Transversal relative vibrations of blanket and plate cylinders in web offset printing press worsen the quality of prints. In the paper, the impact of contact rings upon the quality of prints is discussed upo

I. Iljin

N. Sesok

English

Journal of Vibroengineering

 532. THE INVESTIGATION ON THE IMPACT OF THE CONTACT RINGS OF CYLINDERS AND ON TRANSVERSAL VIBRATIONS OF BLANKET AND PLATE 
CYLINDERS IN OFFSET PRINTING PRESS.   N. ŠEŠOK1, I. ILJIN2 
 
 
 VIBROMECHANIKA. JOURNAL OF VIBROENGINEERING.   MARCH 2010. VOLUME 12, ISSUE 1. ISSN 1392-8716 
95 
532. The investigation on the impact of the contact rings  
        of cylinders and on transversal vibrations of  
        blanket and plate cylinders in offset printing press 
  
N. Šešoka, I. Iljinb 
Department of Printing Machines, Vilnius Gediminas Technical University, 
J. Basanavičius str. 28, LT-03224, Vilnius, Lithuania 
E-mail: a pgses@vgtu.lt;  b pgilj@vgtu.lt 
Phone: +37052744736 
 
(Received  20 October  2009;  accepted 27 November 2009) 
 
Abstract. Transversal relative vibrations of blanket and plate cylinders in web offset printing 
press worsen the quality of prints. In the paper, the impact of contact rings upon the quality of 
prints is discussed upon. 
 
Keywords: printing, offset, printing press, transversal vibrations, investigation. 
 
Introduction  
 
Web offset printing presses are widely used. The principal part of such a press is the printing 
equipment. At present, the most frequently used printing equipment consists of two plate 
cylinders 1, 4 and two blanket cylinders 2, 3 with a paper tape moving between them (see Fig. 1 
and Fig. 2). Its precizity, high speed and other properties predetermine the quality of the prints 
as well as the productivity, economic exploiting and durability of the press. It is known that 
transversal relative vibrations of blanket and plate cylinders of the printing equipment restrict 
technological properties of the printing press. Changes of pressure between blanket cylinders as 
well as between blanket and plate cylinders worsen the quality of the prints, too. Usually, 
changes of pressure between cylinders occur because of relative vibrations between the cylinders 
that appear during operation of the press and static bends of the cylinders that appear on their 
pressing against each other via the blanket. In the first case, the pressure pulsation causes uneven 
transfer of ink onto the paper [1]. 
It was shown in earlier works that transversal vibrations between the cylinders can be 
considerably reduced if their dynamic characteristics and dynamic parameters are identical [2, 
3]. However, it is difficult to produce a printing equipment with cylinders having absolutely 
identical dynamic characteristics. The important problem is an impact of changes of dynamic 
parameters of the cylinders upon the intensity of relative vibrations of the printing equipment. 
The object of the paper is the investigation of the impact of using contact rings in web offset 
printing equipment upon the quality of prints produced by it. In the paper, the results of 
exploiting the printing equipment with and without the contact rings are compared. Two cases 
are analyzed: when all cylinders of the equipment are solid or all of them are pipe-type hollow 
ones, hereinafter referred to as cylinders of „identical“ parameters; and when blanket cylinders 
are solid and plate cylinders are hollow ones, hereinafter referred to as cylinders of „different“ 
parameters. 
 
The object of the investigation and the methods of calculation 
 
In Fig. 1, the scheme of the dynamic model of the printing equipment without contact rings 
is shown. In Fig. 2, the scheme of the general dynamic model of the printing equipment with 
 
 532. THE INVESTIGATION ON THE IMPACT OF THE CONTACT RINGS OF CYLINDERS AND ON TRANSVERSAL VIBRATIONS OF BLANKET AND PLATE 
CYLINDERS IN OFFSET PRINTING PRESS.   N. ŠEŠOK1, I. ILJIN2 
 
 
 VIBROMECHANIKA. JOURNAL OF VIBROENGINEERING.   MARCH 2010. VOLUME 12, ISSUE 1. ISSN 1392-8716 
96 
contact rings is shown. In the first case, the equipment consists of four cylinders pressed against 
their working surfaces via the blanket along their generatrices (blanket is a thin elastic 
rubberized fabric that covers the blanket cylinders), as shown in Fig. 1. In the second case, the 
equipment consists of four cylinders pressed against their working surfaces via the contact rings 
and the blanket, as shown in Fig. 2. The layout of the cylinders shown in the Fig. 1 and 2 is the 
most frequent in web offset printing presses.  
In the dynamic model, cylinders are disintegrated into finite elements. Rolling bearings are 
approximated by elastic mass-free elements with damping, errors of bearing – by kinematic 
excitation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
       a           b 
 
Fig. 1. The scheme of the general dynamic model of the printing equipment without contact rings. 
a – the evolvent of the cylinders; b – the rear image; the blanket and plate cylinders disintegrated to finite 
elements, elastic elements with damping on their ends that simulate assemblies of bearings and the ones 
that simulate the blanket and connect the finite elements of different cylinders are shown; y1÷y4, x2, x3 – the 
generalized coordinates that describe the elastic rectlinear shifts of the middle lines of the cylinders that 
also show the directions chosen for investigation of vibrations of such cylinders; kG ,δ - elements that 
simulate errors of the bearings; k, h – the coefficients of stiffness and resistivity of elastic members 
 
The blanket is approximated by discrete mass-free elastic elements with damping [2, 3].  The 
dynamic model of the system under discussion is complicated, it has multiple degrees of 
freedom. Direct using of it for formation of the equations of the vibrations is not purposeful. For 
this purpose, the computer-aided formation of the mathematical model is used. The proposed 
method of formation of the mathematical model is based on an artificial decomposition of the 
system into less complicated subsystems, formation of equations of vibrations for such systems 
j,j, h;k 11
j,j, h;k 22
j,j, h;k 33
k,Gδ
A
1y
1
2
2y2x
3y3x
3
4y
4
L
n,Gn,G h;k
1α
2y
1
2
2x
3
3x
3y
4y
2α
4
l
D
 532. THE INVESTIGATION ON THE IMPACT OF THE CONTACT RINGS OF CYLINDERS AND ON TRANSVERSAL VIBRATIONS OF BLANKET AND PLATE 
CYLINDERS IN OFFSET PRINTING PRESS.   N. ŠEŠOK1, I. ILJIN2 
 
 
 VIBROMECHANIKA. JOURNAL OF VIBROENGINEERING.   MARCH 2010. VOLUME 12, ISSUE 1. ISSN 1392-8716 
97 
and subsequent uniting of the said equation into the common system of equations that describes 
vibrations of the total system [4]. 
 In the first phase, the following equation is found for each subsystem: 
 
[ ] [ ] [ ] { } 0=+






+





 •••
kk
k
k
k
k qCqBqA ,      (1) 
 
where [ ] [ ] [ ]kkk C,B,A  - the matrices of inertia, damping and stiffness of the k-th subsystem; { }kq  
- the vector of its generalized coordinates (the components of the vector are the principal and 
auxiliary generalized coordinates that define the location of the k-th subsystem). 
 In the second phase, taking into account the external exciting forces that affect the 
subsystems, an auxiliary system of equations of vibrations is formed: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    a)    b) 
Fig. 2. The scheme of the general dynamic model of the printing equipment with contact rings. 
a - the evolvent of the cylinders, b - the rear image; the blanket and plate cylinders disintegrated to finite 
elements, elastic elements with damping on their ends that simulate units of bearings and the ones that 
simulate the blanket and connect the finite elements of different cylinders are shown; y1÷y4, x2, x3 – the 
generalized coordinates that describe the elastic rectlinear shifts of the middle lines of the cylinders that 
also show the directions chosen for investigation of vibrations of such cylinders; 
k,Gδ - elements that 
simulate errors of the bearings; k, h – the coefficients of stiffness and resistivity of elastic members 
 
[ ] [ ] [ ] { } ( ){ }000
0
0
0
0 tFqCqBqA B=+






+





 ••• ;      (2) 
 
where the matrix [ ]0A  is formed of the submatrices [ ]kA   situated on its diagonal and the 
matrices [ ]0B , [ ]0C  are formed of submatrices [ ]kB  or [ ]kC situated in an analogous way; { }0q  - 
the vector that’s components are the principal and auxiliary generalized coordinates included in 
j,j, h;k 11
j,j, h;k 22
j,j, h;k 33
kG ,δ
A
1y
1
2
2y
2x
3y3
x
3
4y
4
L
n,Gn,G h;k
1α
2y
1
2
3
3x
4y
2α
4
l
r,r, h;k 11
r,r, h;k 33
r,r, h;k 22
r,r, h;k 44
3y
D
1y
2x
 532. THE INVESTIGATION ON THE IMPACT OF THE CONTACT RINGS OF CYLINDERS AND ON TRANSVERSAL VIBRATIONS OF BLANKET AND PLATE 
CYLINDERS IN OFFSET PRINTING PRESS.   N. ŠEŠOK1, I. ILJIN2 
 
 
 VIBROMECHANIKA. JOURNAL OF VIBROENGINEERING.   MARCH 2010. VOLUME 12, ISSUE 1. ISSN 1392-8716 
98 
all equations (1); ( ){ }0tFB  - the vector that‘s non-zero components are formed of errors of 
bearings or the elements of kinematic excitation of vibrations of the cylinders through the body 
of the printing equipment. 
 In the third phase, when the auxiliary system of equations for the vibrations (2) and the 
equations of links are known, the principal system of equations (without the auxiliary 
coordinates) that describes vibration of the whole system is found: 
 
[ ] [ ] [ ]{ } ( ){ }tFqCqBqA B=+






+





 •••
;         (3) 
 
where { }q  - the vector of the principal generalized coordinates that defines the position of the 
whole system (here the number of coordinates equals to the number n of the degrees of freedom 
of the system); [ ] [ ] [ ]C,B,A  - the square matrices of inertia, friction and stiffness of the n-th 
degree system; ( ){ }tFB  - the vector of generalized forces obtained from the vector ( ){ }0tFB  after 
elimination of the zero components that conform to the auxiliary coordinates. 
The equations describing vibrations of the printing equipment were formed using the 
methods provided in works [2, 3, 4] and the set of programmes DINCHAR. The forced 
harmonic vibrations of the cylinders are discussed upon. The intensity of the vibrations was 
discussed upon in course of examining the amplitute-frequency responses of the system that are 
obtained on kinematic exciting of the system under discussion by the errors of bearings of 
cylinders and in the vertical direction by the body of the press. It is shown in the works [2, 3] 
that the maximum intensity of forced transversal harmonic vibrations of cylinders is achieved in 
their middle lines, so the relative vibrations of the middle points of the cylinders when they are 
pressed against each other via contact rings are discussed upon herein and this case is compared 
to the case of the equipment where the cylinders are pressed against each other without contact 
rings along their working surfaces. 
 
The results of the investigation 
 
The vibrations are examined using the obtained amplitute-frequency responses – their 
examples are provided in Fig. 3. In the example: the distance between the bearings L=1,36 m; 
length of the working surface l =1,004 m; the external diameters of the cylinders D=0,2 m; the 
diameters of holes dk=0,17 m; the length of the holes lk=0,95 m; kB,n=1,7⋅106 N/m; hB,n=49022 
N⋅s/m; k1,j=k3,j=6,91⋅106÷1,39⋅107 N/m; k2,j =6,91⋅106÷1,209⋅107 N/m; h1,j=h3,j=9,79⋅102 ÷ 
1,963⋅103  N⋅s/m; h2,j=9,21⋅102 ÷ 1,818⋅103 N⋅s/m (the values of ki,j and hi,j are smaller in the 
middle part of cylinders); α1=30°, α2=50°. 
Forced transversal vibrations of the cylinders are excited in the kinematic way by the errors 
of bearings of cylinders or the vibrations of the stand of the printing equipment in the vertical 
direction. The intensity of the transversal vibrations of the centers of the cylinders was 
examined. In all cases, the amplitudes of kinematic harmonic excitation equaled to 1 µm. The 
amplitudes of transversal vibrations of the cylinders are expressed in micrometers. The 
following results were obtained for frequencies up to 500 Hz. 
It was found that on changing the parameters of the printing equipment, i.e. using cylinders 
with „identical“ or „different“ dynamic parameters, as well as taking into account whether the 
cylinders were pressed against each other via the contact rings and blanket or via the blanket 
along their working surfaces, a narrow zone of resonances of transversal relative vibrations is 
formed. The zone with the expressed resonance peak that conformed to the vibrations of the 
maximum intensity is situated in the range of 170 – 210 Hz. The zone is well identified in all 
cases. 
 532. THE INVESTIGATION ON THE IMPACT OF THE CONTACT RINGS OF CYLINDERS AND ON TRANSVERSAL VIBRATIONS OF BLANKET AND PLATE 
CYLINDERS IN OFFSET PRINTING PRESS.   N. ŠEŠOK1, I. ILJIN2 
 
 
 VIBROMECHANIKA. JOURNAL OF VIBROENGINEERING.   MARCH 2010. VOLUME 12, ISSUE 1. ISSN 1392-8716 
99 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 3. The amplitude-frequency responses of transversal relative vibrations of cylinders in the printing 
equipment (a, c, e, g – the equipment without contact rings; b, d, f, h – the equipment with contact rings);   
1 - vibrations between the upper blanket and plate cylinders; 2 – between blanket cylinders; 3 – between 
a) b) 
c) d) 
1 2 
3 1 
0,1 
0,01 
0 100 200 300 400 500 (Hz) 
A, µm 
1 
2 
3 
1 
0,1 
0,01 
0 100 200 300 400 500 (Hz) 
A, µm 
1 
2 
3 
1 
0,1 
0,01 
0 100 200 300 400 500 (Hz) 
A, µm 
1 
2 
3 1 
0,1 
0,01 
0 100 200 300 400 500 (Hz) 
A, µm 
1 
0,1 
0,01 
0 100 200 300 400 500 (Hz) 
A, µm 
1 2 
3 1 
0,1 
0,01 
0 100 200 300 400 500 (Hz) 
A, µm 
1 2 
3 
4 
500 
150 
0 
0 100 200 300 400 500 (Hz) 
A, µm 
4 
100 
1 
1E-4 
0 100 200 300 400 500 (Hz) 
A, µm 
0,01 
e) f) 
g) h) 
 532. THE INVESTIGATION ON THE IMPACT OF THE CONTACT RINGS OF CYLINDERS AND ON TRANSVERSAL VIBRATIONS OF BLANKET AND PLATE 
CYLINDERS IN OFFSET PRINTING PRESS.   N. ŠEŠOK1, I. ILJIN2 
 
 
 VIBROMECHANIKA. JOURNAL OF VIBROENGINEERING.   MARCH 2010. VOLUME 12, ISSUE 1. ISSN 1392-8716 
100 
the lower blanket and plate cylinders; 4 – tangential vibrations between blanket cylinders. a, b – vibrations 
excited in kinematic way by errors of one bearing of the upper plate cylinder; c, d – vibrations excited in 
kinematic way by errors of one bearing of the lower plate cylinder; e, f  - vibrations excited in kinematic 
way by both bearings of the lower plate cylinder with identical errors; g, h – kinematic excitation in the 
vertical direction via the stand of the press. The values of the amplitudes of kinematic excitation equal to 
1/µm. a, b, c, d, e, f – cylinders with „identical“ parameters; g, h – cylinders with „different“ parameters 
 
 
 
On exciting the relative vibrations via the left bearing of one of blanket cylinders of web 
offset printing equipment, it was found that the intensity of the vibrations between the blanket 
cylinders reduces inconsiderably, if contact rings are used; in certain moments, it increases 
inconsiderably. However, if contact rings are used, the intensity of the vibrations between the 
blanket and plate cylinders reduced from 20 to 50% and in certain cases – even by 100%. 
It was found that if relative vibrations are excited from both bearings of one cylinder of the 
web printing press with the identical errors, the intensity of the vibrations between the blanket 
cylinders reduces by about 10 – 15%, when contact rings are used. The intensity of vibrations 
between plate and blanket cylinders is reduced from 40 to 65%, if contact rings are used. 
If the system is excited in the vertical direction via the stand of the press and contact rings 
are used, no changes of the intensity of vibrations between the blanket cylinders occur. The 
intensity of vibrations between plate cylinders reduces about 40%. However, the intensity of 
tangential vibrations fell down close to zero, when the cylinders had „identical“ parameters and 
contact rings were used. However, no changes of the intensity of tangential vibrations took place 
when the parameters of the cylinders were „different“, irrespectively of using the contact rings. 
 
Conclusions 
 
 After the assessment of the results obtained, it may be concluded that in most cases contact 
rings reduce transversal vibrations. Such reduction improves the quality of the prints, increases 
the productivity and the service life of web printing machines. 
 
5. References 
 
[1] Kipphan H. Handbook of Print Media. Berlin, Springer Verlag, Heidelberg, 2001, p. 1700. 
[2] Augustaitis Vytautas, Šešok Nikolaj. Analytical Investigation Method of the Transversal Vibrations 
of Plate and Blanket Cylinders of Web Offset Presses // Mechanika. ISSN 1392-1207. 2000, Nr. 1. p. 
46-53. 
[3] Augustaitis Vytautas, Šešok Nikolaj. Relativne prečne vibracije valjev tiskarskega stroja, ki 
pritiskajo drug ob drugega preko gumijaste obloge // Strojniški vestnik. ISSN 0039-2480. 2004, Vol. 
50, no. 5. p. 277-290. 
[4] Аугустайтис В. К. Анализ и синтез колебаний машин в применении к приводу 
металлорежущих станков. – Вильнюс: Техника, 1994. – 307 с. 


The investigation on the impact of the contact rings of cylinders and on transversal vibrations of blanket and plate cylinders in offset printing press

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The investigation on the impact of the contact rings of cylinders and on transversal vibrations of blanket and plate cylinders in offset printing press

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