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


Experiment and Transfer Equation of Unadjusted Ink-

Uncoated Paper 42


Experiment and Transfer Equation of Adjusted Ink-

Coated Paper 43


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,"


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.


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.


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,"


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


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


C3 = 0.000085 + 0.596 C2


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


C3 = 0.00333 + 0.807 C2


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

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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

An Investigation of the Applicability of Walker and Fetsko Ink Transfer Equation on and the...

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