Rootori tasakaalustamine: staatiline ja dünaamiline tasakaalustamatus, resonants ja praktiline protseduur
Selles juhendis selgitatakse rootori tasakaalustamine jaoks jäigad rootorid: what “unbalance” means, how static and dynamic unbalance differ, why resonance and non-linearity can prevent a quality result, and how balancing is typically performed in one or two correction planes.
Sisukord
- Mis on rootor ja mida tasakaalustamine korrigeerib?
- Rootorite tüübid ja dünaamilise tasakaalustamatuse tüübid
- Mehhanismide vibratsioon: mida tasakaalustamine suudab eemaldada ja mida mitte
- Resonants: tegur, mis takistab tasakaalustamist
- Lineaarsed vs. mittelineaarsed mudelid: millal arvutused enam ei tööta
- Tasakaalustusseadmed ja tasakaalustusmasinad
- Jäikade rootorite tasakaalustamine (praktilised märkused)
- Dünaamilise tasakaalustamise teostamine (kolme käivitusega meetod)
- Tasakaalustamise kvaliteedi hindamise kriteeriumid
- Standardid ja viited
- KKK
Mis on rootor ja mida tasakaalustamine korrigeerib?
Rootor on keha, mis pöörleb ümber mingi telje ja mida hoiavad toetuspinnad. Rootori laagripinnad edastavad koormusi tugedele veerelaagrite või liuglaagrite kaudu. Laagripinnad on kandepinnad või neid asendavad pinnad.
Ideaalselt tasakaalustatud rootoris on selle mass jaotatud pöörlemistelje suhtes sümmeetriliselt, st iga rootori elementi saab sobitada teise elemendiga, mis asub pöörlemistelje suhtes sümmeetriliselt. Tasakaalustatud rootoris on mis tahes rootorielemendile mõjuv tsentrifugaaljõud tasakaalustatud sümmeetrilisele elemendile mõjuva tsentrifugaaljõuga. Näiteks elementidele 1 ja 2 (joonisel 1 rohelisega tähistatud) mõjuvad võrdse suurusega ja vastupidise suunaga tsentrifugaaljõud F1 ja F2. See kehtib kõigi sümmeetriliste rootorielementide kohta ja seega on rootorile mõjuv kogutsentrifugaaljõud 0 ja rootor on tasakaalus.
Aga kui rootori sümmeetria on rikutud (asümmeetriline element on joonisel 1 märgitud punase värviga), siis mõjub rootorile tasakaalustamata tsentrifugaaljõud F3. Pöörlemise ajal muudab see jõud suunda koos rootori pöörlemisega. Sellest jõust tulenev dünaamiline koormus kandub laagritele, põhjustades kiirenenud kulumist.
In addition, under the influence of this variable-direction force there is a cyclic deformation of supports and foundation, on which the rotor is fixed, i.e. there is vibration. In order to eliminate rotor unbalance and the accompanying vibration, balancing masses must be installed to restore symmetry to the rotor.
Rotor balancing is an operation to correct unbalance by adding balancing masses. In other words, the goal of balancing is to bring the principal central axis of inertia of the rotor as close as possible to its axis of rotation, so that the residual unbalance falls within specified limits.
Tasakaalustamise ülesanne on leida ühe või mitme tasakaalustava massi suurus ja asukoht (nurk).
Rootorite tüübid ja dünaamilise tasakaalustamatuse tüübid
Arvestades rootori materjali tugevust ja sellele mõjuvate tsentrifugaaljõudude suurust, saab rootorid jagada kahte tüüpi - jäigad rootorid ja painduvad rootorid.
Jäigad rootorid deformeeruvad töörežiimidel tsentrifugaaljõu mõjul vähe ja selle deformatsiooni mõju arvutustes võib tähelepanuta jätta.
Deformation of flexible rotors can no longer be neglected. Deformation of flexible rotors complicates the solution of balancing problem and requires application of other mathematical models in comparison with the problem of balancing of rigid rotors. It should be noted that the same rotor at low speeds can behave as rigid, and at high speeds - as flexible. The practical criterion is the service speed relative to the rotor’s first critical (bending) speed: a rotor is treated as rigid — ISO 21940-11 speaks of a rotor with “rigid behaviour” — when it runs well below that speed, in practice below roughly 50–70% of the first critical speed. Above that, the rotor bends into a mode shape that changes with speed: it is flexible and must be balanced by modal or multi-plane methods (ISO 21940-12). In the following, we will consider only the balancing of rigid rotors.
Depending on how the unbalanced masses are distributed along the rotor, ISO 21940-2 distinguishes several states of unbalance:
- staatiline tasakaalustamatus — the principal inertia axis is displaced parallel to the shaft axis; it can be detected without rotation, because the rotor turns under gravity until its heavy spot is at the bottom. A single correction mass in one plane removes it;
- couple (moment) unbalance — the principal inertia axis intersects the shaft axis at the center of mass; the two equal unbalances lie in different planes and 180° apart. It appears only during rotation and requires two correction masses in two planes;
- dünaamiline tasakaalustamatus — the general, real-world case: a combination of static and couple unbalance. The principal inertia axis neither is parallel to, nor intersects, the shaft axis. Two correction planes are necessary and sufficient for a rigid rotor.
The older term “moment unbalance” is a synonym of couple unbalance; it should not be confused with dynamic unbalance, which is the sum of the static and couple components. An example of a rotor with static unbalance is shown in Fig. 2.
Couple unbalance appears only when the rotor is rotating.
An example of a rotor with couple unbalance is shown in Fig. 3.
In this case, the unbalanced equal masses M1 and M2 are in different planes - in different places along the length of the rotor. In static position, i.e. when the rotor does not rotate, only gravity acts on the rotor and the masses balance each other. In dynamics, when the rotor rotates, centrifugal forces Fc1 and Fc2 start acting on the masses M1 and M2. These forces are equal in magnitude and opposite in direction. However, since they are applied at different places along the length of the shaft and are not on the same line, these forces do not compensate each other. The forces Fc1 and Fc2 create a moment applied to the rotor — this is why couple unbalance is also called moment unbalance. Accordingly, uncompensated centrifugal forces act on the bearing positions, which can greatly exceed the calculated values and reduce the service life of the bearings.
Since this type of unbalance appears only during the rotation of the rotor, it cannot be corrected in static conditions by balancing "on knives" or similar methods. In order to eliminate couple unbalance, two compensating weights must be installed, which produce a moment equal in magnitude and opposite in direction to the moment arising from the masses M1 and M2. The compensating masses do not have to be set opposite and equal in magnitude to the masses M1 and M2. The main thing is that they produce a moment that fully compensates for the unbalance moment.
In general, the masses M1 and M2 may not be equal to each other, so there will be a combination of static and couple unbalance — this general case is exactly what ISO 21940-2 calls dynamic unbalance. It is theoretically proven that for a rigid rotor, two weights spaced apart along the length of the rotor are necessary and sufficient to eliminate its unbalance. These weights will compensate both the moment resulting from the couple unbalance and the centrifugal force resulting from the asymmetry of the mass relative to the rotor axis (static unbalance). Typically, couple unbalance is characteristic of long rotors, such as shafts, and static unbalance is characteristic of narrow rotors. However, if the narrow rotor is skewed relative to the axis, or deformed ("figure eight"), then couple unbalance will be difficult to eliminate (see Fig. 4), because in this case it is difficult to install correcting weights that create the necessary compensating moment.
Jõud F1 ja F2 ei asu samal joonel ja ei kompenseeri teineteist.
Due to the fact that the arm available to create the compensating moment is small due to the narrow rotor, large correction weights may be required. However, this also results in an "induced unbalance" due to the deformation of the narrow rotor by centrifugal forces from the correction weights. (see, for example, Methodological instructions for balancing rigid rotors to GOST 22061-76 — the modern international counterpart is ISO 21940-11, formerly ISO 1940-1 — Section 10, "Rotor–supports system").
This is noticeable on narrow fan impellers, where, in addition to mass unbalance, an aerodynamic unbalance is also present: unequal blade geometry produces an unequal blade loading and hence a net radial force. Like the centrifugal force of a correction weight, this force scales with the square of speed, but it also depends on the operating point — air density, damper position, duct resistance — so a correction weight balanced at one duty point will not stay optimal at another. The aerodynamic component must therefore be corrected by restoring the blade geometry, not by adding mass.
Elektromagnetilised jõud in an electric machine (unbalanced magnetic pull from an eccentric air gap, broken bars, shorted laminations) behave differently again: they are governed by the air-gap flux, not by rotational speed, and they mostly excite the machine at twice the line frequency and at pole-pass sidebands rather than at 1×. Because they act at frequencies other than the rotation frequency, balancing cannot compensate them at all. In short, balancing removes the 1× mass-related excitation only — it cannot eliminate every source of vibration in a machine.
Mehhanismide vibratsioon
Vibratsioon on mehhanismi konstruktsiooni reaktsioon tsüklilise ergutava jõu mõjule. See jõud võib olla erineva iseloomuga.
Tasakaalustamata rootori tekitatud tsentrifugaaljõud on kompenseerimata jõud, mis mõjub "raskele punktile". Just seda jõudu ja sellest tingitud vibratsiooni saab rootori tasakaalustamisega kõrvaldada.
"Geomeetrilise" iseloomuga vastastikmõjujõud, mis tulenevad vastastikuste osade tootmis- ja montaaživigadest. Need jõud võivad tekkida näiteks võllikaelte ebaühtlase kuju, hammasrataste hammasprofiilide vigade, laagrite radade lainelisuse, vastastikuste võllide joonduse hälbe jms tagajärjel. Mitteümmarguse laagritapi korral nihkub võlli telg sõltuvalt võlli pöördenurgast. Kuigi see vibratsioon tekib ka rootori kiirusel, on seda tasakaalustamise abil peaaegu võimatu kõrvaldada.
Ventilaatorite tiivikute ja muude tiivikumehhanismide pöörlemisest tulenevad aerodünaamilised jõud. Hüdrodünaamilised jõud, mis tulenevad hüdropumpade, turbiinide jne. tiivikute pöörlemisest.
Elektromagnetilised jõud, mis tulenevad elektrimasinate töötamisest, nt ebasümmeetrilised rootori mähised, lühisesse lülitatud mähised jne.
The magnitude of the vibration (e.g. its amplitude Av) depends not only on the excitatory force Fv acting on the mechanism with circular frequency ω, but also on the rigidity k of the mechanism, its mass m, as well as the damping coefficient C, as formula (1) below shows.
Vibratsiooni ja tasakaalumehhanismide mõõtmiseks saab kasutada eri tüüpi andureid, sealhulgas:
- absoluutsed vibratsiooniandurid, mis on ette nähtud vibratsioonikiirenduse (kiirendusandurid) ja vibratsioonikiiruse mõõtmiseks;
- suhtelise vibratsiooni andurid - pöörisvoolu- või mahtuvuslikud, mis on loodud vibratsiooni nihke mõõtmiseks;
- Mõnel juhul (kui mehhanismi konstruktsioon seda võimaldab) saab jõuandureid kasutada ka selle vibratsioonikoormuse hindamiseks; eelkõige kasutatakse neid laialdaselt jäiga tugisüsteemiga tasakaalustusmasinate tugede vibratsioonikoormuse mõõtmiseks.
Seega on vibratsioon masina reaktsioon väliste jõudude mõjule. Vibratsiooni suurus ei sõltu mitte ainult mehhanismi suhtes toimiva jõu suurusest, vaid ka mehhanismi konstruktsiooni jäikusest. Üks ja sama jõud võib põhjustada erinevaid vibratsioone. Jäikade tugedega masina puhul võib laagritele mõjuda märkimisväärne dünaamiline koormus, isegi kui vibratsioon on väike. Seetõttu kasutatakse jäikade tugedega masinate tasakaalustamisel vibratsiooniandurite (vibratsioonikiirendusmõõturite) asemel jõuandureid.
Vibratsiooniandureid kasutatakse suhteliselt nõtkete tugedega mehhanismidel, kui tasakaalustamata tsentrifugaaljõudude toime põhjustab tugede märgatavat deformatsiooni ja vibratsiooni. Jõuandureid kasutatakse jäikade tugede puhul, kui isegi tasakaalustamatusest tingitud märkimisväärsed jõud ei põhjusta märkimisväärset vibratsiooni.
Resonants on tegur, mis takistab tasakaalustamist.
Varem mainisime, et rootorid jagunevad jäigaks ja paindlikuks. Rootori jäikust või paindlikkust ei tohi segi ajada nende tugede (vundament) jäikuse või liikuvusega, millele rootor on paigaldatud. Rootor loetakse jäigaks, kui selle deformatsioon (paindumine) tsentrifugaaljõudude mõjul on tähelepanuta jäetav. Paindliku rootori deformatsioon on suhteliselt suur ja seda ei saa tähelepanuta jätta.
Käesolevas artiklis käsitleme ainult jäikade rootorite tasakaalustamist. Jäik (mitte deformeeruv) rootor võib omakorda olla paigaldatud jäigale või liikuvale (painduvale) toele. On selge, et see tugede jäikus/vedruvus on samuti suhteline, sõltuvalt rootori kiirusest ja sellest tulenevate tsentrifugaaljõudude suurusest. Tingimuslikuks piiriks on rootori tugede omavõngete sagedus.
For mechanical systems, the shape and frequency of natural vibrations are determined by the mass and the elasticity of the elements of mechanical system. That is, the frequency of natural vibrations is an internal characteristic of the mechanical system and does not depend on external forces. Being deflected from the state of equilibrium, supports due to elasticity tend to return to the position of equilibrium. But due to the inertia of the massive rotor, this process is in the nature of damped oscillations. These vibrations are the natural vibrations of the rotor-support system. Their frequency depends on the ratio of the mass of the rotor to the elasticity of the supports, as formula (2) below shows.
Kui rootor hakkab pöörlema ja selle pöörlemissagedus läheneb omavõngete sagedusele, suureneb vibratsiooni amplituud järsult, mis võib viia konstruktsiooni hävitamiseni.
The phenomenon of mechanical resonance occurs. Near resonance the response is amplified by the quality factor Q = 1/(2ζ), typically 3–17 for machine structures, and the peak can be narrow: a speed change of the order of a few percent may change the vibration level several-fold. Across the resonance the phase lag swings by 180°, passing through 90° at the peak.
If the design of the mechanism is unsuccessful and the operating frequency of the rotor is close to the frequency of natural vibrations, then the operation of the mechanism becomes impossible because of the inadmissibly high vibration. Balancing by the usual methods is then impossible, because even a small change in speed drastically changes the vibration parameters. For balancing in the area of resonance, special methods not considered in this article are used.
Võimalik on määrata mehhanismi omavõnkumissagedus vabajooksul (rootori pöörlemise väljalülitamisel) või löögimeetodil koos sellele järgneva süsteemi löögile reageerimise spektraalanalüüsiga.
For mechanisms, which working frequency of rotation is above the resonance frequency, i.e. working in the supercritical (post-resonant) regime, the supports are considered to be moving and vibration sensors are used for measurement, mainly vibration accelerometers, measuring acceleration of structural elements. For mechanisms operating in pre-resonance mode, the supports are considered rigid. In this case, force sensors are used.
Mehaanilise süsteemi lineaarsed ja mittelineaarsed mudelid. Mittelineaarsus on tegur, mis takistab tasakaalustamist
Jäikade rootorite tasakaalustamisel kasutatakse tasakaalustamisarvutuste tegemiseks matemaatilisi mudeleid, mida nimetatakse lineaarseteks mudeliteks. Lineaarne mudel tähendab, et sellises mudelis on üks suurus proportsionaalne (lineaarne) teise suurusega. Näiteks kui rootori kompenseerimata massi kahekordistatakse, siis kahekordistub ka vibratsiooni väärtus. Jäikade rootorite puhul võib kasutada lineaarset mudelit, kuna need ei deformeeru.
Paindlike rootorite puhul ei saa enam kasutada lineaarset mudelit. Kui painduva rootori puhul suureneb raskuspunkti mass pöörlemise ajal, tekib täiendav deformatsioon ja lisaks massile suureneb ka raskuspunkti asukoha raadius. Seetõttu suureneb vibratsioon painduva rootori puhul rohkem kui kaks korda ja tavalised arvutusmeetodid ei toimi.
Another source of non-linearity is a change in support stiffness at large deflections: at small deflections one set of structural elements carries the load, at large ones others come into play. This is why you cannot balance mechanisms that are not fixed on a foundation, but, for example, simply placed on the floor. With significant vibrations, the force of the unbalance can pull the mechanism off the floor, thereby significantly changing the stiffness characteristics of the system. Motor feet must be securely fastened, bolt mounts must be tightened, washer thickness must provide sufficient mounting rigidity, etc. If the bearings are broken, significant shaft misalignment and shocks are possible, which will also result in poor linearity and an inability to perform a quality balance.
Tasakaalustusseadmed ja tasakaalustusmasinad
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
Seda protsessi saab teostada kahe meetodi abil.
The first method involves machining the rotor trunnions in such a way that the axis passing through the centers of the trunnions coincides with the main central axis of inertia of the rotor. Such a technique is rarely used in practice and will not be discussed in detail in this article.
Teine (kõige tavalisem) meetod hõlmab rootorile korrektsioonikaalide teisaldamist, paigaldamist või eemaldamist, mis paigutatakse nii, et rootori inertsustelg oleks võimalikult lähedal selle pöörlemisteljele.
Tasakaalustamise käigus võib korrektsioonikaalu liigutada, lisada või eemaldada mitmesuguste tehnoloogiliste toimingute abil, sealhulgas: puurimine, freesimine, pindamine, keevitamine, kruvimine või lahti kruvimine, laser- või elektronkiirega põletamine, elektrolüüs, elektromagnetiline pindamine jne.
Tasakaalustamisprotsessi saab teostada kahel viisil:
- Field balancing (in situ) — the assembled rotor is balanced in its own bearings, on its own foundation, at its own operating speed, using a portable balancing kit;
- Shop balancing — the rotor is dismounted and balanced on a dedicated balancing machine.
For balancing of rotors in their own bearings, specialized balancing devices (kits) are usually used, which allow measuring the vibration of the balanced rotor at its frequency of rotation in vector form, i.e. to measure both the amplitude and the phase of vibration. At present, the above devices are manufactured on the basis of microprocessor technology and (apart from vibration measurement and analysis) provide automatic calculation of parameters of correcting weights, which should be installed on the rotor to compensate its unbalance.
Nende seadmete hulka kuuluvad:
- arvutil või tööstuslikul kontrolleril põhinev mõõte- ja arvutusüksus;
- kaks (või enam) vibratsiooniandurit;
- a phase angle sensor;
- tarvikud andurite paigaldamiseks kohapeal;
- spetsialiseeritud tarkvara, mis on mõeldud rootori vibratsiooniparameetrite mõõtmise täielikuks tsükliks ühes, kahes või mitmes korrigeerimistasandis.
Praegu on kõige levinumad kaks tasakaalustusmasina tüüpi:
- Soft-bearing machines (with pliable supports);
- Hard-bearing machines (with rigid supports).
Soft-bearing (above-resonance) machines have relatively pliable supports, for example, based on flat springs. The frequency of natural vibrations of these supports is usually 2-3 times lower than the rotation frequency of the balanced rotor, which is mounted on them, so the machine runs above resonance. Vibration sensors (accelerometers, vibration velocity sensors, etc.) are usually used to measure the motion of the supports of these above-resonance machines.
Hard-bearing (pre-resonance) machines use relatively rigid supports, whose natural frequencies of vibration should be 2-3 times higher than the rotation frequency of the rotor being balanced, so the machine runs below resonance. Force transducers are usually used to measure the dynamic load on the supports of the pre-resonance machine.
The advantage of pre-resonance (hard-bearing) balancing machines is that balancing on them can be performed at relatively low rotor speeds (up to 400 - 500 rpm), which greatly simplifies the design of the machine and its foundation, and increases the productivity and safety of balancing.
Jäikade rootorite tasakaalustamine
Oluline!
- Tasakaalustamine kõrvaldab ainult rootori massi ebasümmeetrilisest jaotumisest põhjustatud vibratsiooni selle pöörlemistelje suhtes. Muid vibratsiooniliike tasakaalustamine ei kõrvalda!
- Tehnilised mehhanismid, mille konstruktsioon tagab resonantside puudumise töösagedusel, mis on usaldusväärselt kinnitatud vundamendile, paigaldatud töökorras laagritesse, kuuluvad tasakaalustamisele.
- Defektne masin tuleb enne tasakaalustamist parandada. Vastasel juhul ei ole kvaliteetne tasakaalustamine võimalik.
Tasakaalustamine ei asenda remonti!
Tasakaalustamise peamine ülesanne on leida kompenseerivate raskuste mass ja asukoht, mis tasakaalustavad tsentrifugaaljõude.
As mentioned above, for rigid rotors, it is generally necessary and sufficient to install two compensating weights. This will eliminate both the static and the couple components of the rotor unbalance. The general scheme for measuring vibration during balancing is as follows.
Vibration sensors are installed on the bearing supports at points 1 and 2. A revolution mark is attached to the rotor, usually with reflective tape. The revolution mark is used by the laser tachometer to determine the rotor speed and phase of the vibration signal.
Dünaamilise tasakaalustamise teostamine (kolme käivitusega meetod)
In most cases dynamic balancing is carried out by the method of three starts. The method is based on the fact that trial weights of known mass are placed on the rotor in series in plane 1 and 2 and the weights and the location of the balancing weights are calculated based on the results of changes in the vibration parameters.
The plane in which a correction weight is installed is called a parandustasand. Correction planes are located on the rotor itself — typically at the two ends of the rotor body, on the fan or impeller disks, or on dedicated balancing rings. They should be chosen as far apart along the shaft as the design allows, so that a moderate weight produces a sufficient correcting moment. This is not the same as the measuring points, which are on the bearing housings (see Fig. 6).
At the first start-up the initial vibration is measured (in the Balanset software this is Run 0). Then a trial weight of known mass is placed on the rotor closer to one of the bearings. A second start-up is carried out (Run 1) and the vibration parameters are measured, which should change due to the test weight installation. Then the test weight in the first plane is removed and installed in the second plane. A third test run is performed (Run 2) and the vibration parameters are measured. The test weight is removed and the software automatically calculates the masses and installation angles of the balance weights.
The calculated correction weights are then installed in their planes and a check run is made — in the Balanset software this is Run T (Trim). The residual vibration is compared with the tolerance. If the result is still above the target, the software reuses the influence coefficients already determined, so no new trial-weight runs are needed — only a small additional trim correction is computed and installed.
The point of installing the test weights is to determine how the system reacts to changes in unbalance. The weights and locations of the test weights are known, so the software can calculate so called influence coefficients, showing how introducing a known unbalance affects the vibration parameters. The influence coefficients are characteristics of the mechanical system itself and depend on the rigidity of the supports and the mass (inertia) of the rotor-support system.
Sama tüüpi ja sama konstruktsiooniga mehhanismide puhul on mõju koefitsiendid lähedased. Neid on võimalik salvestada arvuti mällu ja kasutada neid sama tüüpi mehhanismide tasakaalustamiseks ilma katsesõitudeta, mis suurendab oluliselt tasakaalustamise tootlikkust. Pange tähele, et katseraskuste mass tuleks valida nii, et vibratsiooniparameetrid muutuksid katseraskuste paigaldamisel märgatavalt. Vastasel juhul suureneb mõju koefitsientide arvutamise viga ja tasakaalustamise kvaliteet halveneb.
Nagu näete jooniselt 1, mõjub tsentrifugaaljõud radiaalsuunas, s.t. risti rootori teljega. Seetõttu tuleb vibratsiooniandurid paigaldada nii, et ka nende tundlikkustelg oleks suunatud radiaalselt. Tavaliselt on vundamendi jäikus horisontaalsuunas väiksem, seega on vibratsioon horisontaalsuunas suurem. Seetõttu tuleks tundlikkuse suurendamiseks andurid paigaldada nii, et nende tundlikkustelg oleks samuti suunatud horisontaalselt. Kuigi põhimõttelist erinevust ei ole. Lisaks radiaalsuunalisele vibratsioonile tuleb jälgida ka aksiaalsuunalist vibratsiooni piki rootori pöörlemistelge. See vibratsioon ei ole tavaliselt põhjustatud tasakaalustamatusest, vaid muudest põhjustest, peamiselt võllide joondusveast, kui need on ühendatud siduri kaudu.
This vibration cannot be eliminated by balancing, in which case alignment is required. In practice, such machines usually have both rotor unbalance and shaft misalignment, which makes the task of eliminating vibration much more difficult. In such cases, it is necessary to center the machine first and then balance it. (Although with strong torque unbalance, vibration also occurs in the axial direction due to "twisting" of the foundation structure.)
Seotud artiklid (näited tasakaalustuspukkidest)
- Tasakaalustusalus pehme toega
- Elektrimootorite rootorite tasakaalustamine
- Lihtsad, kuid tõhusad tasakaalustusseadmed
Mehhanismide tasakaalustamise kvaliteedi hindamise kriteeriumid
The balancing quality of rotors (mechanisms) can be evaluated in two ways. The first method involves comparing the amount of residual unbalance determined during the balancing process with the tolerance for residual unbalance. These tolerances for the different rotor classes are specified in ISO 21940-11 (formerly ISO 1940-1).
How the tolerance is computed (ISO 21940-11). The standard specifies a balance quality grade G, which is the product of the permissible specific unbalance eiga and the service angular velocity ω, expressed in mm/s:
- ω = 2π·n / 60 [rad/s], where n is the service speed in rpm;
- eiga = G · 1000 / ω [g·mm/kg] (numerically equal to µm of center-of-mass offset) — equivalently eiga = 9549 · G / n;
- Uiga = eiga · m [g·mm], where m is the rotor mass in kg.
Worked example. Rotor m = 50 kg, service speed n = 3000 rpm, grade G 6.3 (fans, pumps, standard electric motors): ω = 2π·3000/60 = 314.2 rad/s; eiga = 6.3 · 1000 / 314.2 = 20.1 g·mm/kg (cross-check: 9549 · 6.3 / 3000 ≈ 20.1); Uiga = 20.1 · 50 ≈ 1000 g·mm for the whole rotor.
Splitting the tolerance between two planes. For a rotor whose center of mass lies between the correction planes, the total tolerance is divided in inverse proportion to the distance from the center of mass to each plane; for a symmetrical rotor this is simply half in each plane — about 500 g·mm per plane in the example above. Neither plane should be allocated more than 70% or less than 30% of Uiga.
Typical grades: G 0.4 — gyroscopes, spindles of precision grinders · G 1 — grinding-machine spindles, precision armatures · G 2.5 — turbines, turbo-generators, machine-tool drives · G 6.3 — general engineering: fans, pump impellers, flywheels, standard electric motors · G 16 — cardan shafts with special requirements, agricultural machinery, crushers · G 40 — car wheels, drive shafts (cardan shafts) · G 100 — crankshaft drives of high-speed diesel engines.
Siiski ei saa ettenähtud tolerantside järgimine täielikult tagada mehhanismi töökindlust, mis on seotud selle vibratsiooni miinimumtaseme saavutamisega. See on seletatav asjaoluga, et mehhanismi vibratsiooni suurus ei sõltu mitte ainult selle rootori jääktasakaalustamatusega seotud jõu suurusest, vaid ka mitmetest muudest parameetritest, sealhulgas mehhanismi konstruktsioonielementide jäikusest k, selle massist m, summutustegurist ja pöörlemissagedusest. Seetõttu on mehhanismi dünaamiliste omaduste (sealhulgas selle tasakaalu kvaliteedi) hindamiseks mitmel juhul soovitatav hinnata mehhanismi jääkvibratsiooni taset, mida reguleerivad mitmed standardid.
The most widely used standard for permissible vibration levels of industrial machines is ISO 20816-3 (formerly ISO 10816-3). It covers machines above 15 kW running at 120–15,000 rpm, and it classifies them in two dimensions: by power group (Group 1 — above 300 kW; Group 2 — 15 to 300 kW) and by support type (rigid or flexible). Each combination has its own A/B, B/C and C/D zone boundaries in mm/s RMS. Machines outside this scope have dedicated parts of the series (turbine sets — ISO 20816-2, hydraulic machines, reciprocating machines, pumps) or product standards such as ISO 14694 for industrial fans.
For general machines evaluated on non-rotating parts, the classic ISO 10816-1 zones (now part of ISO 20816-1) give the following boundaries of vibration velocity, mm/s RMS:
| Klass | A/B | B/C | C/D |
|---|---|---|---|
| Class I (small machines, up to 15 kW) | 0.71 | 1.80 | 4.50 |
| Class II (medium machines, 15–75 kW) | 1.12 | 2.80 | 7.10 |
| Class III (large machines, rigid foundation) | 1.80 | 4.50 | 11.20 |
| Class IV (large machines, flexible foundation) | 2.80 | 7.10 | 18.00 |
Zone A corresponds to the vibration of new machines; zone B is acceptable for unrestricted long-term operation; zone C allows only restricted operation; zone D indicates vibration severe enough to cause damage.
Standardid ja viited
- ISO 21940-11:2016 — Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors with rigid behaviour. (Replaces ISO 1940-1, which is withdrawn.) G-grades and tolerance calculator →
- ISO 21940-2 — Mechanical vibration — Rotor balancing — Part 2: Vocabulary. (Definitions of static, couple, quasi-static and dynamic unbalance.)
- ISO 20816-1:2016 — Mechanical vibration — Measurement and evaluation of machine vibration — Part 1: General guidelines. (Replaces ISO 10816-1 and ISO 7919-1.) Evaluation zones →
- ISO 20816-3:2022 — Mechanical vibration — Measurement and evaluation of machine vibration — Part 3: Industrial machines with nominal power above 15 kW and nominal speeds between 120 r/min and 15 000 r/min. (Replaces ISO 10816-3:2009.)
- ISO 14694:2003 — Industrial fans — Specifications for balance quality and vibration levels.
KKK
Kas tasakaalustamine eemaldab kogu vibratsiooni?
Ei. Tasakaalustamine eemaldab vibratsiooni, mis on põhjustatud rootori massi asümmeetrilisest jaotusest selle pöörlemistelje suhtes. Vibratsioon, mis on tingitud joondusveast, laagrivigadest, aerodünaamilistest/hüdrodünaamilistest jõududest, elektromagnetilistest jõududest ja muudest põhjustest, nõuab eraldi diagnostikat ja parandusmeetmeid.
Miks võib tasakaalustamine resonantsi lähedal ebaõnnestuda?
Resonantsi lähedal võivad väikesed kiiruse muutused põhjustada suuri muutusi vibratsiooni amplituudis ja 180° faasinihet. Sellistes tingimustes muutuvad mõõtmistulemused ebastabiilseks ja tavapärased tasakaalustusprotseduurid ei pruugi ilma spetsiaalsete meetoditeta koonduda.
Millal on vaja ühetasandilist ja millal kahetasandilist tasakaalustamist?
One plane is enough for disk-shaped rotors, where the axial length of the rotor is small compared with the diameter — as a rule of thumb L/D < 0.5 — and the service speed is well below the first critical speed. Typical examples: a grinding wheel, a single-disk fan impeller, a pulley, a car wheel. Such a rotor carries almost purely static unbalance.
Kaks tasandit are required for elongated rotors (L/D ≥ 0.5), for any rotor with two or more impellers or disks spaced along the shaft, and whenever the vibration phase at the two bearings differs markedly — a sign of a couple component. A rigid rotor never needs more than two planes.
When in doubt, measure both bearings: if a one-plane correction reduces the vibration at one bearing and increases it at the other, the rotor has a couple component and needs two-plane balancing.
Mida tuleks enne tasakaalustamist teha?
Veenduge, et masin on töökorras: usaldusväärne kinnitus vundamendile, terved laagrid, tõsine lõtk puudub ja puuduvad ilmsed mittelineaarsuse allikad. Tasakaalustamine ei asenda remonti.
Peamised järeldused
- Tasakaalustamine korrigeerib massiga seotud (tsentrifugaal)ergastust; see ei lahenda joondusvigu, laagrikahjustusi ega elektromagnetilisi/aerodünaamilisi allikaid.
- Resonants ja mittelineaarsus võivad muuta tavapärase tasakaalustamise ebaefektiivseks või ohtlikuks.
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
