Rotorbalancering: statisk og dynamisk ubalance, resonans og praktisk procedure
Denne guide forklarer Rotorafbalancering for stive rotorer: 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.
Indhold
- Hvad er en rotor, og hvad korrigerer balancering?
- Typer af rotorer og typer af ubalance
- Vibrationer i mekanismer: hvad balancering kan og ikke kan fjerne
- Resonans: en faktor, der forhindrer balancering
- Lineære vs. ikke-lineære modeller: Når beregninger holder op med at virke
- Afbalanceringsanordninger og afbalanceringsmaskiner
- Afbalancering af stive rotorer (praktiske noter)
- Hvordan dynamisk afbalancering udføres (trekørselsmetoden)
- Kriterier for vurdering af balanceringskvalitet
- Standarder og referencer
- OFTE STILLEDE SPØRGSMÅL
Hvad er en rotor, og hvad korrigerer balancering?
Rotoren er et legeme, der roterer om en akse og holdes fast af sine lejeflader i støtterne. Rotorens lejeflader overfører belastninger til støtterne via rulle- eller glidelejer. Lejeoverfladerne er overfladerne på drejetapperne eller de overflader, der erstatter dem.
I en perfekt afbalanceret rotor er dens masse fordelt symmetrisk omkring rotationsaksen, dvs. ethvert element i rotoren kan parres med et andet element, der er placeret symmetrisk omkring rotationsaksen. I en afbalanceret rotor er centrifugalkraften, der virker på ethvert rotorelement, afbalanceret af centrifugalkraften, der virker på det symmetriske element. For eksempel virker centrifugalkræfterne F1 og F2, der er lige store og modsatrettede i retning, på element 1 og 2 (markeret grønt i figur 1). Dette gælder for alle symmetriske rotorelementer, og dermed er den samlede centrifugalkraft, der virker på rotoren, 0, og rotoren er afbalanceret.
Men hvis rotorens symmetri brydes (et asymmetrisk element er markeret med rød farve i fig. 1), virker en ubalanceret centrifugalkraft F3 på rotoren. Under rotation ændrer denne kraft retning med rotorens rotation. Den dynamiske belastning som følge af denne kraft overføres til lejerne, hvilket resulterer i accelereret slitage.
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.
Opgaven med afbalancering er at finde størrelsen og placeringen (vinklen) af en eller flere afbalanceringsmasser.
Typer af rotorer og typer af ubalance
Under hensyntagen til rotorens materiales styrke og størrelsen af de centrifugalkræfter, der virker på den, kan rotorer opdeles i to typer - stive rotorer og fleksible rotorer.
Stive rotorer deformeres ubetydeligt under påvirkning af centrifugalkraften ved arbejdstilstande, og indflydelsen af denne deformation i beregningerne kan negligeres.
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:
- statisk ubalance — 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;
- dynamisk ubalance — 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.
Kræfterne F1 og F2 ligger ikke på samme linje og udligner ikke hinanden.
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.
Elektromagnetiske kræfter 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.
Vibration af mekanismer
Vibration er reaktionen fra mekanismens design på virkningerne af en cyklisk excitatorisk kraft. Denne kraft kan være af forskellig art.
Centrifugalkraften, der stammer fra den ubalancerede rotor, er en ukompenseret kraft, der virker på det "tunge punkt". Det er denne kraft og den vibration, der forårsages af den, som kan elimineres ved at afbalancere rotoren.
Interaktionskræfter af "geometrisk" karakter, der stammer fra fremstillings- og monteringsfejl i de modstående dele. Disse kræfter kan for eksempel opstå som følge af urunde akselhalse, fejl i tandprofiler i gear, bølgede lejebaner, forkert justering af modstående aksler osv. I tilfælde af urunde akseltappe vil akselaksen blive forskudt afhængigt af akselens rotationsvinkel. Selvom denne vibration også forekommer ved rotorhastighed, er det næsten umuligt at eliminere den ved afbalancering.
Aerodynamiske kræfter som følge af rotationen af ventilatorhjul og andre vingemekanismer. Hydrodynamiske kræfter som følge af rotation af løbehjul i hydrauliske pumper, turbiner osv.
Elektromagnetiske kræfter som følge af driften af elektriske maskiner, f.eks. asymmetriske rotorviklinger, kortsluttede viklinger osv.
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.
Forskellige typer sensorer kan bruges til at måle vibration og balance af mekanismer, herunder:
- Absolutte vibrationssensorer designet til at måle vibrationsacceleration (accelerometre) og vibrationshastighedssensorer;
- sensorer for relativ vibration - hvirvelstrøm eller kapacitiv, designet til at måle vibrationsforskydning;
- I nogle tilfælde (når mekanismens design tillader det) kan kraftsensorer også bruges til at vurdere dens vibrationsbelastning; især bruges de i vid udstrækning til at måle vibrationsbelastningen på understøtningerne i hard-bearing balanceringsmaskiner.
Vibrationer er altså en maskines reaktion på eksterne kræfter. Vibrationernes størrelse afhænger ikke kun af størrelsen af den kraft, der virker på mekanismen, men også af stivheden af mekanismens design. En og samme kraft kan føre til forskellige vibrationer. I en maskine med hårde lejer kan lejerne blive udsat for betydelige dynamiske belastninger, selv om vibrationerne er små. Det er derfor, man bruger kraftsensorer i stedet for vibrationssensorer (vibrationsaccelerometre) til afbalancering af maskiner med hårde lejer.
Vibrationssensorer bruges på mekanismer med relativt bøjelige understøtninger, når virkningen af ubalancerede centrifugalkræfter fører til en mærkbar deformation af understøtningerne og vibrationer. Kraftsensorer bruges til stive understøtninger, når selv betydelige kræfter på grund af ubalance ikke fører til betydelige vibrationer.
Resonans er en faktor, der forhindrer balancering
Vi har tidligere nævnt, at rotorer opdeles i stive og fleksible. Rotorens stivhed eller fleksibilitet må ikke forveksles med stivheden eller mobiliteten af de understøtninger (fundamenter), som rotoren er installeret på. En rotor betragtes som stiv, når dens deformation (bøjning) under påvirkning af centrifugalkræfter kan negligeres. Deformationen af en fleksibel rotor er relativt stor og kan ikke negligeres.
I denne artikel ser vi kun på afbalancering af stive rotorer. En stiv (ikke-deformerbar) rotor kan til gengæld være monteret på stive eller bevægelige (bøjelige) understøtninger. Det er klart, at understøtningernes stivhed/suspenderbarhed også er relativ, afhængigt af rotorens hastighed og størrelsen af de resulterende centrifugalkræfter. En betinget grænse er frekvensen af de naturlige vibrationer i rotorens understøtninger.
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.
Når rotoren begynder at rotere, og dens rotationsfrekvens nærmer sig frekvensen for naturlige vibrationer, øges vibrationsamplituden kraftigt, hvilket kan føre til ødelæggelse af strukturen.
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.
Det er muligt at bestemme frekvensen af mekanismens naturlige vibrationer ved udkørsel (ved at slukke for rotorens rotation) eller ved stødmetoden med den efterfølgende spektralanalyse af systemets reaktion på stødet.
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.
Lineære og ikke-lineære modeller af et mekanisk system. Ikke-linearitet er en faktor, der forhindrer afbalancering
Ved afbalancering af stive rotorer bruges matematiske modeller kaldet lineære modeller til afbalanceringsberegninger. En lineær model betyder, at i en sådan model er den ene størrelse proportional (lineær) med den anden. Hvis f.eks. den ukompenserede masse på rotoren fordobles, vil vibrationsværdien også fordobles. For stive rotorer kan man bruge en lineær model, da de ikke deformeres.
For fleksible rotorer kan den lineære model ikke længere bruges. For en fleksibel rotor, hvis massen af det tunge punkt øges under rotationen, vil der opstå yderligere deformation, og ud over massen vil radius for det tunge punkts placering også øges. For en fleksibel rotor vil vibrationerne derfor blive mere end fordoblet, og de sædvanlige beregningsmetoder vil ikke fungere.
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.
Afbalanceringsanordninger og afbalanceringsmaskiner
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
Denne proces kan udføres ved hjælp af to metoder.
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.
Den anden (mest almindelige) metode går ud på at flytte, installere eller fjerne korrektionsvægte på rotoren, som placeres, så rotorens inertiakse er så tæt på dens rotationsakse som muligt.
Flytning, tilføjelse eller fjernelse af korrektionsvægte under afbalancering kan udføres ved forskellige teknologiske operationer, herunder: boring, fræsning, overfladebehandling, svejsning, skruing eller afskruing, laser- eller elektronstrålebrænding, elektrolyse, elektromagnetisk overfladebehandling osv.
Afbalanceringsprocessen kan udføres på to måder:
- 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.
Disse enheder omfatter:
- en måle- og computerenhed baseret på en computer eller industriel controller;
- to (eller flere) vibrationssensorer;
- a phase angle sensor;
- tilbehør til montering af sensorerne på stedet;
- specialiseret software, der er designet til at udføre en fuld cyklus af måling af rotorvibrationsparametre i et, to eller flere korrektionsplaner.
To typer afbalanceringsmaskiner er i øjeblikket de mest almindelige:
- 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.
Afbalancering af stive rotorer
Vigtigt!
- Afbalancering eliminerer kun vibrationer, der skyldes asymmetrisk fordeling af rotormassen i forhold til rotationsaksen. Andre typer vibrationer elimineres ikke ved afbalancering!
- Tekniske mekanismer, hvis design sikrer fravær af resonanser ved driftsfrekvensen for rotation, pålideligt fastgjort på fundamentet, installeret i driftssikre lejer, er underlagt balancering.
- Defekte maskiner skal repareres før afbalancering. Ellers er kvalitetsafbalancering ikke mulig.
Afbalancering er ikke en erstatning for reparation!
Hovedopgaven ved afbalancering er at finde massen og placeringen af korrektionsvægte, som modvirker centrifugalkræfterne.
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.
Hvordan dynamisk afbalancering udføres (trekørselsmetoden)
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 korrektionsplan. 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.
For den samme type mekanismer med det samme design vil indflydelseskoefficienterne være tæt på hinanden. Det er muligt at gemme dem i computerens hukommelse og bruge dem til afbalancering af mekanismer af samme type uden testkørsler, hvilket øger produktiviteten ved afbalancering betydeligt. Bemærk, at testvægtenes masse skal vælges således, at vibrationsparametrene ændres mærkbart, når testvægtene installeres. Ellers øges fejlen ved beregning af indflydelseskoefficienter, og kvaliteten af afbalanceringen forringes.
Som det ses af fig. 1, virker centrifugalkraften i radial retning, dvs. vinkelret på rotoraksen. Derfor skal vibrationssensorerne installeres, så deres følsomhedsakse også peger i radial retning. Normalt er fundamentets stivhed i vandret retning mindre, så vibrationerne i vandret retning er højere. For at øge følsomheden bør sensorerne derfor installeres, så deres følsomhedsakse også er rettet vandret. Selvom der ikke er nogen grundlæggende forskel. Ud over vibration i radial retning skal vibration i aksial retning langs rotorens rotationsakse overvåges. Denne vibration skyldes normalt ikke ubalance, men andre årsager, hovedsageligt relateret til fejljustering af de aksler, der er forbundet via koblingen.
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.)
Relaterede artikler (eksempler på balanceringsstativer)
- Balanceringsstativ med blød støtte
- Afbalancering af rotorerne i elektriske motorer
- Enkle, men effektive balancestativer
Kriterier for vurdering af kvaliteten af balanceringsmekanismer
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 epr. and the service angular velocity ω, expressed in mm/s:
- ω = 2π·n / 60 [rad/s], where n is the service speed in rpm;
- epr. = G · 1000 / ω [g·mm/kg] (numerically equal to µm of center-of-mass offset) — equivalently epr. = 9549 · G / n;
- Upr. = epr. · 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; epr. = 6.3 · 1000 / 314.2 = 20.1 g·mm/kg (cross-check: 9549 · 6.3 / 3000 ≈ 20.1); Upr. = 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 Upr..
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.
Overholdelse af de specificerede tolerancer kan dog ikke fuldt ud garantere mekanismens driftssikkerhed i forbindelse med opnåelse af et minimumsniveau for dens vibrationer. Det skyldes, at størrelsen af mekanismens vibrationer ikke kun bestemmes af størrelsen af den kraft, der er forbundet med den resterende ubalance i rotoren, men også afhænger af flere andre parametre, herunder: stivheden k af mekanismens strukturelle elementer, dens masse m, dæmpningsfaktoren samt rotationsfrekvensen. For at estimere mekanismens dynamiske egenskaber (herunder kvaliteten af dens balance) anbefales det derfor i en række tilfælde at estimere mekanismens restvibrationsniveau, som er reguleret af en række standarder.
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:
| Klasse | 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.
Standarder og referencer
- 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.
OFTE STILLEDE SPØRGSMÅL
Fjerner balancering alle vibrationer?
Nej. Afbalancering fjerner vibrationer forårsaget af den asymmetriske fordeling af rotormasse i forhold til dens rotationsakse. Vibrationer fra forkert justering, lejefejl, aerodynamiske/hydrodynamiske kræfter, elektromagnetiske kræfter og andre årsager kræver separat diagnosticering og korrigerende handlinger.
Hvorfor kan balancering svigte nær resonans?
Nær resonans kan små hastighedsændringer forårsage store ændringer i vibrationsamplitude og et faseskift på 180°. Under sådanne forhold bliver måleresultaterne ustabile, og konventionelle afbalanceringsprocedurer kan muligvis ikke konvergere uden særlige metoder.
Hvornår har du brug for balancering i ét plan vs. i to plan?
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.
To fly 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.
Hvad skal der gøres før balancering?
Sørg for, at maskinen er brugbar: pålidelig montering på fundamentet, sunde lejer, ingen alvorlig løshed og ingen åbenlyse kilder til ikke-linearitet. Afbalancering er ikke en erstatning for reparation.
Vigtige konklusioner
- Afbalancering korrigerer masserelateret (centrifugal) eksitation; det løser ikke fejljustering, lejeskader eller elektromagnetiske/aerodynamiske kilder.
- Resonans og ikke-linearitet kan gøre konventionel balancering ineffektiv eller usikker.
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
