
effect on the frictional forces exerted, a consistent mounting technique
was required,
A method was designed to mount a stationary fiber on the
galvanometer needle parallel to it. A special holder was also constructed for mounting a second fiber on the end of the balance arm at
any tension desired.
For the stationary fiber, a piece of eight thousandths phosphor
bronze was used and fabricated into a U-shaped holder. The spring was
held in a special vise when each fiber was mounted, making reproducible
values of tension possible.
Several glues were used to fix the fiber to
the spring initially but were too slow in drying for practical application. Therefore, small amounts of sealing wax were used and an excellent technique was developed for achieving very rapid mounting.
The
spring was fixed on the galvanometer needle with the sealing wax as
well.
The wax proved very satisfactory since a small quantity was suf-
ficient and as a result, minimum mass was added to the needle.
The holder for the fiber on the balance arm was fabricated from
brass and stainless steel stock. Minimum dimensions were used to prevent increasing the total mass of the arm and thus prevent excessive
friction in the bearings. The holder was designed to handle a range
of lengths by incorporating moveable clamps which operated in a small
slot.
One-eighth inch square rubber pads were glued on the lower surface of the clamps to grip the fibers when mounted. A piece of U-shaped,
phospor bronze was used. Figure 7, to which was fixed the upper rubber
pad.
This piece of metal also acted as a bearing surface for the
screw which applied the force to hold the fiber in each clamp.
27
A cap-screw which was machined to fit the threads on the steel
plug in the end of the balance arm was used to fix the fiber holder onto the end of the arm.
The stainless steel pin soldered to the fiber
holder was inserted into a hole in the end of the cap-screw and a
metal disc was soldered to the pin. The cap-screw was tightened on the
disc in order to hold the fiber mount securely in position.
For mounting each fiber, the holder was first removed from the
arm.
A fiber was selected and one end was secured in one of the two
clamps on the holder. A one-half gram weight was then clipped to the
other end of the fiber and the weight was allowed to hang freely while
this end of the fiber was fixed in the other clamp. Thus, a consistent
one-half gram tension was applied to each fiber.
The fiber mounted on the needle was not changed with each new
fiber tested, but was used for testing five fibers. A fresh surface
was exposed for each measurement, however, by displacing the fiber
mount slightly along the axis of the needle before each run. No change
in results was noted by using this procedure. However, corresponding
fibers were used in all testing; that is, for testing one inch fibers,
a one inch fiber was employed on the galvanometer needle.
Measurements of Fiber Friction and Data Analysis
Two runs were made on each of 105 cotton fibers consisting of an
equal number of 3/4, 1, and 1-1/4 inch lengths. This particular number
of fibers was derived by observing results of ten samples of each of
the three length groups. From these data, the standard deviation was
obtained and used to determine the necessary number of fibers to be
run to produce accurate results at a 5 per cent significance level.
28
Approximately 35 of each length were deemed necessary.
Therefore, it
was decided to include 50 fibers from each group and select 35 of the
most typical samples for evaluation. The experimental design involved
the investigation of an equal number of each staple length per day.
This procedure minimized differences among fibers caused by the changing
atmosphere or other uncontrolled variableso
Several typical charts ob-
tained in the testing program are shown in Figures 13, 14, 15, 16, and
17,
After 35 fibers from each length group had been tested, the data
was analyzed by obtaining the average of the high and low points occurring for each 1/4 inch of chart movement. The distance in inches of
each of these averages from a zero line, obtained by inscribing a line
on the chart while the fiber was at rest on the needle, was recorded and
an average value obtained.
Previous calibration of the instrument using
known weights on the galvanometer needle showed that a deflection of
one inch on the chart corresponded to 7.7 milligrams force impressed on
the needle. Therefore, for each average distance obtained, a corresponding average force was determined.
Thus, for each data plot, an
average frictional force was obtained, which, when divided by the normal force, yielded the coefficient of friction of the particular fiber
sample.
This procedure was employed on each of the 105 fibers tested.
For each of the three fiber groups, an average coefficient of
friction was computed and an analysis of variance^° performed to determine, statistically, any significant differences which occurred
(Table 1),
The analysis of variance table calculated is shown in
Table 2 as well as the F test statistic used to determine differences.
29
if any.
It was found that no significant difference occurred in the
frictional forces obtained for the various lengths at a significance
level of 5 per cent. The analysis was carried further by determining
confidence intervals for each mean coefficient of friction.
The confi-
dence intervals can be seen in Figure 18. Ninety-five per cent confidence intervals were obtained, meaning that 95 per cent of the time,
the mean coefficient of friction will be included within the bounds of
the particular interval obtained.
Ten samples of de-waxed cotton fibers were also run and compared
with ten samples of normal fibers. Table 3. Although no significant
difference was indicated, additional measurements of a greater number of
fibers appears necessary to verify this finding.
Ten samples of nylon fibers. Table 4, were run for comparison
with results presented by Harris^^, and Bowden and Tabor^^. They computed coefficients of kinetic friction for nylon on nylon which ranged
from 0.40 to 0.50.
The average value obtained with this instrument for
the ten samples was 0.40.
Results of the second method of testing, whereby a single fiber
was retracted from a parallel mass of fibers under slight pressure, are
shown in tabulated form in Table 5. With this method, it was possible
only to determine a force required to cause an initial slip to occur
since no normal force was available.
In this case, the average force
required was approximately 18 milligrams. Variation of approximately
30 per cent occurred. More precise control of pressure between the
pads should reduce this variation.
An indication of forces developed
within slivers being drawn is offered by this method.
30
Discussion of Sources of Error and Recommendations for Further Work
A problem of immediate importance is that of applying the normal
force between the fibers being tested. While data was being obtained,
it was necessary to re-check the normal force at least three times
daily by dismantling the assembly and placing the Mettler balance in
position to measure the force. Even with these precautions, error in
normal force was obtained as high as 10 per cent. A recent observation
of the bearing surfaces showed badly marred areas which definitely
caused excessive friction and, consequently, greatly increased variability in the normal force. Attempts are being made to obtain more
desirable bearings along with a more suitable pin for supporting the
balance arm. A special taut-band suspension system may prove to be superior and is being studied.
However, it is believed that the ultimate
suspension would be some method of positively applying the normal force,
which, in addition to decreasing variation, would hopefully prevent any
oscillation of the balance arm as the fibers stick and slip during test.
Some method of damping is a possibility.
Under present conditions, os-
cillations occurred occasionally to the extent that the fibers were
completely separated, at which time a zero normal force was experienced.
Another source of error appeared to occur from slight misalignment of the stationary fiber from a vertical plane passing through the
fiber and galvanometer needle.
In a case of this type, the normal
force also applies a slight torque to the galvanometer coil resulting
in a high or low reading of the zero registry.
Additional work is also needed on the servo-system so that it
will be possible to maintain sufficient gain and possess stability
31
simultaneously.
Original intentions for using a double amplifier sys-
tem were to install an integrating circuit in the amplifier.
It is be-
lieved that a single amplifier would give increased stability but would,
of course, eliminate the possibility of later installing the integrating circuit. This does not seem to be the best method of correction.
32
CHAPTER IV
DISCUSSION
Complete evaluation of the instrument has not been completed,
and many aspects must be studied before the full value can be realized.
Of principle concern is the variation in zero values occurring from
beginning to end of several test runs.
Before testing any specimen,
the two fibers were placed in contact and isolated for a short period
to allow all oscillations in the balance arm to cease. The pen was
then started and a short zero line scribed before the fiber was moved,
as shown in Figures 13 through 17. After termination of the run, the
arm was raised until the fibers were clear and a second zero line was
scribed.
Ultimately, these two lines should coincide, as was the case
in about 60 per cent of the tests. At the start of the run, the normal
force was being applied to the galvanometer coil; whereas, it was not
when the second zero line was made.
Therefore, one concludes that a
horizontal component of the normal force was developed and induced on
the galvanometer coil.
Several explanations are possible.
The fiber
mounted on the needle, one-eighth inch above its axis, could have been
slightly off center causing a moment to develop when the normal force
was applied.
Because the fibers are not rigid and tend to deflect when
placed in contact, a horizontal force could have been applied to the
needle, causing a deflection.
However, this is doubtful because the
variation did not occur every time, while the deflection of the fibers
did. An interesting possibility is that at the point of fiber contact.
33
a convolution or other surface irregularity occurs which could cause a
horizontal force to develop.
Undoubtedly, the initial position assumed by the fibers prior to
starting a test run influences, to some extent, the data obtained from
that specimen. Therefore, to insure approximate consistency, the entire operation should be observed microscopically to prevent the positioning of one fiber in a "valley" and another fiber on a "peak" of the
fiber surface.
A definite decrease in the frictional coefficient was noted as
the normal forces were increased.
During the testing program, normal
forces were used in two ranges, one being 11 to 12 milligrams and the
other 26 to 28 milligrams.
Typical charts were taken from each of
these groups and the values averaged.
It was found that at the lower
normal force a value of 0.40 was obtained for the frictional coefficient, while the higher force produced an average value of only 0.29,
considerably less.
This deduction is in agreement with Bowden and
Tabor^^, who state that the frictional coefficient varies inversely
with the normal force applied.
An interesting observation was the relation between the frequency of stick-slip of nylon and de-waxed cotton as compared to typical
one inch cotton fibers.
In addition to the smaller amplitude of pen
deflection of the nylon and de-waxed specimens, they displayed approximately 18 to 20 peaks per inch, compared to about ten for the typical
cotton.
The character of the curves is a very important characteristic
of the data provided by this instrument, and may be of equal or greater
34
importance than numerical values for the coefficient of friction.
Secondly, whereas the average displacement was used to calculate the coefficient of friction, the maximum displacements provide a value for
the static coefficient of friction. As may be seen from the data, this
value is larger for natural cotton than for nylon or de-waxed cotton.
In fact, the static coefficient may well be one of the more important
items in frictional behavior.
A further evaluation program should be conducted to study these
observations as soon as necessary modifications to the instrument can
be made.
35
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
Conclusions
An instrument was developed which offered very significant potentialities. The validity of results from the instrument is indicated,
somewhat, by a correlation of data obtained with it, and data obtained
by Harris, Bowden, and Tabor.
These individuals obtained results for
the coefficient of friction of nylon staple in the range of 0.40 to
0.50.
Data obtained in this investigation showed an average friction
coefficient of 0.40. A more extensive investigation is needed to verify this coordination because this average figure is based on only ten
samples.
No significant difference in the coefficient of friction was obtained for any of the length groups tested.
Values taken for ten de-
waxed fibers, corresponding to ten normal fibers indicated differences
in the character of the data plots and a lower coefficient of static
friction than for natural cotton.
The coefficient of friction was vir-
tually the same, however. The author believes this finding should be
investigated further.
According to Adderley^*^, friction varies with convolutions and
crimp.
T.R. Boys^^ showed that 3/4 inch and 1 inch fibers contained
more crimp and convolutions than the 1-1/4 inch fibers and therefore
should show different frictional results. However, this was not the
case here. The results obtained in this investigation cannot be used
36
to indicate a fallacy in Boys' data because of the evident weaknesses of
the instrument in its current form; however, they should not be considered insignificant.
Variations in normal forces and coil instability
make considerable error possible and must be corrected.
Recommendations
The instrument developed to date has exhibited high potential.
However, as experienced in most initial research, many problems have arisen, and the true potential and value has not as yet been fully realized.
The major problem was found in the method of applying the normal
force between fibers and work has begun to correct this problem.
Error
in normal force was obtained as high as 20 per cent, with the larger
errors occurring as normal force decreased. Before completely satisfactory results are obtained, it will be necessary to reduce this error to approximately 2 per cent, particularly in the lower ranges of
normal force.
A second major problem occurred in the servo—system.
It was
impossible to supply sufficient gain to the galvanometer coil for optimum results and maintain stability simultaneously.
These two problems
must be corrected before completely satisfactory results can be obtained.
The next step in the development program should be to increase
the versatility of the instrument.
It would be interesting and, indeed,
is necessary to study friction of fibers being slid over each other in
a parallel nature, as is the case in textile processing operations.
37
For this purpose, the installation of a more adaptable fiber holder on
the galvanometer needle is needed.
This holder should permit rotation
of the fiber in a horizontal plane to any angle, thus making possible an
angle of fiber contact ranging from 90 degrees to about 5 or 10 degrees.
Also, with only minor adjustments or additions, the instrument could
be used for testing friction acting on any single fiber within yarns
or slivers. This would make the study of internal friction of yarns
possible and thus increase the potential of this instrument to the extent that the frictional behavior of almost any form of textile product could be evaluated.
As the instrument is improved to make more accurate, dependable
results possible, it would be interesting to make a thorough study of
friction properties as related to fiber lengths. This was not possible
because of time limitations.
Fiber lengths ranging from one-half inch
to one and one-fourth inch (increasing in one-eighth inch increments)
should be evaluated to produce conclusive results. Also, a thorough
investigation should be made to determine the behavior of friction in
accordance with variation of the normal force.
Ultimately, the microscopical and infrared studies progressing
at this time should be correlated with the frictional measurements. Attempts should be made to correlate the peaks on the XY curve with characteristics of specific fiber zones. This could be done observing
the fiber slippage microscopically.
In conclusion, a highly versatile, dependable and accurate instrument has been developed and used successfully to measure fiber-tofiber friction. However, the instrument needs further refinement to
38
make absolutely precise, reproducible measurement of the friction of
cotton fibers possible. New work has been posed and should begin as
soon as the few major problems aforementioned have been corrected.
Furthermore, a second apparatus was constructed and employed to give
a measure of the frictional forces acting within consolidated fiber
mechanisms such as encountered in textile processing operations. This
instrument is expected to be of increasing value as the over-all research program on fiber friction advances into areas of practical applications.
APPENDIX
AO
Table 1.
Test
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Average
Computed Average Friction Coefficients for
Three Staple Lengths of Cotton Fibers
3/4
F i b e r Length
1
(Inches)
1-1/4
0.47
0.40
0.49
0.40
0.44
0.39
0.46
0.45
0.28
0.37
0.31
0.25
0.32
0.35
0.31
0.40
0.29
0.35
0.34
0.33
0.48
0.37
0.52
0.36
0.38
0.38
0.34
0.40
0.42
0.52
0.42
0.44
0.40
0.35
0.41
0.31
0.34
0.32
0.38
0.30
0.30
0.28
0.29
0.27
0.50
0.51
0.43
0.34
0.36
0.41
0.52
0.36
0.51
0.52
0.36
0.33
0.29
0.32
0.33
0.54
0.36
0.42
0.49
0.32
0.38
0.37
0.35
0.38
0.29
0.35
0.30
0.31
0.25
0.51
0.43
0.28
0.47
0.50
0.41
0.40
0.44
0.47
0.32
0.29
0.37
0.38
0.24
0.23
0.42
0.24
0.51
0.41
0.46
0.50
0.39
0.38
0.41
0.40
0.50
0.43
0.40
0.53
0.34
0.50
0.55
0.42
0.50
0.53
41
Table 2. Analysis of Variance Calculations
Source of Visrriance
Degrees of Freedom
Sum of Squares
Mean Squares
Between Lengths
2
0.0178
0.0089
Within Lengths
103
0.6740
0.0065
Total
105
0.6918
Test of Hypothesis:
^2
103
"
0.0089/0.0065
=
1.37
From Statistical Tables: F« --.^
1.37 < 3.06
Conclude:
Not significant at 95%
=
3.06 (a 95 % level
42
Table 3.
Coefficient of Friction of Ten
Samples of Staple Nylon on Nylon
Average
Force (mg.)
Normal
Force (mg.)
Friction
Coefficient
1
2
3
4
5
6
7
8
9
10
4.95
4.62
5.29
3.91
3.22
4.14
3.91
6.44
4.37
4.84
11.5
11.5
11.5
11.5
11.5
11.5
11.5
11.5
11.5
11.5
0.43
0.41
0.46
0.34
0.28
0.36
0.34
0.56
0.38
0.42
Average
4.57
11.5
0.40
Test
Number
Table 4.
Test
Number
Coefficient of Friction of Ten Samples
of De-Waxed Cotton Fibers
Average
Force (mg.)
Normal
Force (mg.)
Friction
Coefficient
1
2
3
4
5
6
7
8
9
10
4.37
4.14
4.83
5.40
4.49
5.18
4.95
2.64
5.86
3.34
11.5
11.5
11.5
11.5
11.5
11.5
11.5
11.5
11.5
11.5
0.38
0.36
0.42
0.47
0.39
0.45
0.43
0.23
0.51
0.29
Average
4.52
11.5
0.39
43
Table 5. Static Frictional Force Developed Between Single
Fiber and Parcel of Parallel Fibers
Test
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Average
Recorder Pen Deflection
(Inches)
Force (mg.)
2.90
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as a Function of Fiber Displacement.
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BIBLIOGRAPHY
58
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62
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