Rotora balansēšana: statiskais un dinamiskais disbalanss, rezonanse un praktiskā procedūra
Šajā rokasgrāmatā ir izskaidrots rotora balansēšana par stingri 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.
Saturs
- Kas ir rotors un ko balansēšana labo?
- Rotoru veidi un nelīdzsvarotības veidi
- Mehānismu vibrācija: ko balansēšana var un ko nevar novērst
- Rezonanse: faktors, kas novērš balansēšanu
- Lineārie un nelineārie modeļi: kad aprēķini pārstāj darboties
- Balansēšanas ierīces un balansēšanas mašīnas
- Cieto rotoru balansēšana (praktiskas piezīmes)
- Kā tiek veikta dinamiskā balansēšana (trīs palaidienu metode)
- Balansēšanas kvalitātes novērtēšanas kritēriji
- Standarti un atsauces
- BIEŽĀK UZDOTIE JAUTĀJUMI
Kas ir rotors un ko balansēšana labo?
Rotors ir korpuss, kas griežas ap kādu asi un ko balstos notur gultņu virsmas. Rotora gultņu virsmas pārnes slodzi uz balstiem, izmantojot rites vai slīdošos gultņus. Gultņu virsmas ir trunnionu virsmas vai virsmas, kas tos aizstāj.
Perfekti līdzsvarotā rotorā tā masa ir sadalīta simetriski ap rotācijas asi, t.i., jebkuru rotora elementu var saskaņot ar citu elementu, kas atrodas simetriski ap rotācijas asi. Līdzsvarotā rotorā centrbēdzes spēks, kas iedarbojas uz jebkuru rotora elementu, ir līdzsvarots ar centrbēdzes spēku, kas iedarbojas uz simetrisko elementu. Piemēram, uz 1. un 2. elementu (1. attēlā atzīmēti ar zaļu krāsu) iedarbojas centrbēdzes spēki F1 un F2, kuru lielums ir vienāds un virziens pretējs. Tas attiecas uz visiem simetriskajiem rotora elementiem, un tādējādi kopējais centrbēdzes spēks, kas iedarbojas uz rotoru, ir 0, un rotors ir līdzsvarots.
Taču, ja rotora simetrija ir izjaukta (asimetriskais elements 1. att. atzīmēts sarkanā krāsā), tad uz rotoru iedarbojas nelīdzsvarots centrbēdzes spēks F3. Rotācijai notiekot, šis spēks maina virzienu līdz ar rotora pagriešanos. Šī spēka radītā dinamiskā slodze tiek pārnesta uz gultņiem, izraisot paātrinātu nolietojumu.
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.
Balansēšanas uzdevums ir atrast vienas vai vairāku balansēšanas masu lielumu un atrašanās vietu (leņķi).
Rotoru veidi un nelīdzsvarotības veidi
Ņemot vērā rotora materiāla izturību un uz to iedarbojošos centrbēdzes spēku lielumu, rotorus var iedalīt divos veidos - stingros rotoros un elastīgos rotoros.
Pie darba režīmiem stingrie rotori centrbēdzes spēka iedarbībā deformējas nenozīmīgi, un šīs deformācijas ietekmi aprēķinos var neņemt vērā.
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:
- statiskais disbalanss — 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;
- dinamiskais disbalanss — 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.
Spēki F1 un F2 neatrodas uz vienas līnijas un nekompensē viens otru.
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.
Elektromagnētiskie spēki 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.
Mehānismu vibrācija
Vibrācija ir mehānisma konstrukcijas reakcija uz ciklisku uzbudinoša spēka iedarbību. Šim spēkam var būt dažāda rakstura.
Centrbēdzes spēks, kas rodas nelīdzsvarota rotora dēļ, ir nekompensēts spēks, kas iedarbojas uz "smago punktu". Tieši šo spēku un tā radīto vibrāciju var novērst, līdzsvarojot rotoru.
"Ģeometriska" rakstura mijiedarbības spēki, kas rodas savienojošo detaļu ražošanas un montāžas kļūdu dēļ. Šie spēki var rasties, piemēram, vārpstas kakliņu neapaļīguma, zobratu zobu profilu kļūdu, gultņu skrejceļu viļņošanās, savienojošo vārpstu nepareizas izlīdzināšanas u. c. rezultātā. Ja vārpstas kakliņi nav apaļi, vārpstas ass tiks nobīdīta atkarībā no vārpstas griešanās leņķa. Lai gan šī vibrācija rodas arī pie rotora ātruma, to ir gandrīz neiespējami novērst ar balansēšanu.
Aerodinamiskie spēki, ko rada ventilatoru lāpstiņrati un citi lāpstiņu mehānismi. Hidrodinamiskie spēki, ko rada hidraulisko sūkņu, turbīnu u. c. mehānismu lāpstiņrati.
Elektromagnētiskie spēki, kas rodas elektrisko mašīnu darbības rezultātā, piemēram, asimetriski rotora tinumi, īssavienoti tinumi utt.
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.
Vibrācijas un līdzsvara mehānismu mērīšanai var izmantot dažāda veida sensorus, tostarp:
- absolūtie vibrācijas sensori, kas paredzēti vibrācijas paātrinājuma mērīšanai (akselerometri) un vibrācijas ātruma sensori;
- relatīvās vibrācijas sensori - virpuļstrāvas vai kapacitatīvie, kas paredzēti vibrācijas pārvietojuma mērīšanai;
- Dažos gadījumos (ja mehānisma konstrukcija to atļauj) spēka sensorus var izmantot arī tā vibrācijas slodzes novērtēšanai; jo īpaši tos plaši izmanto cieto gultņu balansēšanas mašīnu balstu vibrācijas slodzes mērīšanai.
Tātad vibrācija ir mašīnas reakcija uz ārējo spēku iedarbību. Vibrācijas lielums ir atkarīgs ne tikai no spēka lieluma, kas iedarbojas uz mehānismu, bet arī no mehānisma konstrukcijas stingrības. Viens un tas pats spēks var izraisīt dažādas vibrācijas. Mašīnā ar cietajiem balstiem, pat ja vibrācija ir neliela, gultņi var tikt pakļauti ievērojamai dinamiskai slodzei. Tāpēc, balansējot mašīnas ar cietajiem balstiem, izmanto spēka, nevis vibrācijas sensorus (vibrācijas akselerometrus).
Vibrāciju sensorus izmanto mehānismos ar relatīvi lokaniem balstiem, kad nelīdzsvarota centrbēdzes spēka iedarbība izraisa ievērojamu balstu deformāciju un vibrāciju. Spēka sensorus izmanto cietiem balstiem, kad pat ievērojami spēki, ko izraisa nelīdzsvarotība, nerada ievērojamu vibrāciju.
Rezonanse ir faktors, kas kavē balansēšanu.
Iepriekš minējām, ka rotori ir iedalīti cietajos un elastīgajos. Rotora stingrību vai elastību nedrīkst sajaukt ar balstu (pamatu), uz kuriem rotors ir uzstādīts, stingrību vai kustīgumu. Rotoru uzskata par cietu, ja tā deformāciju (saliekumu) centrbēdzes spēku ietekmē var neņemt vērā. Elastīga rotora deformācija ir relatīvi liela, un to nevar neņemt vērā.
Šajā rakstā mēs aplūkojam tikai cieto rotoru balansēšanu. Savukārt cietu (nedeformējamu) rotoru var uzstādīt uz nekustīgiem vai kustīgiem (lokaniem) balstiem. Skaidrs, ka arī šī balstu stingrība/atlaidība ir relatīva atkarībā no rotora ātruma un no tā izrietošo centrbēdzes spēku lieluma. Nosacījuma robeža ir rotora balstu dabisko vibrāciju frekvence.
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.
Kad rotors sāk griezties un tā rotācijas frekvence tuvojas dabisko vibrāciju frekvencei, vibrāciju amplitūda strauji palielinās, kas var izraisīt konstrukcijas sabrukšanu.
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.
Ir iespējams noteikt mehānisma dabisko svārstību frekvenci brīvgaitas laikā (izslēdzot rotora rotāciju) vai ar trieciena metodi, pēc tam veicot sistēmas reakcijas uz triecienu spektrālo analīzi.
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.
Mehāniskas sistēmas lineārie un nelineārie modeļi. Nelinearitāte ir faktors, kas kavē balansēšanu.
Balansējot stingrus rotorus, balansēšanas aprēķiniem izmanto matemātiskos modeļus, ko sauc par lineārajiem modeļiem. Lineārs modelis nozīmē, ka šādā modelī viens lielums ir proporcionāls (lineārs) otram. Piemēram, ja rotora nekompensētā masa tiek dubultota, tad arī vibrācijas vērtība dubultosies. Stingriem rotoriem var izmantot lineāro modeli, jo tie nedeformējas.
Elastīgiem rotoriem lineāro modeli vairs nevar izmantot. Elastīgam rotoram, ja rotācijas laikā palielinās smagā punkta masa, rodas papildu deformācija, un papildus masai palielināsies arī smagā punkta atrašanās vietas rādiuss. Tāpēc elastīgam rotoram vibrācijas palielināsies vairāk nekā divas reizes, un parastās aprēķinu metodes nedarbosies.
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.
Balansēšanas ierīces un balansēšanas mašīnas
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
Šo procesu var veikt, izmantojot divas metodes.
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.
Otrā (visizplatītākā) metode ietver korekcijas atsvaru pārvietošanu, uzstādīšanu vai noņemšanu uz rotora, kas tiek novietoti tā, lai rotora inerces ass atrastos pēc iespējas tuvāk tā rotācijas asij.
Korekcijas atsvaru pārvietošanu, pievienošanu vai noņemšanu balansēšanas laikā var veikt ar dažādām tehnoloģiskām operācijām, tostarp urbšanu, frēzēšanu, virsmas apstrādi, metināšanu, skrūvēšanu vai atskrūvēšanu, dedzināšanu ar lāzeru vai elektronu staru kūli, elektrolīzi, elektromagnētisko virsmas apstrādi utt.
Balansēšanas procesu var veikt divējādi:
- 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.
Šīs ierīces ietver:
- mērīšanas un skaitļošanas bloks, kura pamatā ir dators vai rūpnieciskais kontrolieris;
- divi (vai vairāki) vibrācijas sensori;
- a phase angle sensor;
- piederumi sensoru uzstādīšanai uz vietas;
- specializēta programmatūra, kas izstrādāta, lai veiktu pilnu rotora vibrācijas parametru mērījumu ciklu vienā, divās vai vairākās korekcijas plaknēs.
Pašlaik visizplatītākās ir divu veidu balansēšanas mašīnas:
- 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.
Cieto rotoru balansēšana
Svarīgi!
- Balansēšana novērš tikai vibrāciju, ko izraisa rotora masas asimetrisks sadalījums attiecībā pret rotācijas asi. Balansēšana nenovērš cita veida vibrāciju!
- Balansēšanai tiek pakļauti tehniskie mehānismi, kuru konstrukcija nodrošina rezonanses neesamību rotācijas darba frekvencē, kas ir droši nostiprināti uz pamatnes, uzstādīti ekspluatācijā derīgos gultņos.
- Pirms balansēšanas jālabo bojātas mašīnas. Pretējā gadījumā kvalitatīva balansēšana nav iespējama.
Balansēšana neaizstāj remontu!
Balansēšanas galvenais uzdevums ir noteikt kompensācijas atsvaru masu un novietojumu, kas kompensē centrbēdzes spēkus.
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.
Kā tiek veikta dinamiskā balansēšana (trīs palaidienu metode)
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 korekcijas plakne. 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.
Vienāda tipa mehānismiem ar vienādu konstrukciju ietekmes koeficienti būs tuvi. Tos ir iespējams saglabāt datora atmiņā un izmantot vienāda tipa mehānismu balansēšanai bez testa palaidieniem, kas ievērojami palielina balansēšanas produktivitāti. Jāņem vērā, ka testa atsvaru masa jāizvēlas tāda, lai vibrācijas parametri ievērojami mainītos, kad tiek uzstādīti testa atsvari. Pretējā gadījumā palielinās ietekmes koeficientu aprēķina kļūda un pasliktinās balansēšanas kvalitāte.
Kā redzams 1. attēlā, centrbēdzes spēks darbojas radiālā virzienā, t. i., perpendikulāri rotora asij. Tāpēc vibrācijas sensori jāuzstāda tā, lai to jutības ass arī būtu vērsta radiālā virzienā. Parasti pamatnes stingrība horizontālajā virzienā ir mazāka, tāpēc vibrācija horizontālajā virzienā ir lielāka. Tādēļ, lai palielinātu jutību, sensorus ieteicams uzstādīt tā, lai to jutības ass būtu vērsta arī horizontāli. Lai gan principiālas atšķirības nav. Papildus vibrācijai radiālajā virzienā jāuzrauga arī vibrācija aksiālajā virzienā, gar rotora griešanās asi. Šo vibrāciju parasti neizraisa nelīdzsvarotība, bet citi cēloņi, galvenokārt saistīti ar caur sakabi savienoto vārpstu neizlīdzinājumu.
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.)
Saistītie raksti (balansēšanas statīvu piemēri)
- Balansēšanas statīvs ar mīkstu balstu
- Elektromotoru rotoru balansēšana
- Vienkārši, bet efektīvi balansēšanas statīvi
Balansēšanas mehānismu kvalitātes novērtēšanas kritēriji
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 euz vienu and the service angular velocity ω, expressed in mm/s:
- ω = 2π·n / 60 [rad/s], where n is the service speed in rpm;
- euz vienu = G · 1000 / ω [g·mm/kg] (numerically equal to µm of center-of-mass offset) — equivalently euz vienu = 9549 · G / n;
- Uuz vienu = euz vienu · 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; euz vienu = 6.3 · 1000 / 314.2 = 20.1 g·mm/kg (cross-check: 9549 · 6.3 / 3000 ≈ 20.1); Uuz vienu = 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 Uuz vienu.
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.
Tomēr atbilstība noteiktajām pielaidēm nevar pilnībā garantēt mehānisma darbības uzticamību, kas saistīta ar tā vibrācijas minimālā līmeņa sasniegšanu. Tas izskaidrojams ar to, ka mehānisma vibrācijas lielumu nosaka ne tikai spēka lielums, kas saistīts ar rotora atlikušo nelīdzsvarotību, bet tas ir atkarīgs arī no vairākiem citiem parametriem, tostarp no mehānisma konstrukcijas elementu stingrības k, tā masas m, slāpēšanas koeficienta, kā arī rotācijas frekvences. Tāpēc, lai novērtētu mehānisma dinamiskās īpašības (tostarp tā līdzsvara kvalitāti), vairākos gadījumos ieteicams novērtēt mehānisma atlikušo vibrāciju līmeni, ko reglamentē vairāki standarti.
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:
| Klase | 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.
Standarti un atsauces
- 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.
BIEŽĀK UZDOTIE JAUTĀJUMI
Vai balansēšana likvidē visas vibrācijas?
Nē. Balansēšana novērš vibrāciju, ko izraisa rotora masas asimetrisks sadalījums attiecībā pret tā rotācijas asi. Vibrācijai, ko izraisa asu nesakritība, gultņu defekti, aerodinamiskie/hidrodinamiskie spēki, elektromagnētiskie spēki un citi cēloņi, nepieciešama atsevišķa diagnostika un korektīvās darbības.
Kāpēc balansēšana var neizdoties rezonanses tuvumā?
Rezonanses tuvumā nelielas ātruma izmaiņas var izraisīt lielas vibrācijas amplitūdas izmaiņas un 180° fāzes nobīdi. Šādos apstākļos mērījumu rezultāti kļūst nestabili, un parastās balansēšanas procedūras var nekonverģēt bez īpašām metodēm.
Kad nepieciešama vienas plaknes vai divu plakņu balansēšana?
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.
Divas plaknes 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.
Kas jādara pirms balansēšanas?
Pārliecinieties, vai mašīna ir darbspējīga: drošs stiprinājums pie pamatnes, veseli gultņi, nav ievērojama vaļīguma un nav acīmredzamu nelinearitātes avotu. Balansēšana neaizstāj remontu.
Galvenie secinājumi
- Balansēšana koriģē ar masu saistīto (centrbēdzes) ierosmi; tā nenovērš vārpstu asu nesakritību, gultņu bojājumus vai elektromagnētiskus/aerodinamiskus ierosmes avotus.
- Rezonanse un nelinearitāte var padarīt tradicionālo balansēšanu neefektīvu vai nedrošu.
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
