Balansiranje rotora: statička i dinamička neuravnoteženost, rezonancija i praktični postupak
Ovaj vodič objašnjava Balansiranje rotora za kruti rotori: 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.
Sadržaj
- Što je rotor i što ispravlja balansiranje?
- Vrste rotora i vrste neuravnoteženosti
- Vibracije mehanizama: što balansiranje može, a što ne može ukloniti
- Rezonancija: faktor koji sprječava balansiranje
- Linearni i nelinearni modeli: kada izračuni prestanu raditi
- Uređaji za balansiranje i balansirni strojevi
- Balansiranje krutih rotora (praktične napomene)
- Kako se izvodi dinamičko balansiranje (metoda s tri prolaza)
- Kriteriji za procjenu kvalitete uravnoteženja
- Standardi i reference
- FAQ
Što je rotor i što ispravlja balansiranje?
Rotor je tijelo koje se okreće oko neke osi i koje je u ležajevima poduprto svojim ležajnim površinama. Ležajne površine rotora prenose opterećenja na ležajeve, a preko njih na potpore. Ležajne površine su površine rukavaca ili površine koje ih zamjenjuju.
U savršeno uravnoteženom rotoru, njegova masa je simetrično raspoređena oko osi rotacije, tj. bilo koji element rotora može se uskladiti s drugim elementom koji se nalazi simetrično oko osi rotacije. U uravnoteženom rotoru, centrifugalna sila koja djeluje na bilo koji element rotora uravnotežena je centrifugalnom silom koja djeluje na simetrični element. Na primjer, centrifugalne sile F1 i F2, jednake veličine i suprotnog smjera, djeluju na elemente 1 i 2 (označeni zelenom bojom na slici 1). To vrijedi za sve simetrične elemente rotora, te je stoga ukupna centrifugalna sila koja djeluje na rotor jednaka 0 i rotor je uravnotežen.
Ali ako je simetrija rotora narušena (asimetrični element je označen crvenom bojom na slici 1), na rotor djeluje neuravnotežena centrifugalna sila F3. Tijekom rotacije ta sila mijenja smjer zajedno s rotacijom rotora. Dinamičko opterećenje koje proizlazi iz ove sile prenosi se na ležajeve, što dovodi do ubrzanog habanja i trošenja.
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.
Zadatak uravnoteženja je pronaći veličinu i položaj (kut) jedne ili više masa za uravnoteženje.
Vrste rotora i vrste neuravnoteženosti
Uzimajući u obzir čvrstoću materijala rotora i veličinu centrifugalnih sila koje na njega djeluju, rotori se mogu podijeliti u dvije vrste - krute rotore i fleksibilne rotore.
Kruti rotori neznatno se deformiraju pod djelovanjem centrifugalne sile u radnim režimima, a utjecaj te deformacije u proračunima može se zanemariti.
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:
- statička neravnoteža — 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;
- dinamička neravnoteža — 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.
Sile F1 i F2 ne leže na istoj liniji i ne nadoknađuju se međusobno.
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.
Elektromagnetske sile 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.
Vibracije mehanizama
Vibracija je reakcija konstrukcije mehanizma na učinke cikličke uzbudne sile. Ta sila može biti različitog karaktera.
Centrifugalna sila koja nastaje zbog neuravnoteženog rotora je nekompenzirana sila koja djeluje na "tešku točku". Upravo se ta sila i vibracije uzrokovane njome mogu eliminirati uravnoteženjem rotora.
Interakcijske sile "geometrijske" prirode koje proizlaze iz pogrešaka u proizvodnji i montaži spojnih dijelova. Ove sile mogu, na primjer, nastati kao rezultat nekružnosti vratova vratila, pogrešaka u profilima zuba u zupčanicima, valovitosti staza ležajeva, neporavnatosti spojnih vratila itd. U slučaju nekružnosti rukavaca, os vratila će se pomaknuti ovisno o kutu rotacije vratila. Iako se ova vibracija javlja i pri brzini rotora, gotovo ju je nemoguće eliminirati balansiranjem.
Aerodinamske sile koje nastaju rotacijom lopatica ventilatora i drugih mehanizama s lopaticama. Hidrodinamske sile koje nastaju rotacijom lopatica hidrauličnih pumpi, turbina itd.
Elektromagnetske sile koje nastaju pri radu električnih strojeva, npr. asimetričnih namotaja rotora, kratko spojenih namotaja itd.
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.
Za mjerenje vibracija i mehanizama za balansiranje mogu se koristiti različite vrste senzora, uključujući:
- apsolutni senzori vibracija namijenjeni mjerenju ubrzanja vibracija (akcelerometri) i senzori brzine vibracija;
- senzori relativnih vibracija - senzori vrtložnih struja ili kapacitivni, dizajnirani za mjerenje vibracijskog pomaka;
- U nekim slučajevima (kada to dizajn mehanizma dopušta), senzori sile mogu se koristiti i za procjenu njegovog vibracijskog opterećenja; posebno se široko koriste za mjerenje vibracijskog opterećenja nosača strojeva za balansiranje s tvrdim ležajevima.
Dakle, vibracija je reakcija stroja na djelovanje vanjskih sila. Veličina vibracije ovisi ne samo o veličini sile koja djeluje na mehanizam, već i o krutosti konstrukcije mehanizma. Jedna i ista sila može dovesti do različitih vibracija. U stroju s tvrdim ležajevima, čak i ako je vibracija mala, ležajevi mogu biti izloženi značajnim dinamičkim opterećenjima. Zato se pri balansiranju strojeva s tvrdim ležajevima koriste senzori sile, a ne senzori vibracija (vibracijski akcelerometri).
Senzori vibracija koriste se na mehanizmima s relativno savitljivim osloncima, kada djelovanje neuravnoteženih centrifugalnih sila dovodi do primjetne deformacije oslonaca i vibracija. Senzori sile koriste se za krute oslonce, kada čak ni značajne sile zbog neuravnoteženosti ne dovode do značajnih vibracija.
Rezonancija je faktor koji sprječava balansiranje.
Ranije smo spomenuli da se rotori dijele na krute i fleksibilne. Krutost ili fleksibilnost rotora ne treba miješati s krutošću ili pokretljivošću oslonaca (temelja) na kojima je rotor postavljen. Rotor se smatra krutim kada se njegova deformacija (savijanje) pod djelovanjem centrifugalnih sila može zanemariti. Deformacija fleksibilnog rotora je relativno velika i ne može se zanemariti.
U ovom članku razmatramo samo uravnoteženje krutih rotora. Kruti (neelastični) rotor može biti montiran na krutim ili pokretnim (fleksibilnim) nosačima. Jasno je da je ta krutost/fleksibilnost nosača također relativna, ovisno o brzini rotora i veličini nastalih centrifugalnih sila. Uvjetna granica je frekvencija prirodnih vibracija nosača rotora.
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.
Kada rotor počne rotirati i frekvencija njegove rotacije se približi frekvenciji prirodnih vibracija, amplituda vibracija naglo raste, što može dovesti do uništenja strukture.
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.
Moguće je odrediti frekvenciju prirodnih vibracija mehanizma pri slobodnom zaustavljanju (pri isključivanju rotacije rotora) ili metodom udarnog uzbuđenja uz naknadnu spektralnu analizu reakcije sustava na udar.
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.
Linearni i nelinearni modeli mehaničkog sustava. Nelinearnost je čimbenik koji sprječava balansiranje.
Pri balansiranju krutih rotora za izračune balansiranja koriste se matematički modeli nazvani linearnim modelima. Linearni model znači da je u takvom modelu jedna veličina proporcionalna (linearno) drugoj. Na primjer, ako se nekompenzirana masa na rotoru udvostruči, vrijednost vibracija također će se udvostručiti. Za krute rotore može se koristiti linearni model, budući da se ne deformiraju.
Za fleksibilne rotore više se ne može koristiti linearan model. Kod fleksibilnog rotora, ako se masa teške točke povećava tijekom rotacije, nastaje dodatna deformacija, a uz masu se povećava i radijus položaja teške točke. Stoga će se kod fleksibilnog rotora vibracija povećati više od dvostruko, a uobičajene metode izračuna neće raditi.
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.
Uređaji za balansiranje i balansirni strojevi
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
Ovaj se proces može izvesti na dva načina.
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.
Druga (najčešća) metoda uključuje pomicanje, postavljanje ili uklanjanje korekcijskih utega na rotoru, koji se postavljaju tako da je os inercije rotora što je moguće bliža njegovoj osi vrtnje.
Pomicanje, dodavanje ili uklanjanje korektivnih utega tijekom balansiranja može se izvesti raznim tehnološkim operacijama, uključujući: bušenje, glodanje, navarivanje, zavarivanje, vijčanje ili odvijanje, lasersko ili elektronskim snopom gorenje, elektrolizu, elektromagnetsko navarivanje itd.
Proces balansiranja može se izvesti na dva načina:
- 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.
Ovi uređaji uključuju:
- jedinica za mjerenje i izračunavanje temeljena na računalu ili industrijskom upravljaču;
- dva (ili više) senzora vibracija;
- a phase angle sensor;
- pribor za montažu senzora na lokaciji;
- specijalizirani softver, dizajniran za izvođenje punog ciklusa mjerenja parametara vibracija rotora u jednoj, dvjema ili više korektivnih ravnina.
Dvije vrste balansirnih strojeva trenutno su najčešće:
- 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.
Uravnoteženje krutih rotora
Važno!
- Balansiranje uklanja samo vibracije uzrokovane asimetričnom raspodjelom mase rotora u odnosu na njegovu os rotacije. Druge vrste vibracija balansiranjem se ne uklanjaju!
- Tehnički mehanizmi čiji dizajn osigurava odsutnost rezonancija na radnoj frekvenciji rotacije, pouzdano pričvršćeni na temelj i ugrađeni u radne ležajeve, podliježu balansiranju.
- Neispravan stroj mora se popraviti prije uravnoteženja. Inače nije moguće postići kvalitetno uravnoteženje.
Uravnoteženje nije zamjena za popravak!
Glavni zadatak balansiranja je pronaći masu i položaj kompenzacijskih utega koji neutraliziraju centrifugalne sile.
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.
Kako se izvodi dinamičko balansiranje (metoda s tri prolaza)
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 korekcijska ravnina. 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.
Za iste vrste mehanizama istog dizajna koeficijenti utjecaja bit će bliski. Mogu se spremiti u memoriju računala i koristiti za balansiranje mehanizama iste vrste bez probnih pokretanja, što značajno povećava produktivnost balansiranja. Imajte na umu da masu probnih utega treba odabrati tako da se parametri vibracija primjetno promijene kada se probni utezi postave. Inače se pogreška u izračunu koeficijenata utjecaja povećava i kvaliteta balansiranja se pogoršava.
Kao što možete vidjeti na slici 1, centrifugalna sila djeluje u radijalnom smjeru, tj. okomito na os rotora. Stoga vibracijski senzori moraju biti postavljeni tako da je i njihova os osjetljivosti usmjerena u radijalnom smjeru. Obično je krutost temelja u vodoravnom smjeru manja, pa su vibracije u vodoravnom smjeru veće. Zato, radi povećanja osjetljivosti, senzore treba postaviti tako da je njihova os osjetljivosti također usmjerena vodoravno. Iako nema bitne razlike. Osim vibracija u radijalnom smjeru, moraju se pratiti i vibracije u aksijalnom smjeru, duž osi vrtnje rotora. Te vibracije obično nisu uzrokovane neuravnoteženošću, već drugim uzrocima, uglavnom povezanima s neporavnatošću vratila spojenih preko spojke.
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.)
Povezani članci (primjeri balansirnih postolja)
- Stalak za balansiranje s mekom potporom
- Balansiranje rotora elektromotora
- Jednostavni, ali učinkoviti stalci za balansiranje
Kriteriji za procjenu kvalitete mehanizama uravnoteženja
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 epo and the service angular velocity ω, expressed in mm/s:
- ω = 2π·n / 60 [rad/s], where n is the service speed in rpm;
- epo = G · 1000 / ω [g·mm/kg] (numerically equal to µm of center-of-mass offset) — equivalently epo = 9549 · G / n;
- Upo = epo · 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; epo = 6.3 · 1000 / 314.2 = 20.1 g·mm/kg (cross-check: 9549 · 6.3 / 3000 ≈ 20.1); Upo = 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 Upo.
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.
Međutim, poštivanje navedenih tolerancija ne može u potpunosti jamčiti operativnu pouzdanost mehanizma, povezanu s postizanjem minimalne razine njegove vibracije. To se objašnjava činjenicom da se amplituda vibracija mehanizma ne određuje samo silom povezanom s preostalim disbalansom njegovog rotora, već ovisi i o nekoliko drugih parametara, uključujući: krutost k strukturnih elemenata mehanizma, njegovu masu m, faktor prigušenja, kao i frekvenciju rotacije. Stoga se, za procjenu dinamičkih svojstava mehanizma (uključujući kvalitetu njegove uravnoteženosti), u nizu slučajeva preporučuje procjena razine preostale vibracije mehanizma, koja je regulirana nizom standarda.
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:
| Razred | A/B | B/C | CD |
|---|---|---|---|
| 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.
Standardi i reference
- 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.
FAQ
Uklanja li balansiranje sve vibracije?
Ne. Balansiranje uklanja vibracije uzrokovane asimetričnom raspodjelom mase rotora u odnosu na njegovu rotacijsku os. Vibracije uzrokovane neusklađenošću, nedostacima ležajeva, aerodinamičkim/hidrodinamičkim silama, elektromagnetskim silama i drugim uzrocima zahtijevaju zasebnu dijagnostiku i korektivne radnje.
Zašto balansiranje može propasti blizu rezonancije?
Blizu rezonancije, male promjene brzine mogu uzrokovati velike promjene amplitude vibracija i fazni pomak od 180°. U takvim uvjetima rezultati mjerenja postaju nestabilni, a konvencionalni postupci balansiranja možda neće konvergirati bez posebnih metoda.
Kada vam je potrebno balansiranje u jednoj ravnini u odnosu na balansiranje u dvije ravnine?
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.
Dva aviona 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.
Što treba učiniti prije balansiranja?
Provjerite je li stroj ispravan: pouzdano pričvršćivanje na temelj, ispravni ležajevi, bez ozbiljnih labavosti i bez očitih izvora nelinearnosti. Balansiranje nije zamjena za popravak.
Ključni zaključci
- Balansiranjem se ispravlja pobuda povezana s masom (centrifugalna pobuda); ne rješava neusklađenost, oštećenje ležaja ni elektromagnetske/aerodinamičke izvore.
- Rezonancija i nelinearnost mogu učiniti konvencionalno balansiranje neučinkovitim ili nesigurnim.
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
