fondasi mesin pembuat kertas

5/23/2018 Fondasi Mesin Pembuat Kertas

1/5

Dynamic analysis o fpa . . machine foundationsSaurenGuha-MajumdarandMakramA Khoury

fats w h p a p e r m b i n e s have F m i c anabszj ofmbi ne f ounh t i onsa routine part of the esignprocess. Tbzibas created an urgent needfir indmrywzdeguidelinescovering tbe use of tbzjdesign tool.The rotating rolls in todays high-speed fine paper machinescan initiate dynamic excitationwithin a frequency rang e of 2-20Hz. Dynamic and static analyses of the machine and its supp ortstructure a re essentialif the m achine is to runsmoothly, herebyreducing the number of shutdow ns, the amoun t of off-qualityproduction, and maintenance costs. The adven t of fast, high-capacity, cost-efficient computers has made it possible to ana-lyze the interaction between complex machines and their supportstructures.A fine paper machine generally comprises the followingsections: wire, press, d ryer, size press, calender and reel, andwinder. The machine foundation includes the structural ele-men ts below the machine sole plates: sill beams, cross beams,columns,walls, and th e building foundation, ncluding the soilorpile support. I n this pape r, the combined machine and founda-tion is defined as a system.The machine manufacturer and the consulting engineer re-sponsible for designing the machines foundation must thor-oughly understand each others analyses and work closely toconstruct a structurally sound system a t the lowest cost. Thisarticle outlines the information requirements for dynamic analy-sisof a paper machine and its support structure. Th e repo rt alsoprovides a framework for analyzing and designing paper ma-chine foundations.Dynamic analysisEffect ofmachine speedand widthEfforts to increase productivity have resulted in faster papermachines, with speeds increasing from 2500 ft/min to 5000 ft/min over the last 30 years 1-5). The higher machine speedshave mad e th e vibration level an increasingly critical factor inanalyzing machine operation. The sinusoidal hannonic excita-tion forces generated by a rotating roll is proportional to thesquare of t he rolls rotational frequency. Thus t he unbalanceddynamic force of a roll at 5000 ft/min is 1.56 times th at of thesame roll a t 4000 ft/min and four times t hat of th e roll a t 2500 f tmin.

Guha-Majumdar, senior engineer, and Khoury, structuralengineer, a re affiliated with Brown and Root, Inc., 4100Clinton Dr., Houston, TX 770020-6299.

Machine widths also have increased to accommodate demandsfor higher productivity. Fine paper machines are being manufac-turedw ith widths exceeding400 in. Wider machines mply heaviermachine components and sill beams. Since system frequency isinversely proportional to the sq uare root of the mass, heaviercomponentswill result in a lower system frequencyIncrea ses in machine speed an d width have made it difficultto achieve a high-tuned system, i.e., a system whose first natu-ral frequency is higher than the excitation of the highest rollfrequency a t he highest machine speed (for a roll of significantmass). Consequently , the machine-foundation system will, inmany cases, have to be designed to operate under resonantconditions.Data requirementsMachine manufacturers develop technical data, including vi-bration criteria and an analytical model, for each machine sec-tion. The consulting engineer must have access to thisinformation in order to design an effective and efficient founda-tion for the paper machine.

Analyticalmodel.The manufacturer develops an analyticalmodel for dynamic analysis to simulate the properties of themachine components.Figure 1 is a simplified two-dimensionalanalytical model of th e fron t and back sides of a machine sec-tion. The model consists of lumped masses at th e joints con-nected by beam or truss elements tha t represent p arts of themachine section. The dynamic models prepared by machinemanufacturers are similar to this. The models accuracy di-rectly affects the resu lts of the dynamic analysis of the system.To demonstrate this point, the fundamental natural fre-quency of a system was determined using two different models:Model 1-A model of a machine section with 225 degreesof freedom and 85members representing front and backsides. This is the model illustrated in Fig. 1.

Model 2-A single-degree-of-freedom model of the samemachine section. This model is illustrated in Fig. 2. Thesingle-degree-of-freedom model ha s a n equivalent ma ss,center of gravity, and stiffness, producing an equivalentfundamental natu ral frequency of the m achine in the ma-chine direction.Both models were attached to the same foundation. Model 1resulted in a fundamental natural frequency 20% higher than

August 1992Tappi Journal 69


2/5

1. Machine Model 1 with 225 degrees of freedom

Model 2. Thu s Model 2 would produce (a) a conservative andexpensive foundation for a high-tuned sy stem or (b) an unsafefoundation for a low-tuned system, i.e., a system whose firstnatu ral frequency is lower than the excitation of the lowest rollfrequency at th e lowest machine speed.In a force-response analysis, the resu lts from Model2wouldhave been unre liable. Although this difference in frequency wasobtained for a particular case, a simplified single degree offreedom represe nting a machine section will generally yield alower frequency. Model 1detected coupled modes that would bemissed in a model with a single degree of freedom . Given theseresults, it is imperative tha t machine manufa cturer s provide adetailed repre senta tive m odel of each machine section.Damping ratios.Damping dissipates the ener gy in a vibrat-ing system by suppressing vibratory motion. Energy is oftendissipated in the form of heat loss. The dissipation of vibratoryenerg y reduces the amplitude of vibration and makes i t possibleto opera te a system even if it is in resonance.The damping ratio is the actual resistance in damped har-monic motion t o that necessary to produce critical damping. Inorder to perform a force-response an alysis, it is necessary t oknow the damping ratio of the system or its components 5). nthe structural analysis, damping is in the form of dry frictionand hystere sis loss, which are not well understood and thereforear e approxim ated. Measurement of vibration amplitudes of op-erating machines will help determine the damping ratios ofgene ral paper machine components and system s. Such informa-tion will be helpful for future designs.The ma nufac turer provides the consulting engineer with thedamping ratio for the machine. The effect of dam ping is illus-trated in Fig.3 6), where the dynamic magnification factors aresubstantially higher for frequency ratios in the ran ge of 0.75-

1.25,especially whe re syst em damping ratios are low. The mag-nification fac tor, or dynamic load amplification factor, increasesby a factor of up to 50 for a damping ratio of 1 .Vibration criteria.Vibration analysis is done in the threeprincipal axes of each machine section. Vibration cr iteria differfor each of the following situations:High-tuned or low-tuned systemSystem in resonance.

2. Machine Model 2, single-degree-of-freedom system. El is rigidity ofmember, and 144.31 in. is the location of center of gravity of machinemass.I

144.31 in.l

A\\

High-tuned OT low-tuned sy stem In a high-tuned system,the first natural frequency of the system is higher than theexcitation of the highest roll frequen cy at the highest machinespeed (for a roll of s i m c a n t mass). In a low-tuned system, thefirst natura l frequency of the system is lower than the excitationof the lowest roll frequency at the lowest machine speed. Excita-tion frequencies are determined using Eq. 1.

J = 12S/60D,n (1)wheref iDzSt

Manufacturers commonly recommend th e following crite riafor the vertical frequencyU;)and horizontal frequencyg f thesystem:

excitation frequency U; highest,& lowest), Hzroll diameter D1 smallest, D, largest), in.design speed (SI highest, S, lowest), ft/min

70 August 1992TappiJournal


3/5

f ,> 2J , > 1.2 or < 0.7

For a system satisfying the high-tuned criteria, a force-resp onse analysis is generally not req uired because of the ex-cellent track record of machine performance.Operating speeds for h e aper machines typically rangefrom 2500 Wmin to 4500 in. Th e excitation frequency of a38 h- di am . roll ranges from 4.19 Hz to 7.55 Hz for this speedrange , while the excitation frequency of a Win.-diam. roll rang esfrom 2.65 Hz to 4.78 Hz. In a machine section co n t a i i g both38-in. and 60-in. rolls, excitation frequencies can range from2.65 Hz to 7.55 Hz. Using the design-crite ria factors of 0 7 and1.2 for horizontal frequency, the design rang e in the machinedirection would be 1.86Hz to 9.06Hz. Based on our experience,the fundam ental natural frequency of a system ran ges from 3Hz to 7 Hz, depending on the machine and foundation prop er-ties. Resonan t conditions prevail at different production rate swith different m achine rolls.

System in esonance. In addition to a model, damping ratio,and pseudodynam ic loading of each machine section, the follow-ing information is needed to perform a force-response analysisof the system:Forcing functionVibration amplitudePha se angle.1.Forcing function: The design criteria include the unbal-anced force for each roll a t different machine-speed intervals.

The unbalanced forces repres ent dynam ic time-dependent ex-citation on the machine components tha t the indu strywill oler-ate, considering the effect on equipm ent wear and pap er quality.The exciting force,F , for an unbalanced rotating mass is givenin Eq.2 .F =med[sin(wt +@)] 2)

wherem unbalanced rota ting masseot =timeQ

2. Vibration amplitude: Fo r each m achine section, this crite-rion specifies allowable vibration amplitudes a t critical loca-tions. Limits for vibration of general rotating machinery ar eshown in Fig. 4 (7, 8),where the upper line in zone B is theallowable vibration amplitude. Similar vibration criteria areneeded for the pulp and pap er industry.3. Pha se angle: The phase angle specifies the time relation-ship between two rolls with th e sam e frequency rotating suchtha t their peak values of the s am e sign (positive or negative) donot occur simultaneously (6, 9). A common statistical approachis to use the sq uare root of the sum of squa res of responses of

eccentricityof unbalanced massangular frequency of the roll

phase angle of the rotating mass

each roll. A conservative approach is to add the absolute responseof the two rolls.

Designing the bundationThe structural engineer must satisfy both static and dynamicrequ irem ents while resolving layout problems.static analysisThe consulting engineer applies the loads provided by the manu-facturer at the specified locations. Analysis is performed usingcommonly available finite-element computer software 10-13). Theconcrete and steel members of the foundation are designed tocomply with ACI 14) and ASCE (15) codes and to meet themanufacturer's deflection criteria 16).Several factors ar e considered in the analysis and design of thefoundations:

Shear deformation (especially when depth-to-span ratio issmall)Prop erties of unc racked conc rete sections (when the level ofstress is low)Clear span-the effective leng th of the beam-and the use ofrigid links at joints where structural members overlapDesig n of sill beam s using deep-beam theory.

Isolation of machine sectionsDesigners have not always routinely performed dynamic analysesof pap er machine systems. The need was not as compelling as t ison today's h igh-speed machines, and analysis was complicated bythe widesp read practice of attaching machine foundations to theoperatin g floor.Foundations for modern paper machines are not connected tothe opera ting floor, and the foundation for each machine section istypically isolated from the others. Isolation eliminates transmis-sion of vibration between the building and the machine sectionsand from one section to anothe r. Isolation of the dry er sectionsalso helps control deflection from th erm al expansion 3).Frequency analysisThe consulting engineer must satisfy the frequency requirem entsspecified by the machine manufacturer. The first step in thisprocess is to perform a frequency analysis on the combined ana-lytical model of the machine, its su ppo rt structure, and the founda-tion piles (or the soil). Fo r a rigid foundation suppo rted on soil, theequivalent spring constants and damping ratios can be obtainedfrom Tables 10-13 and 10-14 of Richart et al 17).The springconstants for piles or shear modulusof soil ar e determined by soilconsultants. Methods of interpre ting field test are described byRichart et al 17) .A three-dimensional analytical model is recommended in caseswhere geometry and mass distribution are asymmetrical. If thefundamental frequency of the system is much higher than 1.2times the highest excitation frequency, cost can be reduced byreducing the stiffness of the stru cture. If frequency criteria a re notmet, a force-response analysis is performed.

August 1992TappiJournal 71


4/5

3. Vibration magnification factor as a function of frequency ratioexcitation requenc yhatural frequency) at various levelso damping0)

0.2

501 I

- D = 0.601 1 1 1

403020

10865432

1 o0.80.60.50.40.3

Force-responseanalysisDynamic loading and the steady-state response of each ma-chine section is harmonic and sinusoidal. The displacements,velocities, or accelerations at o r near resonance are obtainedfrom a force-response analysis. Th e equation of dynamic equi-librium solved in a harmonic-response analysis is given in E q. 3:

{FI= [Iwl{Ol+ [Cl{Ol + [KJ{D) (3)where{ F } load amplitude vector[M =massmatrix[a dampingmatrix[ K stiffness matrixD} acceleration vector

{ D } = velocityvector{D} displacement vector

Mathematically, the equation represen ts a series of second-order differential equations. Some commonly used computerprograms for performing force-response analysis are STR UDL ,NASTRAN, ANSYS, and SAP 10-13). System response isdetermined over the frequency range t hat corresponds to theopera tingran ge of the roll under consideration. Sepa rate analy-

4. Peak horizontal vibration amplitude measu red at the bearing) as afunction of rotational requency. U pper limit o zone B is the maximumallowable amplitude for general rotating machinery.

0.01siP

nIc

a.

.-

s0.001

0 100 1000 ro mFREQUENCY cycleslmin

ses are performed for each exciting roll, and the respo nse ismeasured at the requir ed locations. Since the analysis is linear,the method of superposition is used to determine the finalresponse.In finite-element analysis, a damping matr ix is created tosolve the resp ons e of the time-related dynamic forcing function.A common method (9, 18) is to combine a fraction, a, f thestiffness m atrix with a fraction, p of the mass m atrix, shown inEq. 4.[cl= m P [M l (4)

Equation 4 s the Rayleigh or the proportional damping.With this damping matrix, the set of second-order differentialequations described are linear, and the mode shapes aredecoupled. If p 0 the higher modes a re lightly damped. If a0, the higher modes are heavily damped. The term a s thedominating factor in dynamic analysis of machine systems,since the excitation is close to the first few natural frequenciesof the system. The stiffness of the system is the most criticalfactor in d eterminingvibration amplitude.The damping ratio can be incorporated in the computeranalysis by one of the following two methods.Method 1-Perform force-response analysis of the sys temusing the lowest damping ratio, i.e., the damping ratio of themachines steel frame and steel suppo rt base frame. This damp-ing ratio, 0.5-1 , will yield conservative results. Method 1 isrecommended for structures supportedwith a steel base frame.

72 August 1992TappiJournal


5/5

MethodM a m e asMethod 1,except damping ratios of eachsystem elem ent are specified. Concrete dam ping is in the ra ngeof 3-5 , while soil damping can be as high as 50 1 ) .Method 2is recommended unless restricted by com puter capacity.ConclusionThe quest for g reate r productivity has led to the developmentof faster, wider paper machines, and this trend is likely t ocontinue. Efficient opera tion of todays high-speed pape r ma-chines requires a well-designed foundation that can sustainvibration within a tolerable range. Dynamic considerations endto determine the sizes of major components of the foundation.Dynamic analysis, in turn, h as become an essential pa rt of thedesign process.The analysis is elaborate and req uires close interaction be-tween the machine manufacturer and t he consulting engineerresponsible for designing the machines foundation. This isespecially tru e for m achines whose speed and w idth stimulateroll frequencies tha t a re in resonance with system frequency.Ahigh-tuned system is preferable and provides the safest design,but a force-response analysis is imperative in low-tuned andreson ant conditions.Models of the machine and foundation are requ ired to deter-mine frequencies and vibration amplitudes. An adequate modelwith sufficient mass points isessentialto obtain accurate results.The model can be reduced in sizeonly if the engineer thoroughlyunderstands the system response. Reducing a machine model toa single degree of freedom resu lts in unreliable outpu t.The recommended practice is to isolate each machine sectionwith a separa te foundation and to isolate each of these founda-tions from the operating floor. Isolation prev ents transmissionof vibrations from one section to another and between thebuilding and the pap er machine. Isolation also makes the sizeand the cost of the dynam ic analysis manageable.

The pulp and paper industry urgently needs standardizedcriteria to streamline the task of analyzing and d esigning pap ermachines and their foundations.A good star ting point would bedevelopment of guidelines for frequency analysis, force-re-sponse analysis, forcing function, vibration amplitude, damp-ing,and phase angle of response.Studies nvolving field mea surem entson operating m achinesare needed to dete rmin e acceptable limits of machine opera-tion. Such studies would best be canied out by committeesconsisting of pap erm ake rs, machine manufacturers, and con-sulting engineers. The TAPPI committee on paper machinedynamic foundation design would be a good candida te for un-dertaking this essential task.Literaturecited1.2.3.4.

5.6.7 .

McKevitt, W. E., Pulp Paper 40(7): 82(1987).Roisum, D. R., Tappi J. 71(1): 87(1988).Baldwin, J.W., Bon net, H. P., an d Re is, W. W., Ta ppiS l(10): 75A(1968).Lee,J. P., Proceedin gs of Second Internationa l Conference on RecentAdvances in Geotechnical Earth quak e Eng ineering and Soil Dynam-ics, Vol. 11, S. rak ash , Ed.), Rolla, MI, March 1991, pp. 1525-30.Abdulezer, A., an d C lark, K. B., P ulp Pa per C an. 88(5): ll(1987).Arya, S. C., ONeill, M W., and Pincus, G., Design of Struc tures andFoundations for Vibrating M achines,Gulf Publishing, Houston, TX, 979.Blake, M. P., Hydrocarbon Processing Petroleum Refiner 43(1):11 (1964).

8. Mechanical vibration of machines with o perating speed s from 10 toZOOrev/s-Basisfor spec@ing evalu ation standards, 1902372-1974(3),International Stan dards O rganization, 1974.9. Hu rty , W. C., and Rubinstein, M. F.,Dynamics of Struc tures, PrenticeHall, Englewo od Cliffs, NJ , 1964.10. Structural Design Language (STRU DL) computer program, Massa-chusetts Institute of Technology, Dep artme nt of Civil Engineering ,Cambridge, MA.11. NASA Stru ctural Analysis (NASTRAN) comp uter program, NASASP-222, National Aeronautics and Space Administration, GoddardSpace Flight C enter, Greenbelt, MD.12. Engin eering Analysis System (ANSYS) compu ter program, SwansonAnalysis Systems, Houston, PA.13. Wilson, E. L., et al., Structural Analysis Program SA P )computerprog ram , University of California, Berkeley.14. Building code requireme nts of reinforced concrete, ACI 318-89; andCommentary, ACI 318R-89, American Concrete Institute, Detroit,1989.15. Manual of Steel Construction (9th edn.), American Institute of SteelConstruction, Chicago, 1989, pp.5.1-5.195.16. Ma chin ebui ldin g nterface design considerations, K095-96-0101-0001,Beloit Corp., Beloit, WI.17. Richart, F. E., Hall, J. R., and Woods, R. D., Vibration of Soils andFoundations, P rentice H all, Englewood Cliffs, NJ, 1970, pp.191-243.18. Cook, R. D., Concepts and Applications of Finite Element Analysis(2nd edn.), Joh n Wiley Sons, New York, pp. 302-25.

Received for review May 31,1991.Accepted Feb. 19,1992.Keywords: Analysis, damping, dynamic tests, force, foundations, high veloc-ity, models, paper machines, resonance, respo nse time, standar ds, vibration.

August 1992Tappi Journal 73

fondasi mesin pembuat kertas

Documents