Gas Turbine Engineering Handbook 2 Episode 13 ppt

In balancing proceduresonly the synchronous vibrations vibration in which the frequency is thesame as the rotor rotating speed are considered.In a real rotor system the amount and locati

done Rotor mass unbalance from dissymmetry, nonhomogeneous material,distortion, and eccentricity can be corrected so that the rotor can run with-out exerting undue forces on the bearing housings In balancing proceduresonly the synchronous vibrations (vibration in which the frequency is thesame as the rotor rotating speed) are considered.

In a real rotor system the amount and location of unbalances cannotalways be found The only way to detect them is with the study of rotorvibration Through careful operation, the amount and the phase angle ofvibration amplitude can be precisely recorded by electronic equipment Therelation between vibration amplitude and its generating force for anuncoupled mass station is

force direction is not the same as the maximum amplitude Thus, for imum benefit, the correction weight must be applied opposite to the forcedirection

max-Figure 17-1 Typical phase lag between force and vibration amplitude chart.

Figure 17-2 Distribution of unbalance in a rotor

The existence of unbalance in a rotor system may be in continuous form

or discrete form, as shown in Figure 17-2 Ascertaining an exact distribution

is an extremely difficult, if not impossible, task by today's techniques.For a perfectly balanced rotor, not only should the center of gravity belocated at the axis of rotation, but also the inertial axis should coincide withthe axis of rotation shown in Figure 17-3 This condition is almost impos-sible to achieve Balancing may be defined as a procedure for adjusting themass distribution of a rotor so that the once-per-revolution vibration motion

of the journals or forces on the bearings is reduced or controlled Balancingfunctions can be separated into two major areas: (1) determining the amountand location of the unbalance and (2) installing a mass or masses equal to

Figure 17-3 Balanced rotor

the unbalance to counteract its effects or removing the mass of the ance exactly at its location.

unbal-Static techniques to determine unbalance can be performed by setting arotor on a set of frictionless supports; the heavy point of the rotor will have

a tendency to roll down Noting the location of this point, the resultantunbalance force can be found, and the rotor can be statically balanced.Static balancing makes the center of gravity of the rotor approach thecenterline of two end supports

Dynamic balancing can be achieved by rotating the rotor either on its ownsupports or on an external stand Unbalance can be detected by studyingrotor vibration with various types of probes or sensors Balancing is thenachieved by placing correction weights in various planes that are perpen-dicular to the rotor axis The weights reduce both the unbalanced forces andunbalanced moments Placing the correction weights in as many planes aspossible minimizes the bending moments along the shaft introduced by theoriginal unbalance and/or the balance correction weights

Flexible rotors are designed to operate at speeds above those ing to their first natural frequencies of transverse vibrations The phaserelation of the maximum amplitude of vibration experiences a significantshift as the rotor operates above a different critical speed Hence, theunbalance in a flexible rotor cannot simply be considered in terms of a forceand moment when the response of the vibration system is in-line (or in-phase) with the generating force (the unbalance) Consequently, thetwo-plane dynamic balancing usually applied to a rigid rotor is inadequate

correspond-to assure the rocorrespond-tor is balanced in its flexible mode

The best balance technique for high-speed flexible rotors is to balancethem not in low-speed machines, but at their rated speed This is not alwayspossible in the shop; therefore, it is often done in the field New facilities arebeing built that can run a rotor in an evacuated chamber at running speeds

in a shop Figure 17-4 shows the evacuation chamber, and Figure 17-5 showsthe control room

High-speed balancing should be considered for one or more of the ing reasons:

follow-1 The actual field rotor operates with characteristic mode shapes nificantly different than those that occur during a standard produc-tion balance

sig-2 Flexible rotor balancing must be performed with the rotor whirlconfiguration approximating the mode in question The operatingspeed(s) is in the vicinity of a major flexible mode resonance (dampedcritical speed) As these two speeds approach one another, a tighter

Figure 17-4 Evacuation chamber for a high-speed balancing rig (Courtesy ofTransamerica Delaval, Inc.)

Figure 17-5 Control room for high-speed balancing rig (Courtesy of TransamericaDelaval, Inc.)

FPO

FPO

balance tolerance will be required Those designs that have a lowrotor-bearing stiffness ratio or bearings in the vicinity of mode nodalpoints are of special concern.

3 The predicted rotor response of an anticipated unbalance distribution

is significant This type of analysis may indicate a sensitive rotorwhich should be balanced at rated speed It will also indicate whichcomponents need to be carefully balanced prior to assembly

4 The available balance planes are far removed from locations ofexpected unbalance and are thus relatively ineffective at the operatingspeed The rule of balancing is to compensate in the planes of unbal-ance when possible A low-speed balance using inappropriate planeshas an adverse effect on the high-speed operation of the rotor Inmany cases, implementation of an incremental low-speed balance asthe rotor is assembled will provide an adequate balance, since com-pensations are being made in the planes of unbalance This is particu-larly effective with designs incorporating solid-rotor construction

5 A very low-production balance tolerance is needed to meet rigorousvibration specifications Vibration levels below those associated with

a standard production-balanced rotor are often best obtained with amultiple-plane balance at the operating speed(s)

6 The rotors on other similar designs have experienced field vibrationproblems Even a well-designed and constructed rotor may experienceexcessive vibrations from improper or ineffective balancing Thissituation can often occur when the rotor has had multiple rebalancesover a long service period and thus contains unknown balance dis-tributions A rotor originally balanced at high speed should not berebalanced at low speed

A wealth of technical literature concerning balancing has been published.Various phases of a variety of balancing procedures have been discussed inthese papers Jackson and Bently discuss in detail the orbital techniques.Bishop and Gladwell, as well as Lindsey, discuss the modal method of balan-cing Thearle, Legrow, and Goodman discuss early forms of influence coeffi-cient balancing The author, Tessarzik, and Badgley have presented improvedforms of the influence coefficient method that provide for the balancing offlexible rotors over a wide speed range and multiple-bending critical speeds.Practical applications of the influence coefficient method to multiplane,multispeed balancing are presented by Badgley and the author The separateproblem of choosing balancing planes is discussed at some length by DenHartog, Kellenberger, and Miwa for the (N ‡ 2)-plane method, and byBishop and Parkinson in the N-plane method

Balancing ProceduresThere are three basic rotor balancing procedures: (1) orbital balancing,(2) modal balancing, and (3) multiplane balancing These methods are sub-ject to certain conditions that determine their effectiveness.

Orbital Balancing

This procedure is based on the observation of the orbital movement of theshaft centerline Three signal pickups are employed, of which two probesmeasure the vibration amplitudes of the rotor in two mutually perpendiculardirections These two signals trace the orbit of the shaft centerline The thirdprobe is used to register the once-per-revolution reference point and is calledthe keyphazor A schematic arrangement of these probes is shown in Figure17-6

The three signals are fed into an oscilloscope as vertical-, horizontal-, andexternal-intensity marker input The keyphazor appears as a bright spot onthe screen In cases where the orbit obtained is completely circular, themaximum amplitude of vibration occurs in the direction of the keyphazor

To estimate the magnitude of the correction mass, a trial-and-error process

is initiated With the rotor perfectly balanced, the orbit finally shrinks to a

Figure 17-6 Typical arrangement for orbit

point In the event of an elliptic orbit, a simple geometric construction allowsfor the establishment of the phase location of the unbalance (force).Through the keyphazor spot, a perpendicular is dropped on the major axis

of the ellipse to intersect its circumcircle as shown in Figure 17-7 Thisintersecting point defines the desired phase angle Correction mass is found

as described earlier It is important to note that for speeds above the firstcritical, the keyphazor will appear opposite the heavy point

In the orbital method, the damping is not taken into account Therefore,

in reality, this method is effective only for very lightly damped systems.Further, as no distinction is made between the deflected mass and thecentrifugal unbalance due to its rotation, the balance weights are mean-ingful only at a particular speed The optimum balancing plane considered

is the plane containing the center of gravity of the rotor system or,alternately, any convenient plane that allows for the orbit to be shrunk

to a spot

Modal Balancing

Modal balancing is based on the fact that a flexible rotor may be balanced

by eliminating the effect of the unbalance distribution in a mode-by-modesequence Typical principal modes of a symmetric, uniform shaft are shown

Figure 17-7 Typical probe positions and the phase angle in an elliptic orbit

in Figure 17-8 The deflections of a rotor at any speed may be represented bythe sum of various modal deflections multiplied by constants dependent onspeed

Thus, a rotor, which has been balanced at all critical speeds, is alsobalanced at any other speed For end-bearing rotors, the recommendedprocedure is: (1) balance the shaft as a rigid body, (2) balance for eachcritical speed in the operating range, and (3) balance out the remainingnoncritical modes as far as possible at the running speed Balance planespicked are the ones wherein the maximum amplitudes of vibration occur.Modal balancing is one of the proven methods for flexible rotor balan-cing Modal balancing has also been applied to problems of dissimilar lateralstiffness, hysteretic whirl, and to complexshaft-bearing problems In manydiscussions on modal balancing fluid-film damping is not included In other

Figure 17-8 Typical principal modes for a symmetric and uniform shaft

instances rolling-element bearing effects are neglected In such cases, thepractical usefulness of the modal method is not fully defined.

Several problems hinder the application of the modal technique to morecomplexsystems To use the technique, calculated information is required

on the mode shapes and natural frequencies of the system to be balanced.The accuracy of the computed results depends on the capabilities of thecomputer program used and on the input data (dimension, coefficients,system model effectiveness) used in the calculations In turbomachinerywhere system damping is significant, as with fluid-film bearings, problemsarise The mode shapes and resonant frequencies of heavily damped systemsoften bear little resemblance to undamped mode shapes and frequencies Thereliance of modal balancing on predicted modes and frequencies is at least aninconvenience and, without proper response programs, can be a significantdisadvantage

At present, no general-purpose modal balancing computer programs existthat are comparable in nature to the programs developed for the influencecoefficient (multiplane) method Such a program would require calculatedmodal amplitudes and phase angles, and that the measured amplitudesand phase angles of the rotor bearing system be balanced The programwould then be run for each separate rotor whirl mode, including the full-speed residual balance correction At present, no general analysis suitablefor programming exists

Multiplane Balancing (Influence Coefficient Method)

Modal balancing came into being to alleviate the problems of thesupercritical rotor unbalance of the steam turbine-generator industry Itcombined the then available techniques for calculating response amplitudesfor the various rotor vibrational modes with the available instruments formeasuring actual installed vibration levels In recent years, more systemshave been designed for supercritical operation Newer types of sensors andinstruments are becoming available, making it feasible to obtain precision

in amplitude and phase measurement Minicomputers for operation on theshop floor or in balancing pits, and time-sharing terminals for in-the-fieldaccess to large computers, are now commonly available The newest multi-plane balancing techniques owe their success to advancement in theseareas

The influence coefficient method is simple to apply, and data are noweasily obtainable Consider a rotor with n discs The method of influencecoefficients provides the means for measuring the compliance characteristics

of the rotor

Let P1, , Pj, , Pn be the forces acting on the shaft Then the

jˆ1

matrixare called the influence coefficients The compliance matrixisobtained by making

varied from 1 to n, each column of the compliance matrixis obtained Oncethe compliance matrixis obtained, knowing the initial vibration level in each

jˆ1

com-puted from the correction forces

In general, 2N sets of amplitude and phase are all that is required by theexact-point speed-balancing method In balancing with the influence coef-ficient method: (1) initial unbalance amplitudes and phases are recorded,(2) trial weights are inserted sequentially at selected locations along therotor, (3) resultant amplitudes and phases are measured at convenientlocations, and (4) required corrective weights are computed and added tothe system Balance planes are obviously where the trial weights areinserted The influence coefficients (or system parameters) can be storedfor future trim balance The method requires no foreknowledge of thesystem dynamic response characteristics (although such knowledge is help-ful in selecting the most effective balance planes, readout locations, andtrial weights)

The influence coefficient method examines relative displacements ratherthan absolute displacements No assumptions about perfect balancingconditions are made Its effectiveness is not influenced by damping, bymotions of the locations at which readings are taken, or by initially bentrotors The least-square technique for data processing is applied to find an

optimum set of correction weights for a rotor that has a range of operatingspeeds.

A number of investigations have concerned themselves with the optimumselections of the number of balancing planes necessary to balance a flexiblerotor To perform an ideal balance on a flexible rotor, as many balancingplanes as unbalances are needed The perfect balance is either impractical oruneconomical Two substitute approaches for deciding the number of bal-ancing planes have been proposed

One is the so-called N-plane approach This approach states that onlyN-planes are necessary for a rotor system running over N critical speeds Theother technique, called the (N ‡ 2)-plane approach, requires two additionalplanes These two additional planes are for the two-bearing system and arenecessary in this school of balancing

The N-plane is based on the concepts of the modal technique FromEquation (17-5), there are N principal modes that need to be zero forthe perfect balance of a rotor, which runs through Nth critical speed Thus,N-planes located at the peaks of the principal modes will be enoughfor cancelling these modes From the point of view of residual forces andmoments at the support bearings, (N ‡ 2)-planes are better than N-planes

If one can balance at design speed, that point is ideal, but there may beproblems while trying to go through the various criticals Thus, it is best to

Figure 17-9 Rotor amplitudes for least-square balance

balance the unit through the entire operation range The number of speeds

to be selected is also very important Tests conducted show that when thepoints were taken at the critical speed and at a point just after the criticalspeed, the best balance results throughout the operating range wereobtained, as seen in Figure 17-9

Application of Balancing TechniquesUsing the influence coefficient technique for multiplane balancing is sim-ply an extension of the logic, which is ``hardwired'' into the standard balan-cing machine This extension has been made possible by the availability ofbetter electronics and easier access to computers

Practical balancing may now be performed in any reasonable number ofplanes at virtually any reasonable number of speeds The one-plane, low-speed balancing operation is perhaps the simplest application of the method,where a known weight at a known radial location (often in the form of waxadded by hand) is used to determine balance sensitivity of the part to bebalanced in a spin-up fixture This procedure can effectively remove anunbalance force from a component Two-plane balancing is simply anextension to permit unbalance moments as well as forces to be removed Inseveral instances, the sensitivities associated with these types of machines can

be predetermined (the machine may be calibrated) and the values stored topermit one-start balancing Balancing a fully assembled rotor operating inits running environment, whether rigid or flexible in nature, represents theultimate application

The balancing process must be in accord with the rotor dynamics,

as specified by the operating environment Unfortunately, the dynamiccharacteristics are often not properly recognized when the balancing proced-ure is specified As a result, the unbalance distribution problem may not beidentified; not enough planes may be provided; sensors may be located atnonoptimum positions, or critical speeds may be overlooked entirely It isthe responsibility of the machinery end user to satisfy himself that themanufacturer has considered:

1 The locations of the critical speeds in the running-speed range for theentire rotor system

2 The mode shapes (problem unbalance distributions) of the rotor atthe criticals

3 The most probable distribution of unbalance in the finally installedrotor, considering manufacturing tolerances, balancing residuals afterlow-speed balance, assembly tolerances, etc

4 The response of the entire rotor-bearing system to this unbalance,considering damping in bearings, joints, dampers, etc.

5 Provisions for eliminating ``unbalance distribution problems'' at eachmanufacturing step, whether by machining, low-speed balancing, orhigh-speed balancing

6 Provisions for future balancing of the final rotor assembly, when and

Design of the production-rotor balancing process begins with an ical optimization process, usually best conducted during system design Anunbalance-response computer program is coupled with a balancing com-puter program to calculate vibration amplitude as a function of unbalance.These programs yield the optimum location of vibration sensors, correctionplanes, and optimum balance speeds Multiplane balancing of the rotorassembly may be done conveniently in a balancing fixture that simulatesdynamically the actual environment in which the rotor will operate A drivemotor is required, and possibly a vacuum system, depending on rotor con-figuration and balancing speed

analyt-It is important that final balancing corrections not be made on anycomponents that are later to be replaced under field operation conditions.Items such as turbine wheels, which are to be replaced as balanced itemsduring field maintenance, obviously cannot be removed and replaced with-out altering the assembly balance if they have been utilized for balancecorrections The balancing process design should therefore also be integratedwith the maintainability design for best results

Once the rotor system has been installed, downtime is the key cost ciated with vibration For example, it is not unusual for lost production costs

asso-to be measured in tens of thousands of dollars per day for a chemical plantcompressor Obviously, shutting down the machine to rebalance the rotor

is a decision not taken lightly The optimum approach is to determine rections while the machine is running, and shutdown only long enough toinstall the trim balance weights The multiplane balancing procedure permits

cor-this procedure to be done with ease after the rotor sensitivities have beenmeasured.

In field balancing (trim balancing), however, rotor speed and systemtemperatures are the key considerations It will often be difficult to controlspeed because of process considerations; system temperatures may requirehours, or even days, to stabilize Vibration should be recorded each time theunit is stopped for trial weight insertion to determine the length of timerequired for thermal stabilization Consideration of critical speed locations,vibratory mode shapes, and the like obtained by a separate rotor dynamicsstudy can also greatly improve the results by providing better guidance tothe best sensor and balancing plane locations

Minimization of the number of startups is an important considerationbecause the number of starts reduces engine life The critical aspect in thisminimization is the correct selection of balance planes at the start of theprocess This selection is essential because the rotor to be balanced oftenconsists of a number of units (turbine, compressor) connected by couplingsand has a great number of available correction planes Usually, balancing isrequired only in one ``zone'' (on the turbine or at the coupling) at a particularspeed The critical location can be pinpointed almost exactly by reference to

a prior analytical unbalance-response sensitivity study Such a study, whichinvolves the entire rotor and couplings, will indicate those planes whereparticular unbalance distributions, if present, will cause vibration at a par-ticular speed For example, a machinery train, consisting of a preciselybalanced compressor with a precisely balanced coupling, will sometimesvibrate excessively at one or more speeds This vibration usually resultsbecause the rotor assembly has one or more bending critical speeds in therunning range where the mode shapes are forced by the residual unbalancesleft in the precision-balanced subassemblies It must be stressed that abalanced rotor subassembly does not have zero unbalance In reality, ithas a residual unbalance distribution, which does not excite the subassemblyunder the balance conditions If an analytical study does not exist, thebalancing engineer must depend on vibration readings from available sen-sors and, ultimately, on judgment or past experience for selection of correc-tion locations

Once the critical zones along the rotor axis have been identified, thesensitivity factors of those planes must be calculated If unbalance sensitivityfactors of those planes must be calculated If unbalance sensitivity factorsare not available for the balance planes and sensors at the speeds of interest,trial weight runs are required Thermal stabilization times become import-ant, since the process can consume significant periods of time If thesensitivities are available, then corrections may be calculated based on

vibration levels measured inservice just before shutdown, and the unit can bebalanced and restarted very rapidly.

It is often tempting to try to shortcut the sensitivity factor gatheringprocess by inserting correction weights in available planes one at a timebased on hunches or one-plane vector plots Occasionally, this shortcut willresult in a balanced rotor; but more often, the opposite result is achieved.This unbalance results because the trial weights in later planes are then notthe only perturbation from the ``as-is'' condition Data Sheets A, B, and Cshow a typical process for field balancing with a computer program thatemploys this balancing technique

The balancing engineer must try to maintain a balance record for eachmachine he balances, since in most cases the machinery system itself willoften contain some nonrepeatable element Components sensitive to thermalvariations, such as dampers and bearing alignments, etc., may often causeproblems When a nonrepeatability is present, the engineer must first deter-mine whether or not another corrective action is indicated If not, then thebalance quality that may be obtained is limited strictly by the range of thenonrepeatable element's variability This level of quality is difficult to ascer-tain without experience, either on the individual machine or on a family ofsimilar machines The balance engineer must balance each rotor by usingmean values for each parameter, and he must keep a detailed record of thedifferent results This record consists, essentially, of residual unbalanceexperience in each case From the standpoint of the multiplane balancingprocedure, the record consists of sensitivity parameters for each machine,which are obtained as a matter of due course in the trial weight procedure

User's Guide for Multiplane BalancingThe following are suggested steps for balancing a rotor using a multiplanebalancing technique The steps are applicable to a specific program; how-ever, other programs will require about the same information:

1 Choose the number of balancing planes and install an equal or greaternumber of proximity probes Install a tachometer that gives a once-per-revolution pulse anywhere on the rotor Feed the tach signal andthe probe signal from one plane at a time into a phase meter toindicate the rotating speed in rpm, the vibration amplitude in peak-to-peak mils, and the phase angle of the maximum amplitude indegrees from the tach pulse

2 Note the number of balancing planes and the balancing speed in rpm

on Data Sheet A Next, rotate the machine at a slow speed (less than

25% of balancing speed), and measure the initial runout amplitudeand phase in each plane Now, rotate the machine at the balancingspeed, and measure the final vibration amplitude and phase in eachplane Record all this data on Data Sheet A.

3 Take a blank Data Sheet B Enter the plane number Place a trialweight at any radius and any angle in that plane Enter these values

on the sheet Now, operate the machine at the balancing speed, andmeasure the vibration amplitude and phase in each plane Repeat theprocedure for each plane (Place only one trial weight in only oneplane at a time.) When finished, you should have as many Data Sheets

B as the number of planes

4 Data Sheet C describes the options available to the user Enter theproper choice for each option

and Phase Before

2 2 4 5

Data Sheet C Options

1 If the same weight as the trial weight is to be used for balancing, then the program will locate radius (NS1 ˆ 1) For computing the weight at a fixed radius NS1 ˆ 2.

NS1 ˆ _

2 Radius at which balancing weights will be placed If NS1 ˆ 2, give the locating

radius in each plane (This is not applicable if NS1 ˆ 1.)

Radius

3 If balancing is to be done to the initial run-out, then NS2 ˆ 1.

If balancing is to be done to zero amplitude, NS2 ˆ 2.

NS2 ˆ _

4 If add-on weights will be used, NS3 ˆ 1.

5 If weights can only be placed or removed at a certain number of evenly spaced

locations, NS4 ˆ 1.

6 If NS4 ˆ 1, then give the number of holes and the angle to the first hole in each plane.

1 2 3 4 5

BibliographyBadgley, R.H., ``Recent Development in Multiplane-Multispeed Balancing

of Flexible Rotors in the United States,'' presented at the Symposium onDynamics of Rotors, IUTAM, Lyngby, Denmark, August 12, 1974

Bently Nevada Corp., ``Balancing Rotating Machinery,'' Report 1970, Minden,Nevada

Bishop, R.E.D., and Parkinson, A.G., ``On the Use of Balancing Machines forFlexible Rotors,'' ASME Paper No 71-Vibr-73

Bishop, R.E.D., and Gladwell, G.M.L., ``The Vibration and Balancing of

an Unbalanced Flexible Rotor,'' Journal of Mechanical Engineering Society,

Den Hartog, J.P., ``The Balancing of Flexible Rotors,'' Air, Space, and Industr.,McGraw-Hill, New York, 1963

East, J.R., ``Turbomachinery Balancing Considerations,'' Proceedings of the20th Turbomachinery Symposium, Texas A&M University, p 209, 1991.Goodman, T.P., ``A Least-Squares Method for Computing Balance Correc-tions,'' ASME Paper No 63-WA-295

February 1971

Kellenberger, W., ``Should a Flexible Rotor be Balanced in N or (N ‡ 2)

Miwa, S., ``Balancing of a Flexible Rotor (3rd Report),'' Bulletin of the ASME,

Stroh C.G., MacKenzie J.R., Rebstock, and Jordan, ``Options for Low Speedand Operating Speed Balancing of Rotating Equipment, Proceedings of the25th Turbomachinery Symposium, Texas A&M University,'' p 253, 1996.Tessarzik, J.M., Badgley, R.H., and Anderson, W.J., ``Flexible Rotor Balancing

by the Exact-Point Speed Influence Coefficient Method,'' Transactions

ASME, Inst of Engineering for Industry, Vol 94, Series B, No 1, p 148,February 1972.

Thearle, E.L., ``Dynamic Balancing of Rotating Machinery in the Field,'' Trans

Couplings and Alignment

Couplings in most turbomachines attach the driver to the driven piece

of machinery High-performance flexible couplings used in turbomachinesmust perform three major functions: (1) efficiently transmit mechanicalpower directly from one shaft to another with constant velocity,(2) com-pensate for misalignment without inducing high stress and with minimumpower loss,and (3) allow for axial movement of either shaft without creatingexcessive thrust on the other

There are three basic types of flexible couplings that satisfy these ments The first type is the mechanical-joint coupling In this coupling,flexibility is accomplished by a sliding and rolling action Mechanical-jointcouplings include gear tooth couplings,chain and sprocket couplings,andslider or Oldham couplings

require-The second type is the resilient-material coupling In resilient-materialcouplings flexibility is a function of flexing of material Resilient-materialcouplings include those that use elastomer in compression (pin and bushing,block,spider,and elastomer-annulus,metal-insert types); elastomer in shear(sandwich type,tire type); steel springs (radial leaf,peripheral coil types);and steel-disc and diaphragm couplings

The third type is the combined mechanical and material couplingswhere flexibility is provided by sliding,or rolling and flexing Combinationcouplings include continuous and interrupted metallic-spring grid couplings,nonmetallic gear couplings,nonmetallic chain couplings,and slider coup-lings that have nonmetallic sliding elements

In choosing a coupling,the loading and speed must be known Figure 18-1shows the relation between coupling type,peripheral velocity coupling size,and speed The loadings in these high-performance flexible couplings are asfollows:

605

1 Centrifugal force Varies in importance,depending on the systemspeed.

2 Steady transmitted torque Smooth nonfluctuating torque in electricmotors,turbines,and a variety of smooth torque-absorbing load(driven) machines

3 Cyclically transmitted torque Pulsating or cyclic torque in ating prime movers and load machines such as reciprocating compres-sors,pumps,and marine propellers

reciproc-4 Additional cyclic torque Caused by machining imperfections of drivecomponents (particularly gearing) and imbalance of rotating drivecomponents

Figure 18-1 Flexible coupling operating spectrum

5 Peak torque, (transience) Caused by starting conditions,momentaryshock,or overload.

6 Impact torque A function of system looseness or backlash Generally,mechanical-joint flexible couplings have inherent backlash

7 Misalignment loads All flexible couplings generate cyclic or steadymoments within themselves when misaligned

8 Sliding velocity A factor in mechanical-joint couplings only

9 Resonant vibration Any of the forced vibration loads,such as cyclic

or misalignment loads,may have a frequency that coincides with anatural frequency of the rotating-shaft system,or any component ofthe complete power plant and its foundation,and may,thus,excitevibration resonance

The gas turbine is a high-speed,high-torque drive and requires that itscoupling have the following characteristics:

1 Low-weight,low-overhung moment

2 High-speed,capacity-acceptable centrifugal stresses

3 High balancing potential

4 Misalignment capability

Table 18-1 Disc, Diaphragm, and Gear Couplings*

Misalignment capacity

(fatigue) Abrupt(fatigue) Progressive(wear) Overhung moment on

Generated moment,misaligned,

Resistance to axial movement

*This table is intended as a rough guide only.

Gear couplings,disc couplings,and diaphragm-type couplings are bestsuited for this type of service Table 18-1 shows some of the major char-acteristics of these types of couplings.

Gear Couplings

A gear coupling consists of two sets of meshing gears Each mesh has aninternal and external gear with the same number of teeth There are twomajor types of gear couplings that are used in turbomachinery The first type

of gear coupling has the male teeth integral with the hub as seen in Figure18-2 In this coupling type the heat generated at the teeth flows in a differentway into the shaft than it does through the sleeve to the surrounding air Thesleeve will therefore heat up and expand more than the hub This expansionplus the centrifugal force acting on the sleeve will cause it to grow rapidlyÐ

lead to a large,unbalanced force Thus,this coupling type is more useful inlow-horsepower units

The second type of coupling,shown in Figure 18-3,has the male teethintegral with the spool In this coupling type the same amount of heat isproduced,but the hollow-bored spool will accept heat in a manner similar tothe sleeve so that no differential growth occurs

Gear couplings have a pilot incorporated into the male tooth form tosupport the loose member of the coupling in a concentric manner at speed,

and expand This relative sliding motion between the coupling elementstakes care of the misalignment problem in gear couplings.

Relative motion between the meshing gears is oscillatory in the axialdirection and has a low amplitude and a relatively high frequency Some

of the major advantages of the gear couplings are:

1 They can transmit more power per pound of steel,or per inch ofdiameter,than any other coupling

2 They are forgiving; they accept errors in installation and mistreatmentmore readily than other types of couplings

3 They are reliable and safe; they do not throw around pieces of metal

or rubber even when they fail,and they can work longer in corrosiveconditions than many other couplings

Figure 18-3 Gear coupling (male teeth integral with the spool)

Figure 18-4 Schematic ofgear used in coupling applications