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Transcript of An Investigation of the Applicability of Walker and Fetsko Ink Transfer Equation on and the...
AN INVESTIGATION OF THE APPLICABILITY OF
WALKER AND FETSKO INK TRANSFER EQUATION ON
AND THE INFLUENCE OF INK VISCOSITY ON
HEAT SET INK USED ON THE WEB OFFSET PROCESS
by
Dein Wang
A thesis submitted in partial fulfillment of the
requirements for the degree of Master of Science in the
School of Printing in the College of Graphic Arts and
Photography of the Rochester Institute of Technology
September, 1986
Thesis Advisor: Dr. Julius L. Silver
Schoo l of Prin t i ngRochester I ns ti t u t e of Technology
Rochester , New York
CERTIF ICATE OF APPROVAL
MASTER 'S THESIS
Th is i s to cert ify that the Master's Thesis of
De in Wang
with a major in Printing Technology has beenapproved b y the Thes is Committee assatisfactory fo r the thesis requirement fo rt he Master of Science degree at theconvocation of
January 1987
Thesis committee: Julius L. silverThes is Adv iso r
Joseph NogaGraduate Adv isor
Miles SouthworthDirector Designate
'1tle of Thesia AYl T>\ v« hr !j'M af 14 Afr'~~'1z 1ts 0 1-rck Tr"",, ~ . rIO " t o' <rI\ fh,. cv.-I .1~(fl 7 Yl k
1m Hoe ,u -r",k.. U-,./ e»: fA< w'Lb a f y"o<,£SS_______________________ hereb~. (grAnt,
1I!!iV) permis.ion to the WAllace MemoriAl Library, of R.I '-T., to
epr oduce my the.i. in whole or in pArt. Any reproduction will
>t be for cOllllllerciAl use or profit.
Or
_______________________ prefer to be
~tActed eAch time A request for reproduction is mAde. I CAn be
,Ache d at the following Address.
te _
TABLE OF CONTENTS
page
LIST OF TABLES iv
LIST OF FIGURES v
ABSTRACT 1
CHAPTER I - INTRODUCTION 1
Significance and Background of Ink Transfer in
the Printing Process 1
Statement of the Problem 3
Footnotes for Chapter I 6
CHAPTER I I - BACKGROUND OF THEORY 7
Walker and Fetsko Ink Transfer Equation 8
1 . Low Ink Film Thickness 8
2. High Ink Film Thickness 12
3. Transfer Constants k, b and f 14
i . Constant k 14
ii. Constant k 15
iii . Constant f 16
Viscosity17
1. Definition 17
Footnotes for Chapter II 21
11
CHAPTER III - LITERATURE REVIEW 23
Walker and Fetsko Ink Transfer Equation 23
Rheology of Printing Inks 24
Footnotes for Chapter III 25
CHAPTER IV - METHODOLOGY 27
Hypothesis 27
Experiment Design 27
1 . Preliminary Test 28
i. Test of the Effect of Solvent
Evaperation Rate 28
ii. Test of the Ink Transfer Consistancy 29
2 . The Experiment 30
CHAPTER V - DATA ANALYSIS 32
Viscosity Measurement 32
Calculation 33
CHAPTER VI - DISCUSSION OF RESULTS 45
CHAPTER VII - CONCLUSION AND SUMMARY 54
Summary 57
CHAPTER VIII - RECOMMENDATION FOR FURTHER STUDY 58
BIBLIOGRAPHY 59
APPENDIX
A . How to Use Viscometer 61
in
LIST OF TABLES
1. Viscosity of Printing Inks 18
2. Viscosity Measurement of the Two Inks Used 33
3. Regression Data of the Unadjusted Ink-Coated
Paper 35
4. Regression Data of the Unadjusted Ink-Oncoated
Paper 35
5. Regression Data of the Adjusted Ink-Coated
Paper 35
6. Regression Data of the Adjusted Ink-Uncoated
Paper 35
7. List of b, f and R-square Value of the Linear
Regression Model 36
8. Unadjusted Ink-Coated Paper Calculation 37
9. Unadjusted Ink-Uncoated Paper Calculation 38
10. Adjusted Ink-Coated Paper Calculation 39
11. Adjusted Ink-Uncoated Paper Calculation 40
12. List of Parameter b, f and k Values 50
IV
LIST OF FIGURES
1. Percent Ink Transfer for a Coated Paper 8
2. Fraction Contact as a Function of Ink Film
Thickness 10
3. Ink Transfer per Unit of Contact Area as a
Function of Ink Film Thickness 11
4. The Amount of Ink Transferred as a Function of Ink
Film Thickness 12
5. Linear Relation of y vs. x at High Ink Film
Thickness 13
6. Change in k with Printing Pressure 14
7. Typical Flow Curve for Pseudo-Plastic Ink System 19
8. Percent Transfer Plot Comparison Between
Experiment and Transfer Equation of Unadjusted Ink-
Coated Paper 41
9. Percent Transfer Plot Comparison Between
Experiment and Transfer Equation of Unadjusted Ink-
Uncoated Paper 42
10. Percent Transfer Plot Comparison Between
Experiment and Transfer Equation of Adjusted Ink-
Coated Paper 43
11. Percent Transfer Plot Comparison Between
Experiment and Transfer Equation of Adjusted Ink-
Uncoated Paper 44
12. Linear Model of Unadjusted Ink-Coated Paper 46
13. Linear Model of Unadjusted Ink-Uncoated Paper ... 47
14. Linear Model of Adjusted Ink-Coated Paper 48
15. Linear Model of Ajusted Ink-Uncoated Paper 49
v
ABSTRACT
The Walker and Fetsko ink transfer equation is the most
used ink transfer equation to predict the ink and paper
behavior on the ink transfer step in the printing process.
All previous studies have shown that this equation is mostly
applicable in the three major printing processes, letterpress,
lithography and gravure.
A study by Schaeffer, Fisch and Zettlemoyer reported
extensive measurements for several oil-base ink and paper
combination over a range of proof-press printing
conditions. Yuri Bery did a series of studies for modifying
the Walker and Fetsko equation in gravure inks for
Weyerhaeuser Company.
All the studies showed that although generally the Walker
and Fetsko ink transfer equation can be applied to all three
major printing processes, there are always some modifications
needed for different rheological characteristics and printing
conditions .
The trends for the lithographic process is toward Web Offset
printing. The components of Web Offset ink is quite different
from conventional sheetfed lithographic ink in the pigment
and vehicle used.
This paper is to find out if the Walker and Fetsko ink
transfer equation can be also applied to the Web Offset ink.
By investigating the effect of viscosity- one of the most
important characteristics in rheology of ink - on the
transfer parameters, the ink transfer mechanism model can be
examined to see whether it is the same for oil base ink as
for the heat-set Web Offset ink.
The result of this experiment showed there is a
significant different absorption behavior between coated
paper and uncoated paper. This difference is effecting the
applicability of the Walker and Fetsko ink transfer equation
in this particular type of ink and paper combination.
CHAPTER I
INTRODUCTION
Significance and Background of Ink Transfer in the PrintingProcess
The main goal of the Graphic Arts Industry is to produce
consistent quality prints by transferring ink from plate to
paper or any other substrates. In the attempt to gain better
control of quality consistency of final prints, the transfer
of ink onto paper is a critical step. Such transfer can be
much improved if we have a better understanding of the
behaviors of inks, the characteristics of papers, and the
mechanism of ink transfer to paper in the printing process.
The first attempt to set a mathematical model for the
ink transfer process was done by Pilh and Olsson in the early
1950 's. They introduced the "transfernumber"
as the ratio
of the amount of ink on the paper to the amount of ink on the
plate after printing. This transfer number is only constant
for large amounts initial ink on the plate.
The research in ink transfer done at the National
Printing Ink Institute by William. C. Walker and Jacqueline M.
Fetsko in19551
tried to identify the major printing
solids using the letterpress process. They also tried to
identify the variables of the quality of prints being
produced. The variables studies in this experiment were the
characteristics of inks and papers, ink film thickness,
printing pressure and printing speed. From the data obtained
from this experiment, a concept of ink transfer mechanism
during printing was introduced by the authors.
The contact of the ink with the paper is
incomplete at very low ink film thickness
but improves rapidly with increasing ink
film thickness. The paper surface has a
definite capacity for taking up or
immobilizing a given amount of ink
during impression. Aconstant fraction
of the remaining or free ink is
transferred to the paper.^
The data obtained from the experiment gave the authors
a best-fit curve, from which an equation was derived. In the
equation the authors defined three constants which were the
printing smoothness of the paper, the immobilization
capacity of the ink, paper combination and the fraction of
3free ink transferred. The equation is as follows:
Y=(l-e"kx){b(l-e"x/b)+f(x-b(l-e"x/b))}
where Y = amount of ink transferred,
x = initial amount of ink on the plate,
e = base of natural logarithms, approximately
2.718,
k = (paper smoothness parameter) a constant
related to the printing smoothness of the paper,
b = (immobilization parameter) the immediate
immobilization or acceptance capacity of the
paper surface for ink,
f = fraction of free ink transferred to paper.
The equation is reduced to a simple form at high ink
film thickness as follows:
y= b + f(x-b)
This Walker-Fetsko ink transfer equation has been
generally accepted by the industry although there are a
number of studies on the parameters in the equation and on
the modifications of the equation. The modifications allow
us to have a better fit to the particular printing process
4condition. Of all the studies done in ink transfer in the
past years, there has been no major achievement in a new
quantitatively defined ink transfer mechanism. The Walker and
Fetsko ink transfer equation is still the most applicable,
quantitative and most referred to mathematical model in all
5of the three major printing methods.
Statement of Problem
The Walker and Fetsko equation is composed of two
dominant factors which are the coefficient (k) of how rapidly
printing contact area reaches 100%, and the rate of
immobilization (b) by the paper. The coefficient k is
determined by the characteristics of the substrate used and
should be an indicator of printing smoothness. A large k
value stands for high printing smoothness. The transfer
constant b indicates the maximum amount of ink which can be
absorbed or immobilized by the substrate during the
impression time the pressure is applied. It is determined
by the ink properties that are used. In the Walker and
Fetsko experiment, the vehicle viscosity of the ink used
apparently has a greater effect on the transfer constant b
than any other ink properties. Another observation made in
the Walker and Fetsko experiment regarding vehicle viscosity
is that with the decreasing vehicle viscoisty, the fraction
of free ink split factor f increases.
The interest of this experiment lies in how well the
Walker and Fetsko ink transfer equation fits a heat set
type ink and the effects of different ink viscosity. As we
know, heat set ink is a solvent type ink. The vehicle of
heat set type ink is composed of different kinds of solvent
compared to the varnish used in the oil base letter press and
sheetfed offset lithographic ink where the drying mechanism
and ink property are quite different from each other.
The question arises, can the well known Walker and
Fetsko ink transfer equation be applied to a heat set solvent
type ink, with the knowledge that the equation is derived
from data yielded by experimentation oil base letterpress inks?
If the Walker and Fetsko equation is applicable to the heat set
Web offset ink, will the ink viscosity have the same dominant
effect on the immobilization parameter b and the factor of
how free ink splits, f, as in the oil base ink? If so, can
the ink viscosity effect in the Walker and Fetsko ink
transfer equation be quantitatively defined? Or will there
be no visible effect at all?
The author hopes to find the answers for the above
questions in this experiment.
FOOTNOTES FOR CHAPTER I
J.M. Fetsko and W.C. Walker, "Measurement of Ink
Transfer in the Printing of Coated Paper,"TAGA Proceeding,
TAGA, 1955, pp. 130-137.
2W.C. Walker and J.M. Fetsko, "A Concept of Ink
Transfer in Printing,"TAGE Proceeding, TAGA, 1955, pp.
134-
149.
3Ibid.
4W.C. Walker, "Determination of Ink Transfer
Parameters,"
Tappi, Vol. 64, No. 5, 1981, pp. 71-75.
5Y. Bery, "An Ink Transfer
Equation,"TAGA Proceeding,
TAGA, 1978, pp. 172-191.
6W.C. Walker and J.M. Fetsko, "A Concept of Ink
Transfer inPrinting,"
TAGA Proceeding, TAGA, 1955, pp.134-
149.
7Ibid.
8Ibid.
CHAPTER II
BACKGROUND OF THEORY
The Walker and Fetsko Ink Transfer Equation
By examining the prints at various film thicknesses,
Walker and Fetsko had three findings:
1. When initially small amount of ink was used, the ink
film was thin and had incomplete contact to paper.
Such condition would not satisfy the ink absorption
by the paper.
2. When ink film thickness increases, the ink absorption
by the paper increased to a maximum capacity.
3. The remaining ink between the plate and the paper
would split between the plate and paper at a certain
constant ration.
4. typical ink transfer curve shown in Figure 1 is the
3"Percent Ink Transfer Curve for Coated
Paper."
Figure 1 - Percent Ink Transfer for
Coated Paper
1. Low Ink Film Thickness
The Walker and Fetsko equation is derived from low ink
film thickness which is much more complicated compared to the
high ink film thickness.
At low ink film thickness condition, the ink film is
not continuous due to incomplete contact of ink to paper.
Hence, there is not enough ink to satisfy the absorbance
4
capacity of the paper. The equation for this condition is:
y= F . Y (D
where y= amount of ink transferred to the paper,
F = fraction of area of paper contacted by ink,
Y =amount of ink transferred to the paper where
the ink and paper have actual contact.
In this condition of incomplete contact, y is determined
by the fraction of contact area F. When F reaches 100% that
is the contact is complete, y= Y. The fraction F is
the fraction constant that tells us when ink film and paper
reach a 100% contact. Walker and Fetsko analyzed many
functions to find the one to express the increase in contact
with increase in ink film thickness. In general, Figure 2
shows a general shape of the curve for this relationship.
The function that corresponds to the curve in Figure 2
is as follows :
F = 1 - (2)
where F = contact fraction,
e = base of natural logarithms, approximately
2.718,
k = coefficient that shows how fast F reaches one,
x = initial amount of ink on the plate.
10
Figure 2 - Fraction Contact as a
Function of Ink Film Thickness
The"k"
value is the printing smoothness of a particular
5paper under specified printing condition.
Since the amount of ink immobilized by the paper is
smaller than the maximum absorption capacity,b'
is used to
describe the function of the maximum immobilization or
absorption.b'
is the function of b. The relationship
betweenb'
and b is illustrated in Figure 3.
The Y, the total ink transferred, can be written as:
Y =b'
+ f(x-b'
) (3)
whereb'
= function of maximum absorption, b
11
f - the fraction of excess or free ink film split
between plate and paper.
rx-
>
r
zy^
b
'(*-?!>)
Figure 3 - Ink Transfer per Unit of Contact
Area as a Function of Ink Film
Thickness
When Walker and Fetsko examined the total transfer
curve shown in Figure 4, they selected a function which
representedb'
most adequately.
b'= b(l-e x/b) (4)
12
16
12
y
0
0
0
O
Of'
SLOPC
b=INTCRCCPT/Vf
%1
a
12
X
16 20 24
Figure 4 - The Amount of Ink Transferred
as a Function of Ink Film Thickness
From equations (3) and (4):
Y = b(l-e x/b) + f [x-b(l-e~x/b)] (5)
Substituting equations (2) and (5) into (1), we have
the well known ink transfer equation:
(l-e"kx){b(l-e x/b) + f[x-b(l-e x/b)]} (6)
2. High Ink Film Thickness
Using equation (6), in high ink film thickness condition
where the initial amount of ink on the plate, x is large, e-x
-x
approaches zero, and 1-e approaches 1.0. Hence, when x is
13
large, equation (6) is reduced to:
y= b + f(x-b) (7)
or rearranged as:
b(l-f) + fx (8)
Since equation (8) is a linear equation, and if y is
plotted against x, the slope of the straight line plotted
will be f. The intercept of the straight line is equal to
b(l-f). This relation is illustrated in Figure 5.
y= b( 1-f) + fx
'b( 1-f)
Figure 5 - Linear Relation of y vs x
at High Ink Film Thickness
14
3. Trnasfer Constants k, b and f
i. Constant k
The value of k was solved by Walker and Fetsko by using
data obtained at low ink film thickness with the values of b
and f from equation (8). Substituting equation (8) into
equation (6), we have:
i-2.303 . ,, y .
k =
xlog (1 "
T} (9)
where Y = b'+f (x-b'
)
b'= b(l-e~x/b)
The transfer constant k indicates how fast the full
contact between ink film and paper. Therefore, k should be
an index of printing smoothness.
200 *oo 600
PRINTING PRESSURE- PLI
600
Figure 6 - Change in k with PrintingPressure
15
The following statement is shown in Figure 6.
The amount of increase ink is dependent
upon the paper; papers differ in
mechanical properties such as compress
ibility, and the order in which a series
of paper is ranked for smoothness may
change with printing pressure.6
ii. Constant b
Constant b is the immobilization parameter. It
indicates the maximum amount of ink that can be immobilized
or absorbed by the paper during the brief time of impression,
The result of Walker andFetsko'
s experiment shows that b is
not directly related to those of paper absorbancy
7measurements such as setting time or final hold-out. Their
result also shows that b is greatly influenced by the ink
viscosity .
Despite the different pigment to vehicle
ratio, the mixing of varnishes and the
different ink viscosities, the vehicle
viscosity of the ink lined up remarkably
well with the b values obtained on a
particular stock.
The relationship between ink viscosity and the b value is
that as the viscosity of ink increases, the b value decreases.
This relationship is true for a series of inks similar in
components .
16
iii. Constant f
The factor f was discovered to increase with decreasing
speed and decreasingviscosity.9
This ink film splitting
mechanism was studied by Zettlemoyer and very
thoroughly. They discovered that the ink film splitting of
the excess free ink was ocrrelated with the function of the
yield value. The yield value describes the state of the ink
film when the rates of shear approach zero. The Zettlemoyer
study observed an inverse relationship between the splitting
behavior of an ink film and the shortness of the ink. The
shortness of the ink was expressed as the ratio of yield
value to plastic viscosity. They also observed that the
physical and chemical properties of the vehicle and the
pigment-vehicle interface would influence the level of
splitting.
The mechanism of ink film splitting suggested by
Zettlemoyer is as follows:
The level in the film at which ultimate
rupture occurs must depend upon the growth
of these cavities to macroscopic bubbles.
.... the cavities can probably grow best in
regions of lowest pigment loading or low
viscosity. Thus, expansion of the bubbles
from the upper to middle or lower half of
the free ink film might be expected to
occur more readily in the lower viscosity
vehicles, and lead to the higher average
splitobserved.12
17
Viscosity
1. Definition
All fluids possess a definite resistance to change of
form and many solids show a gradual yielding to forces that
tend to change their forms. This property, a sort of
internal friction, is called viscosity which is expressed in
dyne-seconds per cm or poises with a dimension of
1 1 1 3fm 1 t ] The flow of liquids through a tube, the
volume escaping per second is:
v -
Pr4
V "
8 1 n (10)
where 1 = the length of the tube,
r = tube radius,
p= difference of pressure at the ends,
n = the coefficient of viscosity.
3The volume can be given in cm /second if 1 and r are in
2 14cm, p in dynes/cm and n in poise.
Viscosity is the most important character of printing
ink. It also describes printing ink dispersion. Since
printing ink is composed of solic pigment particles in
different kinds of vehicles, different types of ink have
quite different pigment concentrations and viscosities as
15shown in Table 1.
18
Table 1
Viscosity of Printing Inks
Type Percent pigment V iscosity (poise)
Gravure 10-30 0.5-10
Flexographic 10-40 1-100
Letterpress 20-80 10-500
News ink 8-12 2-10
Lithographic 20-80 100-800
As stated in Zettlemoyer's paper, the rheological flow
curve of letterpress and lithographic inks are similar to
flow curve, in Figure 7.
The following statement explains how to measure the
rheology property of the"pseudo-plastic"
system as shown in
*>
n16
Figure 7.
The slope of the linear portion is a
measure of the plastic viscosity, u.
The intercept on the ordinate, obtained
by extrapolating to zero rate of shear,
is the yield value, SQ ,and represents
a hypothetical stress which causes flow
to begin. The quantities are related
by
S = S +UD' (H)
o
where S = stress applied to pseudo-plastic film,
17D'
= rate of shear produced by S.
19
SO 100
SHEAR, D(itc-0
ISO 200
Figure 7 - Typical Flow Curve for
Pseudo-Plastic Ink System
In the case of the pseudo-plastic system, there are
18three mechanisms in dispersion of the rheology aspect.
I. The interaction between particle and liquid
The interaction between particle and liquid is found at
low shearing stress applied which can cause the increase of
immobilization or absorption or can lead to anomalies of the
system in an opposite direction.
II. The interaction between particle and particle
The vehicle is held in the interstices of the particle
clusters. The pseuod-plasticity is shown when these clusters
are broken by the shear stress.
III. The disturbances
20
When the particles are not in sphere or rigid shape,
they could be distorted or re-aligned by the shear stress.
Such distortion would cause the disturbance in the system.
There are four factors recognized regarding the disturbance,
"the response of relative viscosity to temperature; the
reversibility of the flow curve, the existence of a lower
limit of nonlinearity and the relation of inherent viscosity
at zero rate of shear to that at infinite shear as the
19concentration of pigment is
increased."
21
FOOTNOTES FOR CHAPTER II
W.C. Walker and J.M. Fetsko, "A Concept of Ink Transferin Printing,"
TAGA Proceeding, TAGA, 1955, pp. 139-149.
2Y. Bery, "An Ink Transfer Eauation," TAGA Proceeding,
TAGA, 1978, pp. 172-191.-
3W.C. Walker and J.M. Fetsko, "A Concept of Ink Transfer
inPrinting,"
TAGA Proceeding. TAGA, 1955, pp. 139-149.
4Ibid., p. 141.
5Ibid., p. 141.
Ibid., p. 145.
7Ibid.,p. 145.
8Ibid., p. 146.
9Ibid., p. 147.
A.C. Zettlemoyer, R.F. Scarr and W.D. Schaeffer,"Influence of Ink Properties on Transfer During
Printing,"
International Bulletin for the Printing and Allied Trades,No. 13, 1958, pp. 88-94.
11T. ..Ibid.
12Ibid., p. 94.
13R.C. Weast, M.J. Astle and W.H. Beyer, CRC Hand Book
of Chemistry and Physics, CRC Press, Inc., 64th Edition,F - 36, 1983-1984.
14T. . .
Ibid.
15A.C. Zettlemoyer and R.R. Myers, "The Rheology of
PrintingInks,"
Rheology Theory and Applications, Vol. 3,
1960, p. 146.
16A.C. Zettlemoyer, R.F. Scarr and W.D. Schaeffer,
Influence of Ink Properties on Transfer DuringPrinting,"
International Bulletin for the Printing and Allied Trades,
No. 13, 1958, pp. 88-94.
Ibid.
22
A.C. Zettlemoyer and R.R. Myers, "The Rheology of
PrintingInks,"
Rheology Theory and Applications, Vol. 3,
1960, p. 146.
1 9Ibid.
, p. 164.
23
CHAPTER III
LITERATURE REVIEW
The Walker and Fetsko Ink Transfer Equation
The single most important finding in this subject can
be found in the two research papers by William C. Walker and
Jacqueline M. Fetsko, the "Measurements of Ink Transfer in
the Printing of CoatedPapers"
and "A Concept of Ink
Transfer inPrinting."
Walker and Fetsko received the
concept ofPihl3
and Olsson and Pihl'
who created the first
mathematical model for the ink transfer mechanism and
introduced the concept of the "transfernumber"
as the ratio
of the amount of ink on the paper to the amount of ink on the
plate after printing. Several articles were published after
the initial studies done by Olsson and Pihl concerning the
immobilized ink and the split of excess ink.
The Walker and Fetsko equation generated a number of
studies and discussions on its transfer parameters, y, x, k,
b and f. One of the interests to the authors is the
Q
"Influence of Ink Properties on Transfer DuringPrinting."
In Zettlemoyer's paper, a more detailed splitting has been
discussed, relating to the yeild value and viscosity in the
rheology aspect.
Zettlemoyer also explained the ink film splitting
mechanism from the rheological point of view which is quite
24
complicated but can help us gain more understanding in the
mechanism of ink transfer from plate to One of the
most extensive studies is done by Schaeffer and
who have done very extensive measurements for three types of
inks and four kinds of paper over a range of proof-press
printing conditions. In their study, the dependence of the
transfer parameters on the paper-ink-pressure-speed has been
determined.
There are quite a few studies done to propose a new ink
transfer equation or to modify the Walker and Fetsko
equation. Some of the notable works are of ANPA11,
Rupp and Rieche,Laraignon
, Ichikawa14, andBery15
of
Weyerhaeuser Company. But none of them is enough to
overpower the Walker and Fetsko ink transfer equation.
Rheology ov Printing Inks
The publication most frequently referred to on
printing industry in the rheology theory is the Rheology
Theory and Application. "The Rheology of PrintingInks"
by
Zettlemoyer and Myers in Rheology Theory and Application
states the necessary concept of rheology theory in the
printing industry.
25
FOOTNOTES FOR CHAPTER III
J.M. Fetsko and W.C. Walker, "Measurement of Ink
Transfer in the Printing of Coated Paper,"TAGA Proceeding,
TAGA, 1955, pp. 130-137.
2W.C. Walker and J.M. Fetsko, "A Concept of Ink Transfer
in Printing,"TAGA Proceeding, TAGA, 1955, pp. 139-149.
3L. Pihl, "The Ink Transfer to Paper in
Printing,"
Svensk Papperstidning, No. 10, 1952.
4I. Olsson and L. Pihl, "The Ink Transfer to Newsprint
at Printing under VaryingConditions,"
Svensk Papperstidning,No. 12, 1952.
5I. Olsson and L. Pihl, "Printing Studies at the Swedish
Graphic Arts Research Laboratory, Stockholm, Sweden, Tappi,
Vol. 37, No. 1, 1954, p. 42.
6, "Testing Method for Printability of
Paper,"
Progress Report Seven, ANPA Technical Report No. 11, 1953.
7, "Testing Method for Printability of
Paper,"
Progress Report Ten, ANPA Technical Report No. 17, 1954.
8A.C. Zettlemoyer, R.F. Scarr and W.D. Schaeffer,"Influence of Ink Properties on Transfer During
Printing,"
International Bulletin for the Printing and Allied Trades,
No. 13, 1958, pp. 88-94.
9Ibid. ,p. 94.
10W.D. Schaeffer, A.B. Fisch and A.C. Zettlemoyer,
"Transfer and Penetration Aspects of InkReceptivity,"
Tappi,
Vol. 46, No. 6, 1963, pp. 359-375.
11, "Testing Method for Printability of
Paper,"
Progress Report Seven, ANPA Technical Report No. 11, 1953.
12E. Rupp and K. Rieche, "Bertrage zur Bedruckbarkiet
von Papier undFolien,"
Institute fur Grafische Technik,
Leipzig, Germany, 1959.
13R. Laraignou, Asso . Tech. Ind. Papetiere Bull, No. 6,
1960, pp. 217-226.
26
I. Ichikaira, K. Sato and G. Ito, "A New Concept of
Ink TransferEquation,"
Res. Bull. Gov. Printing Bureau,
Japan, No. 1, 1962.
15Y. Bery, "An Ink TransferEquation,"
TAGA Proceeding,
TAGA, 1978, pp. 172-191.
16A.C. Zettlemoyer and R.R. Myers, "The Rheology of
PrintingInks,"
Rheology Theory and Applications, Vol. 3,
1960, p. 165.
27
CHAPTER IV
METHODOLOGY
To reiterate, the purpose of this paper is to find out
if the Walker and Fetsko ink transfer equation is applicable
to the heat set type Web offset ink and what are the effects
of different ink viscosities of the same kind of heat set
ink in ink transfer parameters.
Hypothesis
The hypotheses of this experiment are as follows:
1. The Walker and Fetsko ink transfer equation can be
applied on heat set Web offset ink as well as other oil base
letterpress and lithographic ink.
2. The transfer parameters b and f in the Walker and
Fetsko equation increase as the ink viscosity in the same
kind of ink decreases.
Experiment Design
The instruments used in this experiment are IGT
Printability Tester, viscometer and a balance.
The IGT Printability Tester can give a better control on
the thickness of ink layer and cylinder covering, and keep
the printing speed and pressure in a constant or change it
with little difficulty. There is only a very small amount of
ink and paper needed and the IGT Printability Tester is
28
fairly easy to operate. This will allow the test to be
accomplished in a reasonable time.
The IGT Printability Tester can provide the means of
applying ink film to paper under a set of controlled
conditions. The IGT Printability Tester is designed to
stimulate a mechanical abstraction or rotary printing press.
A Brookfield Viscometer model RV is used to do the
rheology measurement. By placing different spindle in
size in different rotation speeds, we can measure the
shear force of the ink fluid. The measurement is recommended
to be taken 15 seconds after each rotating speed change, the
reading can be of 1 percent accuracy and can be reproduced
in 2 percent accuracy by the manufacturer.
1. Preliminary Test
Two preliminary tests will be conducted before the
experiment .
i. Test of the Effect of Solvent Evaporation Rate
Since heat set ink is a solvent type ink, the
solvent evaporation effect should be investigated first
The concern is if the amount of solvent evaporates in a
time period is significant to the ink in quantity and
rheology property aspect.
The procedure is as follows for the two
measurements :
a. Rheology measurement:
Take the readings of the viscometer in five time
29
intervals to see if there are any changes taking
place. The times are 30, 60, 90, 120 seconds,
and 3 minutes.
b. Weight measurement:
1. Distribute ink evenly on a clean, dry printing
disc.
2. Weight the inked disc in four time intervals,
1 minute, 2, 3, and - minutes.
3. Check if there is any weight difference in
these four measurements.
ii. Test of the Ink Transfer Consistency
This test can help us decide if the experiment
needs to be repeated more than once to achieve an
accurate measurement. The procedure is as follows:
a. Distribute the ink evenly on the printing disc.
b. Measure the disc weight.
c. Put the disc on an IGT Printability Tester of a
set printing speed and pressure, then print it.
d. Weigh the disc after printing.
e. Clean the disc, apply ink on the disc and try to
control the ink film thickness as the previous
one.
f. Print the disc, weigh the disc.
g. Repeat steps 5 and 6 again.
h. Check the difference among the three
measurements .
30
2. The Experiment
i. Measure the viscosity of a heat set Web offset ink.
ii. Weigh a clean, dry disc.
iii. Apply a controlled amount of ink on the printing
disc.
iv. Weigh the disc on the balance.
v. Put the disc on the IGT Printability Tester, put
paper on the cylinder, print it.
vi. Take the disc off the IGT Printability Tester and
weigh on the balance.
vii. Repeat steps 2 to 5 a number of times, as needed
with different amounts of ink.
'iii. Calculate the percentage of transfer.
x =weight of inked disc before printing
-
weight of
clean disc
y= x - (weight of inked disc after printing
-
weight of clean disc)
percentage of ink transferred =
ix. Plot percentage of ink transferred vs x on a piece
of graph paper.
x. Repeat steps 1 to 9 with another ink viscosity. To
change the ink viscosity, add more solvent into ink.
xi. Calculate transfer parameters b, f, and k. Plot y
against x on a piece of graph paper.
In the high ink film thickness portion, the straight
v:
31
line, y= b + f (x -
b), the slope is equal to f,
and the intercept equals b(l - f) since y= b(l - f)
+ fx.
To calculate k from equation (9):
_ 2.303 . .. y NK ~
log (1--^-)
where Y = b'+ f(x - b')
b'= b(l -
e~x/b)
xii. Use the x value of the experiment and the calculated
b, f and k values to calculate the y value by using
the Walker and Fetsko ink transfer equation.
xiii. Use both measured and calculated y values to
calculate percent transfer and plot percent transfer
vs x value on the same piece of graph paper.
xiv. Plot ink transfer curve of 2 different ink
viscosities on the same piece of graph paper to see
the differences.
xv. Calculate b, f and k values of both viscosities of
inks, compare the b, f and k values.
xvi . Analyze the differences of the y values measured
from the experiment and the y values calculated from
the Walker and Fetsko equation.
32
CHAPTER V
Data Analysis
The ink used in the experiment is a (Arroweb Process
Black), a black web offset ink made by Flint Ink Co. The
thinner used to reduce ink viscosity is a solvent type with
low evaporation rate which is made by IPI, Interchemical
Corporation, Print Ink Division. Two kinds of paper were
used in the experiment. They were ARDOR offset 3 85 Regular
#60 coated and ARDOR offset 3 Regular 85 undcoated. The
printing pressure setting of IGT Printability Tester was 40
on the scale which is normal for various testing.
The adjusted ink was made by mixing 5 percent solvent
by weight with unadjusted black web offset ink. There were
four ink-paper combinations being tested. They are,
1. Unadjusted ink on coated paper.
2. Unadjusted ink on uncoated paper.
3. Adjusted ink on coated paper.
4. Adjusted ink on uncoated paper.
Viscosity Measurement
To make sure the viscometer was functioning well, a
calibration measurement was performed on a known viscosity
oil. Two measurements were conducted on both adjusted ink
and unadjusted ink. The viscosity readings are as follows:
33
INK
unadjusted
adjusted
VISCOSITY (POISE)
3900
1680
Table 2. Viscosity Measurement of the Two Inks Used
Calculation
1. Parameter b and f
The calculation of b and f was done by applying
equation (8) using data points in the thick ink film region.
The high ink film region is defined as the region with
maximum absorption which is the region after the peak of the
curve. A linear regression model was set on theMINITAB'
subroutine in R.I.T.'s VAX/ VMS computer system. The model
is as follows:
y= b(l-f) + fx
Tables 2 to 5 are the results of all four ink-paper
combination groups from the linear regression model. Table 6
is a list of b, f and the R-square values of all four ink-
paper groups.
2. Parameter k
From the complete equation (6), we can get
F = y/Y
then
l-e"kx
= y/Y
34
-kx=
-ln(l-y/Y)/x
where, Y = b'+ f(x-b'),
b'=
b(l-e~x/b)
To calculate k, we need to obtain the b', Y and x, f from
calculation. Tables 7, 8, 9 and 10 are the data lists of
each group. The column initials are explained as follows:
INIT: x value of the experiment data, in mg.
TRANS: y value of the experiment data, in mg .
PERT: percent of transfer in weight based on experiment
data.
Y: Y value from the calculation.
k: calculated k value from experiment data.
F: calculated F value from experiment data.
y: calculated value from the transfer equation.
CAL. PERT: calculated percent transfer value from the
transfer equation.
b: b value obtained from the linear regression model.
f: f value obtained from the linear regression model.
AVG k: average k value of the experiment data which is
used in calculation of the transfer equation.
A set of graphic illustrations from Figures 8 to 11 is
presented. These plottings show the differences between the
percent transfer curve of the experiment data and the curve
of the calculated data from the Walker and Fetsko transfer
equation .
35
Table 3. Unadjusted Ink - Coated Paper Regression Data
The regression equation is
C3 = 0.00303 + 0.516 C2
Predictor Coef Stdev t-ratioConstant 0.0030312 0.0009029 3.36C2 0.51564 0.01663 31.00
s = 0.0006403 R-sq = 99.8% R-sq(adj) = 99.7%
Table 4. Unadjusted Ink - Uncoated Paper Regression Data
The regression equation is
C3 = 0.00367 + 0.712 C2
Predictor Coef Stdev t-ratio
Constant 0.0036721 0.0009118 4.03
C2 0.71242 0.01873 38.04
s = 0.0004681 R-sq = 99.7% R-sq(adj) = 99.7%
Table 5. Adjusted Ink - Coated Paper Regression Data
The regression equation is
C3 = 0.000085 + 0.596 C2
Predictor Coef Stdev t-ratio
Constant 0.0000855 0.0002423 0.35
C2 0.59579 0.01867 31.91
s = 0.0003696 R-sq = 98.6% R-sq(adj) = 98.5%
Table 6. Adjusted Ink - Uncoated Paper Regression Data
The regression equation is
C3 = 0.00333 + 0.807 C2
Predictor Coef Stdev t-ratio
Constant 0.003333 0.002047 1.63
C2 0.80746 0.02627 30.74
s= 0.001282 R-sq = 99.5% R-sq(adj)
= 99.4%
36
Table 7. Value of b, f and R-square of the
Linear Regression Model
b f R-sq(adj)
Unadjusted Ink - Coated Paper 0 0063 0. 5160 99 7%
Unadjusted Ink - Uncoated Paper 0 0127 0 7120 99 7%
Adjusted Ink - Coated Paper 0 0002 0 5960 98 5%
Adjusted Ink - Uncoated Paper 0 0173 0 8070 99 .4%
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45
CHAPTER VI
Discussion of Results
The linear regression model of the high ink film region
which the constants b and f were obtained from have a very
high R-square value. This result also can be observed on the
plottings in Figure 12 to 15, which showed all the data
points fell on a straight line except a couple of bad data
points in the adjusted ink -
coated paper group.
The graphic comparison of experiment data and calculated
transfer equation values in Figures 8 to 11 showed the data
and values correlate very well on the two uncoated paper
groups .
In the coated paper groups, the experiment and
calculated data do not correlate very well especially in the
low ink film thickness region. The difference between the
experiment and calculated data is most obvious in the
adjusted ink - coated paper group.
The linear models which transfer parameters b and f are
derived from, have a very high degree of confidence for all
four groups.
b f k
unadjusted ink--coated 0 0063 0 5160 166 .1913
unadjustedink-
-uncoated 0 0127 0 7120 83 .9721
adjusted irik-coated 0 0002 0 5960 287 .2918
46
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50
adjusted ink-uncoated 0.0173 0.807 59.9039
Table 12. Transfer Parameters b, f and k
The relationship that Walker and Fetsko observed between
the immobilization parameter b and the ink viscosity was that
when the viscosity decreases, parameter b increases. This
observation exists only in the uncoated paper group. The
coated paper group showed a reverse result in which the
parameter b decreases sharply when the viscosity decreases.
The transfer parameter f behaved as Walker and Fetsko
predicted; the decrease of viscosity would cause the
parameter f increases in both uncoated and coated paper.
We can see that the b and f value is higher in the
uncoated paper groups than those in the coated paper groups
in both ink viscosity. This result showed that the uncoated
paper has a higher absorptace capacity than the coated paper
and the uncoated paper also has a higher ink film splitting
ratio than the coated paper. This high immobilization and
splitting ratio of the uncoated paper may suggest that the
uncoated paper has a better ink trapping mechanism than the
coated paper in ink transfer. A logical assumption would be
that this trapping mechanism has something to do with the
porosity of the substrate surface.
Parameter k is an indicator of how fast the ink film
reached full contact with the substrate. This parameter k
can only be significant to the equation in the low ink film
51
thickness region where the partial contact between the ink
film and the paper happened. Therefore, only the k value of
the low ink film region will be counted when calculating the
average k value. The data points in the high ink film
region have been discarded in that region. In some cases,
the k cannot be calculated due to Y is greater than the y
value of the experiment since k =-ln(l
-
y/Y) / x. This
may be caused either by the operation error or the improper
approximation of the k value in the ink transfer equation.
Since k is a printing smoothness factor we can assume the
coated paper has a higher k value than the uncoated paper
when applying the same type of ink. The k value increases
when viscosity decreases. But this is reversed in the
uncoated paper; the k value decreases when the viscosity
decreases .
Two types of substrate were used in the experiment; the
coated paper and the uncoated paper in both ink viscosities.
A good correlation between the experimental and calculated
data has been observed in the uncoated paper groups on the
graphic comparison illustration. There is less correlation
between the experimental and calculated data in the low ink
film thickness region of the unadjusted ink-coated paper
groupalthough the data points in the high ink film thickness
region matched well. In the low ink film region of the
unadjusted ink-coated paper group we observed the calculated
rve reaches the peak faster and sharper than thecu
52
experimental curve. This result suggested the calculated k
value from the equation is higher than the actual coefficient
of the experiment data. The almost perfect match in the high
ink film region can be the evidence of a reliable parameter
b and f value of the experiment.
The data of parameter k of the adjusted ink-coated
paper is a reverse of the unadjusted ink-coated paper group.
The calculated transfer curve from the equation arose slowly
to a constant. A sharp rise to the peak then decreased to a
constant for the experiment data curve. The comparison of
the experiment transfer curve and the calculated transfer
curve is plotted in Figure 10. We observed the calculated
transfer curve arise much slower than the actual experimental
transfer curve. This graduate arise of the calculated curve
is caused by the smaller parameter k value than the
coefficient of the actual experiment condition. Again, the
high ink film region of the experiment data and calculated
data correlate very well in this adjusted ink-coated paper
group .
The plots of the unadjusted ink-uncoated paper and
adjusted ink-uncoated paper are on Figure 9 and Figure 11.
The plots showed a very good correlation between the
experiment data and calculated value, although we can still
observe a higher peak value of the experiment data than the
calculated data in both uncoated paper groups. This could
suggest there is a higher actual parameter b value than the
53
b value derived from the transfer equation
54
CHAPTER VII
Summary and Conclusions
Two hypotheses were to be examined in this experiment.
1. The Walker and Fetsko ink transfer equation can be applied
on heat set web offset ink as well as oil base letterpress
and lithographic ink.
2. The transfer parameters b and f in Walker andFetsko'
s
equation increases as the ink viscosity decreases.
When we compared the data points that had been obtained
from the experiment and the calculation values of the Walker
and Fetsko ink transfer equation, we can conclude that the
equation is applicable to the heat set web offset ink used in
this experiment. The Walker and Fetsko equation predicts the
transfer behavior successfully in the high ink film thickness
region and matches the experiment data points very well.
Overall, the Walker and Fetsko equation performs remarkably
successfully in predicting the ink transfer behavior on the
uncoated paper. The calculated transfer curve from the
equation matched the transfer curve from the experiment very
well. There were some differences between the calculated
values and the experiment data in the low ink film region
with the coated paper groups of both ink viscosities. These
differences may be due to the improper parameter k value
being supplied to the equation. This improper k value caused
the calculated transfer curve to peak earlier than the
55
experiment transfer curve in the unadjusted ink-coated paper
group. A reverse result was taking place in the adjusted
ink-coated paper group. The calculated transfer curve failed
to arise and peak as quickly as the transfer curve obtained
from the experiment.
Fluctuated k values were noticed in the transfer data
tables in all four ink-paper groups. But the paper porosity
has a definite influence on the parameter k. A much higher
k value is observed in the coated paper group than in the
uncoated group. Since this parameter k is a dominate factor
in predicting the low ink film transfer behavior and it was
fluctuating in this experiment, some further study is
recommended in order to better understand this parameter.
Overall, the Walker and Fetsko ink transfer equation
performed a very accurate prediction of the ink transfer
behavior of the particular heat set web offset ink used in
this experiment. However, further study of the parameter k
and its relationship to substrate porosity is needed in order
to predict low ink film transfer behavior of certain
substrates .
The second hypothesis predicts that viscosity decreases
and the parameters b and f increase. This hypothesis is
true in the uncoated paper groups where a noticeable increase
of b and f values occurred as the ink viscosity decreased
sharply. In the coated paper groups only the parameter f
increases when ink viscosity decreases. Parameter b
56
decreases significantly when a lower viscosity ink was
applied on the coated paper. This phenomenon is contradic
tory to the Walker and Fetsko observation and the hypothesis
of this experiment. A logical assumption is that in a high
solvent ink system, more vehicle would be immobilized when
stress is applied. This can explain the increase of immobil
ization parameter b when ink viscosity decreases. Apparently
this is not the case in the adjusted ink-coated paper group
of which parameter b decreased sharply as the viscosity
decreased. One possible explanation for this sharply
decreased parameter b in the adjusted ink-coated paper is
that paper coating material somehow interfered with the
paper absorption mechanism and unstablized the ink transfer
process. This unstable transfer condition was evidenced by
the scattering experiment data points of adjusted ink-coated
paper group in Figure 10.
Parameter f behaved as predicted; f increases when ink
viscosity decreases in all four ink-paper test groups. The
free ink splitting mechanism suggested by Zettlemoyer is
that film splits at the level of ultimate rupture occurrence
and this rupture grows best in the lower viscosity. There
fore, an expansion of the rupture from the upper to middle
or lower half of the free ink film is expected in the lower
viscosity ink. The expansion of the rupture with in the free
ink film would give a higher splitting ratio f.
57
Summary
The Walker and Fetsko ink transfer equation is applic
able on the web offset heat set type ink. More modification
is needed to approximate parameter k in order to better
predict ink film transfer behavior in the low ink film
thickness condition. The equation performed an accurate
prediction of ink transfer behavior in the high ink film
condition. An unstable ink transfer situation was noted
when the high solvent ink was applied to the coated paper
condition .
Immobilization of parameter b and splitting parameter f
increases when ink viscosity decreases. An exception of this
phenomena was noticed in the adjusted ink-coated paper group
where immobilization parameter b decreased with the decrease
of ink viscosity.
A fluctuated parameter k was also noticed in all four
test groups.
58
CHAPTER VIII
Recommendation for Further Study
There are three parameters, b; f and k in the Walker
and Fetsko ink transfer equation. The free ink film splitting
mechanism suggested by Zettlemoyer explained the relationship
between the parameter f and ink viscosity. The immobiliza
tion parameter b behaved as predicted in three of the four
test groups. The exceptional result came from the high
solvent ink and coated paper group. Due to the unstable
transfer condition of this group, a further replica test in
this ink-paper combination is recommended to determine the
variables which caused instability in the ink transfer
process .
Parameter k is still the least understood factor in the
Walker and Fetsko equation and the k value fluctuated so much
in all four test groups. Some further study of the parameter
k is highly recommended since this parameter seemed to be a
dominate factor in predicting the ink transfer behavior at
low ink film thickness situations. Because of the instabil
ity of the k value in the experiment, this author suggests
the future study would be best conducted on a large sample
size to obtain a reliable finding. To isolate the k
parameter a non-absorbtive substrate may be used to eliminate
the influenceof the other two parameters.
59
BIBLIOGRAPHY
Bery, Y. "An Ink Transfer Equation."TAGA Proceeding. TAGA
1978.-
Fetsko, J.M. and W.C. Walker. "Measurement of Ink Transferin the Printing of Coated Paper."
TAGA Proceeding;.
TAGA, 1955.
Ichikaira, I., K. Sato and G. I to. "A New Concept of Ink
Transfer Equation."Res. Bui. Gov. Printing Bureau.
Japan: No. 1, 1962.~
"
Laraignou, R. Asso. Tech. Ind. Papetiere Bull., No. 6, 1960.
Olsson, I. and L. Pihl. "The Ink Transfer to Newsprint at
Printing under VaryingConditions."
Svensk Papperstiding,No. 12, 1952.
Olsson, I. and L. Pihl. "Printing Studies at the Swedish
Graphic Arts Research Laboratory, Stockholm,Sweden."
Tappi, Vol. 37, No. 1, 1954.
Pihl, L. "The Ink Transfer to Paper inPrinting."
Svensk
Papperstidning, No. 10, 1952.
Rupp , E. and K. Rieche. "Bertrage zuy Bedruckbarkiet von
Papier undFolien."
Institute fur Grafische Technik.
Leipzig, Germany: 1959.
Shaeffer, W.D., A.B. Fisch, and A.C. Zettlemoyer. "Transfer
and Penetration Aspects of InkReceptivity."
Tappi, Vol.
46, No. 6, 1963.
Walker, W.C. and J.M. Fetsko. "A Concept of Ink Transfer in
Printing."
TAGA Proceeding, TAGA, 1955.
Walker, W.C. "Determination of Ink TransferParameters."
Tappi, Vol. 64, No. 5, 1981.
Weast, R.C., M.J. Astle, and W.H. Beyer. CRC Hand Book of
Chemistry and Physics. CRC Press, Inc., 64th Edition,
F-36, 1983-1984.
60
Zettlemoyer, A.C., Scarr, R.F., and W.D. Shaeffer.
"Influence of Ink Properties on Transfer DuringPrinting."
International Bulletin for the Printing and
Allied Reades, No. 13, 1958.
Zettlemoyer, A.C. and R.R. Myers. "The Rheology of PrintingInks."
Rheology Theory and Applications, Vol. 3, 1960.
. "Testing Method for Printability ofPaper."
Progress Report Seven, ANPA Technical Report No. 11,1953.
"Testing Method for Printability ofPaper."
Progress Report Ten, ANPA Technical Report No. 17.
1954.
APPENIX
61
How to use the viscometer:
The Brookfield has two forms of set up which must be
completed prior to use. Step #1 is to level the mounting
stand. Leveling of the stand is done using the thumb screws
at the bottom. The bubble in the level must be in the
center of the black circle. Step #2 is the leveling of the
viscometer on the stand. This set up is performed the same
way as step #1.
Conditions Which Reduce the Unit's Accuracy
1) When using RV spindles the guard should be attaced.
Using the unit without the guard would cause a slight
reduction in the readings.
2) Spindles which rotate too close to the container's walls
would slightly increase the viscosity readings.
3) Dried ink on spindles would increase contact area. There
fore, the shear force increases. Viscosity readings would
increase a small amount .
4) Improper depth of spindles could cause an increase or
decrease in readings.
Formula for RV spindles:
V = D x F V =viscosity
D = dial reading
F = factor
To find the factor chart A is used. Looking on the chart, a
value of 1 was determined for spindle #1 . Knowing both D
62
and F values, a viscosity of 21 cps was calculated,
Formula for RVT spindles:
V=DxKxF v =
viscosity
K = 0.01
F = factor
\=u7
rn
RV SP TUPLES
left hand thread
- shaft under cut
( depth indicator )
63
left hand thread
coupling
If
RVT SPINDLES
spindle chuck
we ight
RVT spindle
RV Spindles
64
""~^--\^sp indie #
rpm-~^
1 2 3 4 5 6 7
0.5 200 800 2m 4m 8m 20m 80m
1 100 400 lm 2m 4m 10m 40m
2 50 200 500 lm 2m 5m 20m
2.5 40 160 400 800 1.6m 4m 16m
4 25 100 250 500 lm 2.5m 10m
5 20 80 200 400 800 2m 8m
10 10 40 100 200 400 lm 4m
20 5 20 50 100 200 500 2m
50 2 8 20 40 80 200 800
100 1 4 10 20 40 100 400
table A
RVT Spindles
m=l,000
rpm ^^
A B C D E F
0.5 400m 800m 2mm 4mm 10mm 20mm
1 200m 400m 1mm 2mm 5mm 10mm
2.5 80m 160m 400m 800m 2mm 4mm
5 40m 80m 200m 400m 1mm 2mm
m=1,000mm=l,000,000
table B