Penyeimbangan rotor: ketidakseimbangan statis dan dinamis, resonansi, dan prosedur praktis.
Panduan ini menjelaskan penyeimbangan rotor untuk rotor kaku: 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.
Isi
- Apa itu rotor dan apa yang dikoreksi oleh penyeimbangan?
- Jenis-jenis rotor dan jenis-jenis ketidakseimbangan
- Getaran pada mekanisme: apa yang dapat dan tidak dapat dihilangkan oleh penyeimbangan.
- Resonansi: faktor yang mencegah penyeimbangan
- Model linier vs. nonlinier: kapan perhitungan berhenti berfungsi
- Perangkat penyeimbang dan mesin penyeimbang
- Penyeimbangan rotor kaku (catatan praktis)
- Cara melakukan penyeimbangan dinamis (metode tiga kali jalan)
- Kriteria untuk menilai kualitas penyeimbangan
- Standar dan referensi
- FAQ
Apa itu rotor dan apa yang dikoreksi oleh penyeimbangan?
Rotor adalah sebuah benda yang berputar pada suatu sumbu dan dipegang oleh permukaan bantalan pada penyangga. Permukaan bantalan rotor mengirimkan beban ke penyangga melalui bantalan gelinding atau geser. Permukaan bantalan adalah permukaan trunnion atau permukaan yang menggantikannya.
Pada rotor yang seimbang sempurna, massanya terdistribusi secara simetris terhadap sumbu rotasi, yaitu, setiap elemen rotor dapat dipasangkan dengan elemen lain yang terletak simetris terhadap sumbu rotasi. Pada rotor yang seimbang, gaya sentrifugal yang bekerja pada setiap elemen rotor diimbangi oleh gaya sentrifugal yang bekerja pada elemen simetris. Misalnya, gaya sentrifugal F1 dan F2, yang besarnya sama dan arahnya berlawanan, bekerja pada elemen 1 dan 2 (ditandai hijau pada Gambar 1). Hal ini berlaku untuk semua elemen rotor simetris, sehingga total gaya sentrifugal yang bekerja pada rotor adalah 0 dan rotor tersebut seimbang.
Namun jika simetri rotor rusak (elemen asimetris ditandai dengan warna merah pada Fig. 1), maka gaya sentrifugal tak seimbang F3 bekerja pada rotor. Saat berputar, arah gaya ini berubah mengikuti putaran rotor. Beban dinamis yang dihasilkan oleh gaya ini diteruskan ke bantalan, sehingga menyebabkan keausan yang dipercepat.
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 menyeimbangkan adalah menemukan ukuran dan lokasi (sudut) dari satu atau lebih massa penyeimbang.
Jenis-jenis rotor dan jenis-jenis ketidakseimbangan
Dengan mempertimbangkan kekuatan material rotor dan besarnya gaya sentrifugal yang bekerja padanya, rotor dapat dibagi menjadi dua jenis - rotor kaku dan rotor fleksibel.
Rotor yang kaku berubah bentuk secara tidak signifikan di bawah aksi gaya sentrifugal pada mode kerja dan pengaruh deformasi ini dalam perhitungan dapat 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 statis — 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 dinamis — 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 garis yang sama 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.
Kekuatan elektromagnetik 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 adalah reaksi dari desain mekanisme terhadap efek gaya eksitasi siklik. Gaya ini dapat memiliki sifat yang berbeda.
Gaya sentrifugal yang dihasilkan dari rotor yang tidak seimbang adalah gaya yang tidak terkompensasi yang bekerja pada "titik berat". Gaya inilah dan getaran yang ditimbulkannya yang dapat dihilangkan dengan menyeimbangkan rotor.
Gaya interaksi yang bersifat "geometris" yang timbul dari kesalahan manufaktur dan perakitan bagian-bagian yang saling berpasangan. Gaya-gaya ini dapat timbul, misalnya, akibat ketidakbulatan leher poros, kesalahan pada profil gigi roda gigi, gelombang pada jalur bantalan, ketidaksejajaran poros yang saling berpasangan, dan lain-lain. Dalam kasus ketidakbulatan jurnal, sumbu poros akan bergeser tergantung pada sudut putaran poros. Meskipun getaran ini juga terjadi pada kecepatan rotor, hampir tidak mungkin untuk menghilangkannya dengan penyeimbangan.
Gaya aerodinamis yang dihasilkan dari rotasi impeler kipas dan mekanisme baling-baling lainnya. Gaya hidrodinamis yang dihasilkan dari rotasi impeler pompa hidraulik, turbin, dll.
Gaya elektromagnetik yang dihasilkan dari pengoperasian mesin listrik, misalnya belitan rotor asimetris, belitan korsleting, dll.
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.
Berbagai jenis sensor dapat digunakan untuk mengukur getaran dan mekanisme penyeimbangan, termasuk:
- sensor getaran absolut yang dirancang untuk mengukur akselerasi getaran (akselerometer) dan sensor kecepatan getaran;
- sensor getaran relatif - arus eddy atau kapasitif, dirancang untuk mengukur perpindahan getaran;
- Dalam beberapa kasus (bila desain mekanisme memungkinkan), sensor gaya juga dapat digunakan untuk menilai beban getarannya; khususnya, sensor ini banyak digunakan untuk mengukur beban getaran pada penyangga mesin penyeimbang bantalan keras.
Jadi, getaran adalah reaksi mesin terhadap aksi gaya eksternal. Besarnya getaran tidak hanya bergantung pada besarnya gaya yang bekerja pada mekanisme, tetapi juga pada kekakuan desain mekanisme. Satu gaya yang sama dapat menyebabkan getaran yang berbeda. Pada mesin dengan bantalan keras, meskipun getarannya kecil, bantalan dapat mengalami beban dinamis yang signifikan. Inilah sebabnya mengapa sensor gaya dan bukan sensor getaran (akselerometer getaran) digunakan saat menyeimbangkan mesin dengan bantalan keras.
Sensor getaran digunakan pada mekanisme dengan penyangga yang relatif lentur, ketika aksi gaya sentrifugal yang tidak seimbang menyebabkan deformasi penyangga dan getaran yang nyata. Sensor gaya digunakan untuk penyangga yang kaku, bahkan ketika gaya yang signifikan akibat ketidakseimbangan tidak menyebabkan getaran yang signifikan.
Resonansi adalah faktor yang mencegah penyeimbangan
Sebelumnya kami telah menyebutkan bahwa rotor dibagi menjadi kaku dan fleksibel. Kekakuan atau fleksibilitas rotor tidak boleh disamakan dengan kekakuan atau mobilitas penyangga (pondasi) tempat rotor dipasang. Rotor dianggap kaku ketika deformasi (pembengkokan) di bawah aksi gaya sentrifugal dapat diabaikan. Deformasi rotor fleksibel relatif besar dan tidak dapat diabaikan.
Dalam artikel ini, kami hanya membahas penyeimbangan rotor kaku. Rotor yang kaku (tidak dapat diubah bentuknya) pada gilirannya dapat dipasang pada penyangga yang kaku atau dapat digerakkan (lentur). Jelas bahwa kekakuan/kelenturan penyangga ini juga relatif, tergantung pada kecepatan rotor dan besarnya gaya sentrifugal yang dihasilkan. Batas kondisional adalah frekuensi getaran alami penyangga 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.
Ketika rotor mulai berputar dan frekuensi putarannya mendekati frekuensi getaran alami, amplitudo getaran meningkat tajam, yang dapat menyebabkan kerusakan 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.
Dimungkinkan untuk menentukan frekuensi getaran alami mekanisme pada saat meluncur (pada saat mematikan putaran rotor) atau dengan metode guncangan dengan analisis spektral berikutnya dari respons sistem terhadap guncangan.
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 linier dan nonlinier dari suatu sistem mekanis. Non-linearitas adalah faktor yang mencegah penyeimbangan
Ketika menyeimbangkan rotor kaku, model matematis yang disebut model linier digunakan untuk perhitungan penyeimbangan. Model linier berarti bahwa dalam model tersebut, satu kuantitas sebanding (linier) dengan kuantitas lainnya. Sebagai contoh, jika massa yang tidak terkompensasi pada rotor digandakan, maka nilai getaran juga akan menjadi dua kali lipat. Untuk rotor yang kaku, model linier dapat digunakan, karena tidak berubah bentuk.
Untuk rotor fleksibel, model linier tidak dapat lagi digunakan. Untuk rotor fleksibel, jika massa titik berat meningkat selama rotasi, deformasi tambahan akan terjadi, dan selain massa, jari-jari lokasi titik berat juga akan meningkat. Oleh karena itu, untuk rotor fleksibel, getaran akan meningkat lebih dari dua kali lipat, dan metode perhitungan yang biasa tidak akan berhasil.
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.
Perangkat penyeimbang dan mesin penyeimbang
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
Proses ini dapat dilakukan dengan dua metode.
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.
Metode kedua (yang paling umum) melibatkan pemindahan, pemasangan, atau pelepasan bobot koreksi pada rotor, yang ditempatkan sedemikian rupa sehingga sumbu inersia rotor sedekat mungkin dengan sumbu rotasinya.
Memindahkan, menambah, atau melepas bobot koreksi selama penyeimbangan dapat dilakukan dengan berbagai operasi teknologi, termasuk: pengeboran, penggilingan, pengerjaan permukaan, pengelasan, memasang atau melepaskan sekrup, pembakaran sinar laser atau elektron, elektrolisis, pelapisan permukaan elektromagnetik, dll.
Proses penyeimbangan dapat dilakukan 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.
Perangkat-perangkat ini meliputi:
- unit pengukuran dan komputasi berdasarkan komputer atau pengontrol industri;
- dua (atau lebih) sensor getaran;
- a phase angle sensor;
- aksesori untuk memasang sensor di lokasi;
- perangkat lunak khusus, yang dirancang untuk melakukan siklus penuh pengukuran parameter getaran rotor dalam satu, dua, atau lebih bidang koreksi.
Dua jenis mesin balancing saat ini yang paling umum:
- 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.
Penyeimbangan rotor kaku
Penting!
- Penyeimbangan hanya menghilangkan getaran yang disebabkan oleh distribusi asimetris massa rotor relatif terhadap sumbu rotasinya. Jenis getaran lainnya tidak dihilangkan dengan penyeimbangan!
- Mekanisme teknis, yang desainnya memastikan tidak adanya resonansi pada frekuensi operasi rotasi, yang secara andal dipasang pada pondasi, dipasang pada bantalan yang dapat diservis, tunduk pada penyeimbangan.
- Mesin yang rusak harus diperbaiki sebelum melakukan penyeimbangan. Jika tidak, penyeimbangan yang berkualitas tidak dapat dilakukan.
Penyeimbangan bukanlah pengganti perbaikan!
Tugas utama penyeimbangan adalah menemukan massa dan lokasi beban kompensasi yang melawan gaya sentrifugal.
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 melakukan penyeimbangan dinamis (metode tiga kali jalan)
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 bidang koreksi. 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 jenis mekanisme yang sama dengan desain yang sama, koefisien pengaruhnya akan mendekati. Anda dapat menyimpannya dalam memori komputer dan menggunakannya untuk menyeimbangkan mekanisme jenis yang sama tanpa uji coba, yang secara signifikan meningkatkan produktivitas penyeimbangan. Perhatikan bahwa massa bobot percobaan harus dipilih sedemikian rupa sehingga parameter getaran berubah secara nyata ketika bobot percobaan dipasang. Jika tidak, kesalahan perhitungan koefisien pengaruh akan meningkat dan kualitas penyeimbangan akan menurun.
Seperti yang dapat Anda lihat dari Fig. 1, gaya sentrifugal bekerja dalam arah radial, yaitu tegak lurus terhadap sumbu rotor. Karena itu, sensor getaran harus dipasang sehingga sumbu sensitivitasnya juga mengarah ke arah radial. Biasanya, kekakuan fondasi pada arah horizontal lebih rendah, sehingga getaran pada arah horizontal lebih tinggi. Oleh karena itu, untuk meningkatkan sensitivitas, sensor harus dipasang sehingga sumbu sensitivitasnya juga diarahkan secara horizontal. Meskipun demikian, tidak ada perbedaan mendasar. Selain getaran pada arah radial, getaran pada arah aksial, sepanjang sumbu putar rotor, juga harus dipantau. Getaran ini biasanya tidak disebabkan oleh ketidakseimbangan, melainkan oleh penyebab lain, terutama yang berkaitan dengan ketidakselarasan poros yang terhubung melalui kopling.
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 terkait (contoh dudukan penyeimbang)
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Kriteria untuk menilai kualitas mekanisme penyeimbangan
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.
Namun demikian, kepatuhan terhadap toleransi yang ditentukan tidak dapat sepenuhnya menjamin keandalan operasional mekanisme, terkait dengan pencapaian tingkat minimum getarannya. Hal ini dijelaskan oleh fakta bahwa besarnya getaran mekanisme tidak hanya ditentukan oleh besarnya gaya yang terkait dengan ketidakseimbangan sisa rotornya, tetapi juga bergantung pada beberapa parameter lain, termasuk: kekakuan k dari elemen struktur mekanisme, massa m, faktor redaman, serta frekuensi rotasi. Oleh karena itu, untuk memperkirakan kualitas dinamis mekanisme (termasuk kualitas keseimbangannya) dalam beberapa kasus, disarankan untuk memperkirakan tingkat getaran sisa mekanisme, yang diatur oleh sejumlah standar.
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 Standar ISO10816-1 zones (now part of ISO 20816-1) give the following boundaries of vibration velocity, mm/s RMS:
| Kelas | A/B | B/C | CD |
|---|---|---|---|
| Class I (small machines, up to 15 kW) | 0.71 | 1.80 | 4.50 |
| Class II (medium machines, 15–75 kW) | 1.12 | 2.80 | 7.10 |
| Class III (large machines, rigid foundation) | 1.80 | 4.50 | 11.20 |
| Class IV (large machines, flexible foundation) | 2.80 | 7.10 | 18.00 |
Zone A corresponds to the vibration of new machines; zone B is acceptable for unrestricted long-term operation; zone C allows only restricted operation; zone D indicates vibration severe enough to cause damage.
Standar dan referensi
- ISO 21940-11:2016 — Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors with rigid behaviour. (Replaces ISO 1940-1, which is withdrawn.) G-grades and tolerance calculator →
- ISO 21940-2 — Mechanical vibration — Rotor balancing — Part 2: Vocabulary. (Definitions of static, couple, quasi-static and dynamic unbalance.)
- ISO 20816-1:2016 — Mechanical vibration — Measurement and evaluation of machine vibration — Part 1: General guidelines. (Replaces ISO 10816-1 and ISO 7919-1.) Evaluation zones →
- ISO 20816-3:2022 — Mechanical vibration — Measurement and evaluation of machine vibration — Part 3: Industrial machines with nominal power above 15 kW and nominal speeds between 120 r/min and 15 000 r/min. (Replaces ISO 10816-3:2009.)
- ISO 14694:2003 — Industrial fans — Specifications for balance quality and vibration levels.
FAQ
Apakah balancing menghilangkan semua getaran?
Tidak. Penyeimbangan menghilangkan getaran yang disebabkan oleh distribusi massa rotor yang tidak simetris relatif terhadap sumbu rotasinya. Getaran akibat ketidaksejajaran, kerusakan bantalan, gaya aerodinamis/hidrodinamis, gaya elektromagnetik, dan penyebab lainnya memerlukan diagnosis dan tindakan korektif yang terpisah.
Mengapa penyeimbangan bisa gagal di dekat resonansi?
Di dekat resonansi, perubahan kecepatan kecil dapat menyebabkan perubahan besar pada amplitudo getaran dan pergeseran fasa 180°. Dalam kondisi seperti itu, hasil pengukuran menjadi tidak stabil, dan prosedur penyeimbangan konvensional mungkin tidak konvergen tanpa metode khusus.
Kapan Anda membutuhkan penyeimbangan satu bidang dibandingkan dengan penyeimbangan dua bidang?
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.
Apa yang harus dilakukan sebelum melakukan balancing?
Pastikan mesin dalam kondisi layak pakai: pemasangan yang andal pada fondasi, bantalan yang sehat, tidak ada kelonggaran yang parah, dan tidak ada sumber non-linieritas yang jelas. Penyeimbangan bukanlah pengganti perbaikan.
Poin-poin penting
- Penyeimbangan mengoreksi eksitasi yang terkait dengan massa (sentrifugal); hal ini tidak menyelesaikan ketidaksejajaran, kerusakan bantalan, atau sumber elektromagnetik/aerodinamis.
- Resonansi dan non-linearitas dapat membuat penyeimbangan konvensional menjadi tidak efektif atau tidak aman.
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
