09 Energy&Aeronautics&Auronautics

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5thInternational Advanced Technologies Symposium (IATS09), May 13-15, 2009, Karabuk, Turkey

IATS09, Karabk University, Karabk, Turkey

ADVANCED TECHNOLOGIES IN RECIPROCATING COMPRESSOR WITHRESPECT TO PERFORMANCE AND RELIABILITY

Amin ALMASIa, *

a, *

Tecnicas Reunidas S.A., Madrid, Spain, E-mail: [email protected] [email protected]

Abstract

Reciprocating compressors are most common type ofcompressor and most flexible machine to handle widecapacity and condition swings. They offer a most efficientmethod of gas compressing. They are vital machines invarious units of industrial plants. In this paper advancedtechnologies and latest configurations and methodsregarding condition monitoring, performance, flowmanagement, capacity control system, inter-stagearrangement, low suction pressure opertaion, lubricatedcylinder, machine optimum speed, compressor valve,lubrication system, piston rod coating, liner material,barring device, pressure drops, rod load, pin reversal,

discharge temperature, cylinder coolant system, coupling,flywheel, special tools, commercial points, delivery,pulsation and acoustic conditions are presented.

Keywords: Reciprocating Compressor, Performance,Reliability.

1. Introduction

In this paper latest and advanced technologies inreciprocating compressor design, component selection andperformance monitoring and management are presentedand discussed. Reciprocating compressors are the mostcommon type of compressors [1,2,3,4]. Reciprocatingcompressors can generate high head independent ofdensity. They are only option for many applications suchas very high pressure and light gases (for examplehydrogen, etc). Worldwide installed reciprocatingcompressor horsepower is approximately three times thatof centrifugal compressors. Maintenance costs ofreciprocating compressors are approximately three andhalf times greater than those for centrifugal compressors[3]. Design, evaluation, selection and purchasing areciprocating compressor shall be done with respect tolatest available technologies. Otherwise purchasedreciprocating compressor may not be suitable machine forexpected performance, safety and reliability level.

2. Performance

2.1. Load Step Curvature

Advanced design technology recommendation is to avoidsteep load curve. A review of the steepness of the loadcurves can quickly identify which load steps (and where)are quite steep in nature, and thus small changes inpressure can have significant changes in load and flow.Often, steep load curves may indicate improper sizing ofcylinders. Units with steep load step curves can also provedifficult to automate and tune [1].

2.2. Advances in Machine Shop Run Test

Shop mechanical run test is the first test aftermanufacturing of machine and last test before delivery.Shop test results, including vibration, may seem to havelimited usefulness because supporting structure andoperating condition of the machine are different with finalsite installation. However this test is a unique opportunityto find defects in design and manufacturing phases whilemachine is still in fabrication shop. Generally the lager thepower per compressor throw leads to higher the dynamicforces and 370 KW or more per throw is a high riskmachine. Latest method is to record and analyze shop runtest measurements (Kalman Filter can be used to optimallyevaluate machine dynamic characteristics based onmeasured data).

2.3. Advances in Pressure Drop Prediction

Latest recommendation for prediction of pressure dropvalues for basic design stage is as follows: pulsationdampeners: 1% pressure, intercooler: 0,70 bar. The use oforifice plates, especially on high-speed single-act, cancontribute to significant pressure drops [1].

2.4. Rod load and Pin Reversal Details

Maximum Rod Load is recommended be less than 80% ofallowable rod load. Duration and peak magnitude load ofrod reversal shall not less than 15 of crank angle and 3%of the actual combined load in the opposite direction,respectively and shall be checked for all possible operating

cases [1] (especially low suction and part load).

2.5. Highest Expected Discharge Temperature

High discharge temperatures cause problems withlubrication cooking and valve deterioration. It shall bereviewed at least for average and maximum suctiontemperatures [1]. The maximum predicted dischargetemperature [1,2,3,4] shall not exceed 150C and notexceed 135C for hydrogen rich service (MW of 12 orless). Latest technology is to limit gas dischargetemperatures below 118C to extend life of wearing parts.

2.6. Performance Curves

Required performance curves for latest control systemdesign to safely and reliably control the unit across itsdefined operating range [1] are as follows: 1- SuctionPressure vs. Load. 2- Suction Pressure vs. Flow. 3-Discharge Pressure vs. Load. 4- Discharge Pressure vs.Flow 5- Suction Pressure vs. Discharge Pressure, per loadstep.

2.7. Advances in Flow Performance Management

Latest flow management methods require flow details asflow curves from units minimum achievable flow rate to its

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maximum achievable, in specified increments [1].Alternative may be flow versus discharge pressure plots ofspecific suction pressures (more compact and commonwhen suction pressure variation is limited).

3. Advances in Compressor Design

3.1. Advances in Inter-stage Pressure Arrangement

Discharge pressure of each stage is normally protected bypressure relief valves, high pressure discharge switchesare seldom seen [2]. Based on latest optimization methodsand experiences, inter-stage pressures can be obtained byformulation and optimization of performance andinvestment for compressor and inter-stage facilities. Somevendors are intended to change inter-stage pressures,generally higher pressures at early stages and lowerpressure ratio at last stages. Vendor offered inter-stagepressures based on just compressor without respect tointer-stage facilities, are not justified. Inter-stage pressuresare going to increase during part load operation and highsuction pressure. If not tolerate-able, additional clearancepocket on first stage cylinder and part load operationinhabitation by the controlling logic can be studied.Generally it is compromise to fix inter-stage facility designpressure based on vendor recommended PRV set points(around 10-15% higher due to common ranges of part loadoperation and suction pressure variations).

3.2. Advances in Low Suction Pressure Design

Sometimes, due to process requirements, reciprocatingcompressors shall be capable to operate at lowest suctionpressure and full design flow at normal dischargepressure. It can have strong effect on compressor sizingespecially frame rating and motor power (more than 35%power increase for 20% suction below normal). Latestexperiences recommend respecting this condition as

design point in basic design to avoid costly future changes.

3.3. Advances in Capacity Control System

Step-less capacity control system uses finger typeunloader, is pneumatically actuated, and unloads thesuction valve for only a portion of compression cycle toachieve adjusted capacity [2]. Finger type unloaders havepotential for damaging the valve sealing elements andrequire more care for maintenance [2]. Valves andunloaders cause around 44% of unscheduled reciprocatingshut down [5,6] and this selection has a strong effect onreliability [5,6,7,8]. For small machine, 100% spill back islatest recommended solution, because power is low. Forbig machine best and latest configuration is selection ofpart load steps based on plug/port unloader and clearance

pocket.

3.4. Advanced Condition Monitoring

Condition monitoring [9,10,11,12,13] shall be particularlycost effective and include necessary items to identifymalfunctions at an early stage (lower maintenance costsand lower risk of accidents). Advanced vibrationmonitoring: 1- Vibration continuous monitoring (Shutdown). Velocity transducers are preferred overaccelerometers due to better signal to noise ratio [9].Advanced configuration: each end of the crankcase about

halfway up from the base plate in line with a main bearing[9]. 2- Each cross head accelerometer (Alarm). 3- Electricmotor vibration (Shut down). Advanced temperaturemonitoring: 1- High gas discharge temperature - eachcylinder (Alarm and Shutdown). 2- Pressure packing case -piston rod temperature (Alarm). 3- High cross head pintemperature (Alarm). 4- High main and motor bearing

temperature (Alarm). 5- Valve temperature (Monitoring). 6-Oil temperature out of frame (Alarm). 7- High jacket watertemperature - each cylinder (Alarm). Optimumimplementation is properly set trip levels that are just highenough over the normal operating levels to reach tomechanical failures, but not so high as to miss the failureprior to catastrophic release [9]. Proximity probes aretypically located under the piston rods [9] and used tomeasure the rod position and determine wear of the pistonand rider bands, malfunction e.g. cracked piston rodattachment, a broken crosshead shoe, or even a liquidcarryover to a cylinder. Latest method: just for alarm andnot for shut down. Latest operation experiencesrecommend cold run outs and normal conditions operatingrun outs are about 50 microns (2 mils) and on the order of50 to 150 microns (2 to 6 mils) peak to peak, respectively

[9]. All shutdown functions shall be 2 out of 3 voting toavoid unnecessary trip. Usually it can be deviated forcompressor frame vibration and temperature related trips.

3.5. Advance Technology in Valve Selection

Cylinder valves are the most critical components ofreciprocating compressors and strongly influence thereliability and efficiency [5-8,10]. Valve defects areobviously responsible for most of the unscheduledmaintenance events [5-8,10]. Three main valve types: ringtype, ported plate and poppet. For big machines (generallylow speed and high pressure ratios) and small machines(relatively higher speeds) ring type valves and plate typevalves are best choice respectively. Optimum valve size

shall be obtained with respect to efficiency, reliability andperformance requirements including minimum clearancevolume. Lift is the distance travelled by the valves movingelements. The higher the lift, the higher the valve flowarea, lower the valve pressure drop, less consumedpower, higher moving elements impact velocities and lowervalve durability. Acceptable compromise should be found.Optimum valve spring stiffness is also important. Too stiffspring can lead to valve flutter (more compressor powerand considerable wear rate) or early closing of valve(reduce capacity). Too light spring cause valve late closingand the reverse flow (higher velocity, less reliability andreducing capacity). Nonlinear partial differential equationsdescribing the valve differential pressure and the valveelement motion (such as [14]) can be used in optimizationprocess to estimate optimum valve lift, spring stiffness and

gas velocity for each machine and application.

3.6. Advances in Piston Rod Coating

Piston rod seal is second important area for reliability ofreciprocating compressor and most likely path forpotentially hazardous process gas leakage [8]. Packing lifecould be improved three times by adding the propertungsten carbide piston rod coating [10]. It is latesttechnology.

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3.7. Advances in Cylinder Liner Material

Cylinder liner is used to provide a renewable surface to thewearing. The liners made by Ni-Resist cast iron (highNickel content) are not recommended due to problemssuch as permanent distortions. Latest researchesrecommend grey cast iron [8] for all applications except

very high pressure or extremely high corrosiveapplications.

3.8. Advanced Passive Vibration Reduction System

Sometimes odd number of cylinders is avoidable. In thiscase dummy crosshead shall be used to reduce vibration.Also state of art spring-mass-spring system shall bestudied for passive force counter balance and morereduction in vibration, where dummy crosshead is, on theone hand, attached to a movable piston assembly byflexible member and on the other hand, to the stationarycompressor casing using auxiliary mechanical springs.

3.9. Future Expansion

Future expansion planning can save money and time ifprocess changes (capacity increase, molecular weightincrease due to catalyst change, etc) are foreseen [12].Optimum selection is sizing cylinders for economicaloperation at the present rate. The frame can be sized forfuture applications. When the future conditions become areality, the cylinders can be changed while keeping thesame frame. Latest design method is to over size thejournal diameter include margins for future development,thus ensuring that crankshaft size would never become thefirst important limitation of the design [15].

3.10. Minimum speed lubricated Cylinder

Reliable machine is involved low speed (around 350 RPM)

and lubricated cylinder. Optimum piston speed is 3-4.4m/s. Most advanced configuration: horizontal cylinder(s),discharge nozzle on the bottom side. For smallcompressors some vendors intend to deviate lubricatedcylinder or low speed. Optimum option is lubricatedcylinder with available lowest speed machines. Probablyless than 20% of all reciprocating compressors aredesigned for non-lubricated operation just because ofprocess demands (oxygen, high pressure air, etc) [2].

4. Advances in Commercial Management

4.1. Commercial Conditions and Negotiations

It is absolutely necessary to receive at least threeproposals and have minimum two technically accepted

machines. It is completely justified to extend proposal deadtime, clarification time, accept optimum configuration,reasonable deviations and attend extensive clarificationmeetings to have at least two clarified and technicallyaccepted proposals.4.2. Advances in Delivery Methods

Small and medium machines shall be delivered fullyfabricated as one skid mounted package. For very bigmachine, latest and optimum figure is to deliver machineprefabricated (including crankcase, distance pieces, etc)while cylinders are dismantled. Assembled cylinders are

delivered to site separately and installed. Vendor to adviceto offer all site supervision work for cylinder installation asclosed price.

5. Advances in Compressor Auxiliaries andPackaging

5.1. Advances in Flywheel and Irregularity

For all reciprocating compressors, flywheel is mandatory toregulate variable reciprocating torques. Irregularity degreefor mechanical component reliable operation is maximum2%. This value is minimum requirement for allcompressors. Generally in accordance with specificrequirements of driver (especially current pulsation forelectric motors), torsional vibration results, etc, lowerirregularity value is required. It is recommended to obtain1% for special purpose units. Latest studies and designsrecommend irregularity value between 1-1.5%.

5.2. Barring Device

When compressor stopped for an extended time, turn itaround a quarter turn every week by barring device.Manual barring device is for small compressor. Pneumaticis for compressor rated over 750 KW, without areaclassification problem or intermittent power availability andpreferred technically [11].

5.3. Special Tools

Latest recommended check list for special tools [11] for bigmachines: 1- bearing extractor 2- piston extractor 3- valveextractor 4- piston fit up tool 5- hydraulic tightening system6- crosshead assembling tool, 7- special lifting tools 8-partition plate assembling tools 9- mandrels for wearbands. For special tools, tool boxes required and they shallbe delivered with main machines, in separate and tagged

boxes.

5.4. Advanced Lubrication System

API 614 is typically applied only to reciprocatingcompressor trains involving a large turbine driver and gearunit [11]. Optimum oil system shall include two oil pump(for special purpose machine as per API 676), both sizedat least 20% over (Two motor driven identical with rundown tank, or well known crank shaft driven main oil pump,supplying UPS power for one pump is not acceptablealternative), dual removable bundle shell and tube oilcoolers (TEMA C) and double oil filters with removableelement and stainless steel piping.

5.5. Advances in Coupling Selection

For reciprocating machine because of special design, thepotential exits for torsional resonance and torsional fatiguefailure [2]. Coupling is best available option for modificationto tune the system. Coupling configurations: 1- hightorsional stiffness coupling (it is best option if allowed bytorsional analysis). 2- flexible coupling (more elasticity anddamping and more maintenance). 3- direct forged flangedrigid connection (no coupling), with single bearing motor.Coupling for big machines shall be as per API 671.

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5.6. Advanced Coolant System

Liquids should never form inside the cylinder [10,11,12].Liquid contributes to poor reliability, can cause high impactvelocities, can lead to stressing of valve moving elements(slugging) and reduce the lubrication effectiveness. Forany application, a good sized suction drum with a drain

provision shall be in order [12]. It may be a part ofpulsation control, if properly done. Cylinder cooling systemmust be monitored and controlled. Coolant inlettemperature between 6 C and 16 C above inlet gastemperature [12]. For exotic gases or operations nearcritical areas, much care needs to be taken. Also makesure the thermodynamic model is proper.

5.7. Advances in Pulsation Control

Advanced technique trends to dissipate less energy thanreliance on special solutions such as orifices to controlpulsation levels [16]. Acoustic reviews shall be performedfor design and guarantee points as well as all otheroperating cases and combinations of pressures, speedsand load steps. Pulsation can also alter the timing of the

valve motion and decrease efficiency and reliability [5].Based on latest optimization processes, for design stage,pulsation limit is recommended around 95%-85% of API618 (Approach 3) limits to have some margin (around 5-15%) to mitigate risk during construction and installationperiods as well as unpredicted deviations and problems.

5.8. Pulsation Shaking Forces

Reduction of pressure pulsation can be accompanied byan increase in shaking forces (or unbalanced forces) [17].It illustrates that shaking forces shall be determined andcontrolled and piping and vessels properly supported. Themargin of separation between the mechanical naturalfrequency (MNF) of system (including piping and bottles)

and excitation frequency is 20% and MNF shall be greaterthan 2.4 times maximum run speed [11,18]. If not meetlimits, the force response (including stress analysis) isrequired. The cylinder gas forces (also called frame stretchor cylinder stretch force) can be significant source ofexcitation (can cause high frequency vibration on thebottles and piping close to the compressor) and lead toexcessive pulsation bottle vibration even if the pulsationshaking forces meet limits. Flow induced pulsation is rarelyseen [17]. API 618 Design Approach 3 and less rigorousanalysis, to control pulsation and shaking (unbalanced)force levels and avoiding mechanical resonance can resultin an optimized design [17]. Pulsation and vibrationanalysis report shall include Time Domain (TD) andFrequency Domain (FD) simulations, Time Domain (TD)plots of key forces and pressure pulsation, dynamic

pressure drop, models including mounting details(mounting plate, bolts, localized skid, etc) and shellflexibility (nozzle connection flexibility), calculated cylinderstretch forces, mode shape of bottles and piping andcompressor stiffness assumption (compressor framemodelled as flexible support) [18].

5.9. Advances in Inter-state Facilities

Inter-stage facilities and coolers and after coolers shall besized carefully. Undersized lines, facilities and coolers cancause excessive pressure drop and power loss. Pulsation

and shaking force studies are necessary to avoid vibrationproblem in inter-state facilities. Increased cross sectionarea, especially in coolers, to decrease pressure drop cancause significant increase of shaking force and equipment(cooler) vibration. Secondary volumes may be studied toreduce this vibration however in some cases this solutioncan not reduce vibration and modifications to recycle line

are required to significantly lower shaking [17].

5.10. Advances in Torsional Analysis

Typically, for reciprocating compressor, lateral naturalfrequencies will be positioned well above significanttorsional natural frequencies, so lateral critical studies arenot required. A stress analysis shall be performed if thetorsional excitation falls close to the torsional naturalfrequency to ensure that the resonance will not be harmfulfor the system [18,19]. The torsional vibration analysisreport shall include data used in mass elastic system,display of force vs. speed, torsional critical speeds,deflection (mode shape diagram), worst case design,upset condition results (such as valve failure, start up,short circuit, electrical network faults, etc) and how the

input data variance will affect the results (sensitivityanalysis) [18]. Continuous operation at torsional resonanceshall be avoided. Changing the load sequence could helpreduce torsional vibration. Avoid full load shutdowns.Measure and verify torsional vibration during performancetest. Synchronous motor or system started on a frequencybasis need more care (definitely need a transient torsionalstart up analysis). Electric machine (driver) shaft diameterto be equal to or greater than the reciprocating compressorcrankshaft diameter.

5.11. Advances in Dynamic Package Analysis

The dynamic package analysis shall include modeling andsimulation of the foundation at the same time. The

accuracy of this analysis is strongly influenced by thedesign of the foundation especially for pile installation [18].It is even more important for packages mounted onoffshore platforms, FPSO (Floating Production StorageOffloading Vessels) [20], modules mounted on steelstructure, new and unproven skid design and where thelocal soil conditions are suspect. Skid lifting study(including lifting lug details and calculations review) isnecessary. Transit study and environmental loadinganalysis are also recommended [18].

5.12. Advances in Package General Arrangement

Layout is often complex and compromise must be madebetween the support requirements, process requirements,vibration/pulsation conditions, access and maintenance.

Optimum configuration is to install local panel nearcompressor package (around 200 mm away frompackage) but on separate skid (frame) which is installed onfoundation, to avoid vibration damage. For maintenance,consider spool removal and avoid support removal. Accessrequired in front of cylinder for cylinder piston dismantlingand non-drive end of compressor. Pay attention tominimum elevation requirement of pulsation bottle suctionflange to keep suction line, no pocket.

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5.13. Advances in Piping Analysis

The thermal piping design often requires that flexibility beadded to the system which is counter to requirement formore support and increase stiffness to meet vibrationdesign. These analyses shall be conducted by same partyto optimize design iteration and result in an overall

optimized system. Piping thermal analysis is necessary[18] especially when the coolers are off-skid, multiplecompressors on a common header, extremely coldambient temperature, or operation over a very wide rangeof conditions.

5.14. Advanced Cylinder Lubrication System

Using the proper type of lubricant as well as establishingthe proper lubricant rates to the cylinder and packing canbe most important for machine reliability [10]. The life ofthe compressor valves, piston rings, rider bands, andpressure packing can all be significantly affected by thetype and quality of lubrication used. Too much or wrongtype of lubrication can increase the effects of valve stiction(viscous adhesion) and reduction in reliability. Reliable

lubrication system with optimum type and rate oflubrication shall be selected [10].

6. Conclusion

Latest technologies, recommendations and configurationsfor reciprocating compressors regarding component designand selection, commercial points, auxiliary andaccessories, performance and reliability are addressed inthis paper.

References

[1] Dwayne Hickman, Specifying Required PerformanceWhen Purchasing Reciprocating Compressor Part I,

II, Compressor Tech Two, August September-October 2007.

[2] Heinz P. Bloch, A Practical Guide To CompressorTechnology, Second Edition, John Wiley and Sons,2006.

[3] W. A. Griffith, E. B. Flanagan, Online ContinuousMonitoring of Mechanical Condition and PerformanceFor Critical Reciprocating Compressors, Proceeding ofthe 30th Turbo-machinery Symposium, Texas A&MUniversity, Houston, TX, 2001.

[4] Heinz P. Bloch and John J. Hoefner, ReciprocatingCompressors Operation & Maintenance, GulfPublishing Company, 1996.

[5] S. Foreman, Compressor Valves and Unloaders forReciprocating Compressors An OEM's Perspective,Dresser-Rand Technology Paper, http://www.dresser-

rand.com/e-tech/recip.asp.[6] Steve Chaykosky, Resolution of a Compressor Valve

Failure: A Case Study, Dresser-Rand TechnologyReport, Dresser-Rand Technology Paper,http://www.dresser-rand.com/e-tech/recip.asp.

[7] Massimo Schiavone, Evaluation of The FlowCoefficient of Cylinder Valves, Compressor Tech Two,pp. 48-50, April 2007.

[8] Robin S. Wilson, Reciprocating Compressor:Reliability Improvement Focusing on CompressorValves, Piston and Sealing Technology, Compressor

Optimization Conference, Aberdeen, 30-31 January2007.

[9] Steven M. Schultheis, Charles A. Lickteig, RobertParchewsky, Reciprocating Compressor ConditionMonitoring, Proceeding of the Thirty SixthTurbomachinery, pp 107-113, 2007.

[10] Stephen M. Leonard, Increasing the Increase

Reliability of Reciprocating Hydrogen Compressors,Hydrocarbon Processing, pp. 67-74, January 1996.

[11] Reciprocating Compressor for Petroleum, Chemicaland Gas Service Industries, API 618 5th edition,December 2007.

[12] Royce N. Brown, Compressors Selection and Sizing,Third Edition, Gulf Publishing, 2005.

[13] Heinz P. Bloch, Compressor and Modern ProcessApplication, John Wiley and Sons, 2006.

[14] Enzo Giacomelli, Fabio Falciani, Guido Volterrani,Riccardo Fani, Leonardo Galli, Simulation of CylinderValves For Reciprocating Compressors, Proceeding ofESDA 2006, 8th Biennial ASME Conference onEngineering Systems Design and Analysis, July 4-7,2006, Torino, Italy.

[15] Ian Cameron, Thomassen Prescience Pays Dividends,

Compressor Tech Two, pp 12-13, November 2007.[16] A. Eijk, J.P.M. Smeulers, L.E. Blodgett, A.J. Smalley,

Improvements And Extensive to API 618 Related ToPulsation And Mechanical Response Studies, TheResip A State of Art Compressor, European Forumfor Reciprocating Compressor, Dresden, 4-5 Nov.1999.

[17] Brain C. Howes, Shelley D. Greenfield, Guideline inPulsation Studies for Reciprocating Compressors,Proceeding of IPC 02, 4th International PipelineConference, Calgery, Alberta, Canada, Sep. 29 Oct.3, 2002.

[18] Shelley Greenfeld and Kelly Eberle, New APIStandard 618 (5 TH ED.) And Its Impact onReciprocating Compressor Package Design Part I, II

and III, Compressor Tech Two, June July August2008.[19] Alberto Guilherme Fagundes, Nelmo Furtado

Fernandes, Jose Eduardo Caux, On-line Monitoring ofReciprocating Compressors, NPRA MaintenanceConference, San Antonio, May 25-28, 2004.

[20] Kelly Eberle and Chris Harper, Dynamic Analysis OfReciprocating Compressors On FPSO TopsideModules Part I & II, , Compressor Tech Two, pp 10-16 and pp 42-48, April & May 2007.

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ANALYSIS OF COLUMN COLLAPSE FOR ADVANCED OFFSHOREDESIGN

Amin ALMASITecnicas Reunidas S.A., Madrid, SPAIN, E-mail: [email protected] [email protected]

Abstract

In modern offshore installations, thin walled columns areused for energy absorption in accident situation. When thisadvanced offshore shock absorber is subjected to axialcompressive load, plastic hinges are developed on thesides of column and the column crushes with repeatablepatterns. It can absorb considerable impact energy due tolarge and continuous plastic deformation. This paperdevelops a new closed form, energy based, solution forprediction of accurate collapse curves of square section

column under axial impact load. New formulations forsquare section tube collapse with respect to contributionsfrom hinge curvature, strain hardening, second forceoscillation and sensitivity to imperfection are presented.The behavior of a column in dynamic load is investigatedusing a simplified model of an offshore impact withdynamic corrections including strain rate modeling. Goodagreement between experimental and theoretical load-displacement and velocity-time curves verifies theaccuracy of the proposed formulation

Keywords: Offshore, Collapse, Column.

1. Introduction

Design of offshore shock absorbers has great effects onreliability of ships and offshore structures. When arelatively short thin-walled closed section column issubjected to an axial compressive load, horizontal andinclined yield lines are developed along the sides of thecolumn and the column crushes with a repeatable pattern[1,2].

Fig. 1 shows the collapse of a square tube [2]. Thecorresponding experimental load-deflection curveoscillates between an upper and a lower limit wherein themaximum axial force corresponds to the initiation of eachcycle of folding. Due to the large and continuous plasticdeformation of the tube, it can absorb considerable energy.A major issue in the design of offshore shock absorber isits energy absorbing capability so that during a crash, the

integrity of offshore structure is ensured and only minimumforces are applied to the systems. Various analytical andnumerical simulation techniques have been proposed.Numerical techniques such as the finite elements methodare highly sensitive to the topology and density of themesh, and require continual re-meshing of the structure.Furthermore, the results of these simulations cannot bereadily generalized and hence do not support parametricstudies. Analytical methods, on the other hand, useindividual elements with explicit formulation derived fromthe kinematics of the structure. These methodssystematically rely on careful observations of the actual

plastic deformation process in their derivation of therelations and verification of their results.

In the 1980s a number of theories were postulated topredict the mean force of collapse of square tubes. It wasreported [3] that the majority of tubes crushedsymmetrically. Also, for the first time, two asymmetricmodes of square tube plastic folding (asymmetric modesA and B) were identified. Researchers published theirtheoretical results and experimental observations aboutcrushing of tapered sheet metal tubes [4,5], foam-filled

square tubes [6] and multi-corner sheet metal columns [7].Magnitude of force oscillations can be as large as half theaverage crush load [8]. In a design situation, if such astructure is used to absorb energy, or to resist a minimumload over a large range of plastic deformations, it isnecessary to estimate the force-displacement and theforce-time behaviors of the shock absorber under dynamicconditions. Analytical formulation for the load-deformationof round stocky tubes in plastic folding was reported in [8].It was based on concentrated plastic hinge and rigid-plastic model" assumptions and predicts load much lowerthan experimental data. An alternative method fordetermining the behavior of round stocky tubes waspresented based on a model that included the plastic hingecurvature [9]. The formulation, however, was derived fortwo special cases, namely those of the plastic hingecurvature length being equal to one third and one half ofthe folding wavelength and as noted just for cylinders.

Figure 1. Collapse of Column.

In this paper a new analytical formulation for plastic foldingof square section tube is presented which takes intoaccount the effects of plastic hinge curvature, strainhardening, strain rate, second oscillation of force andsensitivity to imperfections. In addition a dynamic model forthe prediction of the plastic folding behavior is presented.

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Analytical results are compared with experimental data forboth quasi-static and dynamic loading.

2. Advanced Model for Column Collapse

Experimental observations show four differentmechanisms for the collapse of square tubes [1,3]. The

first mechanism is the well-known symmetric mode whichtwo opposite sides of each layer move inwards, and theother two move outwards. Each formed layer is oriented at90 degrees to the previous one. The Symmetric mode isthe most common folding mechanism for the crushing ofsquare tubes. This mode is quasi-inextensional, as noextension of the area or the plastic hinge length occurs inthe process except for a minor extension of the toroidalsurface. In the practical geometrical range of thin-walledsquare tubes, the crushing of square tubes under axialimpact is theoretically governed by symmetric mode [1,3].Two asymmetric modes of deformation named type Aand type B were also identified [1,3]. Both modes predicta similar symmetric mode for the first layer. Beyond thefirst layer, the asymmetric mixed mode A has a layer withthree individual lobes deforming outwards and onedeforming inwards. The asymmetric mixed mode B hastwo adjacent lobes deforming outwards with the other twoadjacent lobes deforming inwards [1].

Based on previous observations, the collapse of thick wallsquare tubes is controlled by the extensional mode [3]. Inextensional mode all four sides of each layer moveoutwards. A thorough discussion of the aforementionedcollapse modes is included in [1,3]. Various known foldingmechanisms can be modeled by mixing two basic foldingelements, quasi-inextensible and extensible. They arebuilding blocks for various plastic folding mechanisms ofsquare tubes. Characteristics of these two elements areelaborated in [1,3,10]. Quasi-inextensible folding elementhas two types of plastic hinges. First type is the horizontal

(or fixed) plastic hinge, which appears in the upper andlower limits of the element as well as the midpoint betweenthe two limits. Second type is the inclined (or moving)plastic hinge. As the deformation process proceeds, one ofthe sides between the horizontal hinges folds inwards andthe other folds outwards and a toroidal surface is thusdeveloped. The extensional folding element has horizontalplastic hinges which means that during the folding processthe sides between hinges move outwards. The idealizedsymmetric collapse mode for a square tube consists of fourquasi-inextensible elements [1,3]. The asymmetric mixeddeformation modes A and B consists of six quasi-inextensible plus two extensible elements, and sevenquasi-inextensible plus one extensible folding element,respectively [1]. Both asymmetric patterns consist of twofolding layers. The extensional folding mode consists of

one layer with four extensible elements.

A second smaller peak load is observed in the majority ofexperimental load-displacement curves (two peak loads ineach cycle of plastic folding). This phenomenon isattributed to the non-simultaneous proceeding of the upperand the lower folding sides [9]. Experimental curves showthat the first load cycle is different from the rest of thedeformation process and peaks at a higher value. Theimperfections produced as a result of the initial elastic-plastic deformation of the first loading are depicted in [9].Once the first load cycle is completed, subsequent load

cycles start on a portion of the tube which already has aninitial imperfection. Comparisons show that the analyticalmethods based on concentrated plastic hinges tend tounderestimate the actual collapse load [8]. A significantpart of the energy absorbed by the collapse mechanismcan not be modeled properly in the concentrated hingesapproaches. Furthermore, detailed observations of the

folding mechanism shows that a larger region around thehinge is experiencing plastic deformation because thematerial in the immediate vicinity of the plastic hinge isstrain-hardened and yielding shifts to an immediateneighbouring region. Second oscillation of force, initialimperfection, hinge curvature and strain hardening aremodeled in this paper to represent realistic behavior offorce-displacement and force-time of plastic folding. Fig. 2shows model of a collapse including the plastic hingecurvature.

Figure 2. Model for Collapse (Folding).

3. Advanced Formulation of Collapse

The folding wavelength (H) and the hinge curvature length(r) are both assumed to be constant. Based onformulations of quasi-inextensible and extensible elements(including horizontal and inclined hinges, toroidal surfaceand extension of the sides), the governing equation for thecrush load of the symmetric collapse of a square tube is as(1).

The governing equations for the crush load in asymmetricmode A and mode B and the extensional mode can beobtained in the same manner.

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Almasi, A.

(1)

Where:

The relationship between the axial folding distance and theinclination angle of the folding side () can be written as(2). The locking angle (f) of the folding mechanism isobtained by solving (3). This angle determines themaximum deflection of the layer and defines the end pointof each folding cycle. The angle lies within the range of 90to 180 degrees.

(2)

(3)

Expressions for the mean effective strain are derivedbased on the principle of incompressibility. Different mean

effective strain expressions are derived for the horizontaland inclined hinge plastic zones, boundary and middlehorizontal hinge plastic zones, toroidal surface plasticzones, extension of side plastic zones to incorporate straineffect in model. By integrating axial load over a cycle ofcollapse, and making the same simplification as [1,3,10],the mean crushing load can be formulated. Minimizing thisload with respect to folding parameters (H and b) lead todetermine the folding parameters. The mean folding load,folding wavelength and radius of toroidal surface arerepresented by (4), (5) and (6) respectively.

(4)

(5)

(6)

Where:

Using a similar approach, the mean force and the foldingparameters of asymmetric mode A and B andextensional folding mechanism can be determined. Threecoefficients of these equations are presented below as (7)to (9). Other coefficients can be obtained with similarapproach.

(7)

(8)

(9)

Where:

Factors "Fft", "Ffi" and "Ffb1" are strain rate factorexpressions.

In an offshore accident, the kinetic energy of the ship istransformed to the plastic deformation of shock absorbermembers. Elastic-plastic behavior governs the initialloading of plastic folding [11,12,13] as well as the transitionfrom minimum load to maximum load in each load cycle.The equation of motion can be expressed as (10). Tointroduce the strain rate effects to the model, the empirical"Cowper-Symons" uni-axial constitutive is used [1,3].

(10)

)sin()2(4

)cos(18)2(

2

22rHrrrHH c +

+=

))cos()sin(

()2(4))cos(1(

16

)sin()2()sin()cos(

2

)sin()2(4

))cos(1(8

)2(,)cos()2()sin(

2

23

2

2

2

2

2

++

=

=

+

+

=+=

rHrrM

rHrJ

rHrr

rHMrHrJ

)cos()2()sin(

2

rHr +=

)cos()42()sin(

42

rHrH =

0)cos()2()sin(

22

=+

rHr

rh

3

1

2

12

131213

3

1

13

2

13

13

1112

3

2

12

13

1213

12

12131111

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1

11

,

)(,

)(

=

=

=

=

++=

=

I

IIk

h

ck

h

b

k

I

Ik

h

ck

h

H

k

kI

k

IkIk

h

ck

M

P

p

m

3

1213

3

1312

3

1111

8,

8,

32

J

JI

J

JI

J

JI ===

dFJ

dffffFJ

dfffFJ

f

f

f

fb

fi

ft

=

=

=

0 113

4320

112

530

211

)(

)()()()()(

)()()()(

)cos()21()sin(

2)(

)sin()21(4)

)cos(1(8)21()(

2

2

22

1

kkf

kkkkf

+=

+

+=

d

df =)(

3

))tan(2(tan

)(cos1)(

)(

)(cos,))(sin1()(

1

0 0 25

1

212

1

2

4

=

+

=

=+=

f

dd

f

f

ff

)sin()21()cos(1

2)(6

kkf +

=

+= )sin()21(

)cos(2

)sin(2)(

27

kkkf

)(cos))tan(2(tan 11

cH

==

)2

2

2JMM

JMMJ

d

d

=

0)]sin()2()cos(

2)sin(

2[2

))(cos1

(

))(cos)(34)cos()((2

))(sin1(

)

)(cos)(34

)cos()(1

(2

))(1(

2

0 2

22

2

1

2

22

2

1

1

=+

+

++

+

+

rHrrh

P

d

ddb

P

P

P

P

d

d

b

Hh

P

P

P

P

chP

P

ftft

ft

c

fi

fifi

fb

fb

2

2)(

)]([dt

txdMtxF =

1690


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Almasi, A.

4. Comparison with Experimental Results

Fig. 3 shows the experimental load-displacement curvefrom [1] being compared with three theoretical curves.

Figure 3. Comparison of theoretical and experimental load-displacement curves.

Figure 4. Theoretical versus experimental prediction of thevelocity-time behavior of dynamic collapse.

The experimental curve belongs to the quasi-staticsymmetric crushing of a square section steel tube [1]. Thesolid curves are plotted according to (1). The dash-dottedcurve represents the load-displacement behavior withoutthe strain hardening effect and the dashed curverepresents the same behavior without the hinge curvatureand strain hardening effects. Fig. 3 shows how eachrefinement of the analysis brings the solution closer to the

actual collapse curve of the column.Experimental and theoretical velocity-time curves areplotted in Fig. 4. The theoretical curve represents thevelocity-time behavior of the dynamic model consideringthe plastic hinge curvature, strain hardening, secondoscillation of the force and sensitivity to imperfections.There is good agreement between theoretical results andexperimental data.

Figure 5. Theoretical load-time curve for dynamic collapse.

Fig. 5 shows the theoretical load-time curvescorresponding to Fig. 4. A decrease in the velocity wouldcause the time of each plastic folding cycle to increase.

Force peaks are more than yielding force due to strain rateand strain effects.

5. Conclusions

New method for analysis of collapse of square sectioncolumn is presented. Dynamic collapse of square sectiontube is formulated taking into account contributions fromhinge curvature, strain hardening, strain rate, second forceoscillation and sensitivity to imperfections. Goodagreement between experimental and theoretical load-displacement and velocity-time curves verifies theaccuracy of the proposed formulation.

References

[1] W. Abramowitz and N. Jones, Dynamic Axial Crushingof Square Tubes, Int. J. of Impact Eng., Vol. 2, pp.179-208, 1984.

[2] M. Lanseth and O. S. Hopers tad, Local Buckling ofSquare Thin-Walled Aluminum Extrusions, J. of Thin-Walled Structures, Vol. 27, No. 1, pp. 117-126, 1997.

[3] W. Abramowitz and N. Jones, Dynamic ProgressiveBuckling of Circular and Square Tubes, Int. J. ImpactEng., Vol. 4, No. 4, pp. 243-270, 1986.

[4] S. R. Reid, T. Y. Reddy, Static and Dynamic Crushingof Tapered Sheet Metal Tubes of Rectangular Cross-Section, Int. J. Mech. Sci., Vol. 28, No. 9, pp. 623-637,1986.

[5] A. G. Mamalis, D. E. Melonakos, G. L. Vigilant, The

Axial Crushing of Thin PVC Tubes and Frusta ofSquare Cross-Section, Int. J. Impact Eng., Vol. 8, No.3, pp. 241-264, 1989.

[6] W. Abramowitz and T. Wierzbicki, Axial Crushing ofFoam Filled Columns, Int. J. Mech. Sci., Vol. 30,No.3/4, pp. 263-271, 1988.

[7] W. Abramowitz, T. Wierzbicki, Axial Crushing ofMulticorner Sheet Metal Columns, J. Applied Mech.,Vol. 56, pp.113-120, 1989.

[8] R. H. Grzebieta and N. W. Murray, Rigid-PlasticCollapse Behavior of an Axially Crushed Stocky

0 10 20 30 40 50 60 70 800

20

40

60

80

100

120

x(mm)

P(kN)

c=49.3mm h=1.63mm angle=145degree Lf/L=0.23 (8-4-2)

P(r=0)P(r=H/2)P(r=H/2,Strain)P(Experimental)

5 10 15 20 25 30 350

1

2

3

4

5

6

7

8

9

10

time(ms)

V(m/s)

C=37.1mm h=1.15mm M=73.6kg Vo=10.3m/s

AnalitycalExperimental

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

tVo/(2H1)

P/Py

C=37.1mm h=1.15mm M=73.6kg Vo=10.3m/s

Symmetric

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Almasi, A.

Tubes, Recent Advances in Impact Dynamics ofEngineering Structures, 1989.

[9] R. H. Grzbieta, An Alternative Method for Determiningthe Behavior of Round Stocky Tubes Subjected to anAxial Crush Load, Thin walled Structures, Vol. 9, pp.61-89, 1990.

[10] W. Abramowicz, The Macro Element Approach in

Crash Calculations, Proceeding of the Natal-ASI onCrashworthness of Transportation Systems StructuralImpact and Occupant Protection, July 7-19, Troia,Portugal, 1996.

[11] Paulius Griskevicuis, Antanas Ziliukas, The CrashEnergy Absorption of The Vehicle Front Structures,Transport, Vol XVIII, No2, 97-101, 2003.

[12] C. B. W. Pedersen, Topology Optimization of EnergyAbsorbing Frames, Fifth World Congress onComputational Mechanics, Vienna, Austria, July 7-12,2002.

[13] Denzil G. Vaughn, James M. Canning, John W.Hutchinson, Coupled Plastic Wave Propagation andColumn Buckling, Journal of Applied Mechanics, Vol.72, January 2005.

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ADVANCED TORSIONAL STUDY METHOD AND COUPLING SELECTIONFOR RECIPROCATING MACHINES

Amin ALMASITecnicas Reunidas S.A., Madrid, SPAIN, E-mail: [email protected] [email protected]

Abstract

Trains including reciprocating machines are subject to themost varied and often most severe torsional disturbancesin comparison to other machinery classes. If crankshaft orrotating component failures occur as a result of shafttorsional oscillations, the consequences can becatastrophic. In this paper a new comprehensive modeland solution method using analytical formulations aredeveloped to study both steady state and transientresponse of complex reciprocating trains. Analytical results

are presented and recommendations for torsional reliabletrains are addressed. Couplings being the more accessiblecomponents within the train are often modified to tune theoverall system. Recommendations for coupling: Hightorsional stiffness coupling (best option if allowed bytorsional analysis), or flexible coupling (more elasticity anddamping and more maintenance) or integral rigid forgedflange connection (rugged train, less elasticity anddamping) with single bearing electric machine.

Keywords: Torsional Study, Coupling, ReciprocatingMachine.

1. Introduction

Reciprocating machines (reciprocating compressors,reciprocating pumps, gas and diesel reciprocating engines,reciprocating expanders, etc) are most efficient availablemachines. They are flexible to handle wide capacity andcondition swings [1,2]. The expected level of reliability andavailability of reciprocating machine train is very high and itpresents a real challenge to machine designers andoperators [3,4]. Advanced methods shall be applied inorder to obtain the highest level of safety and reliability.Reciprocating trains have a complex crankshaft, flywheel,electric machine rotor(s) and relatively flexible shaftextensions and coupling. It may also include gear unit(s) orturbo expander in special cases. Since connectedmachines function as spring systems in series, thepotential exits for torsional resonance and torsional fatiguedamage. If shaft and rotating component failures occur on

reciprocating trains as a result of shaft torsionaloscillations, the consequences can be catastrophic. Thereis also potential for vast damage and loss of human life.For these reasons great attention is generally taken toensure that rotating machine trains have the requiredtorsional capacity.

2. Advanced Analytical Model

Torsional vibration involves angular oscillation of the rotorsof machines. Each rotor or crankshaft in the system willoscillate following a torsional disturbance to the train. The

design of train shall include optimization for dynamic loadsacting on foundation, pulsation and shaking forces,irregularity degree and torsional stresses. All these factorsneed detailed torsional analysis to ensure proper designand reliability. The torsional behavior is key determinant ofreliable operation of train [3]. It is vital for ensuring reliablemachine operation due to machine stimuli that range fromrarely occurring high level transients to continuousrelatively low levels of excitation. Correct application oftorsional analysis practice and improved transmissionsystem design and operating practices can generally

rendered train robust to the effects of stimuli from theelectrical transmission network, or from problems withinthe electric machine (such as short circuits or faults), orfault in electrical, mechanical or process systems to whichthe train is connected (such as transformer, etc).

It is of paramount importance to avoid torsional resonance(particularly at or near the lower harmonics of trainoperating speed frequency) and to ensure that shafts andother components are suitably sized to avoid failure orsignificant damage during possible sever transientdisturbances. The procedure for torsoinal analysis includefollowing steps. Modeling of train, calculation of undampednatural frequencies, harmonic components calculation andforced vibration calculation.

Trains usually consist of a large crankshaft, electricmachine rotor, flywheel and relatively flexible shaftextensions and coupling.Typically, lateral critical studiesare not required for reciprocating machine trainapplications. Lateral natural frequencies will be positionedwell above significant torsional natural frequencies of train[5]. The model must be accurate enough to simulate thereal system behavior at least for frequencies below the20th multiple of the maximum rotating speed. Only a modelwith enough details and large number of elements make itpossible to evaluate higher number of vibration modes. Inthe other hand very high frequency additional modes (such as frequencies more than 20th multiple of themaximum rotating speed) have no effect since noresonance is foreseen and they are related to low

amplitude exciting harmonics [4].

Basically the model is represented by a number of rotatingmasses connected to each other by means of mass-lessshaft intervals with appropriate torsional stiffness. Rotatingmasses can represent both the crankshaft and theconnected components (connecting rod, piston rod,crosshead, etc). The mass elastic model of crankshaft iscreated by lumping the inertia at each throw andcalculation the equivalent torsional stiffness betweenthrows. The coupling is modeled as a single torsionalspring (coupling sub-vendor supplied torsional stiffness)

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Almasi, A.

with the inertia of the associated coupling halves at eachend. These inertias are added to elements of both sides ofcoupling. Proper dedicated lumped masses for allaccessories (such as flywheel, gear wheel, exciter,connecting flange, etc) are added to model. Parameters inmodel and formulations are as follows:

i Torsional displacement of mass i (rad).Ji Polar moment of inertia of mass i (kg s3/m).Ki Torsional stiffness of the shaft internal i (N m).Ci Damping coefficient for shaft interval i (kg s2/m).CMiDamping coefficient for the mass i (kg s2/m).n Model lumped mass total number.m Maximum reciprocating torque harmonic order. Torsional natural frequency (rad/s).Mi Applied torque to mass i (N m).

3. Advanced Torsional Study

The next step is calculation of the train undamped torsionalnatural frequencies. The goal is to locate naturalfrequencies away (usually by 10%) from potentialexcitation frequencies that might come from train machines[6,7,8,9,10,11]. In addition, it is recommended that naturalfrequencies be placed 10% outside of electrical netfrequency and 5% outside of its second multiple [4].Natural torsional frequencies reach higher values as theirorder increases and in practice the first three modes ofvibration usually need to be investigated.

Torsional natural frequencies come from solution ofequations (1). The calculation of the undamped naturalfrequencies is a problem of eigenvalues and eigenvectorswhich represent natural frequencies and mode shapesrespectively.

(1)

Generally reciprocating equipment and other rotatingmachines including electric machines have a low level oftorsional damping [3,4,8]. It is found that the amount oftorsional damping in turbomachinery is very low unlessspecial provisions are made. For heavy duty machines, itis impractical and uneconomical to employ mechanicaldamping devices to substantially reduce peak vibrationresponse levels following severe torsional vibration [3].Because of low damping level, undamped naturalfrequencies can represent natural frequencies of real train[4]. Observations are in agreement with this assumptionand the torsional mechanical response will generally bemultimodal with a slow decay rate because of the light

damping [3,7,8].

The main concern is for first torsional natural frequencyposition because higher natural frequency orders areassociated with high harmonics which have little effects.In case the torsional natural frequencies do not meetmentioned margins (10% away from potential excitationfrequencies) individual train component can be modified.Parametric study of presented natural frequencycalculation method can provide information on how to tunerotating machine train if natural frequency separationmargins are discovered to be unacceptable for reliable

performance. Modification of coupling torsional stiffness byan appropriate tuning of the coupling type or spacediameter is primary and easiest solution. Generally thecoupling is the most flexible shaft interval in train and has astrong influence on first torsional natural frequency. Rangeof available coupling options is vast, from flexible couplingto rigid forged flanged connection (without coupling).

However If coupling modification is not sufficient andfurther modification required (mainly in case of moretorsional stiffness required to raise first torsional naturalfrequency) modification of electric machine shaft geometrycan be studied jointly with electric machine sub-vendor. Inany case the modification of reciprocating crankshaftgeometry is very difficult and in most cases it is nevermodified to accommodate torsional applicationrequirements.

The frequency spectrum of shaft torsional oscillations willusually show most response in the lower order torsionalmodes with some components at the harmonics ofelectrical system frequency (the first and secondharmonics generally are the most pronounced).Cylinder arrangement (especially number of cylinders) has

strong effects on excitation of certain torsional harmonics[3,4,9,10,11]. For example in case of 4 cylinders frame, (2xharmonics) are significantly exited and in cases of 6 and 8cylinders frame (3x harmonics) and (4x harmonics) aresignificantly excited, respectively.

If there is interference between torsional naturalfrequencies and excitation harmonics and modification isnot desired or possible, it is necessary to make torsionalstress analysis. Stress analysis shall be performed toensure that the resonance will not be harmful for the train[5]. First step is steady state torsional analysis. Theanalysis should be performed for all possible operatingconditions including all possible speeds and capacities.The governing equations of system to calculate the

damped forced torsional vibration are as (2).

(2)

The general expression of the steady state applied torques(Mi) includes a vibrating component superimposed on anaverage torque level as per (3). Train load torques can bedecomposed, through a Fourier Analysis, into series ofsinusoidal curves which frequencies are multiple ofmachine running speed and modulus generally decreasesas the harmonic order increases. The higher the number ofharmonics considered, the closer the results to real torque.

Optimum solution suggested as calculation of 25harmonics (m=1 to 25).

(3)

The torsional dampening is assumed to be the hysteretic[4,6,7,8]. Each applied torque must be properly phasedwith respect to relatively crankshaft angular position. Theelectric machine torque supposed to be constant duringsteady state load however there are relatively smallfluctuating torque component due to interactions betweenthe current pulsation of electrical elements (such as

( )

( ) ( )

( ) 0

1,...,2,0

0

11

111

21111

=+

==++

=+

+

nnnnn

iiiiiiii

KJ

niKKJ

KJ

&&

&&

&&

( ) ( )( ) ( ) ( )

( )( ) ( )

nnMnnnnnnnnn

iiMiiii

iiiiiiiiiii

M

MCCKJ

niMCC

CKKJ

MCCKJ

=+++

==++

+++

=+++

+

+

&&&&&

&&&

&&&&

&&&&&

1111

1

11111

11121121111

1,...,2,

( )p

m

p

pii tpMM +==

sin0

,

1694


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Almasi, A.

winding) and electrical machine shaft mechanicalirregularity degree. These fluctuations generally can beneglected for steady state response. Solution of (2) can beobtained based on Principle of Linear Superposition. Thesystem is composed of (n) linear differential equations with(n) parameters, tri-diagonal and symmetrical. Its solutioncan be transferred to the solution of (m) differential

equation system (each equation related to differentharmonic of the exciting forces).

A sensitively analysis should be always carried out to takeinto account all possible variances affecting the modelespecially those due to fluctuations of running speed (suchas net frequencies, etc) which can shift the harmonics ofthe running speed. Variations of the mass elastic data (i.e.coupling stiffness, rotor inertia, etc) can shift the torsionalnatural frequencies. Alternative option of considering therelative position of the harmonics and natural frequencies,is to calculate the torques and stresses over a range of10% of the rated speed. The highest values within thatrange can be comparable to correspondence endurancelimit for torsional fatigue. For a train, torsional stress isfunction of related position of torsional natural frequencies

and exciting harmonics. There are usually many cases oftransient disturbance which should be modeled. Thetransient torsional analysis requires a different and moretime consuming calculation method since it requires adirect integration of the motion equations. In this case thesolution is time dependent.

The differential equations of motions are similar to those ofthe steady state (2), but they have different excitingtorques. In this case reciprocating machine torques (Mi)can be given in Fourier Series. Inertia and gas pressurecomponents of reciprocating cylinders can be separatelycalculated since it can be assumed that train speedvariations affect only the inertia components where as thecylinder fluid cycle contributions is assumed without

considerable changes when speed changes. However fortrains which include electric machine, electric machinetorque can not be given in Fourier Series since transientexcitation is not periodic. The transient analysis out put isgenerally represents by the torque and stress plots foreach rotor as a function of time. However the main resultsof the transient analysis can be given in terms of peakshear stress in machines and peak torque on couplings.

The highest stress / torque amplitudes acting on rotatingmachines and coupling shall be compared to theendurance limits of each of the respective components. Incase the alternative torques and stresses are not within theallowable endurance limits a redesign must be carried outin order to achieve a wider separation margin betweentorsional natural vibration and high amplitude harmonics to

obtain lower stresses.The fact that the damping of the trainis low can lead to the generation of extremely hightransient torques in train shafts as a result of responsecompounding if torsional disturbances occur in rapidsuccession. The resulted alternating stresses in the trainshafts and other components need to be below the fatigueendurance limit of the material involved. This is because ofthe very high number of stress cycles that will beexperienced over the life of the machine as the cycles arebeing accumulated continuously.

4. Electrical Effects on Reciprocating MachineTrains

It is most important to study problems from electricalevents that can produce pulsating torques and torsionalvibration in train. There are wide varieties of incidents thatcan cause electrical current oscillations in the electrical

transmission to which the electric machine is connected. Ineach case, the incident results in an oscillating torqueapplied to the train, which can stimulate twistingoscillations in the machine shafts and vibration of variousrotating and non rotating components.

Electrical transient disturbance can be planned orunplanned (emergency) transmission line switch incidence,electrical faults in the transmission network such aselectrical circuit breaker actions or fault caused by storms,electric machine internal faults or terminal short circuits. Incase of power generation (reciprocating engine coupled toelectric generator) transient disturbance can be mal-synchronization of the generator to the electrical network.These transient oscillations generally include a stepchange in torque (impulse) and discrete frequency torquecomponents at the first or second harmonics of the powersystem frequency, with generally low levels at the higherharmonics. The step change torque component decaysquite slowly (order of seconds) however the lowerharmonics of the power system frequency decay rapidly incomparison (order of tenth of seconds) [3].

An example of this is with the use of some forms of highspeed reclosing of electric transmission line circuitbreakers following the electrical faults in network. Asdiscussed electrical line fault can result from eithertemporary or permanent electrical transients (for exampleelectrical lighting strike, transmission line break, a tree fallinto a transmission line causing long term transmission linephase to phase or phase to ground fault, etc ). Following

any type of electrical fault in the transmission line with oneform of high speed reclosing, the power circuit breakersautomatically open after a few electrical cycles (1/50 ofseconds) to isolate the fault and then automatically recloseafter only several tenths of second. If the fault has clearedduring this period then no significant shaft torquecompound occurs. However high percentage of severemultiphase faults are permanent and thus may not benefitfrom high speed reclosing. In case of permanent fault thena second major torsional event will be experienced by themagnitude approximately equal to that of the first one. Asthe damping of the torsional modes is very light theresponse amplitudes in the shafts from the first electricaldisturbance will be decayed only slightly when the circuitbreakers reclose into the fault for the second time. If thetiming of this reclosure is at its most unfavorable, the shaft

torques could approximately double as a result ofresponse compounding .

There is potential for torsional insatiability on trainsconnected to electrical networks that have series capacitorcompensated lines to reduce power transmission losses(sub-synchronous resonance or SSR). Machinesconnected to direct current transmission lines can also beaffected with instability in this case due, for example, toincorrect operation or mal-adjustment of rectifier andinverter control equipment. In such these cases, torquepulsations are produced by electric machine due to current

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Almasi, A.

pulsation and magnetic fields interactions. In general thesetorque pulsations do not cause any harm unless theirfrequency (resistance, inductance and capacitance circuitintroduces an electrical resonance frequency) coincideswith, or is close to, one of the torsoinal natural frequenciesof the train. Under these conditions the shaft responsetorque could build up to extremely high level.

Recommended corrective actions for SSR problemincluded installation of large filters to remove the harmfulcurrent frequency components from entering the electricmachine, installing electrical damping devices, andaddition of protective monitoring and relaying equipment[3]. The rectifiers, inverters, high voltage direct current(HVDC) transmission system or large nonlinear electricalsystems feed significant harmonics of the fundamentalpower frequency into electrical network. Train is subjectedto significant high order harmonic currents entering thearmature of the electric machine which produce pulsatingtorques on the rotor, causing torsional vibration. Thesepulsating torques are at (6n) harmonic frequencies (6, 12,18, etc) and would be of concern only if they becameresonant with a train torsional natural frequency. The

lowest harmonic torque frequency and the one thatgenerally has the highest amplitude is the sixth harmonic.Higher order harmonic torques are therefore rarely ofconcern [3]. Certain harmonic effects arise when anelectric machine is started. Usually the main concern iswith torque dips in induction motors, which affect motor'sability to reach full speed. But there are some effects thatcan result in torque pulsations. These are due tointeractions between various sources of harmonics inmachine magnetomotive forces and fluxes. The mainsources of harmonics are distribution nature of the statorwinding, distribution nature of rotor currents, slotting on thestator (or rotor) which produces a permanent variation atslot pitch frequency and pulsation of main flux because theaverage permeance of the air gap fluctuates as the rotor

moves relative to the stator. The interaction between allthese different harmonic sources can produce torques thatrise and fall with speed, sometimes accelerating the shaft,sometimes slowing down the shaft. Torque pulsationfrequency will vary as the machine speed changes. Thesetorques and their magnitudes depend on the relativenumber of stator and rotor slots, the use of open andclosed slots, the rotor slot skew, and the electric machinereactance and resistances. There have been reportedcases [3] of torques large enough to cause chatter anddamages.

5. Advances in Flywheel and Train Irregularities

For all reciprocating trains, flywheel is mandatory toregulate variable reciprocating torques. Irregularity degree

for mechanical component reliable operation is maximum2%. This value is minimum requirement for all trains.Generally in accordance with specific requirements ofelectric network, electric machine (especially currentpulsation), reciprocating equipment, operation, torsionalvibration results, etc, lower irregularity value is required. Itis recommended to obtain 1% for special purpose units inpetroleum and petrochemical plants. Irregularity valuesbetween 1-1.5% are in common use.

6. New Technology of Variable Speed Machines

Variable frequency motor drives are becoming morepopular [9]. For variable speed reciprocating machinetrains, complex issues of torsional response and feedbackdue to torque pulsation shall be addressed.

Because of the complexity of the reciprocating andelectrical machine train, the system is limited in its turn

down by torsional problems. Torsional analysis is vital fordevelopment of relatively new technology of variablespeed reciprocating trains. In variable frequency drive(VFD), the inverter converts the AC power to a series ofDC voltages, and then varies the frequency of DC pulsesto approximate a sinusoidal waveform at the desiredfrequency. The AC waveform produced by this process isrich in harmonics because the fast switching createsvoltage spikes. This results high order harmonic torques toelectric machine and potential for mechanical damage. It isbecause during the frequency run up and run down thereare large number of potential operating speeds and holdpoints. There are significant risks of the development ofresonant mechanical response. It is important thattorsional natural frequencies be calculated and modified asrequired to avoid resonances. In addition operational

strategies include rapid acceleration through definedcritical speeds and avoidance of operating hold points nearcritical speeds shall be carefully respected. Due to wideoperating speed range, maintaining 10% margins betweenall possible excitation frequencies and natural frequenciesis very difficult and usually impossible. For variable speeddrives comprehensive torsional and stress analysis arenecessary.

Torque harmonics generated by variable speed drive canexcite the resonance during start up, and therefore mustbe evaluated. In addition the ramp rate or frequency atwhich the variable speed drive controls the speed of theunits should not coincide with torsional natural frequencies.A variable speed reciprocating compressor or pump may

have several damaging torsional resonances within thespeed range due to the reciprocating machine excitationharmonics intersecting the first torsional natural frequency.With the use of soft coupling, the first tosional naturalfrequency can be tuned below minimum speed. In manyinstances this is the only way to achieve the full desiredspeed range. Otherwise the speed range has to be limitedor certain speed bands have to be avoided.

Soft coupling in variable speed train can add damping tothe system. However Dynamic torque should be calculatedand compare with coupling limits. In addition limited softcoupling life can be a problem. High tensional stiffnesscoupling can reduce maintenance but large portion ofspeed range should be avoided. Comprehensive torsionalanalysis and study must be used to obtain optimum

solution.

7. Simulation Results

Analytical results are presented for a four throw and threecylinders heavy duty reciprocating compressors. Trainspeed is 327 rpm. Four step capacity control, 0-50-75-100%, using fixed volume pocket at cylinder head end andsuction valve unloaders are provided. Total motor power ofeach train is 6.5 MW. Driver is direct coupled eighteen (18)poles induction electric motor. Based on experienceavailable coupling options are: High torsional stiffness

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coupling (if allowed by torsional analysis), flexible couplingor integral rigid forged flange connection with singlebearing electric machine. Extensive simulations show forthis train regarding natural frequency interfaces and allpossible transient cases, flexible coupling is acceptableoption due to more elasticity and damping effects whichhelp to obtain acceptable frequency margins and reduce

transient stresses. Coupling selection implies an adequateseparation with respect to compressor exciting harmonics,and in particular with the most adverse one (2 x) withrespect to cylinder arrangement. Simulations show acoupling stiffness variance of about 35% would be requiredfor the train to reach resonance. Compressor train integritymust be assessed during a three phase short circuit of theelectric motor. The transient event assumed to last about0.5 seconds. In this case the electric motor is subjected toa high frequency and high amplitude oscillating torque.Motor peak torque is around 3.3 times the normal value.Simulations show that torsional transient response isstrongly reduced by train damping from flexible couplingselection. The peak torques and stresses are about 1.6times their average values. Simulations show electricmachine has a high frequency response at the early stage

of train start. The peak stresses do not reach significantamplitudes. A local amplification occurs several secondafter start when the electric machine variable frequencypulsating component crosses the first torsional naturalfrequency.

0 50 100 150 200 250 300 3500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Crank Angle(Degree)

CompressorBrake

Torque/RatedElectricMotorTorque

Normal Full Load

Unloaded(50%)

Figure 1. Reciprocating Compressor Brake Torque vs.

Crank Angel.

Fig. 1 shows reciprocating compressor brake torque vs.crank angel for one revolution of crankshaft in steady stateconditions. Compressor brake torques are dimensionlessby rated electric motor torque. The solid and dashed-dotted curves represent compressor torque for normal full

load and (50%) unloaded conditions respspectively. Thisfigure show how compressor brake torque variesconsiderably in one shaft revolution (from less than 20% ofmotor rated torque to around 170% of motor rated torque).It shows importance of flywheel to regulate train torquerequirements and strong effects of torsional irregulartorques on train torsional behavior. Different unloadedconditions show completely different torsional loadingbehavior. Simulations show unloaded (50%) conditionrepresents highest irregularity in train among steady stateconditions. It proves necessity to evaluate torsionalbehavior of all operating conditions including all unloaded

stages, high and low suctions, possible process changesand all foreseen transient situations.

8. Coupling Selection

Many operators and vendors prefer high torsional stiffnesscoupling because it results to more rugged train and higher

natural frequencies. Also it decreases maintenance. Thesoft couplings can protect the electric machinecomponents by absorbing the dynamic torque generatedby reciprocating machines. Rubber coupling usuallyincrease maintenance since the rubber degrades over thetime due to heat and environmental factors. Actual rubbercoupling life may be significantly less than couplingmanufacture stated life, if the coupling is subject to heat orharsh condition (such as oil mist, ozone, etc). Specialsilicon block may improve life for high temperatureapplications [12].

For coupling an appropriate service factor should be usedto allow for possible transient conditions. The vibratorytorque and heat dissipation must be reviewed carefully.The allowable vibratory torque is typically 20% to 30% ofthe coupling rated torque. The heat dissipation is afunction of the vibratory torque and frequency and isnormally specified in terms of power loss (Watts). Otherfactors such as end float and allowable misalignmentshould also be addressed. The torsional stiffness of therubber elements can vary with temperature and torque.The actual coupling stiffness can vary by as much as 20%from catalogue values. Also some coupling (such ascoupling with rubber elements) have nonlinear stiffnesswhich depends upon the actual transmitted torque. As asystem starts, the speed increase can result in a loadincrease, natural frequencies will change (couplingstiffness can increase and cause natural frequencies toslightly increase). In these cases coupling are usuallymodeled linear and special attention is required for elastic

data sensitivity analysis. Comprehensive torsional analysisand study, machine arrangement, all possible steady stateand transient conditions, operation and maintenance mustbe considered for optimum coupling selection.

9. Electric Machine Considerations and PracticalRecommendations

Experiences have shown that only accurate modeling of allrotating machines and elements in (especially electricalmachine) can result to accurate torsional analysis of train.Observations show that natural frequencies ofreciprocating trains are sensitive to torsional model ofother machines in train especially electric machine model.Flexibility and inertial distribution through the electricmachine core shall be modeled accurately otherwise it can

result in missed torsioal natural frequency, inaccuratetorsional analysis and torsional problems. Stiffness ofelectric machine shaft can be influenced by the varioustypes of construction. Machined or welded webs can addsignificant stiffness (typically 10-40% more) while keyed orlaminations typically add minimum stiffness. Only adetailed Finite Element Analysis (F.E.A.) of the electricmachine shaft can provide accurate results. Comparisonshowed more than 30% error in shaft stiffness betweendetailed Finite Element Analysis (F.E.A.) and simplifiedmethod [12].

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Experiences have shown that many electric machineshave been designed to couple to non-reciprocating rotatingequipment and may not be adequately sized forreciprocating equipment. An indication can be shaft size.Crankshafts are often constructed with higher strengthmaterial and have lower strength concentration factors. Asrule-of-thumb electric machine shaft diameter to be equal

to or greater than the reciprocating machine crankshaftdiameter. Numerous torsional vibration problems continueto occur in reciprocating trains. Main reasons are lack ofcomprehensive torsional vibration analysis and study,improper application and maintenance of coupling (mainlyflexible couplings), using of electric machines traditionallyused in non-reciprocating application (such as variablespeed motor) and lack of monitoring.

Shaft materials should be high strength steel. If welds arerequired on shaft, a weldable shaft material should beused. Proper weld procedures and material compatibilitymust be considered. Fabrication details such as theelectric machine pole bolt torque, etc should considerloads due to torsional vibration. Continuous operation attorsional resonance shall be avoided. Coupling, flywheel

and electric machine torsional characteristics have stronginfluence on reciprocating train torsional vibration and canbe modified to tune system. Changing the load sequencecould help reduce torsional vibration in reciprocatingcompressor and pump. Avoid full load shutdowns forreciprocating compressor and pump specially in train withtorque sensitive equipment. Some vendors intended to usestiff system with short flanged connection (no coupling)and single bearing electric machine. These trains havemuch lower damping however higher natural frequencies.These trains may be acceptable after careful review oftorsional analysis including all possible operating steadystate and transient torsional situations.Reciprocatingmachines generate a torque excitation due to reciprocatinginertia and gas forces acting on the crankshaft. This can

consist of multiple integer torque harmonics. Half orderexcitation (0.5X, 1.5X, etc) can also occur in four strokereciprocating engine. In reciprocating machine each throwcan create significant primary (1X) and secondary (2X)harmonic torques. For reciprocating compressor andpump, valve failure, fluid pulsation and load steps shall beconsidered. For reciprocating engines, engine misfire,pressure imbalance, ignition problem and leaks (leaks infuel valves or compression pressure) shall be respected.

It is important to measure and verify torsional vibrationduring performance test. Based on site observationsfollowing transient events are critical and shall berespected in details: synchronous electric machine startup, short circuit, reciprocating engine misfire, valve failureand loaded shut down of compressor and pump.

A train which passes through a torsional natural frequencyduring start up may produce significant transient shaftstresses. If the system is started on a frequency basis, astart up analysis should be performed to determine if lowcycle fatigue is a potential problem. Synchronousmachines need more care (than induction machines) inthis regard and they definitely need a transient torsionalstart up analysis. Coupling torque is usually chosen on thebasis of mean requirements for full load. It must have asufficient service factor to handle and likely overload (suchas electrical faults).

10. Conclusion

Reciprocating equipment are very efficient, flexible andhave wide range of application. A comprehensive modeland solutions using analytical formulations are developedto study both steady state and transient response ofcomplex reciprocating trains. The torsional vibration

analysis report shall include data used in mass elasticsystem, torsional natural frequencies, display of torquesvs. speed, torsional critical speed, mode shape diagrams,interface diagrams, definition of coincidence of theexcitation frequencies with the torsional naturalfrequencies, all possible steady state cases (normal and allunloded cases), all possible transient cases (start up, shutdown cases, especially loaded shut down, short circuit,electrical faults, etc ), non-ideal cases (such as enginemisfire or compressor valve failure), worst case design,dynamic torsional stresses (based on dynamic torquemodulations, stress concentration factors, andamplification factors), comparison to determine compliance(with regard to separation margin, stresses, loading, andcoupling dynamic torque), parametric analysis todetermine possible coupling modification (when separationmargin, stress level or coupling torque are not acceptable).The report should also consider how the input datavariance will affect the results (sensitivity analysis).

References

[1] Heinz P. Bloch, Compressor and Modern ProcessApplication, John Wiley and Sons, 2006.

[2] Heinz P. Bloch, A Practical Guide To CompressorTechnology, Second Edition, John Wiley and Sons,2006.

[3] Duncan N. Walker, Torsional Vibration ofTurbomachinery, McGraw-Hill, 2004.

[4] Enzo Giacomelli, Carlo Mazzali, Nicola Campo, PaoloBattagli, Fabio Falciani, Torsional Analysis of A-20

Cylinder Hyper compressor Train, Proceeding ofESDA2006, Engineering System and Analysis, Torino,Italy, 4-7 July, 2006.

[5] Shelley Greenfeld and Kelly Eberle, New APIStandard 618 (5 TH ED.) And Its Impact onReciprocating Compressor Package Design Part I, IIand III, Compressor Tech Two, June July August2008.

[6] Vibration in Reciprocating Machinery and PipingSystems, Engineering Dynamics Incorporated,Engineering Dynamic Incorporated (EDI), SanAntonio, Texas, June 2007,

[7] A. S. Rangwala, Reciprocating Machinery Dynamics,First Edition, New Age International (P) LimitedPublishers, 2006.

[8] Cyril M. Harris, Allan G. Piersol, Harris Shock and

Vibration Handbook, Fifth Edition, McGraw-Hill, 2002.[9] Royce N. Brown, Compressors Selection and Sizing,

Third Edition, Gulf Publishing, 2005.[10] Positive Displacement Pumps - Reciprocating, API

674 2th edition, June 1995.[11] Reciprocating Compressor for Petroleum, Chemical

and Gas Service Industries, API 618 5th edition,December 2007.

[12] Troy Feese and Charles Hill, Guidelines for ImprovingReliability of Reciprocating Machinery By AvoidingTorsional Vibration Problems, Gas MachineryConference, Austin, Texas, October 2001.

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5. Uluslararas leri Teknolojiler Sempozyumu (IATS09), 13-15 Mays 2009, Karabk, Trkiye

IATS09, Karabk niversitesi, Karabk, Trkiye

DALGI POMPA PERFORMANS TESTLERNDE KULLANILANYENTEKNOLOJLER

NEW TECHNOLOGIES USED IN THE PERFORMANCE TESTING OF

SUBMERSIBLE PUMPSErgn KORKMAZa,*, Mustafa GLCb, Cahit KURBANOLUc

a,* Sleyman Demirel ni. Teknik Eitim Fak., Isparta, Trkiye, E-posta: [email protected] Pamukkale ni. Teknik Eitim Fak., Denizli, Trkiye, E-posta: [email protected]

c Sleyman Demirel ni. Mh. Mim. Fak., Isparta, Trkiye, E-posta: [email protected]

zet

Pompa performans testleri, tasarm gerekletirilenpompalarn performanslarnn tespiti veya pompaperformans zerinde etkili olduu dnlenparametrelerin pompa karakteristiklerine etkilerininincelenmesinde olduka nem arz etmektedir. Bu nedenle

testlerde kullanlacak lm yntemleri ve lmecihazlarnn belirlenmesinde gerekli hassasiyetgsterilmelidir. Bu almada; dalg pompakarakteristiklerinin belirlenmesi iin basma ykseklii, debi,efektif g ve motor dnme hz lm ve kontrolndekullanlan yeni teknolojiler incelenmitir. Bu amala yksekhassasiyetli lme ve kontrol cihazlarnn kullanld dalgpompa test nitesi kurulmutur. Kullanlan bir programsayesinde pompa karakteristikleri bilgisayar destekli olarakelde edilmitir. Ayrca, ebeke gerilimi ve motor devrindekideiimlerin pompa karakteristikleri zerindeki olumsuzetkilerinin nasl giderilebilecei de ortaya konulmutur.

Anahtar kelimeler: Dalg pompa, Pompa performans,Pompa karakteristikleri.

Abstract

Pump performance tests are considerably important for theassessment of the performance of pumps designed orstudy of the effects on the pump characteristics ofparameters believed to be affecting pump performance.Therefore, due care should be employed whendetermining the measurement methods and measurementdevices for use in such tests. This study examines newtechnologies used in the measurement and control ofhead, flow rate, brake horsepower and rotation speed ofthe motor. For this purpose, a submersible pump testingunit has been assembled using highly sensitivemeasurement and control devices. The pumpcharacteristics have been obtained in a computer-aided

manner using software. It has been further figured out hownegative impacts of changes in the mains voltage andmotor rotation speed on pump characteristics could beeliminated.

Keywords:Submersible pump, Pump performance, Pumpcharecteristics.

1. Giri

Tketilebilir su potansiyelimizin %13ne yakn bir ksmnoluturan yeralt su kaynaklarnn yeryzne

kartlmasnda; basnl hava sistemleri, dey trbinpompalar ve yaygn olarak da dalg pompalarkullanlmaktadr.

Dalg pompalar; montaj kolayl, derinlik snrnnolmamas, yksek verim, enerji tasarrufu ve ekonomikliinedeniyle teknolojik gelimelere paralel olarak y

09 Energy&Aeronautics&Auronautics

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