BALANCEO ESTATICO Y DINAMICO DE MAQUINARIA

8/13/2019 BALANCEO ESTATICO Y DINAMICO DE MAQUINARIA

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Static and Dynamic Balancing

of Rigid Rotorsby Macdara MacCamhaoil

Briiel&Kj^r

Introduction

Unbal ance is the most comm on centrifuga l forces. Thi s is usually done tion (see Fig. 1). An equal mas s, placedsource of vibrat ion in machi nes with by adding compe nsat ing masse s to the at an angle of 180 to the unbala ncedrotat ing part s. It is a very impo rta nt rotor at prescribed locations. It can mass and at the same radius , is re-factor to be consi dered in mod ern ma- also be done by removing fixed qua n- quired to rest ore the cen tre of gravitychine des ign, especially where high tit ies of materi al, for exam ple by drill - to the cen tre of rot ati on. Static Bal-speed and reliability are significant ing. ancing involves resolving primaryconsider ations. Balancing of rotors forces into one plane and adding apr even ts excessive loadi ng of bear in gs Field Balanc ing is the process of correction mass in th at plan e only.and avoids fatigue failure, thus in- balancing a rotor in its own bearings Many rotat ing part s which have mostcreasing the useful life of machinery. and supp ortin g str uctu re, rath er tha n of their mass conce ntrat ed in or very

in a balancing machin e. near one plan e, such as flywheels,This Applica tion Note will demon- grindst ones, car wheels, etc., can be

strate how simple and straight-for- Static Unbalance is defined as the trea ted as stat ic balancing problems .ward it is to bal ance rigid roto rs in situ eccentri city of the centr e of gravi ty of If a rotor has a dia met er of more tha nusing port able Briiel&Kja3r ins tru - a rotor, caused by a poi nt mass at a 7 to 10 tim es its wid th, it is usual lyments . certain radiu s from the centre of rota- tr eat ed as a single-plan e rotor.

Brtiel&Kjaer balancing machines

that accept rotating parts for production-line balancing and laboratory useare described in separate publications.

Basic Theory andDefinitions

Unbalance in a rotor is the resultof an uneven distribution of mass,which causes the rotor to vibrate. Thevibration is produced by the interaction of an unbalanced mass component with the radial acceleration dueto rotation, which together generate acentrifugal force. Since the mass compo nent ro ta te s, th e force also ro ta te sand tries to move the rotor along theline of action of the force. The vibration will be transmitted to the rotor'sbearings, an d any po in t on th e bear in gwill experience this force once per revolution.

Balancing is the process of attempting to improve the mass distribu tion of a rotor, so that it ro ta te s inits bearings without uncompensated Fig. 1. Static unbalance

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Couple (Moment) Unbalance maybe found in a rotor whose di am et er isless than 7 to 10 times its width. In thecase of a cylinder, shown in Fig. 2, it is

possible to have two equal massesplaced symmetrically about th e cent reof gravity, but positioned at 180 fromeach other. The rotor is in static balance, i.e. there is no eccentricity of thecentre of gravity, but when the rotorturns, the two masses cause a shift inthe inertia axis, so that it is no longeraligned with the rotation axis, leadingto strong vibrations in the bearings.The unbalance can only be correctedby taking vibrat ion meas ur em en tswith the rotor turning and adding correction masses in two planes.

The difference between static balance and couple balance is illustrated

in Fig.3. It can be seen that when the Fig. 2. Couple unbalancerotor is stationary, the end masses balance each other. However, when it ro

tates, a strong unbalance is experienced.

Dynamic Unbalance, illustrated inFig. 4, is a combina tion of static an dcouple unbalance and is the most common type of unbalance found in rotors. To correct dynamic unbalance, itis necessary to make vibration measurements while the machine is running and to add balancing masses intwo planes.

Rotors are classified as being either

rigid or flexible. This ApplicationNote is concerned wi th rigid rotorsonly. A rigid rotor is one whose service speed is less than 50% of its firstcritical speed. Above this speed, therotor is said to be flexible. A rigidrotor can be balanced by making corrections in any two arbitrarily selected

i rnr u i A Fig. 3. Static balance, couple unbalanceplanes . I he bal anc ing procedure tor *flexible rotors is more complicated,because of th e elastic def lections ofthe rotor.

Fig. 4. Dynamic unbalance

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Principle of Balancing

A rotor is balanced by placing a correction mass of a certain size in a position where it counteracts the unbalance in the rotor. The size and position. of the correction mass must bedetermined.

The principle of performing fieldba lancing is to make (usual ly te mp orary) alterations to the mass distribution of the rotor, by adding trialmasses, and to measure the resultingph as e an d ma gn it ud e of b ea ring vibra tion. The effects of these trial corrections enable the amount and positionof the required correction mass to bedetermined. The values are usuallycalculated with the aid of a pocketcalculator.

Fig. 5. The basic measurement chain

Any fixed point on the bearing ex

periences th e cen tr ifu gal force due tothe unbalance, once per revolution ofthe rotor. Therefore in a frequencyspectrum of the vibration signal, unba lance is seen as an increase in th evibration at the frequency of rotation.

The vibration due to the unbalanceis measured by means of an acceler-ometer mounted on the bearing housing, see Fig. 5. Th e vibra tio n signal ispassed th ro ug h a fil ter tu ne d to th erotational frequency of the rotor, sothat only the component of the vibra

tion at the rotational frequency ismeasured. The filtered signal ispassed to a vibrat ion meter, which displays th e ma gn it ud e. The in di ca te dvibration level is directly proportionalto the force produced by the unbalanced mass.

The phase meter measures and displays th e ph as e be tween th e signa lfrom the tachometer probe (the reference signal) and the filtered vibrationsignal. The angle displayed by the meter enables us to locate the angularposi tion on th e ro tor of th e un ba la nce,relative to the datum position.

General BalancingProcedure Fig. 6. Frequency spectra of the vibration signal, (upper) before balancing and (lower) after

balancing

Performing a Frequency

AnalysisBefore an at te mpt is made at bal- alignmen t, or a bent shaft. If a rotor is By performing a frequency analysis

ancing, a frequency analysis should be unbala nced, there will be a peak in the before and after balancing, the reduc-carried out to see wheth er it is unbal - vibration level at its r otati onal fre- tion in vibratio n level due to the bal

ance th at is caus ing th e excess vibra- quency and thi s pea k will usually ancing can also be clearly seen (seetion, or some other fault, such as mis- domina te the spec trum. Fig. 6).

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Selecting the Best Measurement

Parameter

A frequency analysis of the vibration signal before balancing alsoguides us in the selection of the bestpa ra me te r for meas ur in g th e vibra tion. The vibration can be measuredin terms of acceleration, velocity, ordispla cement. Fig. 7 shows th e rela

tionship between the three parametersas a function of frequency. The threecurves have different slopes, but thepeaks in th e sp ec tr um occur at th esame frequencies in each case. Thesame information about the vibrationlevels is contained in each curve, butthe way the information is presenteddiffers considerably.

The parameter with the flattestcurve, i.e. the most horizontally Fig.7.Frequency spectra produced using three different measurement parameters: accelera-aligned spectrum is usually selected tion, velocity and displacement. The signal range for each parameter is shown

for vibration measurement. This pa

rameter requires the smallest dynamicrange in the measuring instruments,so the signal-to-noise ratio is higher.

Experience has shown that velocityusually has the flattest curve, so it isthe parameter most often selected.Use of acceleration levels tends to emphasize highe r frequ ency co mp on en ts ,so acceleration is chosen where lowfrequency noise is a problem. Displacemen t, on th e othe r ha nd , ten ds toemphasize the lower frequency compo nent s an d is therefore used to avoidhigh frequency noise.

Determining Balance Quality

Ideally a balanced machine wouldshow no unbalance at all. In practicehowever, due to machining tolerances,per fec t balance can never be achieved .For different types and sizes of machines, the level of vibration regardedas excessive varies considerably: forexample, an acceptable vibration levelin the crankshaft of a motorcar wouldprobably dest roy a record-player. It isimportant therefore to classify the rotor to be balanced according to thelevel of vibration that is acceptable.

Tablet shows a Briiel&Kjaer Unba lance Nomogram, based on ISOStandard 1940. The Nomogram listsQuality Grades and some typical examples of each grade. Once the gradehas been decided, the maximum allowable residual unbalance can be determined, if the rotor service speed isknown. The value obtained is themaximum allowable level of specificunbal ance (in g mm/k g) after balan cing-

Table1. Specific Unbalance (gmm/kg) as a function of Balance Quality Grade and RotorMaximum Service Speed

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The calculation of the maximum allowable residual specific unbalance assumes that the mass of the rotor isevenly distributed about the centre ofgravity. If the mass of the rotor isunevenly distributed, the calculationsare a little more complicated.

In a perfectly balanced rotor, equal

forces act on both ends of the rotorwhen it rotates. If the rotor is shapedas in Fig. 8, however, th e forces at eachend will be equal, but the allowableresidual specific unbalance will be dif-ferent for each bearing. The positionof the centre of gravity divides theroto r in t he rat io V3 :2/3. The sum ofthe moments about the centre of gravity must be zero. Therefore the residu- Fig. 8. A rotor with unevenly distributed mass

al specific unbalance at bearing A is2/3of the total residual specific unbalance, while a t be arin g B it is V3 of th etotal.

Selection of Trial MassesThe specific unbalance is used to

calculate the size of trial masses,which are used during balancing tomake temporary alterations to the

mass distribution of the rotor, to de- Fig. 9, Determining the position of the correction masstermine the relationship between thespecific unbalance and the bearing vi- n ^ . , , , . . 1 . n .i ,. 3. Measu re and record the vibratio n care has been taken with the bai-

level and phase angle. ancing procedu re and proper bairn ,. , ,, n n . , U 1 ancing equi pment , such as th at de-To esti mate the value ol a suitabl e . 0i_ ,. . . , j . -i i li \- r ,

^ . , ,, , ,, , - , 4. htop the machine and moun t a tn - scribed in the section on Instru-tn al mass, th e mas s oi th e rotor in kg , . . . i , ., i i ^ ^ ^ ^

, ^ T i T_- i. 1.x. al mass of suit able size arbi trar ily mentation, has been used, the leveland the radius m mm at which the . n ,. . , . , . , , ., ,

, , i , i in the correction circle, i.e. th e or resi dual vibr ation mea sur ed

corrections are to be made mus t be . . . > . - , ^ ^ i

u n i - i i i ,., ^ i rm n/r o - j i plane where the correction is to be should be small and it should notdet ermi ned. Th e Max im um Kesidual i **- , , r , i ^ ^ , i i i, , ,f i made.Mark the position of the tri- be necessary to repea t the balanc-Mass MMR, in gramme s, is given by: . * ' jal mass. ing proced ure.

S U X MMMR = 5. S tar t up th e machin e an d me as ur e Two-Pl ane (Dynamic) Balancing

Re and record the new vibratio n level The proced ure for two-plan e bal-

whe re and phase angle. ancing is very similar to tha t for single-plane balancing. In this case, how-

S.U. = Specific Unbalan ce re- 6. Stop the machi ne and remove the ever, two accelerome ters mu st bequired (in g mm/kg) ^ ^ mass. used, since measure ments in two

MR = Rotor Mass (kg) planes are required . Unbala nce in one. 7. Calculat e the values of the correc- plane affects the other ; thi s is known

Rc - Correction Radi us (mm) t[Qn m a g s a n d a n g l e r e q u i r e d ? u s i n g a s the cross effect. Before balancing, a

. 1, . 1 . r. one of the met hod s deta iled in the frequency analysi s of both plan es is

A suitable trial mass is five to ten g e c t i o n Q n Calculatim Methods. m a de.times the value of the Maximum Re

sidual Mass. 8 j y j o u n t t n e correction mass at the The steps involved in two-pla ne bal-

Single-Plane (Static) Balancing P 0 s i t l 0 n indi cat ed by th e correc- ancing are as follows:Having made a frequency analysis t l 0 n , a n g ' e : A P o s fv e correction

of the vibration and calculat ed the angle indica tes th at the angle 1. Moun t the accelerome ters and ta-value of a suitable trial mass, the pro- s h o u l d f

b e meas ured m the direc- chometer probe and connect them, r i i u i tion of rotat ion. For a negative cor- to the ins trum ent s.

cedu re for singl e-plane balancin g is as . - ,follows- rection angle, mea sur e agains t th e

direction of rot atio n, see Fig. 9. 2. Run the machine at its norma l op-1. Mou nt an acceleromete r and ta- The correction mass should be erating speed*.

chomete r probe and connect the m moun ted at the same radiu s as theto the instrum ents. trial mass.

* It is preferable, b ut no t in fact nec essary toD3.l9.nc6 s. rotor 9t its scrvicG SDGGCI SP G th.6

2.Ru n the machine at its norm al op- 9. St ar t up the machin e again and sectionSpecial Balancing Casesfor details onerat ing speed* . measure th e res idu al unb alance . If balancing at less than service speed.

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3.Measure and record the vibration I I Av < 25/ I AV> ?50/ I u e s c a n ^ e use


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ba lancing re po rt can be found in Ap pend ix 3. T hi s can be ph otocopied an dfilled in by the user during the balancing operation.

Procedure for BalancingOverhanging Rotors

Figs.11, 12 and 13 show typical examples of overhung rotors. If thelength of the rotor is approximately lhto Vio of its di ame ter (Fig. 11) th ensingle-plane balancing can be performed, making measurements at thebear ing which is most in fluenced bythe trial mass. For other cases, however, it is necessary to use two correctionplanes wi th one of th e following me th ods:

1. Use a single-plane balancing proce

dure twice:

Firstly, carry out the static balancing procedure with the trial mass divided into two equal masses andmounted as shown in Fiff 12 a Mea- Fig. 12. Overhung rotor balanced using a single-plane procedure twice

sure on the bearing which is most influenced by the trial mass. The calculated correction mass should also bedivided into two equal masses.

Secondly, carry out the static balancing procedure again, this time withthe trial masses mounted as a couple,

i.e. the two trial masses mounted inthe two correction planes, but 180from on e ano ther , as i n Fig. 12 b. Th eforces around the centre of gravity ofthe rotor should be equal and in opposite directions. The calculated correction mass should also be made as acouple.

Note that the "trial mass" reauired ^^' ^ ' ^ver^un^ rtr balanced using a two-plane procedure

in the calculator program will be the

sum of the two trial masses used.

2. Perform a two-plan e balanc ing pro- speed. In man y cases it is not possiblecedure using the measur ing planes to run a rotor at full speed during the

and the correction planes as indi- balancing operatio n.cat ed in F ig. 13.

The only consideration necessaryNote that th e tr ia l masses can be when balancing at less than th e service

moun ted as in the normal two-plane speed is the grade of Balance Qualityba lancin g pr oced ur e, i.e. ar bi tr ar il y on requ ir ed . If it is st ip ul at ed that a ro to rthe correction circle. must be balanc ed to a certai n quality

grade then, when balancing the samerotor at less than the service speed,

t the balance quality mus t be increas edS p e c i a l B a l a n c i n g C a s e s correspondingly. Using the example

shown earlier in Table 1, where aBalancing at Less than Service Grad e 6,3 is req uire d at 3000 RP M,Speed the n if the rotor is to be balanc ed at

Fig. 11. Overhung rotor balanced using a It is prefe rable , bu t not in fact nee- only 500 RP M it mu st be bal ance d tosingle-plane procedure essary to bala nce a roto r at its service a Grad e 1.

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Correction Mass and Correction

Radius

It is sometimes impossible to mountthe correction mass at the same radiusas the trial mass, because of the structu re of the rotor, see Fig. 14.

In this case, to correct the unbalance, we use the relation:

_>. m r

where

e = specific unb alancem = unbalance massr - correction radius

M = rotor mass.

This can also be written:

e M = m r

Therefore, Fig. 14. Mounting the correction mass at a radius different from the radius at which the trial__> ..^ _. _> mass was mountedeM = mr = m^r^ = m2r2 =

So, if the radius, r2, at which thecorrection mass is to be mounted, isdifferent from the radius, r1} at whichthe trial mass was mounted, we simplychange the value of the correctionmass, m2, so that the product m r remains constant, i.e. so that:

> >

m2 r2 = m1 rx

Checking Residual Unbalance

After a balancing job has been compl et ed the resi dual un ba la nce sh ou ldbe de te rmin ed . Th is can be done di

rectly using proper balancing equipment, such as that described earlier inthis Application Note. However, in asituation where no adequate equipment is available, a procedure described in ISO Standard 1940 may beused, as follows:

1 Mark out eaual intervals of for ex- ^ ' ^' ^raP^ca^ method of checking for residual unbalance using just a vibration meter

ample 45 on the rotor, see Fig. 15.dal. Otherwise the residual unbal- 7. The position of the residual unbal-

2.Mou nt a tria l mass at the 0 posi- ance is below th e limit of rep rod uc- ance mass (


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Calculation Methods

When suitable test results have beenobtained, the next step is to calculatethe values of the correction mass(es)and angle(s) required. There are twomethods of finding the necessary data:

Calculator and Balancing Program

WW9021The easiest method of calculation is

to use the Bruel&KjaBr balancing program WW9021. The program runs onthe Hewlett-Packard HP41 CV andCX calculators (and discontinued Cversion, with Memory Modules fitted).Using this method, even an inexperienced operator can soon learn to perform the whole calculation in abouttwo minutes. The program providesthe calculations for both single-Diane Fig. 16. Balancing Program WW'9021, for use with the HP41CVand CX ProgrammableCal-

and two-plane balancing. A calculator cu a ors

overlay, supplied with the program,

displays clearly the keys used with theprogram and thei r functions.

The program is supplied on fivemagnetic cards each with two tracks.A sixth card is provided for storingdata using the SAVE function.

The calculation procedure is as follows:

1. Load the calculator with theWW9021 program, see theWW9021 Instruction Manual forloading instructions.

2.Select [1-P LANE] or [2-PLAN E]balanci ng.

3. Key in the data as prompted by thecalculator display, e.g. A10 = amplitude me asured in plane 1 with notrial mass; L2\ = phase angle measured in plane 2 with trial massmounted in plane 1. The order inwhich the items of data are requested follows the numbering system in the Bruel&Kjaer BalancingReport. After each value has been

keyed in, [DATA ENTER] is Pig- 17-Vectorial representation of the vibration levels: (a & b) measured values, (c, d & e)pressed calculated values

4.When all the e ntri es have beenmade, the calculator carries out a Other functions of the WW 9021 can only be made at certain perm itt edset of calc ulat ions for up to 30 sec- prog ram allow for cases where tri al locati ons; see the exam ple at the endonds and the n a "beep " is sounded. corrections are perm anen t, e.g. where of this section.

trial masses are welded on, or material5.The calculated correction masses is drilled from the rotor; see the Vector Dia gram Calculations

and angles are the n displayed re- WW90 21 Inst ructi on Manu al for de-pea tedly , for a few seconds at a ta il s. (a) Single-Plane Balancing

time, until the calculator is The values of the correction massswitched off. Th e [RESOL] facility enabl es cor- and angle can be det erm ine d by repr e-

rection masses to be resolved into sep- senting the measur emen ts vectorially,

arat e component s, where corrections as shown in Fig. 17:

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1.Avector* V0 isdrawn representing rotor indicating th e point where With the Balancing Program, thethe initial unbalance. The length of the trial ma ss was mounte d.If it is procedure is as follows:V0 isequal to thevibration ampli- a positive angle it is measured intude and its direction is given by the direction of rotation. A nega- Press [RESOL]. Thefollowing dat athe phase angle. tive angle ismeasured in theoppo- are then requested in turn:

site sense.

2.Another vector V] is drawn repre- CRM:Requir ed correction mass; 2gsenting the amplitude and phase Example One, in Appendix 1 is a in our example;measured with th e trial mass worked example of th e use of this ^

mounted. method forcalculating thecorrections

CRL: R e ^ e d

correction angle i measured trom one ot the permittedXt^ ULJ.1X c Ll * , , y \ rt *

3.Th e tipB of vectors V0 and V, are ZTllOO^- WY " ^ " "joined by means of a third vector (b) Two-Plane Balancing ^ ' 'VT, which is^marked sothat itindi- RESL: The angle between the twocates the V0 to Vs direction, as The correction masses an dtheir po- permitt ed positions; in this case, 72.shown. This vector represents the sitions can be found using a methodeffect of the tria l mass alone. similar to that used in thesingle-plane The calculator t hen ca lculates and

case, but the calculations are rather displays, in sequence, th e resolved4.A vector is drawn parallel to the complicated, so the pocket calculator masses atposition zero {MLO)and the

vector VT,with thesame amplitu de is usually used. Example Two in Ap- other permitt ed position (MLRES).and direction, bu t starting atjthe pendix 1 is a worked example of the For the given example, th e calculatororigin. This vector isalso called VT. use of this method. returns th e following infor mation:

>

5.Th e vector V0 is continued A Ma ss Resolution Exampl e: Bal- MLO

=l,5g ML_72

=l,0g.through th eorigin, in theopposite anci ng a Fandirection to V0. This vector is Fig. 18 shows an example of a five- This indica tes th at l, 5g of the 2g cor-calledV(_

:OMP a n d it represents th e bladed fan, where mass corrections rection mass should be mounted on

posi tion an d magnitude of the can only be made on the blades, i.e. the 72 blade, and the o the r 1,0 gmass required to counteract th e there are only five perm itt ed correc- should bemounted on the 144 blade.original unbal ance. tion positions, with an angle of 72

be tween pe rm itt ed posi tions. If, as a6.Ifwe assume that the amplitude of result of a balancing job, the correc-

the vibration isproportional to the tion mass is found to be 2g and theunbalance mass, we get the rela- correction angle 100, it seems impos- T n Q f r n T n p n t a f i n n "Pnrtion: sible to mount the correction mass.

The solution is todividet hecorrection BalancingMr Mrf)MP M() mass between the blades at 72 and

- y = = r~ 144. Some of the instru ments availableVT VCOMP VQ for balancing have been specially de-This can bedone using avector dia- signed for this purpose, while others

=>M('OMP - g

r am>but it is more easily done using are vibration measuring or analysing

y an HP41C calculator and WW9021 instr uments which can alsobeusedforM() = x MT Balancing Progr am. balancing.

VT

This expression enables us to findthe valueofMC0MP, th ecompensating mass.

7. The position of the mass relativetothe position of the trial mass canbe de te rm in ed from th e vector dia

gram using a protractor, or can befound from the expression:

U:OMP ~ - LT + Lo + 180

The angle calculated is measuredfrom th e position marked on the

* Strictly sp eaking this is a phasor and not avector, since we aredealing with a "vector"inthe complex plane, with real and imaginarycomponents.In the worldofbalancing, however, the convention is to refer to the graphicrepresentation of theunbalance as a "vectordiagram", and not a "phasor diagram". Theuse of terms such as "unbalance vector" conforms to ISOstand ard 1925 onbalancing. Fig. 18. Dividing a correction mass into two components for mounting on afive-blade fan

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Fig. 19. To the left, the Vibration Analyzer Type 25,5. To the right, balancing a 275 MW turbo-generator set at Kyndby^rket power station

When choosing an instrumentforbalancing, it isimportant to lookatthe other things it can do. Likewise,when selecting equipment for generalvibration measurement or machinecondition monitoring, it isimportantto consider whether itcan be ada pte deasily for balancing.

Briiel & Kjser offers thr ee ins tru ments suitable for balancing rotorsinsitu. They are the Type 2515 VibrationAnalyzer, and theTypes 3517and3537 Balancing Sets.

Pig. 20. Single-plane balancing with the Type 2515 Vibration Analyzer

Vibration Analyzer Type 2515

TT h e

9 P r ^1 ' Vib ft ion Analyzer plane balancing, two fortwo-plane) machine runni ng speed can beseen

liiiil' ;g- 'is drgned frbo th andconnectingcabiesAO

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the tachoprobe and controls the external sampling of the analyzer. If themachine speed changes, the analyzersampling frequency will change propor tiona lly so that th e peak at th e rotational frequency always remains atthe same line on the screen.

Another useful feature of the 2515 isits facility for storing, retrieving andcomparing spectra. The vibrationspectra for before and after balancingshould be stored in memory, so thatthe reduction in vibration due to balancing can be seen. Also the spectra ofthe balanced and unbalanced machinecan be directly compared using theMEMORY "Compare" function. Fig. 22. Signal paths in the Type 3517 Balancing Set

Field Balancing Set Type 3517

The portable Balancing Set Type3517, Fig.21 , is an ideal tool for field

ba lancing of r otors. The se t is su pp li ed

in a hard-foam carrying-case, togetherwith built-in rechargeable batteries.

The set consists of a Type 2511 Vibrat io n Me te r an d a Ty pe 1621 Tunable Band Pass Filter (which togethercomprise the Type 3513 Vibration Analyzer) plus a Type 2976 Phase Indicator. As well as for balancing, the 3517can be employed for the same widerange of vibration analysis functionsas the 3513, and therefore forms a veryuseful dual-purpose analysis tool.

Two Type 4370 Piezoelectric Accel-erometers are supplied with the set,together with a Photoelectric Tachometer Probe MM0 012 and connection _ OQ _ , 7 , . . , , ^ ri^ , .

, , tig. 23. 1wo-plane balancing with the lype 3517 Balancing Set

Fig. 22 shows how the 3517 o pera tes .The vibration signal from one of the

Fig.24. To the left, the Balancing Set Type 3537.To the right, balancing a Alfa-Laval NX 418 decanter centrifuge

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accelerometers is chosen using the"Ch.l/Ch.2" CHA NNE L SELE CTORswitch. This signal is amplified andpassed thr ou gh th e filter, which istuned to the rotational frequency ofthe rotor. The level of vibration is displayed by th e vibrat ion meter. Th eph as e in dica tor co mpar es th e signalfrom the tachoprobe with the filtered

accelerometer signal and displays thephase be tween th em . Th e eq ui pm en tset -up is shown in Fig. 23.

Field Balancing Set Type 3537

The Field Balancing Set Type 3537,shown in Fig. 24, is similar to the Type3517. The princip al difference be- _ 0_ c . , . . . rp __ D , . c ,,., . ,, , , . r 1 1 tig.zb. Signal paths in the lype 3oo/ Balancing Settween the two is the tracking filter,incorporated into the Type 3537. The3537 is ideal for applications where anarrowband tracking filter is necessary, e.g. when balancin g at f luct uati ng

speeds, or to suppress vibrations fromother sources. Automatic frequencyanalyses up to 2kHz are also possibl ewith the set.

The set consists of a Type 2635 Preamplifier, a Type 2433 Indicator Unit,a Type 1626 Tracking Filter, and aType 2976 Phase Indicator. Two Type4370 Piezoelectric Accelerometers, anMM 0024 Photoe lectr ic Tachopr obeand connecting cables complete theset. The set is supplied in a carryingcase, together with rechargeable batteries. p^ 26. Two-plane balancing with the Type 3537 Balancing Set

Fig. 25 shows a simplifi ed block d iagram of the signal paths in the 3537,and Fig. 26 the e quip ment set up. T hetachoprobe provides one pulse per revolution of the rotor. The filter is thenautomatically and continuously ad

ju st ed so tha t it is always cor rectlytuned to the rotational frequency ofthe rotor. The automatic tuning meansthat the 3537 can give stable phasereadings, even when there are smallfluctuations in rotor speed.

Three filter bandwidths are available: 0,1 Hz ( up to 20 Hz), 1 Hz (20 to Fig. 27. Using a stroboscope to measure phase angles200Hz), and 10Hz (200Hz to 2kHz).However, if required, it is possible toselect any of thes e filter band widt hs displayed on the Indic ator Unit. The The vibra tion level is meas ured us-over the entire frequency range. Thi s Pha se Indicat or measu res and dis- ing a Type 3513 Porta ble Vibrationis a useful feature when, for exam ple, plays th e phase between the pulse sig- Analyzer, which consi sts of a 2511 Vi-there is anot her peak in the spec trum nal from the tacho probe and the fil- brati on Meter a nd a 1621 Tuna bleclose to the rota tiona l frequency of the tered vibrati on signal. Band Pass Filter.rotor and it is necessary to measurethe amplitude of one of these peaks. Usi ng a Strobosco pe to Mea sur e Inst ead of using a Pha se Indica tor

Phase Angles to meas ure the phas e, a Type 4912The vibrat ion signal from one of the The alte rnati ve ins tru men tat ion Portab le Stroboscope is employed. A

acce lero mete rs is amplif ied an d fil- shown in Fig. 27 can be used for bal- scale gr adu ated in angu lar uni ts is

tered , and the level of the signal com- ancing, where proper balancing equip- tap ed or mark ed on the rotor. T hepo ne nt at th e ro ta ti on al frequency is men t is no t available. scale is il lu mi na te d du ri ng tr ia l ba l-

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ancing runs with the light from thestroboscope, which is triggered by thefiltered vibration signal. The phase ofthe vibration signal is then simplyread from the scale.

Portable Level Recorder Type

2317

The three instruments described

above can all be used with the Portable Level Recorder Ty pe 2317 to pro- P . 0 0 r , ,, ~ ___ , ++ , T . . rtoi^

, . , y \ , (. rig. 28. brequency spectrum from the lype 251 a plotted on a Level Recorder Type 2317duce a hard copy ol the irequencyspectrum. The 2317 is a handy, complete ly se lf -conta ined level recorderdesigned for field use. Rechargeableba tt er ie s an d an (op tiona l) le athe r car - th e probe. An LED on top of th e probe to hav e decreased to 1,8 mm /s , whi lerying-case make it truly porta ble. flashes to indicat e triggering. the phase angle had changed to +4 2 .

With the Balanci ng Sets Types 3517 The MM 0012 probe is supplied The position and magn itud e of theand 3537, the Level Recorder is used with the 3517 Balanci ng Set, while the compens ating m ass were det ermin edto obta in a pic tur e of th e frequency MM 0024 is sup pli ed with the 3537 from the vector diagr am shown inspec trum, which can be used for fault Balancing Set. All thre e ins trum ent s, Fig. 30.diagnos is. Spe ctr a of th e machin e vi- the 3517, the 3537 and the 2515, can

br at io n before an d aft er ba lancing can use ei ther probe for tr igger ing. Th e original unba la nce is given by:be produced so tha t th e reduct io n in yvibration due to the balancing can be M() = x MT

clearly seen. Appendix 1: Worked Vr

The Vibration Analyzer Type 2515 E x a m p l e s = ~^- x 2displays a spec trum for imme diat e 'fault diagnosis, but the Level Recorder Exampl e One: = 2,03 g.is very useful if a hard copy is re- To balance a rotor statically using thequired. An example of a hard-copy equipment shown in Fig.29. So the compen satin g massfrom the 2515/2317 is shown in Fig. 28,note how the 2515 mea sur eme nt set- Mea sure ment of peak- to-pe ak vi- MC0MP = 2,03 gup is also given on the hard-co py re- bra tio n velocity level was selected oncording. the Vibration Meter, and a band wid th and its position is given by

of 3% on the Band Pass Filter. ThePhotoelectric Probes Types machine was run up to its norma l op- ^COMP - -LT + L0 + 180MM0012 and MM0024 erating speed, 1490 r/mi n, after which

One final note on ins tru men tat ion the Band Pass Filter centr e frequency = -3 27 + 116 + 180concerns photoele ctric tach omet er was adjuste d to the rota tion frequency.probes . Bri iel&Kjaer offers two probes A vibrat io n level of 3,4 mm /s was re- = -31 referred to th e po-for use with balancing equi pment . corded, and when the band widt h was sition of the trial mass .Both probes are of the non-c ontac t broadene d to 23 %, the Pha se Metertype and they function by projecting a indica ted +11 6. As the angle indic ated is negative,beam of in fra-red light at th e rotor th e co mpen sa ti ng ma ss is to be fas-surface an d genera ting an electrical The machi ne was stoppe d, and a 2g tene d at an angle of 31 from the posi-signal related to the proport ion of trial mass was fixed to it. When the tion where the trial mass was moun t-light reflected back. Triggering is indi- machine was run up to speed again, ed, meas ured in the opposite directio ncated by a periodic change in the value the vibr ation velocity level was found to the dire ction of rot ati on.of this signal.

The M M 0012 has an operat ing distan ce of betwe en 1 and 20 mm fromthe rotor. The probe is triggered by acontrast mark on the rotor. The circumference of the rotor, in the planewhere the probe is to be mounted, isfirst covered by a band of matt blacktape or paint.

The MM 0024 probe has an operat-ing dist ance of 50 to 800 mm from therotor. A matt black background is notnecessary, as the probe is triggered

only by special, hexagonally patternedreflective tape QA0137, supplied with Fig. 29. Instrument set-up for Example One

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Example Two:

Performing two-plane (dynamic) bal

ancing on a machine that has a rigid

rotor supported in two bearings.

The equipment was set up as shownin Fig.31 . A WB0968 Channel Selector was employed to enable switchingbe tween th e two me as ur em en t pl an es .

To avoid special emphasis of high orlow frequency components, vibrationvelocity was chosen as the measurement parameter. Using the Y-UNITSbu tt on , th e veloci ty un it s were se t tom/s.

The machine was run up to its normal service speed and, with the cursorposi tioned at th e ro ta ti on al sp eed ofthe rotor, the initial vibration level forpl ane 1 was read from th e disp layscreen and noted in the Balancing Re

port . Pu sh in g th e "P ha se " bu tt on , th eP h a s e was read from the screen, andits value was noted.

Choosing channel 2 on the ChannelSelector, the initial vibration level andph as e were meas ur ed an d recorded , inthe same way, for plane 2. The valuesrecorded are shown in Table 3.

The machine was stopped and a2,5g trial mass was mounted at a suitable position in plane 1, and its position marked. The level and phasemeasurements for both planes were Fig. 30. Vectordiagram for Example One

repeated and the data recorded.

The machine was stopped and thesame 2,5 g trial mass wa s at tach ed toplane 2 an d it s posi tion mark ed . Themeasurement and data recording procedure was repeated.

Using the dat a show n in Ta ble 3,the masses and angles required to balance the rotor were calculated, usingtwo different methods: firstly bymeans of an HP41CV calculator andWW9021 Balancing Program, andsecondly, using the vector diagrammethod.

The calculator ret urne d the follow- _. OT T t + + , . . . , . rig. ol. Instrument set-up for Example 1 wo

ing values tor the correction massesand angles:

P l a n e 1 : 1 I Trial Mass I

= Measured Effect of Triaf Mass3,0 g at an angle of 50,2 from th e 1posi tion of th e tr ia l mass , me as ur ed Size and Location Plane1 Plane 2

in the dire ction of rot ati on, i.e. None 7,2mm/s 238 V1i0 13,5mm/s 296 V20+ 5 0

'2

- 2,5g Plane1 4,9mm/s 114 V^ 9,2mm/s 347 V2i1

2,5gP lane 2 4,0mm/s 79 V1i2 12,0mm/s 292 V22T01940GBO

Table3. Measured vibration levels and phase angles for Example Two

16

Trial Mass

Size and Location

Measured Effect of Triai MassTrial Mass

Size and Location Phane 1 Plane 2

None 7,2mm/s 238 v 1 i0 13,5mm/s 296 V2|0

2,5 g Plane 1 4,9mm/s 114 V1.1 9,2mm/s 347 V2l i

2,5g Plane 2 4,0 mm/ s 79 v 1 i2 12,0mm/s 292 v 2 ,2T01940GBO


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Fig. 32. Vectorial representation of the vibration levels

Pla ne 2: In vector notat ion: V]2- VL0 is the effect in Plane 1 off ?

2,8g at anangle of81,9 from the atrial mass moun ted in Plane2.posi tion of th e tr ia l mass , me as ur ed Vlj0 isthe original unbala nce mea- _> _^against the direct ion of rota tion , i.e. sured in Plane 1. V2tl- V20 is the effect in Plane 2 of- 81,9. atrial mass mou nted in Plane1.

V2io isthe original unbalan ce mea- _^Using the vector diagram meth od to sured in Plan e 2. V2>2 ~ ^.o is the effect in Plane 2 of

calculate the correction masses and _^ _^ atrial mass mou nted in Plane2.angles, the first step was to represent V u- VUI is the effect in Plane 1 of

the measured vibration levels in vector atrial mass mou nted in Plane1.diagram form, see Fig. 32.

Mathematically, the problem was to find two vector operators Q} (with vector length Q, and phase angley^ an d Q2 (withvector length Q2 and phase angle y2), which satisfy th e following equa tio ns:

Q, ( v u - v l i 0 ) +Q2( Vlt2-VI)0) = -Vi,o (i)Qi (V2A - V2>0) + Q2 (V2:1- V2i0) =-V2,o (2)

- V 1 , o - Q 2 (V 1 . 2 - V 1 ,)Writing Q{ in terms of Q2in Equ at io n (1), we get: Qx= (3)

^1,1 _

^1,0

Substituting for Q^ in Equati on (2), and writin g itall in te rms of Q2:

v , , o ( v u - y 1 , 0 ) - v 1 , o ( v 2 , 1 - y 2 ,o)Q2 = (4)

(Vu-V2t0)(Vli2-Vlfi){V2i2-V2t0)(Vltl-VUQ)

The measured values ofvibra tion level and phas e angle are the polar coordinates^for the vector qua ntit y V. WhenaCartesian system of coordinates is used, with real and imaginary components, where V = a +jb amat hema tic al solut ion forEquations (3) and (4) can be calculated.

Polar coordinates are converted to Cartesian coordinates by means of the two equations:

a =Vcosy,a nd b=Vsiny

Converting to Polar coordinates, the values in Table 4 (shown overleaf) can be calculated, for example:

V u - V1(0 = (-2,0 + 4,48;)- (-3,82- 6,1 2; ) = ( + 1,82+10,6; )

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y 1 y I ~ I ~ 1 fo 1 The balancing masses require d to _ co un te ract th e original unba la nce are

Vli0 7,2 238 -3,82 -6.12J a s f o l l o w g .V u 4,9 114 -2,0 +4,48j

V1> 2 4,0 79 +0,76 +3,93j pl an e 1:

V2.0 13,5 296 +5,92 -12, 13j MC0MP = 1,1 72 X 2, 5g

V2i1 9,2 347 +8,96 -2,07j (2,5g being th e tr ia l mas s)

V22 12,0 292 +4,5 -11,13j = 2,93 g at + 50,4.

(Vn-V1 0) +1,82 +10,60j

v ' J f be 1,8mm/s, with 2,2mm/s at Plane 2.

( + 1,82 + 10,6 ;) These results illus trate the importance of the really accurate phase an-

, . , . ,-,. , r, , nnAro , n r i n 0 o - g^e determination possible with

which simplifies to: Q, = +0, 746 8 + 0,9033i f, .. ,0 T r . \_Bruel&Kjser equipment.

Converting to polar coordinates Qx = 1,1720, y1 = +50,4

18

V V 7 a jb

v l i 0 7,2 238 -3,82 -6,12j

Vi.i 4,9 114 -2,0 +4,48j

v1>2 4,0 79 + 0,76 +3,93j

V2.0 13,5 296 + 5,92 -12.13J

V2l i 9,2 347 + 8,96 -2,07j

v 2 , 2 12,0 292 +4,5 -11.13J

( V L I - V ^ Q ) + 1,82 + 10,60j

(v2,-v2,0) +3,04 + 10,06j(V1l2-V1i0) +4,58 +10,05j

(V2,2-V2,0) -1, 42 + 1,00j


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Appendix 2: Fault Tracing

This appe ndix lists possible faults (c) It may be necessary to mask lize before mea sur emen ts areencoun tered when balancing and sug- the tacho probe from extern al made.gests remedies . light sources.

(b) The presence of more than1. If th e tachop rob e is trigge ring (d) If still no trigge ring, check th e one mar k on the rotor. Check

proper ly, th e yellow "Tr igger Lev- ba tt er ie s in th e in st ru me nt s. th e reflection mark .el" lamp of the Type 2976 Phase

Indica tor or the red "Trig' d" LE D 2. If the tachoprob e is triggering (c) The photoelec tric probe isof th e 2515 Vibr ation Analyze r properly, but the disp lay of the picking up reflec tions fromshoul d be lit (or flashin g, if the 2976 indi cat es "E " for "Er ror" or flickering light sources. Tryrotor is rota ting slowly). An LE D is blank, or the 2515 display shows moving the probe to anoth eron top of the MM 0024 Photoe lec- N. A. DEG as a P h a s e reading , position.trie Probe should flash to indic ate or the phase readin g on either in-triggering. If the tachop robe is not str ume nt is not steady within 2, (d) The photoel ectric probe is vi-trigger ing properly, th en th e fol- the n the error is proba bly due to bra tin g at a level above itslowing shou ld be checked: one or more of the following prob - limi t. Remove it from the vi-

lems: brat ing body or stiffen the(a) The orient ation of the tachoprobe suppo rt.

probe. (a) Er ra ti c ro tor speed va ri at io ns .Check the rotor speed and en- (e) The unbal ance compo nent of

(b) Th at the correct tacho cable sure th at sufficient time is al- the vibratio n is insufficient

AO0158 has been used. lowed for the speed to stabi- for read ings to be mad e.

Acknowledgements

Much of the mater ial in this Appli- mater ial on balancing prep are d bycation Note is based on Briiel&Kjser Aage Courrech-N ielsen and Caitrion ainter nal lite ratu re, in parti cula r course Ni Aonghusa.

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BALANCEO ESTATICO Y DINAMICO DE MAQUINARIA

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