Uravnoteženje rotorja: statična in dinamična neuravnoteženost, resonanca in praktični postopek
V tem priročniku je pojasnjeno. uravnoteženje rotorja za togi rotorji: 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.
Vsebina
- Kaj je rotor in kaj uravnoteževanje popravi?
- Vrste rotorjev in vrste neuravnoteženosti
- Vibracije mehanizmov: kaj lahko in česa ne more odpraviti uravnoteženje
- Resonanca: dejavnik, ki preprečuje uravnoteženje
- Linearni v primerjavi z nelinearnimi modeli: kdaj izračuni prenehajo delovati
- Balansirne naprave in balansirni stroji
- Uravnoteženje togih rotorjev (praktične opombe)
- Kako se izvaja dinamično uravnoteženje (metoda treh zagonov)
- Merila za ocenjevanje kakovosti uravnoteženja
- Standardi in reference
- POGOSTA VPRAŠANJA
Kaj je rotor in kaj uravnoteževanje popravi?
Rotor je telo, ki se vrti okoli neke osi in ga držijo ležajne površine v nosilcih. Ležajne površine rotorja prenašajo obremenitve na nosilce prek kotalnih ali drsnih ležajev. Ležajne površine so površine stebričkov ali površine, ki jih nadomeščajo.
V popolnoma uravnoteženem rotorju je njegova masa simetrično porazdeljena glede na os vrtenja, tj. kateri koli element rotorja se lahko ujema z drugim elementom, ki se nahaja simetrično glede na os vrtenja. V uravnoteženem rotorju je centrifugalna sila, ki deluje na kateri koli element rotorja, uravnotežena s centrifugalno silo, ki deluje na simetrični element. Na primer, centrifugalni sili F1 in F2, ki sta enake velikosti in nasprotne smeri, delujeta na elementa 1 in 2 (označena z zeleno na sliki 1). To velja za vse simetrične elemente rotorja, zato je skupna centrifugalna sila, ki deluje na rotor, enaka 0 in rotor je uravnotežen.
Če pa je simetrija rotorja porušena (asimetrični element je na sliki 1 označen z rdečo barvo), potem na rotor deluje neuravnotežena centrifugalna sila F3. Pri vrtenju ta sila spreminja smer skupaj z vrtenjem rotorja. Dinamična obremenitev, ki nastane zaradi te sile, se prenaša na ležaje, kar povzroča pospešeno obrabo.
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.
Naloga uravnoteženja je poiskati velikost in položaj (kot) ene ali več korekcijskih mas.
Vrste rotorjev in vrste neuravnoteženosti
Glede na trdnost materiala rotorja in velikost centrifugalnih sil, ki delujejo nanj, lahko rotorje razdelimo na dve vrsti - toge rotorje in fleksibilne rotorje.
Togi rotorji se pod vplivom centrifugalne sile pri delovnih načinih deformirajo neznatno in vpliv te deformacije pri izračunih lahko zanemarimo.
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:
- statična neuravnoteženost — 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;
- dinamična neuravnoteženost — 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.
Sili F1 in F2 ne ležita na isti premici in se ne kompenzirata.
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.
Elektromagnetne 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 mehanizmov
Vibracije so reakcija konstrukcije mehanizma na učinke ciklične vzbujevalne sile. Ta sila je lahko različne narave.
Centrifugalna sila, ki nastane zaradi neuravnoteženega rotorja, je nekompenzirana sila, ki deluje na "težko točko". Prav to silo in vibracije, ki jih povzroča, je mogoče odpraviti z uravnoteženjem rotorja.
Interakcijske sile "geometrijske" narave, ki izhajajo iz proizvodnih in montažnih napak ujemajočih se delov. Te sile lahko na primer nastanejo zaradi neokroglosti vratov gredi, napak v profilih zob zobnikov, valovitosti tekalnih stez ležajev, neusklajenosti ujemajočih se gredi itd. V primeru neokroglosti ležajnih čepov se os gredi premika glede na kot vrtenja gredi. Čeprav se te vibracije pojavljajo tudi pri hitrosti rotorja, jih je skoraj nemogoče odpraviti z uravnoteženjem.
Aerodinamične sile, ki nastanejo zaradi vrtenja rotorjev ventilatorjev in drugih mehanizmov z lopaticami. Hidrodinamične sile, ki so posledica vrtenja rotorjev hidravličnih črpalk, turbin itd.
Elektromagnetne sile, ki so posledica delovanja električnih strojev, npr. asimetričnih rotorskih navitij, kratkega stika navitij 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 merjenje vibracij in balansiranje mehanizmov se lahko uporabljajo različne vrste senzorjev, vključno z:
- absolutni senzorji vibracij, namenjeni merjenju pospeška vibracij (akcelerometri), in senzorji hitrosti vibracij;
- senzorji relativnih vibracij - vrtinčnotokovski ali kapacitivni senzorji, zasnovani za merjenje vibracijskega premika;
- V nekaterih primerih (kadar zasnova mehanizma to omogoča) se lahko za oceno njegove vibracijske obremenitve uporabijo tudi senzorji sile; zlasti se pogosto uporabljajo za merjenje vibracijske obremenitve trdno uležajenih nosilcev strojev za uravnoteženje.
Vibracije so torej odziv stroja na delovanje zunanjih sil. Velikost vibracij ni odvisna le od velikosti sile, ki deluje na mehanizem, temveč tudi od togosti konstrukcije mehanizma. Ena in ista sila lahko povzroči različne vibracije. V stroju s trdimi ležaji so lahko ležaji, tudi če so vibracije majhne, izpostavljeni velikim dinamičnim obremenitvam. Zato se pri uravnoteženju strojev s trdimi ležaji uporabljajo senzorji sile in ne vibracij (vibracijski merilniki pospeška).
Senzorji vibracij se uporabljajo na mehanizmih z razmeroma prožnimi nosilci, kadar delovanje neuravnoteženih centrifugalnih sil povzroči opazno deformacijo nosilcev in vibracije. Senzorji sile se uporabljajo pri togih nosilcih, ko tudi znatne sile zaradi neuravnoteženosti ne povzročajo znatnih vibracij.
Resonanca je dejavnik, ki preprečuje uravnoteženje
Prej smo omenili, da se rotorji delijo na toge in prožne. Togosti ali prožnosti rotorja ne smemo zamenjevati s togostjo ali gibljivostjo podpor (temelja), na katerih je rotor nameščen. Rotor velja za tog, kadar lahko zanemarimo njegovo deformacijo (upogibanje) pod vplivom centrifugalnih sil. Deformacija prožnega rotorja je razmeroma velika in je ni mogoče zanemariti.
V tem članku obravnavamo samo uravnoteženje togih rotorjev. Togi (nedeformabilni) rotor je lahko nameščen na toge ali gibljive (upogljive) podpore. Jasno je, da je tudi ta togost/premičnost nosilcev relativna, odvisna od hitrosti rotorja in velikosti posledičnih centrifugalnih sil. Pogojna meja je frekvenca lastnih vibracij nosilcev rotorja.
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.
Ko se rotor začne vrteti in se frekvenca njegovega vrtenja približa frekvenci lastnih vibracij, se amplituda vibracij močno poveča, kar lahko privede do porušitve konstrukcije.
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.
Določiti je mogoče frekvenco lastnih vibracij mehanizma pri izteku (pri izklopu vrtenja rotorja) ali z metodo udarca s poznejšo spektralno analizo odziva sistema na udarec.
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 in nelinearni modeli mehanskega sistema. Nelinearnost je dejavnik, ki preprečuje uravnoteženje
Pri uravnoteženju togih rotorjev se za izračune uravnoteženja uporabljajo matematični modeli, imenovani linearni modeli. Linearni model pomeni, da je v takem modelu ena količina sorazmerna (linearna) z drugo. Če se na primer podvoji nekompenzirana masa na rotorju, se podvoji tudi vrednost vibracij. Za toge rotorje se lahko uporabi linearni model, saj se ne deformirajo.
Pri prožnih rotorjih linearnega modela ni več mogoče uporabiti. Če se pri prožnem rotorju med vrtenjem poveča masa težke točke, pride do dodatne deformacije, poleg mase pa se poveča tudi polmer lokacije težke točke. Zato se pri prožnem rotorju vibracije povečajo za več kot dvakrat in običajne metode izračuna ne delujejo.
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.
Balansirne naprave in balansirni stroji
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
Ta postopek lahko izvedete 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 (najpogostejša) metoda vključuje premikanje, nameščanje ali odstranjevanje korekcijskih uteži na rotorju, ki so nameščene tako, da je vztrajnostna os rotorja čim bližje njegovi osi vrtenja.
Premikanje, dodajanje ali odstranjevanje korekcijskih uteži med uravnoteženjem se lahko izvede z različnimi tehnološkimi postopki, vključno z vrtanjem, rezkanjem, površinskim navarjanjem, varjenjem, vijačenjem ali odvijanjem, žganjem z laserskim ali elektronskim žarkom, elektrolizo, elektromagnetnim navarjanjem itd.
Postopek uravnoteženja je mogoče 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.
Te naprave vključujejo:
- merilno in računsko enoto, ki temelji na računalniku ali industrijskem krmilniku;
- dva (ali več) senzorjev vibracij;
- a phase angle sensor;
- dodatke za namestitev senzorjev na lokaciji;
- specializirana programska oprema, zasnovana za izvedbo celotnega cikla merjenja parametrov vibracij rotorja v eni, dveh ali več korekcijskih ravninah.
Trenutno se najpogosteje uporabljata dve vrsti strojev za uravnoteženje:
- 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 togih rotorjev
Pomembno!
- Z uravnoteženjem se odpravijo le vibracije, ki nastanejo zaradi asimetrične porazdelitve mase rotorja glede na njegovo os vrtenja. Druge vrste vibracij se z uravnoteženjem ne odpravijo!
- Tehnični mehanizmi, katerih zasnova zagotavlja odsotnost resonanc pri delovni frekvenci vrtenja, ki so zanesljivo pritrjeni na temelje in nameščeni v uporabne ležaje, so predmet uravnoteženja.
- Okvarjene stroje je treba pred uravnoteženjem popraviti. V nasprotnem primeru kakovostno uravnoteženje ni mogoče.
Uravnoteženje ne more nadomestiti popravila!
Glavna naloga uravnoteženja je določiti maso in položaj kompenzacijskih uteži, ki delujejo proti centrifugalnim silam.
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 izvaja dinamično uravnoteženje (metoda treh zagonov)
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 isto vrsto mehanizmov enake zasnove bodo koeficienti vpliva blizu. Možno jih je shraniti v pomnilnik računalnika in jih uporabiti za uravnoteženje istovrstnih mehanizmov brez preskusnih voženj, kar znatno poveča produktivnost uravnoteženja. Upoštevajte, da je treba maso preskusnih uteži izbrati tako, da se parametri vibracij ob namestitvi preskusnih uteži opazno spremenijo. V nasprotnem primeru se poveča napaka pri izračunu koeficientov vpliva in poslabša kakovost uravnoteženja.
Kot je razvidno s slike 1, centrifugalna sila deluje v radialni smeri, torej pravokotno na os rotorja. Zato morajo biti senzorji vibracij nameščeni tako, da je tudi njihova os občutljivosti usmerjena v radialno smer. Običajno je togost temelja v vodoravni smeri manjša, zato so vibracije v vodoravni smeri večje. Zato je za povečanje občutljivosti priporočljivo senzorje namestiti tako, da je njihova os občutljivosti usmerjena tudi vodoravno. Čeprav bistvene razlike ni. Poleg vibracij v radialni smeri je treba spremljati tudi vibracije v aksialni smeri, vzdolž osi vrtenja rotorja. Te vibracije običajno ne povzroča neuravnoteženost, temveč drugi vzroki, predvsem povezani z neporavnanostjo gredi, povezanih prek sklopke.
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 članki (primeri balansirnih stojal)
- Stojalo za uravnoteženje z mehko oporo
- Uravnoteženje rotorjev elektromotorjev
- Enostavna, a učinkovita stojala za uravnoteženje
Merila za ocenjevanje kakovosti mehanizmov 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 ena and the service angular velocity ω, expressed in mm/s:
- ω = 2π·n / 60 [rad/s], where n is the service speed in rpm;
- ena = G · 1000 / ω [g·mm/kg] (numerically equal to µm of center-of-mass offset) — equivalently ena = 9549 · G / n;
- Una = ena · 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; ena = 6.3 · 1000 / 314.2 = 20.1 g·mm/kg (cross-check: 9549 · 6.3 / 3000 ≈ 20.1); Una = 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 Una.
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.
Vendar upoštevanje določenih toleranc ne more v celoti zagotoviti zanesljivosti delovanja mehanizma, ki je povezana z doseganjem najnižje ravni vibracij. To pojasnjuje dejstvo, da velikost vibracij mehanizma ni odvisna le od velikosti sile, povezane s preostalo neuravnoteženostjo njegovega rotorja, temveč tudi od več drugih parametrov, vključno s togostjo k konstrukcijskih elementov mehanizma, njegovo maso m, faktorjem dušenja in frekvenco vrtenja. Zato je za oceno dinamičnih lastnosti mehanizma (vključno s kakovostjo njegovega ravnotežja) v številnih primerih priporočljivo oceniti raven preostalih vibracij mehanizma, ki jo urejajo številni standardi.
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 | 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.
Standardi in 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.
POGOSTA VPRAŠANJA
Ali uravnoteženje odstrani vse vibracije?
Ne. Uravnoteženje odstrani vibracije, ki jih povzroča asimetrična porazdelitev mase rotorja glede na njegovo vrtilno os. Vibracije zaradi nepravilne poravnave, napak ležajev, aerodinamičnih/hidrodinamičnih sil, elektromagnetnih sil in drugih vzrokov zahtevajo ločeno diagnostiko in korektivne ukrepe.
Zakaj lahko uravnoteženje odpove blizu resonance?
V bližini resonance lahko majhne spremembe hitrosti povzročijo velike spremembe amplitude vibracij in fazni premik za 180°. V takih pogojih postanejo rezultati meritev nestabilni in običajni postopki uravnoteženja morda ne bodo konvergirali brez posebnih metod.
Kdaj potrebujete uravnoteženje v eni ravnini v primerjavi z uravnoteženjem v dveh ravninah?
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.
Dve letali 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.
Kaj je treba storiti pred uravnoteženjem?
Prepričajte se, da je stroj v dobrem stanju: zanesljiva pritrditev na temelj, zdravi ležaji, odsotnost večje zračnosti in odsotnost očitnih virov nelinearnosti. Uravnoteženje ni nadomestilo za popravilo.
Ključne ugotovitve
- Uravnoteženje popravi vzbujanje, povezano z maso (centrifugalno); ne rešuje pa nepravilne poravnave, poškodb ležajev ali elektromagnetnih/aerodinamičnih virov.
- Resonanca in nelinearnost lahko povzročita, da je konvencionalno uravnoteženje neučinkovito ali nevarno.
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
