=Paper=
{{Paper
|id=Vol-2604/paper51
|storemode=property
|title=Information Technology to Improve the Quality of Printed Image Reproduction by Ink Printing Systems
|pdfUrl=https://ceur-ws.org/Vol-2604/paper51.pdf
|volume=Vol-2604
|authors=Mykhailo Verkhola,Ulyana Panovyk,Ihor Huk,Myron Kalytka
|dblpUrl=https://dblp.org/rec/conf/colins/VerkholaPHK20
}}
==Information Technology to Improve the Quality of Printed Image Reproduction by Ink Printing Systems==
https://ceur-ws.org/Vol-2604/paper51.pdf
Information Technology to Improve the Quality of
Printed Image Reproduction by Ink Printing Systems
Mykhailo Verkhola1[0000-0001-6135-6439], Ulyana Panovyk1[0000-0002-9663-4328],
Ihor Huk1[0000-0002-0815-3496], and Myron Kalytka1[0000-0001-7814-7211]
1
Ukrainian Academy of Printing, Pid Holoskom, St., 19, 79020 Lviv, Ukraine
ulianapanovuk@gmail.com
Abstract. It is proposed the information technology to improve the reproduc-
tion quality of the printed image. In the process of developing information tech-
nology, a signal graph was constructed and a three-dimensional mathematical
model of the branched structure ink printing system was developed, which de-
scribes the process of ink microflows transferring from the ink feeder device to
the imprints. A simulator of an ink printing system was built which simulates
the work of all its elements and reproduces the printing process. Various vari-
ants of form simulation models representation with the same values of the form
filling coefficients in the corresponding zones were developed. An algorithm
for constructing a simulation model of a printing form is proposed, which takes
into account the topology of printing elements placement and reproduces the
image in detail. As a result of the simulation and analysis, it was established
that determining the parameters of the input task using simplified printing form
models does not provide the required accuracy of imprints reproduction. There-
fore, to improve the quality of print products and, accordingly, the accuracy of
the parameters of the input task, it is necessary to use a printing form model,
which takes into account the topology of printing elements.
Keywords: Image, Printing form, Information Technology, Ink printing Sys-
tem, Signal graph, Three-dimensional mathematical model, Simulator.
1 Introduction
1.1 Formulation of the Problem
Offset printing is a leader among other types of printing. Offset printing is used for
printing medium-sized prints of high-quality printing products: books, magazines,
labels or souvenirs. Offset printing provides optimum reproduction of small details
and good transfer of midtones on different media, with high clarity and brightness
[1 – 3]. The quality of the image reproduction by offset printing machines depends on
the technologically necessary ink thickness and its uniformity of application on paper
or other material. This process is ensured by offset printing systems and predeter-
mined to a large extent by the features of their designs and settings.
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
The printing enterprises of Ukraine mainly used medium format machines of dif-
ferent manufacturers: Adast, Heidelberg, KBA, MAN Roland, Ryobi, etc. Depending
on the series, the ink printing systems have different numbers of rollers and cylinders.
Small format machines have 13 rollers, 3 of which are form rollers (13/3); the medi-
um format is 16/4 and the large format is 21/4. However, irrespective of the element
number and their topology, offset ink printing systems must provide the optimal pa-
rameters of replicated imprints that meet the requirements of international standard
ISO 12647. And obtaining such high-quality products depends directly on the adjust-
ment of the ink printing systems. Therefore, improving the accuracy of ink printing
systems setting is an actual problem.
1.2 Analysis of Literary Data and Problem Statement
The analysis of existing offset ink printing systems of well-known companies showed
that all of them are structurally different from each other by the number of rollers in
the ink printing system, by their size and location. The efficiency of these systems can
only be determined by the quality of the products printed on them. The quality of the
printed image depends to a great extent on the accuracy of the determination and the
appropriate adjustment before printing of the ink feeder device that will ensure receipt
of the technologically necessary ink thickness on the imprints [4]. Many years of
research have shown that the amount of ink that must be submitted to the input of the
ink printing system depends on many factors, such as the nature of the printing ele-
ments filling, the coefficients of the ink separation between the elements of the print-
ing system, the design of the printing system, etc. [5–9].
In [10], a computer simulation investigated the distribution of ink thicknesses at
the output of ink printing systems when receiving imprints from a printing form hav-
ing a different intensity of its zonal filling with printing elements. It is found that the
ink from the zone with the high coefficients of the form filling is redistributed to adja-
cent zones, where the coefficients of the form filling are lower. It is concluded that to
align the ink thickness in all zones of the imprint, it is necessary to adjust the zonal
ink supply at the input of the ink printing systems, but it is not suggested how to de-
termine the amount of correction. In [11], the process of ink transferring by an ink
printing system is simulated by a computer, and the ink distribution is used, based on
which a singular matrix is built. The resulting matrix is proposed to use to determine
the input task that would enable the reproduction of imprints from the printing form.
The input task parameters are determined by truncating the singular matrix. This pa-
per does not provide a detailed description of the ink printing system mathematical
model, based on which a singular matrix is obtained. And in determining the coeffi-
cients of the singular matrix does not take into account the mutual movement of the
ink flows in the axial direction, which is caused by the operation of the oscillator
cylinders. In [12], it is argued that the ink transfer system is essential to ensure high
quality printed matter. Based on the model developed it was carried out analysis of
the effect of print speed on the dynamics of the ink transfer. The results show that
increasing printing speed increases the time of ink stabilization. However, this paper
does not show how this data can be used for an ink printing system setting.
In [13], a computer simulation investigated the dynamic properties of an offset ink
printing system. It is revealed that the mode of oscillators' operation and the density of
form filling with printing elements have a significant influence on the duration of the
ink printing system output on the steady mode. In [14] it is noted that the quality of
printing depends on the ink supply system, which is important and complex in offset
printing. Mathematical models of ink printing systems have been developed and
simulations and investigating the effect of ink supply methods on the duration of the
transition process in the ink printing system have been carried out. As a result of
modeling, it is established that the ink supply system, the mode of oscillators’ opera-
tion and the density of form filling with printing elements affect the dynamic proper-
ties of the ink printing system. In researches [13, 14] it is not offered how the ob-
tained results can be used for ink printing systems setting. Therefore, the development
of methods and technologies for improving the setup of ink printing systems is an
important task.
2 Materials and Methods
2.1 Signal Graph of the Offset Ink Printing System
To represent the process of developing information technology to improve the accura-
cy of determination before printing the input task, we use a branched structure ink
printing system, a fragment of the signal graph of which is presented in Fig. 1.
The presented signal graph reflects the circulation of the ink microflows in a sepa-
rate j-th zone. The amount of ink microflows in a zone depends on their width and
width of the ink feed zone. The amount of zones is determined by the number of ink
supply regulators at a certain brand of offset machine. The vertex at the input of the
signal graph reflects the ink flow thickness, which is supplied in the j-th zone to a part
of the ductor surface and arrives in the form of k microflows through the vibrator
roller to the surface of the first oscillator cylinder. The vertices of the graph are joined
by arcs or lines that reflect the microflows circulating on the surfaces of the rollers
and cylinders in a circular direction. A closed circuit corresponds to each roller and
cylinder. The movement of the microflows in the axial direction is reflected by hori-
zontal lines. In other zones, the process of ink distributing in a circular direction is
similar, and in the axial direction, ink moves between adjacent zones. The general
graph of the ink printing system consists of n graphs, which is presented in Fig. 1. All
other vertices of the graph, except for the input and output, reflect the ink microflows
thicknesses at the respective contact places of the ink printing system elements. The
vertexes at the output of the ink printing system correspond to the ink microflows
thickness, which are transferred to paper or other material.
2.2 Mathematical Model of the Ink Printing System
In developing the mathematical model, we accept the following assumptions: the
whole ink printing system is conventionally divided into n zones of equal width; in
each zone are transmitted k ink microflows from the ductor cylinder to the imprints.
h dj
j
Pd
l d1 l dk
R 1d T v1 R dk T vk
P v1 R v1 Pvk R vk
1 k
Pvd1 Rdv Pvdk R dv
1
T v11 T vd T vk1 T vdk
R v11 R vk1
P11v 1
P1kv k
1 Rv k Rv
Pv T1 1 Pv T1 k
R1b11gr1 R1b1kgr1
b 1g p1 b kgp1
P1 1 P1 1
P 21 T 21 P2k T 2k
R 21 R 2k
T 31 P 31 T 3k P3k
R 31 R 3k
T 41 T 4k
P 41 R 41 P4k R 4k
R5b51gr 5 T 51 R5b5kgr 5 T 5k
b 1g p 5.2 b kgp5.2
T 61 P5.25 T 6k P5.25
b 1g p 5.1 b kgp5.1
P5.15 P5.15
P 61 T 71 1 P6k T 7k
R 61 P 1 R7 R 6k P k R 7k k
7.1 7.1
T 1f 1 T 81 T fk1 T8
T f1 2 P7.2
1
R8b81gr8
k
T fk 2 P7.2 R8b8kgr8
R 1f R kf
b 1g p8 b k g p8
P 1f 2 P8 8 P fk 2 P8 8
T o1f T1 T okf T 9k
P f1 3 T 1f 3 1 9 P fk 3 T f 3
k
Po1f 1 P
R9 9 Pokf R 9k P9k
1
R of R ofk
h 1p h pk
T p1 P p1 T pk P pk
Fig. 1. Signal graph of the three-dimensional model of the branched structure ink printing sys-
tem with three oscillators
The lengths of the rollers and cylinders circles are divided by integer of conditional
units; the time of passage of the ink microflow by the surface of the roller or cylinder
by the path of one length unit corresponds to one relative unit; the linear velocities of
the ink rollers surfaces, the plate and offset cylinders are constant; the cycle of oscilla-
tor movement in the axial direction is equal to the time of one revolution of the plate
cylinder; the width of the ink flow in each zone of the ink printing system consists of
k microflows by width Δb = 1 conditional unit; the balance of ink supply and selec-
tion in the ink printing system is maintained.
Taking into account the above assumptions, based on works [15–18] according to
the scheme of the signal graph (Fig. 1), we compose a three-dimensional mathemati-
cal model of the ink printing system:
for the first ink microflow circulating on the surface of the rollers and cylinders,
the equation system will have the following form:
Tv1 ( z ) Pd1 ( z ) hd1 ( z ) Rv1 ( z )Tvd1 ( z ) Rv1 ( z ) Rdv
1
( z )T11 ( z );
Tvd1 ( z ) Pv1 ( z ) Pg ( z )Tv1 ( z ) Rv11 ( z )Tv11 ( z );
Tv11 ( z ) Pvd1 ( z )Tvd1 ( z ) Rv1 ( z ) Pr ( z )T11 ( z );
T1b 1 g (z) g r 1 (z) ( z ) Pv1 ( z ) P11v ( z )Tv1 ( z ) Pv1 ( z )Tv11 ( z ) R1b 1 g r 1 (z) ( z )T2b 1 g (z) ( z );
b 1 g (z) g p1 (z) b 1 g p1 (z)
T2 ( z ) P1 ( z )T1b 1 g (z) ( z ) R21 ( z )T31 ( z );
T31 ( z ) P21 ( z )T21 ( z ) R31 ( z )T41 ( z );
T41 ( z ) P31 ( z )T31 ( z ) R41 ( z )T51 ( z );
T5b 1 g (z) gr 5 (z) ( z ) P41 ( z )T41 ( z ) R5b 1 gr 5 (z) ( z )T6b 1 g (z) ( z );
b 1 g (z) g p 5 (z) b 1 g p 5 (z)
T6 ( z ) P5.2 ( z )T7b 1 g (z) ( z ) R61 ( z )T71 ( z );
b 1 g (z) g p 5 (z) b 1 g p 5 (z)
T 7 ( z) P 5.1 ( z )T5b 1 g (z) ( z ) R71 ( z )T81 ( z );
T8b 1 g (z) g r 8 (z) ( z ) P7.2
1
( z )T f1 2 ( z ) R8b 1 g r 8 (z) ( z )T9b 1 g (z) ( z );
b 1 g (z) g p 8 (z) b 1 g p 8 (z)
T9 ( z ) P8 ( z )T8b 1 g (z) ( z ) R91 ( z )T f13 ( z );
T f11 ( z ) P61 ( z )T61 ( z ) R1f ( z )Tof1 ( z );
T f12 ( z ) P7.1
1
( z )T71 ( z ) R1f 1 ( z )T f11 ( z );
T f13 ( z ) P91 ( z )T91 ( z ) R1f 2 ( z )T f12 ( z );
Tof1 ( z ) Pf13 ( z )T f13 ( z ) Rof1 ( z )Tc1 ( z );
Tp1 ( z ) Pof1 ( z )Tof1 ( z ); h1p ( z ) Pp1 ( z )Tp1 ( z );
……………………………………………………..
for the last k-th microflow of the first zone:
Tvk ( z ) Pdk ( z ) hdk ( z ) Rvk ( z )Tvdk ( z ) Rvk ( z ) Rdvk ( z )T1k ( z );
Tvdk ( z ) Pvk ( z ) Pg ( z )Tvk ( z ) Rvk1 ( z )Tvk1 ( z );
Tvk1 ( z ) Pvdk ( z )Tvdk ( z ) Rvk ( z ) Pr ( z )T1k ( z );
T1b k g (z) g r 1 (z) ( z ) Pvk ( z ) P1kv ( z )Tvk ( z ) Pvk ( z )Tvk1 ( z ) R1b k g r 1 (z) ( z )T2b k g (z) ( z );
b k g (z) g p 1 (z) b k g p 1 (z)
T2 ( z ) P1 ( z )T1b k g (z) ( z ) R2k ( z )T3k ( z );
T3k ( z ) P2k ( z )T2k ( z ) R3k ( z )T4k ( z );
T4k ( z ) P3k ( z )T3k ( z ) R4k ( z )T5k ( z );
T5b k g (z) gr 5 (z) ( z ) P4k ( z )T4k ( z ) R5b k gr 5 (z) ( z )T6b k g (z) ( z );
b k g (z) g p 5 (z) b k g p 5 (z)
T6 ( z ) P5.2 ( z )T7b k g (z) ( z ) R6k ( z )T7k ( z );
b k g (z) g p 5 (z) b k g p 5 (z)
T7 ( z ) P5.1 ( z )T5b k g (z) ( z ) R7k ( z )T8k ( z );
T8b k g (z) g r 8 (z) ( z ) P7.2
k
( z )T fk2 ( z ) R8b k g r 8 (z) ( z )T9b k g (z) ( z );
b k g (z) g p 8 (z) b k g p 8 (z)
T9 ( z ) P8 ( z )T8b k g (z) ( z ) R9k ( z )T fk3 ( z );
T fk1 ( z ) P6k ( z )T6k ( z ) R kf ( z )Tofk ( z );
T fk2 ( z ) P7.1
k
( z )T7k ( z ) R kf 1 ( z )T fk1 ( z );
T fk3 ( z ) P9k ( z )T9k ( z ) R kf 2 ( z )T fk2 ( z );
Tofk ( z ) Pfk3 ( z )T fk3 ( z ) Rofk ( z )Tck ( z );
Tpk ( z ) Pofk ( z )Tofk ( z ); hpk ( z ) Ppk ( z )Tpk ( z ) (1)
where Pd ( z ) , Rd ( z ) is operators of supply and selection of ink microflows by a
ductor cylinder; n is the number of the ink supplying zones into the ink printing sys-
tem; k is the number of microflows in a separate j-th zone; nk is the number of
microflows in the ink printing system; Pv ( z ) , Rv ( z ) , Pv (z) , Rv ( z ) is operators of
ink microflows transfer by the vibrator roller at the time of contact with the ductor
cylinder and the first oscillator cylinder, respectively; Pvd ( z ) , P1v ( z ) , Rv1 ( z ) , Rdv ( z )
is operators of ink microflows transfer during oscillatory movement of the vibrator
roller from ductor to an oscillator cylinder and in the opposite direction; Pg ( z ) ,
Pr ( z ) is operators displaying the cyclic mode of the vibrator roller operation in the
ink feeder device; Ti ( z ) is z-image of the total -th ink microflows thickness at the
contact places of the rollers and cylinders; T fi ( z ) , Tof ( z ) is z-image of the total ink
microflows thickness at the contact places of the printing form with the form rollers
and offset cylinder; Pi ( z ) , Ri ( z ) is transfer operators of directs and reverse ink
b g pi (z)
microflows in a circular direction; Pi i ( z ) , Ribi gri (z) ( z ) is transfer operators
of directs and reverse ink microflows by oscillator cylinders; b is number of micro-
flows in a separate zone; g i ( z ) is movement of ink microflows in the axial direction
by oscillator cylinders; g p (z) , g r (z) is z-image of the direct and reverse ink mi-
croflows displacement by the surface of the oscillator cylinders between adjacent
rollers in contact with the cylinders; Pp ( z ) is operator of ink microflows transfer
from an offset cylinder to paper; h p ( z ) is z-image of the ink microflows thickness on
pf 1
the surface of the imprint; R6 ( z) (1 f F ( z)) z r6 , R7 ( z) (1 f F ( z) z ) z r7 ,
( p f 1 p f 2 )
R9 ( z) (1 f F ( z) z ) zr9 is transfer operators of the reverse ink microflows
pf 1 ( p f 1 p f 2 )
by a surface of the form rollers; Pf1 ( z ) f F ( z ) z , Pf2 ( z ) f F ( z ) z ,
( p f 1 p f 2 p f 3 ) rf pof rof
Pf 3 ( z) f F ( z ) z
, Rf ( z) (1 of ) z
, Pof (z) of z
, Rof ( z) (1 ) z
is transfer operators of direct and reverse ink microflows by a surface of the plate and
offset cylinders; F ( z ) is display operator of printing elements placed on a printing
form within the width of μ-th ink microflow; f , of , is coefficients of ink trans-
fer at an exit from contact places of the plate and offset cylinders.
The printing form consists of printing and whitespace elements, which differ in
their physicochemical properties. The printing elements are the areas that transmit the
images and they are oleophilic, whitespace elements are hydrophilic and do not per-
ceive ink. Therefore, when contacting the form rollers with the form ink is perceived
only by the printing elements [19]. The printing form is attached to the cylinder and
rotated with it during the machine operation with a period Df equal to the time in rela-
tive units for which point on the surface of the plate cylinder will pass the path Lf:
n n 1
L f ai ci cn (2)
i 1 i 1
where аi , сi is the size of the printing and whitespace elements at the printing form
within the width of the raster dot, which determines the width of the μ-th ink micro-
flow; сn is the size of the whitespace in the circular direction formed by the cylinder
gap to secure the form; n is number of elements.
The scan of form F(m) in the circular direction can be represented through the scan
of the respective microstrips as a finite sequence system:
F 1 m 1 m 1 m g11 1 m g11 e11 1 m g11 e11 g12 ...
... 1 m g11 e11 ... g1n 1 e1n 1 1 m g11 e11 ... e1n 1 g1n
…………………………………………………………………………… (3)
F k m 1 m 1 m g1k 1 m g1k e1k 1 m g1k e1k g2k ...
... 1 m g1k e1k ... g nk1 e 1 m g e ... e
k
n 1
k
1
k
1
k
n 1 g nk
where g i , ei is the time at which the point on the surface of the printing form dur-
ing the machine operation will pass a path responding to the size of the corresponding
printing and whitespace elements; m is the plural of finite sequences.
The sequences described by the system of equations (3) can be represented in the
form of z-transformations:
1 1 1 1 1 1 1 1 1 1 1 1 1 1
z{F 1[m]}[1 z g1 z ( g1 e1 ) z ( g1 e1 g 2 ) z ( g1 e1 g n1 en1 ) z ( g1 e1 en1 g n ) ]
……………………….…….…………………………………………………. (4)
g1k ( g1k e1k ) ( g1k e1k g 2k ) ( g1k e1k g nk 1 e nk 1 ) ( g1k e1k e nk1 g nk )
z{F k [ m]} [1 z z z z z ]
Based on the systems of equations (3) and (4), taking into account the displacement
theorem in the field of originals and images [20], we write a periodic function that
reflects the character of the printing elements displacement in μ-th microstrip of the
printing form:
F ( z ) (1 z g1 z ( g1 e1 ) z ( g1 e1 g2 ) z ( g1 e1 g2 e2 ) z ( g1 e1 g2 e2 g3 ) ...
Df
... z ( g1 e1 ... gn1 en1 ) z ( g1 e1 ... en1 g n ) ) (1 z ) 1 (5)
Based on expression (5), a structural diagram of a printing form universal model for
the j-th zone is constructed (Fig. 2).
1 k
z g1 z g1
1 1 k k
z (g1 e1 ) z (g1 e1 )
1 1 1 k k k
z (g1 e1 g2 ) z (g1 e1 g 2 )
1 1 1 1 k k k k
z (g1 e1 g2 e2 ) z (g1 e1 g 2 e2 )
1 1 1 1 1 k k k k k
z (g1 e1 g 2 e2 e3 ) z (g1 e1 g2 e2 e3 )
z (g1 e1 g2 gn 1 en 1 ) z (g1 e1 g 2 gn 1 en 1 )
1 1 1 1 1 k k k k k
z (g1 e1 g 2 gn 1 en 1 gn ) z (g1 e1 g 2 gn 1 en 1 gn )
1 1 1 1 1 1 k k k k k k
Df Df
z z
Df Df
z 1 z 1
Fig. 2. Structural scheme of printing elements display in a separate j-th zone of the printing
form
3 Results of Modeling
To study the process of ink transfer from the ductor cylinder to the imprints, we build
a simulator of a branched ink printing system using a signal graph (Fig. 1) and a
three-dimensional mathematical model (1) in the Matlab-Simulink. The geometric
dimensions of such an ink printing system are introduced into the simulator in the
form of appropriate transport delays. Set the value of the ink transfer coefficients at
the contact points of the ink printing system elements by 0.5, and the ink transfer
coefficient from the surface of the cylinder to the paper – 0.7. We assume that the
axial movement of the oscillator cylinders is carried out by sinusoidal law.
The printing form in the Matlab-Simulink can be submitted as a structural scheme,
as shown in Fig. 2. Reproduction only a snippet of such an image with a resolution of
25 dpi and a width equal to the width of the ink feed will require 32 structural blocks.
Accordingly, the structural model of the entire form will consist of 32xn blocks,
where n is the number of printing form zones corresponding to the number of ink
supply zones. This representation of the form provides the topology of printing ele-
ments placement, which corresponds to the drawing of the form. To simplify the de-
velopment of the form model in the Matlab-Simulink environment, we take a different
approach. To generate the image of the printing form, we develop a subroutine that
algorithm is presented in Fig. 3.
Fig. 3. The algorithm of creating a printing form model
Images that should be reproduced by a form should be processed in a graphical editor
(for example, in Adobe Photoshop). Resize the image to the correct format of the
form, change the extension and convert to bit form. The resulting bitmap must be
saved with the extension *.bmp and open it with the function (imread). This creates
an object of variable time data. All bitmaps from an open image are copied to the field
“Value” of the data variable object, and an array of integers from zero to the length of
the form Lf is created for the field “time”. The subroutine then selects the elements of
each zone one by one (in a loop) and copies them to a separate array. Based on these
data, the number of bit units Nf corresponding to the form printing elements and the
total number of bits Nf in the j-th zone are determined. The coefficients of the form's
filling in each zone are then determined as the ratio of the total number of bit units in
the j-th zone to the total number of bits (printing and whitespace elements) in that
zone. Arrays of the form filling coefficients in each zone become available for use in
the model and can be modified in the window Workspace. After placing the name of
the time-variable data object in the block “From Workspace”, the construction of the
ink printing simulator is completed. This representation of the form makes it possible
to reproduce the image on the surface of the prints.
For research the influence of the mathematical form model presentation method on
the accuracy of determining the input task parameters of the printing system, we use
the test form, the image of which is presented in Fig. 4a and equivalent plate form
(Fig. 4b), which differ in composition but have the same form's filling zonal coeffi-
cients with the printing elements.
a) b)
Fig. 4. Image of: a) test form; b) equivalent plate form
The mathematical model of equivalent plate form (Fig. 4b) is much simpler and its
use reduces the duration of modeling. But it remains an open question whether deter-
mining the input task parameters using an equivalent plate form will provide the re-
quired quality of imprints. To answer the question, we simulate and determine the
input task parameters with the printing forms, which are presented in Fig. 4a and
Fig. 4b. In the first stage, we export the form model (Fig. 4b) to the ink printing sys-
tem simulator and by modeling determine the input task parameters hdj , which pro-
vide at the output of the ink printing system to the set mode the ink transferring to all
zones of imprints hcj with an accuracy of ± 2%, which is significantly higher than
ISO (Table 1).
Table 1. Input task parameters for equivalent plate form.
№ zone 1 2 3 4 5 6 7 8 9 10 11 12
kzj 0.498 0.731 0.209 0.602 0.246 0.317 0.400 0.479 0.300 0.298 0.415 0.262
hdj , μm 22.6 47.2 5.3 38.8 12.6 16.8 23.4 29.4 16.3 16.4 26.1 17.4
hсj , μm 1.012 0.983 1.019 0.987 1.012 1.006 0.998 0.992 1.007 1.009 0.998 0.998
,% 1.20 -1.70 1.90 -1.30 1.20 0.60 -0.20 -0.80 0.70 0.90 -0.20 -0.20
In the next step, we use the model of the printing form presented in Fig. 4a, which
takes into account the topology of printing and space elements placement. Set the
predefined parameters of the input task hdj contained in table 1 in the model of the ink
printing system and simulate before the system enters the operating mode. The image
of the obtained imprints is presented in Fig. 5a, and the profiles in the j-th zones of the
imprint in Fig. 5b. The profiles (Fig. 5b), which represent the cross-sections of the
imprint’s j-th zones middle, determine the minimum hсj min and maximum hсj max val-
ues of the ink thickness (table 2).
Table 2. The results of the simulation using the test form.
№ zone 1 2 3 4 5 6 7 8 9 10 11 12
kzj 0.498 0.731 0.209 0.602 0.246 0.317 0.400 0.479 0.300 0.298 0.415 0.262
hdj , μm 22.6 47.2 5.3 38.8 12.6 16.8 23.4 29.4 16.3 16.4 26.1 17.4
h j
, μm 1.107 0.952 1.156 0.946 1.078 1.031 0.986 0.963 1.065 1.110 1.039 1.062
с m ax
h с m in , μm 1.040 0.898 1.112 0.899 1.057 0.996 0.925 0.902 1.030 1.080 1.016 1.012
j
hсj , μm 1.077 0.935 1.090 0.945 1.040 1.020 0.996 0.969 1.011 0.996 0.948 1.036
,% 7.70 -6.50 9.00 -5.50 4.00 2.00 -0.40 -3.10 1.10 -0.40 -5.20 3.60
a) b)
Fig. 5. Three-dimensional image of the imprint (a) and its cross sections in the j-th zones (b)
obtained at the determined hdj based on an equivalent plate form
As can be seen from the data presented in Table 2, the average values of the ink
thicknesses in some zones of the imprint beyond the tolerances of ISO, which are
± 5%, and the amplitude of the ink microflows deviation in the middle of the j-th
zones is in the range of –11.0% up to 15.6%. Based on the obtained results, we con-
clude that the determined input task parameters as a result of simulation using an
equivalent plate form do not provide the required quality of printed products. There-
fore, we simulate and adjust the input task using the test printing form (Fig. 4a). As a
result of model experiments, we get the parameters of the input task (table 3).
Table 3. Input task parameters for test form.
№ zone 1 2 3 4 5 6 7 8 9 10 11 12
hdj , μm 18.8 53.1 2.8 41.6 10.7 17.1 23.1 31.2 15.3 16.8 28.8 13.6
hсj m ax , μm 1.001 1.026 1.044 1.008 1.005 1.006 1.020 1.028 1.031 1.042 1.038 1.025
h сj m in , μm 0.951 0.959 1.008 0.952 0.991 0.971 0.959 0.968 0.990 1.020 0.995 0.977
hсj , μm 0.985 0.987 1.019 0.986 0.991 0.990 1.009 1.010 1.004 1.003 0.997 1.010
,% -1.50 -1.30 1.90 -1.40 -0.90 -1.00 0.90 1.00 0.40 0.30 -0.30 1.00
Enter the refined parameters of the input task (table 3) in the simulator ink printing
system and conduct a simulation to output it in the set mode. The obtained images of
the imprints and cross sections in the j-th zones of the imprints are presented in Fig. 6.
In this case, the deviation error of the ink thicknesses averages values is much smaller
than admissible and ranges from -1.5% to 1.9%. The range of oscillation amplitude of
the section profiles in the j-th imprint zones is in the range of –4.9% to 4.4%, which
corresponds to the permissible parameters of ISO.
a) b)
Fig. 6. Three-dimensional image of the imprint (a) and its cross sections in the j-th zones (b)
obtained at the determined hdj based on a test form
4 Conclusions
It was developed the information technology to improve the quality of printed images,
which consists of the following steps:
─ creation of a three-dimensional mathematical model of the ink printing system,
which describes in detail the work of all components of the offset machine system,
the work of which is researched and its adjustment will be improved;
─ development of an ink printing system simulator, which reproduces the work of the
ink feeder device with the possibility of changing the general and zonal ink supply;
operation mode of ink rollers, oscillator, plate and offset cylinders;
─ developing options of the printing form imitation model: printing form as a plural
of form's filling zonal coefficients or as a structural scheme; the form model repro-
duces the topology of the printing elements placement, which is fully compliant
with the image; creation of an algorithm for generating a printing form model in
the Matlab-Simulink taking into account the composition of the image;
─ export of the form model to the simulator of the ink printing system;
─ testing the imitation model and verifying it matches the physical object based on
the balance of supply and selection of ink.
Based on model experiments and analysis of the obtained results, it is established
that to improve the accuracy of ink printing systems adjustment, accordingly, the
quality of printed images, the models of printing forms need to be developed that
convey in detail the topology of printing elements placement for image reproduction.
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