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DETERMINISTIC AND PROBABILITY ANALYSIS
OF PAPER MACHINE VIBRATION IMPACT
TO THE STRUCTURE SAFETY AND HUMAN COMFORT
Ju aj KRÁLIK1, Ju aj KRÁLIK, j . 2
1Depa men o S uc u al mechanics, Facul y o Ci il Enginee ing, STU B a isla a, Radlinského 11, 810 05 B a isla a,
Slo akia
2Academy o Fine A s and Design in B a isla a, H iezdosla o o nam. 18, 814 37, B a isla a, Slo akia
ju aj.k alik@s uba.sk, [email p o ec ed]
DOI: 10.35181/ ces-2019-0004
Abs ac . This pape desc ibes he p obabili y and
sensi i i y analysis o he conc e e ame and pape
machine in e ac ion. On he base o he expe imen al
esul s, he calcula ion FEM model was e i ied. The
unce ain ies o he loads le el, he ma e ial p ope ies and
o he in luences ollowing he inaccu acy o he calcula ed
model and nume ical me hods we e conside ed in he
app oxima ion me hod RSM.
Keywo ds
ANSYS, Machine Vib a ion, P obabili y, Sa e y, Human
Com o , FEM, RSM.
1. In oduc ion
The pape p esen s solu ions o he p oblems ha ha e
a isen a e ins alling a new echnology o a highe -end
pape machine in o he o iginal ac o y building. A e he
s a o he ope a ion, he e we e p oblems wi h he
in e ac ion o he machine wi h he load-bea ing s uc u e,
which h ea ened bo h he load-bea ing s uc u e and he
impac on he human com o o he pe son wo king in he
hall.
Due o he p oblems o in e ac ion be ween he pape
machine and he exis ing indus ial hall s uc u e, i was
necessa y o expe imen ally measu e hese e ec s and o
modi y a compu a ional model and analyse he e ec o
in e ac ion on he s uc u es and human com o o he
wo ke s, and o p opose o he econs uc ion o he
exis ing s uc u e o design o dampe s o maximally
elimina e he e ec s o machine and s uc u e in e ac ion.
On base o he p oblems wi h he pape machine and
hall s uc u e in e ac ion, i was necessa y o analyse he
e ec o he dynamic in e ac ion by he expe imen al
measu emen s o he ib a ions o he s ool- echnology-
hall sys em o elimina e he ad e se esonan e ec s o he
p oposed echnology on he hall s uc u e. The econs uc-
ion wo k in ol ed he exchange o pa o he echnology
in he sc een, winding and ups eam pa o he machine.
Fig. 1: The sec ion o he hall ame
The suppo ing s uc u e o he hall consis s o a
ein o ced conc e e ame wi h a mason y walls. The
indi idual loo s o one hall sec ion a e ein o ced wi h
monoli hic conc e e pla es wi h g id beams. The sec ion o
he ein o ced conc e e columns is 45/70 cm, he ame
modulus is 9-4.5-4.5-6 m in ame plane and 6 m in
pe pendicula di ec ion. The machine is placed a le el
5.65 m. The bo om/ op le els o he columns a e a -
0.25/18.23 m.
The ollowing expe imen al and nume ical analyses
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we e ca ied ou based on he need o e iew he concep
o cons uc ion wo k on he gi en objec :
• Expe imen al es ing and e alua ion o he
dynamic in e ac ion o he in e ac ion sys em in
all holding s a es o he pape machine,
• Nume ical Analysis o he P oblem o In e ac ion
wi h he P esen S a e Gi en Designed Machine
Pa ame e s.
As pa o he nume ical analysis, i was necessa y o
make a comple e dynamic calcula ion o he spa ial
sys em, a modal analysis conside ing he in e ac ion o he
subs uc u e-cons uc ion- echnology [6-21, 28].
2. Design c i e ia o he s uc u e
eliabili y and human com o
F om he poin o iew o he Eu ocode ecommenda ions
[5, 7, 13, 14] and na ional s anda ds [24, 25], he designe
should assess he e ec s o machine ib a ions on he
ollowing e ec s:
• Impac o machine ib a ions on building
cons uc ion
• In luence o ib a ions on man and on ope a ion
(mechanical, acous ic and op ical)
• Impac o Machine Vib a ion on Machine y
(manu ac u e 's ecommenda ions and
limi a ions)
• Based on he assessmen o all impac s, he
ollowing c i e ia [7] a e equi ed:
• C i e ia o he limi s a e o load-bea ing
capaci y and ins abili y o s uc u es [5]
• Physiological c i e ia [25]
• Ope a ional pe o mance c i e ia (manu ac u e 's
equi emen s)
In s anda d [25], he ca ego iza ion o s uc u es in
e ms o c i e ia o he 1s limi s a e is made based on
alues o e ec i e oscilla ion eloci y depending on he
eliabili y classes and he signi icance o he objec .
Rein o ced conc e e s uc u es o indus ial buildings a e
classi ied in he esis ance class E and he consequen ion
classes II.
The equi emen s o he design o he human com o
and i s p o ec ion a e de ined in he s anda ds [25]. The
s anda ds de ine he c i e ions o he human com o s om
he poin o he in e up ed and common ib a ions.
The c i e ions o he quali y o he ib a ion in luences
on he human com o a e no de ined only in dependency
on he in ensi y o ib a ions bu om he poin o iew o
he unc ionali y o he building ooms and he equency
and he ime o he ib a ion ac ion o he human. The ype
o he diag ams de ined in s anda d [25] is used o he
design o he in luence he ib a ions on human com o .
3. Expe imen al modal analysis
In o de o check he dynamic p ope ies o he s uc u e,
i was necessa y o measu e he ib a ion esponse in he
c i ical places [2-4, 18, 19]. A measu ing sys em was used,
he basic elemen o which was he piezoelec ic
accele ome e KD 35 and KD 22. Thei signal was led o
he in eg a ing RFT 00OLS ampli ie and a e
ampli ica ion o bo h he Tesla EMM 140 and he TRACE
860SA digi al oscilloscope.
Vib a ion accele a ion a es and alues we e measu ed
a i e loca ions [4]:
• on he main beam by he ope a o a he same si e,
• on he ou side o he building,
• on he loo in he cen e o he monoli hic slab,
• on he ope a o 's side,
• on he loo a he con ol loo ,
• on he loo .
a) Accele a ions a loo in ime
b) Accele a ion spec um a loo
Fig. 2: E alua ion o he expe imen al accele a ion eco d on he
bo om o cylinde d i e mo o [4]
F om he numbe o ib a ion spec a e alua ed, i was
possible o see he di e en equencies o indi idual
equencies om place o loca ion. The dominan eigen
equencies o he building s uc u e we e de e mined.
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4. Nume ical analysis
Wi hin he nume ical analysis o he soil-s uc u e-
echnology in e ac ion sys em, i was necessa y o p o e
ha he s ool unde he pape machine mee s he c i e ia
se by he manu ac u e and, on he o he hand, he load-
bea ing s uc u e can ans e he dynamic load caused by
he echnology [1, 6, 11-15, 18, 19, 23, 26-28].
The spa ial disc e iza ion o he s uc u e was
pe o med by he one-dimensional elemen s LINK8 and
BEAM4 and wo-dimensional shell elemen s SHELL43.
Th ee calcu-la ion models we e cons uc ed - F am1,
F am2 and F am3 (Fig.3). The F am1 model esponds o
he o iginal design and o iginal load, F am2 o iginal
design and new load, and F am3 ein o ced cons uc ion
and new load. The o al calcula ion model consis s o 686
nodes and 1216 elemen s wi h six deg ees o eedom. The
pilla s a e ixed on he ounda ion pad.
Fig. 3: Calcula ion ame models - F am1, 2 and F am3
The dynamic calcula ion o he sys em consis ed o :
• modal analysis
• dynamic analysis o he esponse o ha monic
oscilla ion
()
=Mu + Cu + Ku F
  (1)
whe e M, C, K a e he mass, damping and s i ness
ma ices, ,anduu u
  a e ec o s o nodal accele a ion,
eloci ies and displacemen s. In he case o ha monic
exci ing o ces, we exp ess he ec o o he displacemen s
and exci a ion o ces as ollows
12
i
ie
Ω
=+uu u and 12
i
ie
Ω
=+FF F (2)
whe e u1 (o u2) is he eal (o imagina y) componen o
he ec o o displacemen s and F1 (o F2) is he eal (o
imagina y) componen o he exci a ion ec o o o ces.
A e we pu ela ionships (2) in o (1) we ge dynamic
equa ions (1) in he o m o complex equa ions
()
()
2
12 12
iii−Ω + Ω + = +KMCuuFF
(3)
The columns o ames a e join ed wi h he pad oo ing
embedded on he subsoil consis ing o a g a el wi h a
eloci y o shea wa es s = 700 m/s. The pad oo ing has
been modelled by LINK8 wea e elemen s, whose igidi y
and damping cha ac e is ics we e de e mined by [6],
whe e
ρ
is he speci ic g a i y o he soil, B, L a e g ound
plan dimensions o he base oo ,
β
x,
β
z,
β
ψ a e coe icien s
dependen on he shape o he oo acco ding o [6].
()
BLGk xx
βν
+= 12 ,
()
1
zz
kBLG
β
ν
=−
,
()
21kBLG
ψψ
β
ν
=−
, 3
16 3
kGR=,
()
422 6/
π
LBBLR += , (4)
GRkc xx
ρ
576,0=, GRkc zz
ρ
85,0=,
()
0.3 1ckRGB
ψψ ψ
ρ
=+
,
()
[]
RIikc k 5
21
ρ
+=
,
whe e kx, ky, kz a e longi udinal s i ness, kψ, k a e
o a ional and o sional s i ness, cx, cy, cz a e longi udinal
damping, cψ, c a e o a ional and o sional damping.
Due o he signi ican in luence o he s i ness o he
soil on he dynamic cha ac e is ics o he s uc u e o he
building [1, 11-15, 18], i is ad isable o conside h ee
low-medium-high alues, based on he median alue and
he alues o he lowe and uppe quan um, assuming he
no mal dis ibu ion [22]. The uppe and lowe alue kp
de ined o no mal dis ibu ion o he s i ness o he soil
a e exp essed in he o m [7]:
()
1
p
mpw
kk.u.k=± (5)
whe e kp is he quo ien o he s i ness o he subsoil ( o
p obabili y p = 0.05 and p = 0.95), km is he mean s i ness
o he subsoil, kw is he alue o he soil s i ness a ia ion
(kw = k a s/km), up is he no malized alue o he quo ien ,
quan i y. I you conside 24% o he s anda d de ia ion and
he no mal dis ibu ion, i is a ac o o 0.6 / 1 / 1.4 (Low /
Medium / High).
The in luence o soil s i ness on he equency
cha ac e is ics o he s uc u e is shown in Tab. 1. Modal
analysis was pe o med using he Lanczos i e a ion
me hod based on Cholean me hod o ac o iza ion o mass
and s i ness ma ix. The mode shape o wo o he c i ical
equencies can be seen in Fig. 4.
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Tab. 1: Compa ison o he in luence o he soil s i ness o signi ican
modes
Model Mode in di ec . X/Y/Z
F ame Soil ype F equency
[Hz] Rela i e masses [%]
F1 L 1.03/1.04/5.05 58.51/58.35/44.82
and M 1.07/1.05/5.82 23.68/57.58/88.29
F2 H 1.09/1.06/6.2 58.50/57.34/49.56
L 1.15/4.24/6.14 55.01/41.81/46.10
F3 M 1.28/5.21/6.60 34.50/29.32/60.61
H 1.29/6.21/10.35 33.54/26.85/33.34
*) No e - L / M / H- lowe / middle / uppe s i ness o he soil
By compa ing he alues o he deciding eigen
equencies o he s uc u e, he igidi y o he soil
signi ican ly a ec s he alues o he equencies in he
ho izon al di ec ion. The e is a jump o decisi e
equencies a he low and medium s i ness o he soil. I
should be no ed ha he o he equencies a e close o
equencies han o he o iginal design.
a) The decisi e shape o oscilla ion in X di ec ion
b) The decisi e shape o oscilla ion in Y di ec ion
Fig. 4: P incipal modes o he o iginal s uc u e
A a pape speed o 450 m/min, he o a ion speed o
he 1.6 Hz d ying olle s is a s a e ha has exis ed o 10
yea s and does no esona e [4]. Inc easing he speed o
pape mo emen o 700 m/min ep esen s an inc ease in
he o a ion speed o cylinde s o 2.5 Hz. In he ange o
1.6 - 2.5 Hz, we ind ou own equencies, which ha e a
small sha e in he o al e ec i e weigh o he sys em. We
ha e deal wi h he di ec me hod o sol ing he complex
equa ions o he ha monic load by he oscilla ion o he
pape machine.
5. Loads and load combina ions
The load and load combina ion in he case o de e minis ic
as well as p obabilis ic assessmen o he limi s a e o load
capaci y and se iceabili y o he s uc u e a e conside ed
acco ding o STN ENV 1991-1 [7] as ollows:
A) De e minis ic combina ions
.in .in .1 .1
1
Gj kj Q k
j
GQ
γγ
≥
+
 (6)
.sup .sup .1 .1
1
Gj kj Q k
j
GQ
γγ
≥
+

B) P obabilis ic combina ions
a a
1
kj k
j
g
GqQ
≥
+
 (7)
whe e Gkj is he cha ac e is ic alue o cons an loads ( o
he ad e se e ec Gkj.in and he bene icial e ec o Gkj.sup),
Qk1 - he cha ac e is ic alue o he p edominan a iable
load,
γ
Gj - he pa ial coe icien o pe manen load, γQ1 -
he pa ial coe icien o a iable load 1, g a , q a -
a iable coe icien s in he o m o a s anda d his og am.
The pa ial coe icien alues in ela ions (6) and (7) a e
conside ed o he limi s a e o capaci y and usabili y as
ollows [7]:
• limi s a e o load capaci y
(
γ
Gj.in = 0.9;
γ
Gj.sup = 1.1;
γ
Q.1 = 1.5)
• limi s a e o se iceabili y
(
γ
Gj.in = 1.0;
γ
Gj.sup = 1.0;
γ
Q.1 = 1.0)
6. Unce ain ies o inpu pa ame e s
The a iabili y o he e ical s i ness o he soil (Table 2)
is de ined by he cha ac e is ic kz.k s i ness ob ained om
he in-si u measu emen s and he a iable coe icien
o kz. a .
Tab. 2: P obabili y model o inpu pa ame e s
Type Quan i ies Cha ac .
alues
Va iabil.
pa ame .
His o-
g am
*)
Mean
μ
De .
σ
Soil S i ness
k
z,k
k
z. a
N 1 0.24
Ma e ial Modulus
E
k
e
a
LN 1 0.05
Load Dead
G
k
g
a
N 1 0.10
Li e
Q
k
q
a
G 1 0.35
Ampli ude
F
k
a
LN 1 0.10
F equency
F
k
a
N 1 0.10
Model Ac ion
θ
E
Te
a
N 1 0.05
Resis ance
θ
R
T
a
N 1 0.05
*) N - No mal, LN - Logno mal, G - Gama
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The s i ness o he s uc u e is de e mined by he
cha ac e is ic alue o he Young's Ek module and he
coe icien o a iabili y e a . The load is cha ac e ized by
he alues Gk, Fk, F .k and a iable ac o s g a , a and . a
(Tab. 2). The unce ain y o he compu a ional model is
conside ed by he a iable model coe icien s and he
a iable coe icien o load e ec o Gaussian no mal
dis ibu ion. The p obabilis ic analysis was pe o med
unde he ANSYS sys em by he app oxima e RSM
me hod using he CCD [14] expe imen al design me hod
o 79 simula ions. F om he esul s o he p obabilis ic
analysis models "F am1" and "F am2" show, ha he
dominan equency is changing in he di ec ion X ( om
0.83 Hz in 1.41 Hz), Y ( om 0.83 Hz o 1.37 Hz) and Z
( om 4.19 Hz-7.48 Hz). F om he esul s o he
p obabilis ic analysis models "F am1" and "F am2" show
ha he dominan equency is changing in he di ec ion X
( om 0.83 Hz in 1.41 Hz), Y (since in he case o pa ed
cons uc ion o "F am3" is he dominan equency o he
change in he di ec ion o X ( om 1.02 HZ-1.68 Hz), Y
(3.86 Hz o 6.63 Hz) and Z ( om 4.99 Hz o 8.35 Hz).
These anges o equencies can ha e a signi ican impac
on he esponse o ha monic oscilla ion he pape machine.
7. Compa ison o de e minis ic and
p obabilis ic analysis
Compa ison o de e minis ic and p obabilis ic solu ion o
he sa e y and eliabili y o he design o building is
documen ed in Table 3. F om he able see a compa ison
o he ho izon al and e ical displacemen s o he h ee
calcula ion models, he s uc u es (F am1, F am2 and
F am3) ob ained om he de e minis ic analysis ( o h ee
a ia ions o he soil s i ness) and om he p obabilis ic
analysis. The alues o maximum displacemen s,
eloci ies and accele a ion a he le el o he ounda ions
does no exceed he limi alues gi en in he s anda ds
STN 73 0032 and DIN 4150. Maximum e ical
displacemen s o he s uc u e indica e a possibili y o
ailu es in acco dance wi h he c i e ia STN 730036
(Tab.1).
Tab. 3: A compa ison o he maximum peak o he displacemen s a op
o ames
Model
Analysis
Di ec ion
*)
Displacemen [mm]
P obabili y o exceedance De .
5% 50% 95% σ
F am1 De e min. H 2.80 3.06 3.29 -
V 7.26 8.88 12.72 -
S ochas ic H 1.21 4.80 8.42 2.19
V 4.88 8.59 12.31 2.26
F am2 De e min. H 2.02 2.22 2.85 -
V 7.81 9.74 14.63 -
S ochas ic H 1.73 2.63 3.52 0.54
V 4.93 9.39 13.85 2.72
F am3 De e min. H 0.91 0.91 1.02 -
V 4.37 5.06 8.08 -
S ochas ic H 1.01 1.38 1.76 0.23
V 3.72 5.85 7.98 1.30
*) H – ho izon al, V - e ical
F om he poin o he human com o he peak eloci y
a loo le el we e calcula ed on o iginal and ein o ced
ame and compa ed wi h he g aph No.8 in nomog am o
s anda d [25]. The limi alue is equal 2.7 mm/s o
equency 2.5 Hz. The peak eloci ies in he ho izon al and
e ical di ec ions we e equal x.peak = 5.65 mm/s >
2.7 mm/s and z.peak=5.59 mm/s > 2.7 mm/s a o iginal
ame (F ame2). A e ein o cemen o he ame by
sys em o he conc e e walls he peak eloci ies in he
ho izon al and e ical di ec ions we e equal x.peak =
1.4 mm/s < 2.7 mm/s and z.peak = 0.44 mm/s < 2.7 mm/s
(F ame3) calcula ed de e minis ic. In he case o he
p obabilis ic analysis he peak eloci y o he p obabili y
o exceedance 95% in he ho izon al and e ical di ec ions
we e equal x.peak = 2.41 mm/s < 2.7 mm/s and z.peak =
0.43 mm/s < 2.7 mm/s (F ame3).
8. Conclusions
The eliabili y analysis o he sa e y and eliabili y o he
hall s uc u e wi h he pape machine, depending on he
a iabili y o he s i ness o he sub-soil, mechanical
cha ac e is ics o ma e ials, and he ope a ion o he
machine, as well as he unce ain y o he model and he
esis ance we e p esen ed in his pape . The analy ical
model was es ed by expe imen al measu emen on a eal
s uc u e. The me hodology o he p obabilis ic analysis o
he soil-s uc u e-machine in e ac ions was p esen ed on
he p ac ical p oblem in he pape ac o y a e changing
he echnology. A e ein o cemen o he ame wi h he
conc e e walls, he alues o he displacemen s we e
educed by 30%. The p obabilis ic analysis gi es o he
enginee -designe s a mo e complex in o ma ion’s abou
he in e ac ion o he sys em soil-s uc u e-machine as
de e minis ic.
Acknowledgemen
The p ojec was pe o med wi h he inancial suppo o
he G an Agency SR (VEGA 1/0265/16).
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[2] ČAJKA, R., M. KREJSA. Measu ed Da a P ocessing
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[3] ČAJKA, R. e al. Expe imen al soil - conc e e pla e
in e ac ion es and nume ical models, Jou nal - Key
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[4] DRŽÍK, M. e al. Ha monize he s ool- echnology-
hall in e ac ion sys em on a pape machine PM-8 in
SCP Ružombe ok, Enginee ing Buildings, 41 (10),

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1993, pp.337-341. (in Slo ak)
[5] EN 1990, Eu ocode – Basis o s uc u al design. CEN
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Abou Au ho s
Ju aj KRÁLIK was bo n in B a isla a, Slo akia. He
ecei ed his p o . om STU B a isla a in 2011. His
esea ch in e es s include applied mechanics.
Ju aj KRÁLIK, j . in B a isla a, Slo akia. He ecei ed
his PhD. om STU B a isla a in 2008. His esea ch
in e es s include applied mechanics.