Pengimbangan rotor: ketidakseimbangan statik dan dinamik, resonans dan prosedur praktikal
Panduan ini menerangkan pengimbangan rotor untuk rotor tegar: 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.
Kandungan
- Apakah itu rotor dan apakah yang diperbetulkan oleh pengimbangan?
- Jenis-jenis rotor dan jenis ketidakseimbangan
- Getaran mekanisme: apa yang boleh dan tidak boleh disingkirkan oleh pengimbangan
- Resonans: faktor yang menghalang pengimbangan
- Model linear vs. tak linear: apabila pengiraan berhenti berfungsi
- Peranti pengimbangan dan mesin pengimbangan
- Mengimbangi rotor tegar (nota praktikal)
- Cara pengimbangan dinamik dilakukan (kaedah tiga larian)
- Kriteria untuk menilai kualiti pengimbangan
- Piawaian dan rujukan
- Soalan Lazim
Apakah itu rotor dan apakah yang diperbetulkan oleh pengimbangan?
Rotor ialah suatu badan yang berputar di sekitar suatu paksi dan dipegang oleh permukaan galasnya dalam penyokong. Permukaan galas rotor memindahkan beban ke penyokong melalui galas gelinding atau galas gelincir. Permukaan galas ialah permukaan trunnion atau permukaan yang menggantikannya.
Dalam rotor yang seimbang sempurna, jisimnya diagihkan secara simetri mengelilingi paksi putaran, iaitu, mana-mana elemen rotor boleh dipadankan dengan elemen lain yang terletak secara simetri mengelilingi paksi putaran. Dalam rotor yang seimbang, daya emparan yang bertindak pada mana-mana elemen rotor diseimbangkan oleh daya emparan yang bertindak pada elemen simetri tersebut. Contohnya, daya emparan F1 dan F2, yang sama magnitud dan bertentangan arah, bertindak pada elemen 1 dan 2 (ditanda hijau dalam Rajah 1). Ini adalah benar untuk semua elemen rotor simetri, dan dengan itu jumlah daya emparan yang bertindak pada rotor ialah 0 dan rotor seimbang.
Tetapi jika simetri rotor terganggu (elemen tidak simetri ditandakan dengan warna merah pada Rajah 1), maka daya sentrifugal tidak seimbang F3 bertindak ke atas rotor. Semasa berputar, daya ini mengubah arah mengikut putaran rotor. Beban dinamik yang terhasil daripada daya ini disalurkan ke galas, menyebabkan keausan dan kerosakan yang dipercepatkan.
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.
Tugas penyeimbangan ialah mencari saiz dan kedudukan (sudut) satu atau lebih jisim penyeimbang.
Jenis-jenis rotor dan jenis ketidakseimbangan
Dengan mengambil kira kekuatan bahan rotor dan magnitud daya emparan yang bertindak ke atasnya, rotor boleh dibahagikan kepada dua jenis - rotor tegar dan rotor fleksibel.
Rotor kaku mengalami deformasi yang tidak ketara di bawah tindakan daya sentrifugal pada mod operasi, dan pengaruh deformasi ini dalam pengiraan boleh diabaikan.
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:
- ketidakseimbangan statik — 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;
- ketidakseimbangan dinamik — 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.
Gaya F1 dan F2 tidak terletak pada satu garisan dan tidak saling mengimbangi.
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.
Daya elektromagnet 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.
Getaran mekanisme
Getaran ialah tindak balas reka bentuk mekanisme terhadap kesan daya rangsangan kitaran. Daya ini boleh mempunyai pelbagai sifat.
Daya emparan yang terhasil daripada rotor yang tidak seimbang ialah daya tidak terkompensasi yang bertindak pada "titik berat". Daya inilah dan getaran yang disebabkan olehnya yang boleh dihapuskan dengan mengimbangi rotor.
Daya interaksi bersifat "geometri" yang timbul daripada ralat pembuatan dan pemasangan bahagian-bahagian yang sepadan. Daya-daya ini boleh, sebagai contoh, timbul akibat ketidakbulatan leher aci, ralat dalam profil gigi dalam gear, kealunan landasan galas, ketidaksejajaran aci yang sepadan, dsb. Dalam kes ketidakbulatan jurnal, paksi aci akan dialihkan bergantung pada sudut putaran aci. Walaupun getaran ini juga berlaku pada kelajuan rotor, hampir mustahil untuk menghapuskannya dengan mengimbangi.
Gaya aerodinamik yang terhasil daripada putaran impeller kipas dan mekanisme bilah lain. Gaya hidrodinamik yang terhasil daripada putaran impeller pam hidraulik, turbin, dan lain-lain.
Gaya elektromagnetik yang terhasil daripada operasi mesin elektrik, contohnya lilitan rotor tidak simetrik, lilitan litar pintas, dan lain-lain.
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.
Pelbagai jenis sensor boleh digunakan untuk mengukur getaran dan mekanisme imbangan, termasuk:
- penderia getaran mutlak yang direka untuk mengukur pecutan getaran (akselerometer) dan penderia kelajuan getaran;
- sensor getaran relatif - arus pusar atau kapasitif, direka untuk mengukur anjakan getaran;
- dalam beberapa kes (apabila reka bentuk mekanisme membenarkannya), sensor daya juga boleh digunakan untuk menilai beban getarannya; khususnya, ia digunakan secara meluas untuk mengukur beban getaran sokongan mesin pengimbang galas keras.
Jadi, getaran adalah tindak balas mesin terhadap tindakan daya luaran. Amplitud getaran bergantung bukan sahaja pada magnitud daya yang bertindak pada mekanisme, tetapi juga pada kekakuan reka bentuk mekanisme. Satu daya yang sama boleh menyebabkan getaran yang berbeza. Dalam mesin galas keras, walaupun getaran kecil, galas boleh mengalami beban dinamik yang ketara. Inilah sebabnya sensor daya dan bukannya sensor getaran (akselerometer getaran) digunakan semasa mengimbangkan mesin galas keras.
Penderia getaran digunakan pada mekanisme dengan penyokong yang agak lentur apabila tindakan daya sentrifugal tidak seimbang menyebabkan deformasi ketara pada penyokong dan getaran. Penderia daya digunakan untuk penyokong kaku apabila walaupun daya ketara akibat ketidakseimbangan tidak menyebabkan getaran ketara.
Resonans adalah faktor yang menghalang pengimbangan.
Sebelum ini kami menyebut bahawa rotor dibahagikan kepada kaku dan fleksibel. Kekakuan atau kefleksibelan rotor tidak seharusnya dikelirukan dengan kekakuan atau mobiliti penyokong (asas) di mana rotor dipasang. Sesebuah rotor dianggap kaku apabila deformasinya (pembengkokan) di bawah tindakan daya sentrifugal boleh diabaikan. Deformasi rotor fleksibel adalah relatif besar dan tidak boleh diabaikan.
Dalam artikel ini, kami hanya mempertimbangkan penyeimbangan rotor kaku. Rotor kaku (tidak boleh cacat) boleh dipasang pada penyokong kaku atau penyokong boleh alih (lentur). Jelas bahawa kekakuan/keupayaan penggantungan penyokong ini juga bersifat relatif, bergantung pada kelajuan rotor dan magnitudo daya sentrifugal yang terhasil. Ambang bersyarat ialah frekuensi getaran semula jadi penyokong rotor.
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.
Apabila rotor mula berputar dan frekuensi putarannya hampir dengan frekuensi getaran semula jadi, amplitud getaran meningkat dengan mendadak, yang boleh menyebabkan kemusnahan struktur.
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.
Adalah mungkin untuk menentukan frekuensi getaran semula jadi mekanisme semasa meluncur (apabila pemutaran rotor dimatikan) atau melalui kaedah hentakan dengan analisis spektral seterusnya terhadap tindak balas sistem terhadap hentakan.
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.
Model linear dan bukan linear bagi sistem mekanikal. Ketaklinearan adalah faktor yang menghalang pengimbangan.
Apabila mengimbangi rotor kaku, model matematik yang dipanggil model linear digunakan untuk pengiraan pengimbangan. Model linear bermaksud bahawa dalam model sedemikian, satu kuantiti adalah berkadar terus (linear) dengan kuantiti yang lain. Sebagai contoh, jika jisim tidak diimbangi pada rotor digandakan, nilai getaran juga akan digandakan. Bagi rotor kaku, model linear boleh digunakan kerana ia tidak mengalami deformasi.
Untuk rotor fleksibel, model linear tidak lagi boleh digunakan. Bagi rotor fleksibel, jika jisim titik berat meningkat semasa putaran, deformasi tambahan akan berlaku, dan selain jisim, jejari lokasi titik berat juga akan meningkat. Oleh itu, bagi rotor fleksibel, getaran akan meningkat lebih daripada dua kali ganda, dan kaedah pengiraan biasa tidak akan berfungsi.
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.
Peranti pengimbangan dan mesin pengimbangan
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
Proses ini boleh dilakukan melalui dua kaedah.
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.
Kaedah kedua (yang paling biasa) melibatkan memindahkan, memasang atau menanggalkan pemberat pembetulan pada rotor, yang diletakkan supaya paksi inersia rotor sedekat mungkin dengan paksi putarannya.
Memindahkan, menambah atau mengeluarkan berat pembetulan semasa penyeimbangan boleh dilaksanakan melalui pelbagai operasi teknologi termasuk: pengeboran, penggilingan, penimbunan permukaan, pengelasan, pemasangan atau penanggalan skru, pembakaran laser atau sinaran elektron, elektrolisis, pelapisan permukaan elektromagnetik, dan lain-lain.
Proses penyeimbangan boleh dilaksanakan dengan dua cara:
- 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.
Peranti-peranti ini termasuk:
- unit pengukuran dan pengiraan berasaskan komputer atau pengawal industri;
- dua (atau lebih) penderia getaran;
- a phase angle sensor;
- aksesori untuk memasang penderia di tapak;
- perisian khusus, direka untuk menjalankan kitaran penuh pengukuran parameter getaran rotor dalam satu, dua atau lebih satah pembetulan.
Dua jenis mesin penyeimbangan adalah yang paling biasa pada masa ini:
- 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.
Pengimbangan rotor kaku
Penting!
- Pengimbangan hanya menghapuskan getaran yang disebabkan oleh pengagihan jisim rotor secara tidak simetri berbanding paksi putarannya. Jenis getaran lain tidak dihapuskan oleh pengimbangan!
- Mekanisme teknikal yang reka bentuknya memastikan ketiadaan resonans pada frekuensi putaran operasi, dipasang dengan kukuh pada asas, dipasang dalam galas yang boleh diselenggara, dan tertakluk kepada penyeimbangan.
- Mesin yang rosak mesti dibaiki sebelum pengimbangan. Jika tidak, pengimbangan berkualiti tidak dapat dilakukan.
Pengimbangan tidak menggantikan pembaikan!
Tugas utama pengimbangan ialah mencari jisim dan lokasi berat pampasan yang mengimbangi daya emparan
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.
Cara pengimbangan dinamik dilakukan (kaedah tiga larian)
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 satah pembetulan. 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.
Untuk mekanisme jenis yang sama dengan reka bentuk yang sama, koefisien pengaruh akan hampir sama. Ia boleh disimpan dalam memori komputer dan digunakan untuk mengimbangkan mekanisme jenis yang sama tanpa menjalankan ujian, yang meningkatkan produktiviti pengimbangan dengan ketara. Perlu diingat bahawa jisim pemberat ujian hendaklah dipilih supaya parameter getaran berubah dengan ketara apabila pemberat ujian dipasang. Jika tidak, ralat pengiraan koefisien pengaruh akan meningkat dan kualiti pengimbangan akan merosot.
Seperti yang anda lihat dalam Rajah 1, daya emparan bertindak dalam arah jejari, iaitu berserenjang dengan paksi rotor. Oleh itu, sensor getaran mesti dipasang supaya paksi kepekaannya juga menunjuk ke arah jejari. Biasanya, kekakuan asas dalam arah mendatar adalah lebih rendah, jadi getaran dalam arah mendatar lebih tinggi. Oleh itu, untuk meningkatkan kepekaan, sensor hendaklah dipasang supaya paksi kepekaannya juga diarahkan secara mendatar. Walaupun tiada perbezaan asas. Selain getaran dalam arah jejari, getaran dalam arah paksi, sepanjang paksi putaran rotor, juga mesti dipantau. Getaran ini biasanya bukan disebabkan oleh ketidakseimbangan, tetapi oleh punca lain, terutamanya berkaitan dengan ketidakselarasan aci yang disambungkan melalui gandingan.
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.)
Artikel berkaitan (contoh penyangga pengimbang)
- Penyangga imbangan dengan sokongan lembut
- Mengimbangi rotor motor elektrik
- Penyangga imbangan yang ringkas tetapi berkesan
Kriteria untuk menilai kualiti mekanisme pengimbangan
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 eper and the service angular velocity ω, expressed in mm/s:
- ω = 2π·n / 60 [rad/s], where n is the service speed in rpm;
- eper = G · 1000 / ω [g·mm/kg] (numerically equal to µm of center-of-mass offset) — equivalently eper = 9549 · G / n;
- Uper = eper · 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; eper = 6.3 · 1000 / 314.2 = 20.1 g·mm/kg (cross-check: 9549 · 6.3 / 3000 ≈ 20.1); Uper = 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 Uper.
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.
Walau bagaimanapun, pematuhan kepada toleransi yang ditetapkan tidak dapat menjamin sepenuhnya kebolehpercayaan operasi mekanisme, yang berkaitan dengan pencapaian tahap minimum getarannya. Hal ini dijelaskan oleh hakikat bahawa magnitudo getaran mekanisme ditentukan bukan sahaja oleh magnitudo daya yang berkaitan dengan ketidakseimbangan sisa rotornya, tetapi juga bergantung kepada beberapa parameter lain, termasuk: kekakuan k elemen struktur mekanisme, massanya m, faktor peredaman, serta frekuensi putaran. Oleh itu, untuk menilai kualiti dinamik mekanisme (termasuk kualiti imbangannya) dalam beberapa kes, disyorkan untuk menganggarkan tahap getaran baki mekanisme, yang dikawal oleh beberapa piawaian.
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:
| Kelas | 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.
Piawaian dan rujukan
- 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.
Soalan Lazim
Adakah pengimbangan menghapuskan semua getaran?
Tidak. Pengimbangan menghilangkan getaran yang disebabkan oleh taburan jisim rotor yang tidak simetri berbanding paksi putarannya. Getaran daripada ketidaksejajaran, kecacatan galas, daya aerodinamik/hidrodinamik, daya elektromagnet dan punca lain memerlukan tindakan diagnostik dan pembetulan yang berasingan.
Mengapakah pengimbangan boleh gagal berhampiran resonans?
Berhampiran resonans, perubahan kelajuan yang kecil boleh menyebabkan perubahan besar dalam amplitud getaran dan anjakan fasa 180°. Dalam keadaan sedemikian, keputusan pengukuran menjadi tidak stabil dan prosedur pengimbangan konvensional mungkin tidak menumpu tanpa kaedah khas.
Bilakah anda memerlukan pengimbangan satu satah vs. dua satah?
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.
Dua pesawat 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.
Apakah yang perlu dilakukan sebelum melakukan pengimbangan?
Pastikan mesin boleh diservis: pemasangan yang boleh dipercayai pada asas, galas yang sihat, tiada kelonggaran yang teruk dan tiada punca ketidaklinearan yang jelas. Pengimbangan bukanlah pengganti pembaikan.
Kesimpulan penting
- Pengimbangan membetulkan pengujaan (emparan) yang berkaitan dengan jisim; ia tidak menyelesaikan ketidaksejajaran, kerosakan galas atau sumber elektromagnet/aerodinamik.
- Resonans dan ketaklinearan boleh menjadikan pengimbangan konvensional tidak berkesan atau tidak selamat.
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
