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TECHN ICAL AND RESEARCH BULLETIN NO. 2-29A

Measurement and Evaluation of Structuraland Machinery Vibration in Ships

Panel HS-7 (Vibrations)of theHull Structure Committeeand

Panel M-20 (M achinery Vibrations)of theShips' Machinery C omm ittee

Published byThe Society of Naval Arch itects and M arine Engineers601 Pavonia Avenu e, Jersey City, New Jersey 07306

www.sname.org

Copyright O 2004 by the Society of Naval A rchitects and Marine Engineers


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T&R B ulletin No. 2-29A has been prepared fo rTHE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERSTECHNICAL AND RESEARCH PROGRAM

Reviewed and Approved by:PAN EL HS-7 (Vibration) (Joint with ANSI Working G roup S2-11)Richard J. Sonnensch ein, Chairman, HS-7Arthur F. Kilcullen, Ch airman, S2-11

Gary P. A ntonidesSteven P. A ntonidesWilliam BlakeRichard K. Brown, Jr.Frederick J. BurkeArthur J. CautilliJiang-Ren ChangYung-Kuang Chen

Gary P. A ntonidesRobert Gerlach

Kevin F. DanahyJoe GelsominoGeorge D. HillAllan K. KukkJoel H. LeiferMark T. McGownEdward F. NoonanAnthony R. Paladino

SNA ME PAN EL M-20 (Machinery Vibration)Richard T. Woytowich, ChairmanJaroslav V. HavelMoses W . HirschkowitzPatrick 0. Prendergast

Approved by:HULL STRUCTURE COMMITTEEPhillip G. Rynn, Chairma n

Frederick H. Ashcroft William J. FallonBilal M. Ayyub Owen F. HughesRamesw ar Bhattacharyya Roger G. KlineHarry Paul Cojeen Chao H. LinMark Debbink Naresh M. ManiarAllen H. Engle Thoma s Miller

Robert S. BehrKarl E. BriersRoger K. ButturiniAllen ChinJoseph H. Comer 111Thomas F. Conroy Jr.James J. CorbettW. Mark CummingsRichard D. DelpizzoEarl W. Fenstermacher

SHIPS' MACHINERY COMMITTEEDavid R. Rodger, ChairmanJoseph P. FischerRichard W. HarkinsJohn F. HenningsBahadir lnozuThoma s P. MackeyWilliam L . McCarthyCharles A. NarwiczMark F. NittelCharles H . PiersallKevin D. Prince

J. Allen ParkesPaul C. ShangJohn J. SlagerSteve StroubakisRichard F. TaddeoMichael B. W ilsonWilliam A. W ood

Steve StroubakisIvan Zgaljic

Lewis E. MotterStephen E. SharpeRobert A. SielskiRichard J. SonnenscheinRobert J. vom SaalChristopher J. W iernicki

Alan L. RowenE. Gregory SanfordPeter G. SchaedelWilliam J. SemblerKenneth SiegmanRichard P. ThorsenMatthew F. WinklerRichard T. WoytowichIvan Zgaljic

It is understood and agree d that nothing expressed herein is intended or shall be construed to give any person, firm,or corporation any right, remedy, or claim against SN AM E o r any o f its officers or members.


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ABSTRACTThis Bulletin supplements ANSl documents S2.19, S2.25, S2.26,S2.27, S2.28 and S2.29pertaining to ship vibration. The ANSl docume nts contain guidelines for the measurem ent andevaluation of structural and m achinery vibration on ships. They a lso specify data acqu isition andprocessing procedures which will result in consistent and reliable data to compare with theguidelines. Howeve r, the ANSl docum ents do not provide a lot of detail about how to m ake thevibration m easurements or do the ana lytical calculations that are required.This T&R Bulletin is designed to assist in understanding the rationale for many of therequirements, and help the reader in choosing the appropriate techniques for the requiredmeasurem ents and calculations. Where appropriate, it discusses standards issued by otherorganizations, and references texts, reports, etc. where more detail can be found, particularly forthe analytical prediction of vibration magnitudes. This B ulletin, together with the und erlying ANSIdocuments supercedes the existing SNAME T&R Bulletins 2-25 and 2-29 and SN AME Cod es C1,C4, and C5.

ACKNOWLEDGEMENTSThis document was a joint project of SNAME Panel HS-7, chaired by Rich Sonnenschein, andPanel M-20, chaired by Rich Woytow ich. The panels took advantage of research and a numberof reports that were do ne in connection with Navy an d Coast G uard sponsored tasks to improveship vibration standards in the 1990's. That work resulted in a number of ANSl standards,initiated by ANS l Working Group S2-11, chaired by Arthur K ilcullen. It is the function of thisdocume nt to support, explain, and expound on the ANSl standards.There was o ne subject outside the expertise of most of the panel mem bers, that of hull vibrationcalculations. To write that section, Panel HS-7 turned to Jerry Hill, Daniel Curtis, and ArthurSymmes of John J. McM ullen Associates, Inc., Barton McPh eeters of MSC Softw are Corporation,Kevin Arden of Northrop Grumm an Newport News, and George C amp of B ath Iron Works.


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Table of ContentsPART I. ENERAL ......................................................................................................................I INTRODUCTION ................................................................................................................1 1 1 Objective and Scope ..............................................................................................

1 1 2 Background............................................................................................................................................................................................1 3 SNAME and ANSI Standards 21 1 4 History ....................................................................................................................................................................................................2 DEFINITIONS AND TERMINOLOGY 4

...................................................................3 TEST & ANALYSIS PROCEDURES (General) 61.3.1 Test Conditions ....................................................................................................1.3.2 Test Procedures ....................................................................................................1.3.3 Instrumentation .....................................................................................................1.3.4 Vibration Severity.................................................................................................1.3.5 Data Processing ..................................................................................................01.4 REFERENCES ................................................................................................................1

PART II. TRUCTURAL VIBRATION ......................................................................................... 3...............................................................................................................1 INTRODUCTION 13

............................................................................................2 HABITABILITY GUIDELINES 132.2.1 Background..........................................................................................................32.2.2 ANSI S2.25 Criteria.............................................................................................. 42.2.3 Data Processing ..................................................................................................52.3 EQUIPMENT SURVIVABILITY (Mechanical Suitability) GUIDELINES ............................162.3.1 General ................................................................................................................6

2.3.2 Shake Table Tests vs Shipboard Environment ................................................... 62.3.3 Major Propulsion System Problems vs Shipboard Environment .........................172.4 PROPELLER FORCES (Pressure & Bearing forces) ....................................................... 82.4.1 General ................................................................................................................82.4.2 Computer Programs ...........................................................................................82.4.3 Preliminary Estimates ..........................................................................................02.5 DIESEL ENGINE EXCITATION .....................................................................................12.5.1 Introduction ......................................................................................................... 1

........................................................................................................5.2 Inertia Forces 222.5.3 Inertia Moments (Couples) ................................................................................2.........................................................................................................5.4 Firing Forces 22

2.5.5 Summary of Likely Forces and Moments ............................................................ 32.5.6 Design Considerations .........................................................................................4.6 HULL VIBRATION CALCUATIONS ................................................................................ 5...........................................................................................................6.1 Approaches 252.6.2 General ................................................................................................................52.6.3 Empirical Formulas ..............................................................................................62.6.4 Beam Models .......................................................................................................62.6.5 Plate Models ....................................................................................................... 82.6.6 Analysis................................................................................................................9


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2.7 TESTING REQUIREMENTS ............................................................................................12.7.1 Transducer Locations .........................................................................................1...........................................................................................................7.2 Test Report 31

2.8 SHAKE TABLE TESTS .....................................................................................................1...........................................................................................................9 LOCAL VIBRATION 33

.................................................................................................................10 REFERENCES 34PART Il l . AIN PROPULSION & AUXILIARY M ACHINERY VIBRATION ..................................373.1 INTRODUCTION ...........................................................................................................7

...........................................................................................ONGITUDINAL VIBRATION 373.2.1 Historical Background and Perspectives ............................................................. 8.......................................................2.2 Conven tional and Noncon ventional Systems 383.2.3 Mathem atical Mod el.............................................................................................93.2.3 Operational Factors .............................................................................................03.2.4 Measuring Alternating Thrust in the Main Thrust Bea ring ................................... 13.2.5 Turbine and Diesel Thrust Bearings ....................................................................23.2.6 Vibration of Propulsion System Comp onents .....................................................33.2.7 Gear Tooth Stresses ............................................................................................3..................................................................................................3 TORSIONAL VIBRATION 443.3.1 Torsional Calculations ..........................................................................................53.3.2 Torsional Vibration Criteria ..................................................................................73.3.3 ANSI S2.27 Criteria for Torsional Vibration ...................................................... 73.3.4 Com paring Criteria to Measurem ents ..............................................................0

.................................................4 LATERAL VIBRATION OF PROPULSION MACHINERY 513.4.1 Lateral Calculations .............................................................................................23.4.2 Lateral Measurem ents .........................................................................................33.4.3 Lateral Criteria .....................................................................................................3

......................................................................................................................5 BALANCING 543.5.1 Balance Quality Grade ........................................................................................ 53.5.2 Balancing and Vibration Documentation .............................................................. 53.5.3 Shipboard Measurem ents ................................................................................... 53.6 DIESEL ENGINES ............................................................................................................53.6.1 ANSI S2.27 Diesel Engine Criteria ....................................................................63.6.2 Other Criteria .....................................................................................................63.7 GEAR CASE VIBRATION .................................................................................................73.7.1 Calculations and Measurem ents ......................................................................... 83.7.2 Criteria ................................................................................................................83.8 AUXILIARY MACHINERY .................................................................................................83.8.1 ANSI S2.28 - Measurements on Bearing Housings ............................................ 9

...............................................................8.2 ANSI S2.29 - Measurements on Shafts 593.9 REFERENCES ................................................................................................................0


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PART I - GENERAL1.1 INTRODUCTIONI I I Objective and ScopeThe primary objective of this Bulletin is to supplement ANSl guidelines for assessing theacceptability of a ship's performance with respect to structural (hull, superstructure, and local),equipment, and m achinery vibration. It applies to seagoing ships and for inland ships of alllengths. It applies to turbine, electric, and diesel drive n ships, with single or multiple shafts. ThisBulletin also provides information on the measurement and data processing procedures whichresult in reliable data to com pare with the guidelines, and gives g uidance for calculations requiredfor both machinery and structural vibration during the design of the ship. It also includes som ebackground o n how the ANSl standards were deve loped, and the rationale for them.ANSl guidelines for structural vibration (ships' hulls, superstructures, and locat structures) arebased on hum an habitability and equipmen t survivability. If these guidelines are met there willalso be assurance that there are no major shaft rate vibration problems associated with thepropulsion system, or structural fatigue problem s.Machinery vibration guidelines in the ANSl documents are given for the main propulsionmachinery (torsional, lateral, and longitudinal), and for the internally excited vibration of a uxiliarymachinery. To indicate probable compliance with the machinery guidelines certain mathematicalanalyses are required, and these are discussed.This Bulletin is intended for use by naval architects, marine engineers, ship designers,shipbuilders, equipment manufacturers, and ship operators.1.I2 BackgroundStarting in the 1960 's, the Technical Panels of the Soc iety of Naval Architects and MarineEngineers (SNAME) were the driving forces in developing ship vibration standards in the UnitedStates. An indication of their general acceptance wh en they were written is the fact that many ofthe documents were adopted by I S 0 as International Standards. In recent years, however, theAmerican National Standards Institute (ANSI) has included ship vibration as part of their purviewand has issued a number of standards dealing with ship hull and mach inery vibration. Muc h ofthis work was sponso red by the United States Navy. The ANS l documen ts, being more recent,are more compatible with new developments, and, if the SNAME documents were updated, theywould essentially duplicate the ANS l docum ents, or would con fuse shipbuilders and buyers if theycontained different criteria. The members of the SNAME vibration panels have concluded thatthey can provide a more valuable service by issuing documents that explain how best to complywith the ANS l requirements with respect to calculations and measurem ents. This document,issued by Panels HS-7 (Vibrations) and M-20 (Machinery Vibrations), taken together with theunderlying ANSl Standards, supersedes most of the existing SNAME documents on both hull andmachinery vibration, including T&R Bulletins 2-25 and 2-29 and Codes C1, C4, and C5.Many different types of vibration are treated in this Bulletin, and each type is associated with itsown set of problems and analysis methods. In recent years, the treatment of some types ofvibration has changed significantly, while other types are treated essentially the same as yearsago. For this reason, the depth of coverage of the different types varies considerably. Also, som enew innovations in ship design, propulsion systems in particular, do not have a long history, sonot as much is known about them, making the corresponding coverage sketchier. It is hoped thatthis Bulletin will be updated to account for new developments in shipboard vibration, and willeventually cover all types of v ibration in greater depth.


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Numerous industry standards addressing vibration of marine machinery and machinery spaces,in particular, currently exist. The prediction processes and vibration limits contained in thesestandards are sufficient in some cases, but in other cases lack sufficient definition. Reference ismade to the existing industry standards where they may be of assistance. Specifically, some ofthe relevant industry standards are as follows:1. Ame rican Bureau of Shipping (ABS) Rules for Building Steel Vessels;2. Ame rican Society of Testing and Materials (ASTM ) Standards;3. Ame rican National Standards Institute (ANSI) Standards;4. Bureau Veritas (BV) Building and Operation of Vibration-Free Propulsion Plantsand Ships;5. International Standards Organization (ISO) Standards;6. U.S. Dept. of Labor, Oc cupa tional Safety and Health Adm inistration (OSHA );7. Society of Naval Architects and Marine Engineers (SNAM E) T&R B ulletins

1.I3 SNAM E and ANSl StandardsThe existing SNA ME documen ts on ship vibration are as follows:T&R Code C -I , "Code for Shipboard Hull Vibration Measurements," 1975.T&R Code C-4, "Shipboard Local Structure and Machinery Vibration Measurements," 1976.T&R C ode C-5, "Acceptable Vibration of Marine Steam and Gas Turbine Main and AuxiliaryMachinery Plants," 1976.T&R Bulletin 2-25, "Ship Vibration and Nois e Guidelines," 1980.T&R Bulletin 2-29, "Guide for the Analysis & Evaluation of Shipboard Hull Vibration Data," 1992.T&R Bulletin 3-42, "Guidelines for the Use of Vibration Monitoring for Prev entativeMaintenance," 1987.Note that three of the six were written in the 701s , wo in the 80's, and only one in the 90's. Som eof these documents deal only with measurement procedures and analysis methods, both ofwhich, it was felt, had to be standardized to yield consistent results before the actual criteria couldbe developed. Criteria for machinery vibration mag nitudes were established in Cod e C-5, but thefirst guidelines for hull vibration came from an I S 0 document ( IS 0 6954)(Ref. 1-1). Even after itwas issued, the discussions continued about what is the appropriate measure of severity(broadband or narrowband, velocity or acceleration, etc.), and whether the criteria for hullvibration should be related to habitability, equipment survivability, or that which results fromunacceptable machinery problems.The AN SI documents referred to are:ANS l S2.19-1989 , "Mechanical Vibration - Balan ce quality requirements of rigid rotors- Part I:Determination of permissible res idual unbalance."ANS l S2.25-2001 , "Guide for the Meas urement, Reporting, and Evaluation, of Hu ll andSuperstructure Vibration in Ships.ANSl S2.26-2001, "Vibration Testing Requirements and Acceptance Criteria for ShipboardEquipment."ANSl S2.27-2002, "Guidelines for the Measurem ent & Evaluation of Ship PropulsionMachinery Vibration."ANSl S2.28-2003, "Guide for the Measurement and Evaluation of Vibration of ShipboardMachinery."ANSl S2.29-2003, "Guide for the Measurement and Evaluation of Vibration of Machine Shafts onShipboard Machinery."Except for the balancing standard, these were started in the go's, but were approved in 2001,2002, or should be approved in the near future. They all give quantitative guidelines for


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shipboard vibration, and, where appropriate, they specify acceptable data acquisition andprocessing procedures.This B ulletin, which sup ersedes all of the SNA ME docum ents listed above except T&R Bulletin 3-42 (on condition m onitoring), is divided into three parts:

(I) General(11) Stru ctur al Vib ratio n (Ha bitability & Equipme nt Survivability)(Ill) Main Propulsion & Auxiliary M achinery VibrationPanel HS-7 (Vibrations) has the responsibility of maintaining Part II, Panel M-20 (MachineryVibrations) has responsibility for P art Ill, and bo th panels are jointly respons ible for Part I.It is recognized that vibration of hull and machinery (particularly when slow speed diesels areinvolved) should often be considered together, perhaps by using an integrated hull/machinerycompu ter model. Howev er, the exact p rocedure will differ from ship to ship, and there is not yetsufficient agreement within the industry to include such an integrated approach in the ANSIdocum ents or these guidelines. Ship buyers and sellers are encouraged to agree on such anapproach if the de sign of the ship warrants it.II4 HistoryIn April 1959, a Task Group that became the HS-7 Panel (Vibrations), began evaluatinginstrumentation systems and methods of shipboard hull vibration measurement, for the purposeof establishing a recomm ended p rocedure for the collection of shipboard vibration data. Threeshipboard studies were done (1959, 1960, and 1963). A shipboard vibration measurementsystem was developed for the U.S. Maritime Administration (MARAD) in 196 5. The first "Code forShipboard Hull Vibration Measurements" was published by SNAME as T&R Bulletin 2-10 in 1964,was revised in 1967 to include details on the new MARAD instrumentation system, and again in1969 to include longitudinal vibration meas urements on main machinery components. It waspublished as T&R Code C - I in 1974 by SNAME Panels HS-7 and M-20.Code C - I was used as the basis for the International Standards Organ ization 180-4867 , 1984(Ref. 1-2), which was expand ed to include the treatment of large diesel drives. In like manner,T&R Code C-4, "Local Shipboard Structures and Machinery Vibration Measurements" waspublished in December 1976 and was used as the basis for 1S0-4868, "Code for theMeasurement and Reporting of Local Vibration Data of Structures and Equipment," published in1984 (Ref. 1-3). These e vents indicate d a mea sure of international agreeme nt at the time on themethods of evaluating shipboard vibration.In all cases, these codes called for the evaluation and reporting of each frequency componentassessed separately, in terms of their maximum repe titive amplitudes (MRA). The M RA was themost used measure of the severity of vibration since about 1960, when the primary recordingdevice was the oscillograph, and when manual analysis of data was performed as described byManley (Ref. 1-4). In practice, this procedure p roved to be time-consum ing a nd subject to humanerror. Rather than using the ma nual method, a filter can be used to isolate the compo nents ofinterest, and the MRA can be found from the filtered signal. A typical filtered signal mo dulatesconsiderably, and the MRA is the maximum value of the envelope of this filtered signal.However, filters cannot isolate components properly if there are several components present inthe frequency range of interest.These problem s have led to the recent conclusion that MRAs of individual frequency componentsare not appropriate for use in criteria, and that the MRA is only useful when it is applied to abroadband or unfiltered signal. At the sam e time, it has becom e increasingly accepted that hullvibration should be evaluated based on all the frequency com ponents together.


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The use of automatic data analysis equipment also helped to change attitudes significantly. In1972, Panel HS-7 started the process of updating data measurement and analysis procedures,the development of a ship vibration data bank and the publication of a guide for shipboardvibration control. The T&R "Vibration Data Sheets were published by SNAME starting in 1976.Many ev ents took place before the "Ship Vibration Design G uide" (Ref. 1-5) was finally publishedin 1990.In 1982 SNAME recommended a test program to develop "crest factors" to bridge the gapbetween the MRAs and the rms results often obtained by the widely used spectral analyzers.Limited data indicated that the crest factor (the MR A divided by the rm s value) for hu ll vibration isnormally abo ut 2.5, at least for blade frequency vibration. If tests could refine that number forvarious types of ships, a convenient method for estimating the MRAs would be to obtain the rmsvalues of eac h component and simply multiply it by the appropriate crest factor. Further work onthis project was deferred primarily because of cost considerations.Meanw hile, efforts to set reasonable hull vibration limits began in the I S 0 in 1970. 180-6954 waspublished in December 1984 (Ref.1-I), with the same criteria that appeared in SNAME T&RBulletin 2-25. It included a tentative crest factor of 2.5. T&R Bulletin 2-29 was authorized toclarify its usage. Howev er, because of the continuing controversy over the application of the FF Tanalyzer in relation to 130-6954, the Bulletin was no t issued until 1992. lS0 -69 54 had been wellreceived an d was in wide use, but was frequently m isinterpreted. It satisfied the criteria forhuman exposure to w hole bo dy vibration, as defined in 1S0-263111 (Ref.1-6), and is applicable toeach frequency component assessed separately.The attitudes toward M RAs changed also. Rather than finding M RAs by multiplying rms valuesby 2.5, it made mo re sense for the criteria to address rm s magnitudes directly. This is particularlytrue for broadband magnitudes, which, as noted above, were becoming accepted as moreappropriate for c riteria.Work began on a new standard for hull vibration in 1995 when the U.S. Naval Sea SystemsCommand sponsored a task to recommend a commercial standard that could be used by theNavy instead of the existing military standard. Work on the N avy task was done in conjunctionwith SNAME Panel HS-7 (Vibration) which also wore an ANSl hat as Working Group S2-77.Over a period of several years, many improvements were made by this comm ittee, and resultedin ANSl S2.25.For machinery vibration, the U. S. Coast Guard, which had been using a military standard, fundedthe development of a new propulsion system vibration standa rd which they issued in 1999. Thatformed the basis of ANSl S 2.27, developed by Working G roup S2-77.

1.2 DEFINITIONS AND TERMINOLOGYThe definitions in ANSI S2.1-2000/ISO 2041:I90 (Ref. 1-7) apply. In addition, the followingdefinitions and term inology apply.A dd ed Mass. Wh en a plate structure is in conta ct with a fluid, motion of the structure will forcethe fluid to move, causing a reaction force on the structure. For hull girder frequencies, puttingadditional mass on the structure can model this reac tion. This is terme d Added or Virtual Mass.Ax ial Vibra tion. Any forced or natural vibration wherein the various propulsion systemmecha nical elements move in the direction defined by the axis of the shafting.Balancing. A procedure by which the mass distribution of a rotor is checked and, if necessary,adjusted in order to ensure that the vibration of the journals and/or forces on the bearings at afrequency corresponding to operational speed are within sp ecified limits.


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Balance Quality Grade (G). A measure of the allowable unbalance expressed in terms ofvelocity (mmls). G = we, where w = angular rotational speed (radls), and e = eccentricity (mm).Blade Rate. Blade rate or propeller blade frequency is the product of rotational speed and thenumbe r of propeller blades.Broad-band Vibration. Vibration having its frequency components distributed over a broadfrequency b and, usually an octave or greater.Consistent Mass. A real structure usually has Distribute d Mas s rather than idealized Lum pedMasses. If the mass is modeled as lumped, it will generate a diagonal mass matrix. A methodthat is appropriately consistent with the sh ape functions used to generate the stiffness matrices inthe Finite Element method gives a banded m ass matrix. This Co nsistent Mas s matrix gives crosscoupling terms that allows the motion of one grid point to produce an inertia reaction at anadjacent grid point. This can give mo re accurate results in some cases.Coordinate Axes.x longitudinal, + is forwardy, transverse, + is to port

z, vertical, + is upwardsc p , angle of roll, right hand is +x8, angle of pitch, right hand is +yly, angle of yaw, right hand is +z

Coupled Mass. See Consistent Mass.Coupling (mechanical). A mechanical coupling is a fastener connecting two shafts, the rotatingelements of two pieces of equipment, or a shaft and a rotating element of a piece of equipment.Direct Frequency Response Analysis. A meth od that determines the response of a structure todynamic loading at a particular frequency or a series of frequencies by solving the equations ofmotion at each of the loading frequencies. (Compare with M oda l Frequency Response Analysis.)Distributed Mass. Mass that is modeled by describing the distribution of mass on a plateelement or along a bar element. (Compare with Lum ped Mass.)Engine Firing-rate Frequency. The product of rotational speed and the number of enginecylinders firing in each revolution.Environmental Vibration. Environmental vibration with respect to shipboard equipment isfoundation or support vibration excited by sources external to the equipment, either by shipmotion resulting from wave action (rolling, pitching, yawing, heaving, or surging), impacts,propeller or shaft forces, or by other ship machinery.Finite Element. The basic division of a finite element model. A finite element model representsa structure with an assemblage of connected units (e.g., plate and beam elements) that canindividually be easily solved for forces, stresses and motion. The individual elements arecombined using matrix algebra to solve the complete problem and to recover the forces, stressesand m otions of the individual elem ents.Full Matrix. A matrix with no (o r few) zeros.Fully Coupled Matrix. A mass, stiffness, or dampin g matrix with no (or few) zeros. This mea nsthat the local force or motion of any part of the structure will directly affect all other parts of thestructure.


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Grid Point. A location used in for defining the geometry of a finite element.Gyroscopic Moment. Gyroscopic moment is the turning moment which opposes any change ininclination of the rotational axis of a ma ss ha ving a mom ent of inertia.Lateral Vibration. Lateral vibration of a sh afting system is vibration norm al to the sha ft axisLocal Vibration. The accentuated vibration that occurs in various components or at discretelocations within the ve ssel's structure.Longitudinal Vibration. Longitudinal vibration is synonym ous with axial vibration.Lumped Mass. Mass that is modeled by putting discrete values of mass at a grid point; not acoupled mass. (Compare with D istr ibuted Mass; see also Consistent Mass.)Machinery-excited Vibration. Vibration excited by forces or moments generated by machinery.Maximum Repetitive Amplitude (MRA). The maximum displacement, velocity, or accelerationof a vibratory signal that repeats over a given time period. In a modulating signal, the time periodexamined should include several crests. The fact that it repeats indicates that it can be usedwhere fatigue or wear over a long period is a concern.Modal Frequency Response An alysis. A method that determines the response of a structureto dynamic loading at a particular frequency or a series of frequencies by first determining thenatural frequencies and mode shapes of the structure for a large frequenc y range (pe rhaps five orten times the range of loading frequencies). The natural frequencies and mo de shapes are thenused to solve the equations of motion for the desired loadings, which us ually are not at any of thenatural frequencies of the structure. (Compa re with Direc t Freq uenc y Res pons e Analysis.)Nonstructural Mass. The structural mass is the mass of the structure that is modeled as plateand beam elements (volume times density). Any additional mass of equipment, outfitting, orstructure can be included by adding lumped or distr ibuted masses to the model. These massesadd no stiffness to the m odel, and are termed non structura l ma ss.Propeller Blade Frequency. Propeller blade frequency or blade rate is the product of rotationalspeed and the num ber of propeller blades.Rayleigh Damping. Damping that is a linear combination of the stiffness and mass proportionaldamping of a structure. Under these conditions, classical norm al mod es, where everythingvibrates in phase, will exist for the dam ped system .Shaft-rate Frequency. The frequency of sha ft rotation.Structural Damping Coefficient. A measure of the hysteretic dam ping of a structure, equal inthe energy sense to twice the Viscous Da mp ing Ratio.Torsiona l Vibration. Torsional vibration of a rotating shafting system is an oscillatory rotationalmovement of the elements comprising that system.Vibratory Torque. Vibratory torque in a shafting system is a torque fluctuation which generatesor results from torsional vibration.Virtual Mass. See Added Mass.Whirling Shaft Vibration. Whirling shaft vibration is a combination of shaft rotation and lateralvibration.


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1.3 TEST AND ANALYSIS PROCEDURES (General)1.3.1 Test ConditionsThe test conditions required for hull vibration measurements and for propulsion systemmeasurements are listed in S2.25 and S2.27 respectively. There are two significant differencesin the requirements for hull vibration and for propulsion system vibration, as follows:

Sea state must be 3 (SS 3) or less for hull vibration. For propulsion systems: SS 1 orless for small craft, SS 2 for ships of less than 10,000 tons, SS 3 for ships greaterthan 10,000 tons. (S2.27 does not specify type of tonnage, but it is recommendedthat the gross tonnage be used to determine sea state.)Both cases require full immersion of the propeller, but for hull vibration, the sternplating in the vicinity of the propeller should be underwater. (For this requirement,judgement must be used to include the area of the plating subjected to significantpressure fluctuations from the propeller. It is suggested that any plating that comeswithin a propeller radius of the blade tips in any direction as the propeller rotates beincluded.)

If both tests are being done concurrently, the lesser sea state applies, as required by S2.27, andthe stern plating should be underwater, as per S2.25.Individual ship specifications can alter the test conditions for any particular ship.1.3.2 Test ProceduresThe test procedures are generally the same for both the structural and the machinerymeasurements. All transducers should be calibrated in the laboratory before being installed.After installation, each instrumentation channel of the vibration measurement system should bechecked to ensure proper functioning. A field calibration (which normally excludes transducercalibrations, but includes conditioning and recording equipment) should be made before and aftereach major phase of the test. Transducer calibration can sometimes be done on site by placing acalibrated transducer on or immediately adjacent to the installed device, exciting the neighboringstructure (with a shaker or by running nearby machinery) and comparing transducer outputs.In order to allow for limited diagnostics, if they become necessary, provision should be made forobtaining the phases between different locations. This can be done by making all measurementsin a particular direction simultaneously, or by recording a shaft position marker as a reference.

Operating Conditions. The differences in the operating conditions for the hull andpropulsion system during data recording are as follows:

a) Steady acceleration (or deceleration) run from half of rated shaft speed or less to therated speed to determine critical speeds. The rate of change in speed should be 10% of therated RPM per minute or less for the propulsion system, 5% for the hull. If the tests areconcurrent, 5% should be used.

b) Free-route runs at constant speeds from half of rated shaft speed or less to the ratedspeed. The words describing the increments differ somewhat, but, simply put, require 10 or moreequally spaced increments, with additional runs at service speeds and near resonances.In addition, the following optional test conditions, described in Annex A of S2.27 may be requiredby the purchaser for the propulsion system tests, depending on the type of ship and its normaloperating requirements.


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(c) Hard turns to port and starboard at rated speed or speed(s) agreed upon by thepurchaser and the builder. Recording should commence before the turn and continue until themaximum vibration has passed (when settled into the turn). The maximum vibration occurs at thebeginning of the turn and is very dependent on how fast the rudder is applied. Some helmsmenare reluctant to apply the rudder quickly, so that data will be inconsistent from ship to ship. Thevibration after the ship settles into the turn will give more consistent results. Note - turns wouldnormally not be required for ships such as cargo ships and tankers, but would be required forships such as combatant ships and patrol craft, where high speed turns are expected as a part oftheir normal operation.

(d) Bol lard tests (optional). While securely anchored, or tethered to a dock or another ship,perform tests (a) and (b) described above. This would be appropriate for tug and tow boats, etc.Although no guidelines are given for crashbacks (changing speed from full ahead to full astern asquickly as possible), this maneuver sometimes excites natural frequencies that may not otherwisebe detected. If this test is done, it should be done with caution because crashbacks may result instructures or equipment being subjected to very large displacements and/or stresses.In multiple-shaft ships, all shafts should normally be run as closely as possible to the samespeeds. However, in certain instances, it may be appropriate to run with a single shaft.With controllable pitch propellers, all runs should be made using the design pitch, or the range ofpitches, normally used at each shaft speed.In some cases, it may be appropriate to make vibration measurements at different or additionalspeeds to those mentioned above, such as the maximum possible speed. In those cases, suchchanges should be detailed in the ship specifications.Often, data can be obtained during acceptance trials in which ships normally perform enduranceruns for several hours. This may be an opportunity to use roving transducers at successivelocations to define mode shapes or to acquire additional habitability or enviromental data whichmay have been limited due to the number of transducers or limited trial time.1.3.3 InstrumentationAcceleration and velocity transducers suitable for acquiring data between 1 and 100 Hz aregenerally acceptable for hull measurements, and between 1 and 1000 Hz for machinerymeasurements. The limits may be modified for particular ships depending on the expectedexcitation frequencies, and for special requirements such as machinery diagnostics. Virtually allmodern vibration transducers generate signals proportional to acceleration, and it is necessary tointegrate the signals with respect to time to obtain velocities. Integration at low frequencies canbe a problem, and it may be necessary to calibrate at low frequencies.An alternative to integrating the signal in the time domain is to generate spectra fromacceleration data and divide by the angular frequencies to obtain velocity spectra.Measurements should be recorded on an electronic system which produces time domain recordsin a form (magnetic tape, computer disk, etc.) which can be replayed for subsequent analysis.Either digital or analog records are acceptable.1.3.4 Vibration SeverityPerhaps the most significant change in recent thinking, reflected in the new ANSI documents, isthe use of broadband values as measures of vibration severity. Many of the guidelines in thesuperseded documents are based on the maximum repetitive amplitude (MRA) of individual


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frequency components. There are problems in processing data in order to obtain MRAs, andoften it was no t clearly stated that the guidelines applied to M RAs. Test engineers us ing spectralanalyzers often obtained the results in a format convenient for those ma chines.To understand one of the reasons for using broadband values, consider the characteristics of atypical ship vibration record. There could be a single dominant frequency as shown in Figure 1-1,normally blade frequency, or there could be several frequencies involved, perhaps includingengine firing frequency or b lade harmonics. In either case, there is likely to be significantmodulation, due to ship motion, waves, etc. Frequency spectra of single modulating compon entshave sidebands as shown. If the modulation frequency is constant, as in the upper trace, thesidebands will be distinct and will be spaced at the modulation frequency away from the carrierfrequency, most often blade frequency. If the mod ulation frequency varies, as in the lower case,the sidebands will be spread over som e range above and below the carrier frequency.

Time Historie s Frequency SpectraFigure 1-1- Modulating Signals and Corresponding Spectra.

Where it is required to find the MRA or peak magnitude of a single frequency, it can be foundfrom the time history. (The only difference betwe en MRA and peak is that the MRA excludes thelargest excursions, which may be a result of electrical problems, for example, or an impact orother transient phenom ena.) Howeve r, if there are several frequencies present, they mus t beseparated before finding the pe aks. This is norma lly done with a filter, and if the components arespread out, they can b e separated, and the peaks found from the filtered signals. In filtering,however, the pass band must include all of the associated sidebands, or the filter will reduce themodulation, and the peak value found will be too low. This is normally not a problem with turbinedrives where the prop eller blade excitation is relatively isolated. Unfortunately, with diesel drives,there are usually too many frequency components too close together to separate them with afilter and still include all of the appropriate sidebands. Consequ ently, the MRA (or peak ) values ofindividual frequency components are often impossible to measure accurately, and are notappropriate for use in standards.Three useful criteria are left: (a) broadband rms, (b) narrowband rms, and (c) broadband peak.Even though narrowband data are essential in understanding the nature of a vibration, thebroadband quantities are mo re appropriate for limiting criteria. If there are several significantfrequency components involved, it would be the com bined m agnitude that would cause wear orfatigue, or that would b e felt by humans. Rms values have the added advantage that they areaffected less by waves, ship m otion, etc. than peak values. Even though damage is oftenassociated more with peak values, the magnitudes of vibration that will cause damage are notusually known, so there seems to b e little advantage in measu ring peaks.


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In the ca se o f alternating torque, alternating thrust, and torsional stress, however, the m agnitudesthat cause dama ge are usually known. Wh en the alternating torque or thrust exceeds the mean,the resulting torque or thrust reversals could dama ge the gears or thrust bearing. The reversalswould be associated with the peak unfiltered magnitudes, not the rms, and not just bladefrequency. In evaluating the torsional stresses with respect to fatigue, it is the peak values thatdo the mo st damage. For these three quantities, the criteria in ANSl S2.27 are expressed in peakvalues, an d app ly to the unfiltered signal.In propulsion system vibration, peak values are sometimes used in the measurement of therelative radial motion between a shaft and an adjacent bearing. Adequa te clearances must bemaintained in the bearing, so the unfiltered peak-to-peak displacement is the quantity that bestreflects vibration severity in this app lication.In recent years, with data being processed by spectrum analyzers, average amplitudes ofindividual frequency components were often considered instead of MRA s. Frequency spectra arevaluable (and sometimes required by the new ANSl documents) in pointing out the sources ofany excessive vibrations as well as ensuring the quality of the data a nd allowing for diagnostics ifa problem is discovered. How ever, for the new standards, b roadband rrns values have to bedetermined.Com plicating the analysis of the hab itability data so mew hat is the fact that the hu man body is lesssensitive to low frequencies, and therefore the frequency content of the vibration signal must beattenuated below 7 Hz.1.3.5 Data ProcessingIn general there are four types of data presentation that a re required by the ANSl docume nts, andthe data processing procedures must be carefully executed to provide the results required ateach of the m easureme nt locations and directions:

a) Broadband rms magnitudes for free-route runs, including speeds at hull girder,superstructure, and/or machinery resonances. After filtering the a ppropriate band, such as from 1to 100 Hz for hull measurements, rrns magnitudes can be found from an rrns magnitude detectorand averaged. Ship vibration usually has conside rable modulation and irregularity, so a longenough sam ple has to be analyzed to get a goo d average. Alternatively, the rrns value of a signalwithin the specified frequency band can be obtaine d with m ost spectral analyzers. If the signalshave low signal-to-noise ratios, the rrns magnitudes determined by these methods will be toolarge. In this case, it is possible to find the bro adba nd rrns magnitude by obtaining the spectralamplitudes of all frequency components above the noise level (excluding spurious componentssuch as electrical line frequencies) and finding the square root of the sum of the squares of thoseamplitudes.

b) Broadband peak magnitudes for free-route runs or maneuvers as required. Peak valuesare useful when mechanical damage is associated with the largest forces, displacements,velocities, accelerations or strains. Howe ver, it must be kep t in mind that peak values are verysensitive to the conditions present during sea trials, particularly the sea state. The simplestmethod of obtaining broadband peak values is to record the broadband time histories on a stripchart or display them on an analyzer, and man ually me asure the p eaks or find them with a cursor.

c) Rms magnitude frequency spectra, averaged over the length of each run, for the free-route/acceleration runs, including at resonanc es. To obta in the required amplitude spectra, aHanning window and a 114 Hz bandwidth are normally appropriate. Reports must containfrequency spectra for any free-route runs whe re the criteria are not met.d) Plots of rms amplitudes versus rpm of major orders (such as sh aft rate, blade rate, firingrate, and other significant engine orders), as obtaine d from the spectra. The ANSl docu men ts


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require test reports to contain plots of significant orders of vibratory velocity, thrust, or torqueversus rp m, even though there are no criteria associated with these.Low frequency vibration. Care must be taken with respect to the low frequencycompo nents in ship vibration records. The m agnitudes associated with rigid body motions (roll,pitch, yaw) can be very large, but they are normally well below I z for large seagoing ships. If

the instrumentation does not measure below 1 Hz, those signals will not overwhelm the signals ofinterest (those excited by the propeller or machinery).The next lowest frequencies are usually those ass ociated with the fundamental hull modes (in theneighborhood of up to 3 Hz for large seagoing ships). Norma lly, the only excitation of interest inthat range is propeller shaft rate. Unfortunately, during trials, the seaway often excites thosemodes as well. Ideally, sea trials should be conducted in calm water, but ships' schedu les oftendo not allow that luxury. Some times, it will be necessary to judge wh ether these low frequencycomponents are due to the seas or machinery, based on factors such as the constancy of thevibration, or the shaft speeds at which they occur. Any com ponents due to the seas should notbe included in the magnitudes com pared to guidelines.In some cases, such as with smaller ships, it can be reasonably expected that there will be noshaft, machinery, or propeller excitations at very low frequencies, and that there may be shipmotion near 1 Hz due to the seaway. In such cases, the owner and builder should agree on aappropriate lower limit greater than 1 Hz. On the other hand, there are some ships with hullfundamental frequencies below 1 Hz which could be excited by shaft rate. It ma y be appropriatefor the buyer and seller to agree on a lower limit less than 1 Hz. Howeve r, note that, at least forhabitability purposes, the weighting will minim ize such low frequency com ponents.

Beating. Beating occurs when there are two excitations close in frequency so that theirresponses alternately add and subtract, such as two propeller shafts rotating at slightly differentspeeds. The resulting wave form app ears similar to the modu lation of a single frequencycomponent which is shown in Figure 1-1 (top left). It also has "bulges" and "waists," but thespectrum of a beating vibration shows two distinct components rather than the single dominantcompo nent with sidebands such as occurs with m odulation. The difference can also be detectedfrom the waveform becaus e the pe riod of a modulating signal is constant, whereas the pe riod of abeating signal is different in the "bulges" than in the "waists." If the period in the wa ist is shorterthan in the bulge, the larger vibration is at a higher frequency, and the converse also applies.

Evaluating data expressed in terms of acceleration and displacement. Much of thevibration data presented in years past are in terms of individual frequency components (e.g.,blade rate) and may be expressed as acceleration or displacement instead of velocity. Datawhich contain two or more significant frequency components can be converted to broadband rmsvelocities that can be evaluated with the guidelines in this Bulletin. In such cases, where spectraconsist of clear discrete components, conversion to rms velocity can be made by multiplying ordividing each frequency component expressed as an rms displacement or acceleration,respectively, by angular frequency, applying the weighting factor if appropriate (see Section 2.2 -Habitability Guidelines), and then taking the square root of the sum of the squares of all the rmsvelocity components.1.4 REFERENCES(1-1) International Standard I S 0 6954, "Mechanical Vibration and Shock - Guidelines for theOverall Evaluation of Vibration in Me rchan t Ships," Dec. 15, 1984.(1-2) International Standard I S 0 4867, "Code for the measurement and recording of shipboardvibration data," Dec. 15, 1984.


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(1-3) lnternational Standard IS 0 4868, "Code for the Measurement and reporting of localvibration data of ship structures and equipment," Nov. 15,1984.(1-4) Manley, R.G., "Waveform Analysis," John Wiley and Sons, Inc., 1946.(1-5) "Ship Vibration De sign Guide," Ship Structure Comm ittee, SSC 350, 1990.(1-6) International Standard IS 0 263111, "Guide for the evaluation of hum an exposure to whole-body vibration - Part 1 General requirements."(1-7) ANSI S2 .1-2000lISO 2 041 1990, Nationally Adopted International Standard "Vibration andShock - Vocabulary."


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PART II- STRUCTURAL VIBRATION

2.1 INTRODUCTIONIn ANSl S2.25 (R ef. 2- I) , guidelines are given for hum an habitability and equipm ent survivability.If the vibration is low enough to satisfy those guidelines, it would also provide an indication thatthere are no major vibration problems associated with the low speed components of thepropulsion system such as unbalance, misalignment, or pitch variance between propeller blades(pitch unbalance). It is also likely that the hull stresses are not large enough to cause structuralfatigue failure.When ANSl 52.25 was written, I S 0 6954 (Ref. 2-2) was the most established hull vibrationstandard, bu t it only gave levels at which ha bitability complaints were (a ) probable, or (b) unlikely.It used peak m agnitudes of individual frequency components. The IS 0 document has now beenrevised, but the U.S. delegation to I S 0 still has som e reservations about the new version.The guidelines in ANSl S2.25 can be used for the acceptance of new ships or for evaluating aship's performance after an overhaul or at other times as deemed necessary. In some cases,such as for high pe rformance craft, or for short term op eration, criteria other than those containedin S2-25 may be more appropriate. Such cases should be identified by the manufacturer, andchange s mad e to the criteria as agreed to by the m anufacturer and the bu yer.

2.2 HABITAB ILITY GUIDELINES2.2.1 BackgroundWhe reas the old version of IS 0 6954 used two vibration levels for criteria, the new version usesthree levels: A, B and C, intended generally for "passenger cabins, crew accomodations, andworking areas" respectively. For ANS l S2.25, it was felt that a de scription of human reactions tovarious vibration magnitudes would also be useful for shipbuilders and buyers, allowing themdetermine wha t limits are appropriate for which spaces.Guidance on human reactions is given in AN Sl S3.18 (Ref. 2-3), which is similar to I S 0 2631,"Mecha nical vibration and shock - Evaluation of huma n exposure to who le-body vibration," whichhas two parts: "Part 1: General requirements" (Ref.2-4), and "Part 2: Continuous and shock-induced vibration in buildings (1 to 80 Hz)" (Ref. 2-5). It is anticipated that there will be a Part 4"Vibration on board sea-going ships (1 to 80 Hz). In the meantime, Part 2 on buildings helped inthe development of the new version (2000) of I S 0 6954, and, as a result, of ANS I S2.25.But it was an o lder version of 2631 that was mo st useful. It recomme nded three different vibrationlevels for the categories "comfort, work proficiency, and safety or health." There were limits forvarious times of exposure, ranging from one minute to 24 hours. In the newest version of 2631,there seems to be a realization that research has not adeq uately defined the relationship betweenthe time of e xposure and comfort or work proficiency. (Howeve r, there is some indication of howthe time of exposu re affects health.) While mu ch has changed with the new version of 2631, theconcepts of com fort, work p roficiency and h ealthlsa fety seem valid and a re used in S2.25.Another basic difference between the old 6954 and the new one (and S2.25) is that the oldcriteria app lied to individual frequency compon ents, but the n ew criteria, including S2.25 ap ply tobroadba nd rms vibration magnitudes.I S 0 2631 ha s more restrictive guidelines, in general, for vertical than for horizontal vibration, but itdoes provide for "combined" criteria for cases where humans might be sitting, standing, or lying


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down, which is certainly the case for ships' crews. The combined criterion is the same as thevertical criterion for most frequencies, bu t it is the same as the horizontal criterion from about 1 to3 Hz where the horizontal is the most restrictive. The criteria, expressed as rms velocities oraccelerations, are accompanied by "weighting curves" which account for the sensitivity of thehuman body to vibration. The vibration levels in 263112 apply to buildings, and for ships they aresomew hat higher and based on past research and documen ts peculiar to ships.The weighting curves are felt to b e applicable to ships as well as buildings, so the s ame weightingcurves are used in I S 0 6954. They reflect equivalent sensitivities to vibration across thefrequency range of interest. They attenuate the measured vibration at the parts of the frequencyrange at which the body is less sensitive before calculating the broadband rms vibration. Thisallows more vibration at those frequencies. A simplified approximation of those curves is used inANSl S2.25, and reflects the fact that human perception of the vibration severity is the sam e forequal acceleration magnitudes at frequencies below 7 H z, and also the sa me for equ al velocitiesat frequencies above 7 Hz. Each vibration record (of one minute or more) must be expressed asa function of frequency (normally with a Fast Fourier Transform), and the amplitudes "weighted"with respect to frequency, that is, each component amplitudes must be multiplied by theweighting function for that frequency. The 7 Hz break point is a compromise between thehorizontal break point, which o ccurs at about 2 Hz, and the vertical, which occurs at a bout 12 Hz.Note that on ships h orizontal hull vibration is usually less severe than the ve rtical.While I S 0 6954 was often used for merchant ships in the past, the Navy used MIL-STD-1472D(Ref. 2-6) for habitability concerns, including vibration on ships. M IL-STD-1472D co vers vibrationof vehicles, mostly involving shorter time periods than crews normally encounter on ships. MIL-STD-1472D is based on the parts of the 1978 version of 2631 that pertain to land, sea, and airvehicles, much of which has been superceded in the new version of 2631. In the Navy's recentprogram to switch to commercial standards, I S 0 6954 was identified as the mos t comparablecommercial standard available dealing with hull vibration, and efforts were made to improve it,basing it on mechan ical suitability as well as ha bitability. ANSl S2.25 is a result of those efforts.2.2.2 ANSl S2.25 CriteriaIn determining which spaces should be assigned to which categories, it must be recognized thatsome types of work, such as reading, writing, calculating, or precision work, are mo re difficult in asevere environment than physical labor and the more appropriate category may be "comfort,rather than "work proficiency." Normally unoccupied spaces do not require long term workproficiency, but should be "safe." Typical applications for the three habitability categories aregiven in the table below, along with the recommended broadband criteria in ANSl S2.25 in termsof both velocities and accelerations, so either one can be used.

Types ofCategory SpacesBroadband Broadbandrms velocity rms accelerationmm ls (inls) mm/sA2 (inlsA2)

Comfort Cabins, lounges, hospitals < 2.2 (0.09) < 98 (3.8)Some offices a nd shopsWork Workshops, galleys, < 5.0 (0.20) < 220 (8.9)proficiency machinery and control roomsSafety or UnoccupiedHealth spaces

Note - A range of values of 2 to 4 mmls is reasonable for the upper limit of comfort to take intoaccount the environments of various ship types. For example, it is recomm ende d that cruise shipsus e 2 mm/sec for cabins, while for tugboats, other work boats, or military vessels, 4 mm lsec may


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be appropriate. Ship specifications should state this criterion for each ship. Using theserecomm ended limits as a reference, the shipowner could use the individual ship specifications torequire some spaces to have intermediate limits, or to clarify magnitudes for spaces n ot includedin one of the categories above.Velocity weighting is in accordance with the first equation below, and acceleration weighting isgiven in the sec ond equation below.

We ighting function (velocity) = f / 7, 1 Hz < f < 7 Hz= I , >or= 7 HzWeighting function (acceleration) = 1, 1 Hz < f < 7 Hz= 7 / f. f >or= 7 H z

The velocity and acceleration guidelines, with their respective weightings amount to the samething, and reflect the fact that vibration at low frequencies (1 to 7 Hz) are perceived as lesssevere with respect to habitability than higher frequencies. I S 0 8041 (Ref. 2-7) describes otherweighting functions for evaluating human response to vibration that may b e of interest.S2-25 differs from IS 0 6954 in the following respects:

The catego ries are associated with hu man reactions, rather than just the type of space.It has a category for unocc upied spaces (safety) whereas 6954 h as berthing and workingcategories only.It gives definite guidelines rather than a range of values reflecting the vibration"commonly experienced and accepted."It requires that the stern vibration be measured as a referenc e.It uses simp lified weighting functions.It applies to a frequency range of 1 to 100 Hz, whereas 6954 a pplies to 1 to 80 Hz.It has criteria for "Mechanical Suitability" (Equipment survivability) as well as forhabitability. (See Section 2.3.)2.2.3 Data Process ingIf the measured quantity is acceleration, the weighting curve for acceleration can be applied byusing a custom built weighting filter on the acceleration signal before some type of rms levelrecorder. Note that the filter should cut off frequencies below 1 and above 100 Hz, as well asattenuate the signal abov e 7 H z. (Other instrumentation characteristics ma y preclude the need forcutoffs at I nd 100 Hz.) If the measured quantity is velocity, the procedures are the same,except the frequencies below 7 Hz are attenuated.The weighting can also be done with a spectral analyzer by obtaining the spectrum of theacceleration or velocity, multiplying the spectrum by the appropriate weighting curve, andintegrating the area under the spectrum between 1 and 100 Hz. If the weighting functions areapplied while processing the data rather than while recording, many of the same records can beused for evaluating both hum an habitability and mec hanic al suitability.Vertical, athwartship, and fore-aft vibrations should be evaluated separately and each shouldsatisfy the guidelines, a fter applying the necessary we ighting.

2.3 EQUIPMENT SURVIVABILITY (Mechanical S uitab il i ty) GUIDELINES2.3.1 General


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Equipment or machinery to be used on a ship must be designed for the ship's dynamicenvironment, which can be categorized as follows:Low frequency motions evolving from the motion of the ship in the seaway.The vibration of the hull structure on which the equipment is mounted.The vibration where the equipment or instruments are mounted, which may be onmachinery, or on a structure, such as a mast, that might amplify the hull vibration level.

A moving ship responds in a highly complex motion to the forces of waves. The periodic lowfrequency motions of a ship are rolling, pitching, and heaving. Sway, yaw, and surge areunrestrained and therefore not periodic. Roll and pitch are generally objectionable because of thelarge linear motions that they generate at distances remote from the center of gravity of the ship.They may also cause rotating machinery to generate gyroscopic moments. While these motionsare not addressed by the recent ANSl documents, it is sometimes necessary to distinguishbetween vibration and ship motion while evaluating ship vibration measurements.2.3.2 Shake Table Tests vs Shipboard Environment.In ANSl S2.25 the recommended hull vibration level for equipment survivability is based on theshake table tests required by ANSl S2.26 (Ref. 2-8), extrapolated from the testing period to theexpected life of the equipment. That extrapolation requires that the severity of the vibrationenvironment on the ship be correspondingly less than that during the tests. 52.26 requires thatthe equipment be able to perform its normal functions during the shake table tests, and survivewith no damage.The hull vibration criteria assume that major low-frequency propeller or shaft problems, such asunbalance or propeller pitch irregularities are absent, as discussed in the next section.For those areas where equipment is mounted, broadband (1-100 Hz) hull vibration should bebelow about 10.0 mmls rms, with no weighting curve. This is the same as the velocityrequirement for "safety" as identified above, except for the weighting. The criteria for bothhabitability and mechanical suitability must be satisfied, and because most unoccupied spacescontain equipment, this results in a broadband velocity limit of 10.0 mmls in the 1 to 100 Hzrange, with no weighting curve. For occupied spaces, the habitability requirements for "workproficiency" and "comfort" are more restrictive.S2.25 requirements for masts are more severe, as shown in the table:

Hull, Superstructure and Mast Vibration,Equipment Environment Criteria:Broadband (1-100 Hz)Location rms velocityHull and superstructure 10 mmls (0.4 inls)Mast 30 mmls (1.2 inls)

In cases where different environmental vibration magnitudes are appropriate, the owner andbuilder should agree on acceptable criteria. It should be kept in mind, however, that more than 10mmls on the hull or superstructure may indicate a major mechanical deficiency.An analysis that relates shake table amplitudes and equipment survivability vibration levels isgiven as Annex A in S2.25. That analysis indicates that a level of 10 mmls rms for hull vibrationwhere equipment is to be mounted would be acceptable. The analysis makes a number ofassumptions to establish the relationship. If it is felt that a safety factor is warranted because ofthe assumptions, or, for vulnerable equipment, a lesser limit could be used. The shake table


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amplitudes for mast mounted equipment are about three times those required for the hull, so the30 mmls rms limit for mast vibration is also reasonable for most cases.Some equipment is mounted directly on diesel engines or other reciprocating machinery, whichplaces it in a severe environment. ANSl S2.25 has no requirement for the maximum allowablevibration of reciprocating machinery, but ANSl S2.27 (Ref. 2-9) has limits for diesel engineswhich, depending on size, the mounting, and what the engine is driving, vary between 10 and 18mmls rms. As shown in the velocity plot of Figure 2-4 (Section 2.8 on Shake Table Tests), theshake table tests for mast mounted equipment have similar velocity amplitudes as equipmentmounted on reciprocating machinery, but the latter is tested at higher frequencies. Consequently,it is felt that the diesel engine limits will ensure that there is minimal probability of problems withequipment that survives the shake table tests for equipment mounted on reciprocating machinery.S2.27 has no requirements for reciprocating machinery other than diesels, such as compressorsor pumps, but the vibration magnitudes should be about the same or less.Very often equipment is mounted on local structures, and although vibration measurements onlocal structures are not required, measurements are often prudent. In general, the vibrationmagnitudes of local structures should not exceed twice the hull girder vibration magnitude in thesame vicinity. If the natural frequencies of local structures are close to any hull resonances it maybe necessary to modify the local structure to change its natural frequency.2.3.3 Major Propulsion System Problems vs Shipboard Environm ent.Propulsion system components are usually the only items that are massive enough to causesignificant vibratory magnitudes of the hull girder or superstructure. Annex B of S2.25 relates twoof the most likely shaft rate vibration sources to hull vibration magnitudes: propeller unbalance,and pitch variations in the propeller blades. Recommended limits for both sources are used tocalculate the resulting hull vibration magnitudes at hull resonant frequencies of two ships forwhich vibration hull calculations have been performed.Marine propellers normally have a Balance Quality Grade of no worse than G6.3 as defined inIS0 1940/1 (Ref. 2-10). That corresponds to an eccentricity of 0.5 to 0.9 mm for the particularpropellers and hull resonant frequencies of the two ships. Annex B shows that the hull vibrationgenerated by those unbalances are from 0.095 to 0.326 mmls rms.IS0 Recommendation 484-1981 (Ref. 2-11) states that the error in mean pitch per blade shouldbe no more than +I- 1 to 1.5 % for most merchant vessels with large propellers. Relating theworst case, a 1.5% pitch error in one blade to the propeller bearing forces, and then to hullvibration magnitudes of the two ships, gives magnitudes of 0.22 to 0.60 mmls rms. Thesemagnitudes might be greater if more than one blade had that amount of error, but then forces dueto pitch error from different blades would not be in phase.Even adding the two worst cases together, the shaft rate vibration is below 1 mmls, which wouldbe a reasonable expectation for a new ship with no marine growth, etc. A bent shaft or damagedpropeller could easily cause much more severe vibration.Blade frequency vibration magnitudes, at least near the stern, are usually greater than themagnitudes due to pitch error and unbalance, perhaps as much as 3 to 4 mmls rms. Thecombination would still be less than about 5 mmls. Marine growth could cause that to increase,but, at 10 mmls, one would certainly be well advised to check out the source of the vibration,particularly if it is predominately at shaft rate.

2.4 PROPELLER FORCES (Pressure and Bearing Forces)2.4.1 General


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Alternating propeller forces are the result of the propeller operating in a nonuniform wake. Thenonuniformity is caused by a boundary layer along the hull, as it is affected by various obstaclesto the flow before entering the prop eller, such as s kegs, bo ssings, struts, shafts, etc. The flow, ingeneral, is slower in the upper part of the propeller disk since there are more obstacles in thatvicinity. Skeg s also slow the flow in the lower part of the propeller disk. A large part of minimizingpropeller forces involves selecting an afterbody shape and appendages that maintain as muchunformity in the wake as possible.In addition, the interaction of the propeller with the wake is determined by the propellercharacteristics, such as n umber of blades, blade area ratio, rotationa l speed, skew , and pitch.The propeller design proce ss norma lly involves measuring the wake (inflow velocities) of a modelat various points in the propeller disk and resolving the velocities into axial, tangential, and radialcomponents. Most of the axial components, when plotted, show a more or less constant velocityover the 360 degrees of propeller rotation, except for a large dip near 0 degrees (top deadcenter), and, if a skeg is present, another dip near 180 degrees. See Figure 2-1. The axialcomponents are predominant in generating the forces while the radial components have littleeffect. The tangential compon ents are me asured with respect to a rotating blade. In general, nearthe stern the flow has an upward component, resulting in a positive flow with respect to thepropeller direction for half of its rotation, and a n egative flow for the other half.The Fo urier components of all the velocity components ca n be found, and the resu lting forces ona single propeller blade with the anticipated blade geometry can be calculated, also in terms ofthe Fourier components. These forces are added to those of the other blades, resulting in theforces and moments on the whole propeller. Even though the greatest forces on a single bladeare normally first and second-order forces, when all the blade forces are added together to getthe propeller forces, those components add up to zero. The alternating propeller forces areresolved into three forces (thrust, and vertical and horizontal bearing forces) and three moments(torque, and mom ents about the vertical and horizontal axes).For the alternating thrust and torque, only the blade frequency or nth order (no. of blades = n)wake components, and its harmonics, generate any propeller forces. For the vertical andhorizontal bearing forces and the mom ents about the vertical and ho rizontal axes, because of theshaft rotation, only the n-I, n+l, 2n-1, 2n+l, etc. components of the wake generate propellerforces, and those are also at blade frequency and its harmonics. For calculating hull vibrationamplitudes, only the vertical and ho rizontal bearing forces are norm ally used, but other forces andmom ents are very important for propulsion system vibration considerations.The pressure forces generated by the propeller greatly affect the hull vibration. These forces arethe result of the pressure fields that surround the p ropeller blades, an d primarily affect the verticalvibration of the hull because the pressure acts on a mostly horizontal hull bottom. These forcesoccur at blade frequency and its harmonics. The pressure forces are of the same order ofmagnitude as the vertical bearing forces if the propeller is not cavitating. If serious cavitation ispresent, the pres sure forces may be an order of magnitude h igher.More detailed information on prope ller forces can be found in Referen ce 2-12.2.4.2 Computer ProgramsThere are several computer programs that calculate the forces and moments on the propeller,with the input being the wake survey velocities and the geometry of the propeller. Theseprograms have existed for many years and have been used extensively. It should beremembered that these programs assume constant velocities in the wake, whereas, due towaves, rolling, pitching, etc., the velocities actually modulate, causing the propeller forces tomodulate as well. For alternating thrust, as an example, extensive measured data show a crest


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factor (ratio of peak magnitude to rms magnitude) of about 4.0. A lesser set of data shows hullvibration to have a crest factor of about 2.5. These diffferences must be considered whencomparing calculations to measurements and acceptance criteria.

Figure 2-1. Axial and Tangential Wake Velocities for Single Screw Merchant ShipThe development of programs to predict pressure forces is more recent, but they do exist, forcavitating propellers as well as non-cavitating. The results of these programs have not beenextensively compared to measured data. Of course, the objective is usually to have a non-cavitating design.Both bearing forces and pressure forces can be calculated with respect to phase so that, whenfinding the total force exciting the hull, account can be taken as to the extent to which they areadditive.


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2.4.3 Preliminary EstimatesReference 2-13 suggests a simple method of predicting, for preliminary purposes, the propellerforces of a ne w ship design. The estimate of propeller forces (exce pt pressure forces) is based ondata from other, similar ships. To qualify as "similar," a ship should have a similar sternconfiguration with regard to struts, skegs, propeller clearances, and number of screws. It shouldalso have approximately the same block coefficient. Past studies on several ships (Ref. 2-14)have shown that highly skewed propellers can reduce hull vibration levels by about 50%compa red to conventional p ropellers, so the amo unt of skew should be similar also.Whe n us ed to calculate hull vibrations, the results of this preliminary method are multiplied by thefollowing factors:

Hull Pressure Phase TotalShio Tvoe -orce Factor Factor FactorSingle Screw Horizontal 1 1 1Vertical 2 1 2Twin Screw Horizontal 1Vertical 2

The hu ll pressure factor of 2 is applied to the vertical forces since the pressure forces are of thesame order of magnitude as the calculated bearing forces, and it is assumed in the preliminarystages that the two are in phase.The "phase factor" is applied to twin screw ships, and assumes the forces from the two screwsare in phase. Both factors apply to vertical forces of a twin screw ship whe re the total factor is 4.Ref. 2-13 assumes that the results of propeller force calculations are given as single amplitudes,and represent sinusoids. It also suggests the use of a modulation factor (ratio of pe ak to "averagesingle amplitude") of 2 be used for all four forces in the above table. This differs from the crestfactor mentioned above, which uses rms rather than single amplitude. For a modulating sinusoid,the crest factor would be nominally 1.4 times the modulation factor. The hull crest factor of 2.5found from data mentioned above would correspond to a modulation factor of about 1.8. In anycase, if the limiting criterion is expressed in peak vibration mag nitudes, then that factor should beused. However, most of the existing standards, including S2.25, use broadband rms criteria, inwhich case that factor should not be used. Instead, the propeller forces should be expressed asrms quantities (divide single amplitudes b y 1.416 if necessary). Note that the factors above applyto blade frequency forces and harmonics. If engine excited hu ll vibration is also to b e considered,those vibration magnitudes should be add ed before comparing to a broadband criterion.The preliminary estimate suggested by Ref. 2-13 is based on the assumption that, for "similar"ships, the alternating thrust and torque a nd bea ring forces are roughly dependent on the value ofpropeller advance ratio (J) at design speed .

Where: V A = speed of advanc e of p rop relative to the watern = rotational speed of propellerD = diameter of propellerTherefore, the calculated forces (as a percentage of mean thrust) for similar ships can be plottedagainst the various values of J at design speed, and, knowing the J of the new design, the forces


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(as percentages of mean thrust) can be determined from the plot. Ref. 2-13 cites the data forthree ships as sh own in the following table for twin screw nava l ships:Ship # I Ship #2 Ship #3Block Coeff. ,469 589 .480Adv. Ratio 1.08 .839 1.13

Alt. thrust, % mean thrust 1.7 .98 1.79Hor. Force, % mean thrust 1.5 0.32 1.43Vert. force, % mean thrust 1.0 0.42 1 OEven though the block coefficient of Ship #2 is significantly higher than the other two, the data areplotted against the ad vance ratio in Figure 2-2, and if the relationship is valid the points should fallclose to a straight line. Then the percentage forces for a new similar design can be taken from thecurve. The confidence in the m ethod increases according to the nu mber of ships that are includedin the plot, and h ow close the resu lts are to a straight line.

Propeller ForcesVS Advance Ratio

Advance Ratio-0-- Alternating Thrust + orizontal Forces -+ Vertical Forces

Figure 2-2. Alternating Propeller Forces VS Advance Ratio

2.5 DIESEL ENGINE EXCITATION2.5.1 IntroductionThe forces and moments generated by a diesel engine are either internal or external. Internalforces and m oments stress the engine parts, but, if the engine and its foundation are rigid enoughto avoid significant distortion, these forces and moments are not transferred to the foundation orother supporting structure. Consequently, it is not normally necessary to consider these asexcitations to the hull, but it must be a goal in the design process to ensure that such rigidityexists.The external forces include vertical and horizontal forces, and the external moments exist aboutall three axes. The forces and moments occur at engine rotational frequency and variousmultiples of that frequency, and if one of these exciting frequencies coincides with a naturalfrequency of a ship's structure or hull, it could cause a resonant vibration. Forces exciteresonances most efficiently at antinodes of the mode of vibration excited, and moments excite


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resonances most efficiently at the nodes of the mode. A diesel engine also exerts a torsionalexcitation on the shaft, but, at least with a d irect drive, that only affects the rotating comp onents ofthe propulsion system. In a geared drive, the bearing reactions in the reduction gear can betransferred to the foundation of the gear, and again, adequate rigidity of the gear case andfoundation is necessary. Torsional vibration is discussed in Part Ill.Large, low-speed, two-stroke, direct drive diesel engines are the most likely to generate forceslarge enough, and in the frequency range, that could excite structural resonances. The externalforces and moments that the engine generates can be calculated for any engine design, and arenormally prov ided by the engine man ufacturer.2.5.2 lnertia Forceslnertia forces res ult from the rec iprocating motion of the internal parts of the e ngine. For a s inglecylinder engine, the largest inertia force is in line with the p iston motion, opposite in direction, andat the first order. The lower end of the conne cting rod also travels in the horizontal direction (on avertical engine). If the connecting rod were infinitely long, the motion of the piston would besinusoidal. Because the rod is finite in length, second and higher-order vertical forces are alsoproduced. In a two cylinder engine, with the cranks 180 degrees apart, the first-order forcescancel, but the second -order forces add. With four cylinders and the cranks 90 degrees apart, thefirst and second-order vertical forces cancel. This is the normal configuration of a four cylindertwo-stroke engine. A four-stroke engine, however, has two cranks at 0 and two at 180 degrees.This is because firing all four cylinders takes two revolutions, so the firing occurs every 180degrees. This topic gets fairly complicated with various numbers of cylinders, V-engines, andother variables, but the engine manufacturers can provide the forces for each engine. As ageneral rule, most engines will be designed to cancel the first and second-order vertical inertiaforces. In some configurations, such as four-cylinder, four-stroke in-line engines and six-cylinder,two-stroke in-line engines, rotating weights m ay be used to compensa te for otherwise unb alancedforces or moments, as noted below.2.5.3 Inertia Mom ents (Couples)In the above example of a two cylinder engine, we noted that the first-order vertical forces werebalanced when the cranks were 180 degrees apart. Since the two forces are displaced from eachother along the crankshaft, the opposing forces will create a moment or couple about a horizontalaxis, called a pitching couple. Depending on the number of cylinders and whether it is a 2- or 4-stroke engine, the pitching couples may or may not be balanced. Pitching couples can beconverted, wholly or partially into a couple about the vertical axis, or a yawing couple, by addingweights to the crankshaft in addition to those needed to balance the cranks and webs. They arearranged to generate vertical forces that compensate for the pitching moment, but they will haveunbalanced components in the horizontal direction. In general, vertical forces can be counteredwithout generating horizontal forces (or vice versa) by having weights on two shafts spinning inopposite directions, with the order of the correction b eing controlled by the rotational speed of theweights. Similarly, by locating weights near both ends of the engine, out of phase, couples aregenerated which can be used for balancing. Again, the subject is complicated with variousnumbers of cylinders, various V-angles, and different arrangements of compensating weights, sousers should refer to the m anufacturer's data to determ ine the couples for each engine.2.5.4 Firing ForcesThe gas forces in a cylinder peak within a few degrees after top dead center, and then trail offgradually. These forces are far from sinusoidal, and the refore, in addition to providing a firing rateexcitation, will contribute to excitation at harmonics of the firing rate. The expanding gas in acylinder pushes down on the piston, resulting in compression in the connecting rod, and a torqueon the crank, with an opposing force exerted on the crankshaft by the crankshaft bearings. Sincethe connecting rod is at an angle, the piston is forced against the side of the cylinder, or, in a


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at an order equal to half the number of cranks (114 the number of cylinders).14-, 16-, and 20-cylinder, 4-stroke e ngines m ay have mode rate first and second -order pitching, yawing, and rollingcouples.Two-stroke, V-engines have a large first-order pitching couple. Evenly distributed power strokescan be achieved with a 45-degree bank angle in V-8 and V-16 engines, but not in V-12 and V-20engines, although the large number of cylinders and the rigidity of the engine tend to suppressthe net effect.2.5.6 Design ConsiderationsIn the preliminary design stage it may be feasible to select an engine whose major excitationsavoid the lowe r hull natural frequencies. As the design matures, and a more detailed hull model isdeveloped, hull responses can be calculated, and higher hull modes can be considered. Whichorders to examine in the calculations will depend on the orders of major excitation, the hullfrequencies, and the operating speeds.Rolling and racking couples can be restrained by supporting the top of a tall engine withtransverse struts tied in to the ships structure. Direct structural connections sometimes result invery large forces in the struts. Friction connections and hydraulic stays have been used, whichcan reduce the forces, p rovide damping, and provide adjustment to suit a particular situation.Det Norske Veritas (Ref. 2-16) describes a solution to vibration problems caused by first andsecond-order pitching couples exciting a vertical hull mode. A mechanical shaker is placed, noton the engine, which would be near a node of the hull mode shape, but at an antinode of

panel hs-7 vibration.measurement and eval.jan.2004.t-r

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