Deterministic and Probability Analysis of Paper Machine Vibration Impact to the Structure Safety and Human Comfort

SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 19 | NUMBER: 1 | 2019 | JUNE © 2019 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 22 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 SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 19 | NUMBER: 1 | 2019 | JUNE © 2019 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 23 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. SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 19 | NUMBER: 1 | 2019 | JUNE © 2019 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 24 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. SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 19 | NUMBER: 1 | 2019 | JUNE © 2019 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 25 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 SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 19 | NUMBER: 1 | 2019 | JUNE © 2019 TRANSACTIONS OF VSB - TECHNICAL UNIVERSITY OF OSTRAVA CIVIL ENGINEERING SERIES 26 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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Assessmen o Unce ain ies in Mechanical Models, Applied Mecha-nics and Ma e ials, 2013, Vol. 378, pp 13-18, TTP, Swi ze land, doi: 10.4028/www.scien i ic.ne /AMM. 378.13. [27] ŠEJNOHA, M., J. ŠEJNOHA, M. KALOUSKOVÁ and J. ZEMAN. S ochas ic analysis o ailu e o ea h s uc u es, In. P obabilis ic Enginee ing Mechanics, 22(2), pp. 206-218. 2007, doi:10.1016/j.p obengmech .2006.11.003. [28] VAŠKOVÁ, J. and R. ČAJKA. Subsoil-s uc u e in e ac ion sol ed in di e en FEM p og ams, In: In e na ional Con e ence, SGEM, Volume 17, Issue 32, 2017, Pages 555-562, Albena; Bulga ia; 29 June- 5 July 2017, Code 130796, ISSN: 13142704, DOI: 10.5593/sgem2017/ 32/S13.072. 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.