Rotor balancing: static and dynamic unbalance, resonance, and practical procedure
本指南說明 轉子動平衡校正 對於 剛性轉子: 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.
目錄
- What is a rotor and what does balancing correct?
- Types of rotors and types of unbalance
- Vibration of mechanisms: what balancing can and cannot remove
- Resonance: a factor that prevents balancing
- Linear vs. nonlinear models: when calculations stop working
- Balancing devices and balancing machines
- Balancing rigid rotors (practical notes)
- How dynamic balancing is performed (three-run method)
- Criteria for assessing balancing quality
- Standards and references
- 常見問題
What is a rotor and what does balancing correct?
The rotor is a body which rotates about some axis and is held by its bearing surfaces in the supports. The bearing surfaces of the rotor transmit loads to the supports via rolling or sliding bearings. The bearing surfaces are the surfaces of the trunnions or the surfaces that replace them.
在完全平衡的轉子中，其質量相對於旋轉軸呈對稱分布，也就是說，轉子的任何一個質量元素，都能在相對於旋轉軸對稱的位置上找到與之對應的另一個元素。在已平衡的轉子中，作用在任一質量元素上的離心力，都會被作用在其對稱元素上的離心力所抵消。例如，大小相等、方向相反的離心力F1和F2，分別作用在元素1和元素2上（圖1中以綠色標示）。所有對稱的轉子元素都是如此，因此作用在轉子上的合離心力為0，轉子處於平衡狀態。
但如果轉子的對稱性被破壞（圖 1 中以紅色標記的非對稱元素），則不平衡離心力 F3 作用於轉子上。旋轉時，此力隨轉子的旋轉而改變方向。由此力產生的動態負荷傳遞至軸承，導致磨損加速。
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.
The task of balancing is to find the size and location (angle) of one or more balancing masses.
Types of rotors and types of unbalance
Taking into account strength of rotor material and magnitude of centrifugal forces acting on it, rotors can be divided into two kinds - rigid rotors and flexible ones.
Rigid rotors deform insignificantly under action of centrifugal force at working modes and influence of this deformation in calculations can be neglected.
柔性轉子的變形，已經不容忽視。與剛性轉子的動平衡校正問題相比，柔性轉子的變形，使動平衡校正問題的求解變得更加複雜，並且要求採用不同的數學模型。這裡應當指出，同一個轉子，在低速運轉時可以表現得如同剛性轉子，而在高速運轉時，則會表現出柔性轉子的特性。實用的判斷標準，是使用轉速相對於轉子第一臨界（彎曲）轉速的比值：當使用轉速遠低於該臨界轉速時——實用上大致低於第一臨界轉速的50%到70%——這個轉子就被視為剛性轉子，ISO 21940-11標準稱之為具有「剛性行為」的轉子。一旦超過此範圍，轉子就會彎曲成隨轉速變化而變化的振型：此時的轉子已屬於柔性轉子，必須採用模態法或多平面法（依ISO 21940-12標準）進行動平衡校正。在接下來的內容中，我們將只討論剛性轉子的動平衡校正。
Depending on how the unbalanced masses are distributed along the rotor, ISO 21940-2 distinguishes several states of unbalance:
- 靜不平衡 — 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;
- 動不平衡 — 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.
在這種情況下，那兩個不平衡的等質量M1和M2，位於不同的平面上——也就是說，位於沿轉子長度方向的不同位置上。在靜態位置下，也就是轉子並不旋轉的時候，只有重力作用在轉子上，因此這兩個質量彼此是平衡的。而在動態情況下，當轉子開始旋轉時，離心力Fc1和Fc2便開始作用在質量M1和M2上。這兩個力，大小相等，方向相反。但是，由於它們分別作用在軸的長度方向上不同的位置，並不在同一條直線上，所以這兩個力並不能相互抵消。力Fc1和Fc2共同在轉子上產生了一個力矩——這正是力偶不平衡之所以也被稱為力矩不平衡的原因所在。因此，這些未被抵消的離心力，就作用在軸承所在的位置上，其數值有可能大大超過原本的計算值，從而縮短軸承的使用壽命。
由於這種類型的不平衡只有在轉子旋轉時才會出現，因此無法在靜止狀態下透過“刀刃法”一類的方法來校正。要消除偶不平衡，必須安裝兩個補償重塊，使其產生的力矩與質量M1和M2所產生的力矩大小相等、方向相反。補償質量並不需要與M1和M2大小相等、位置相對，關鍵在於它們所產生的力矩能夠完全抵消不平衡力矩。
一般而言，質量M1與M2這兩者，可能互不相等，因此會出現靜態不平衡與力偶不平衡相互組合的情形——而這種一般性的情況，正是ISO 21940-2標準所稱的動態不平衡。理論上已經證明，對於剛性轉子而言，沿轉子長度方向、彼此間隔一定距離布置兩個配重，是消除其不平衡所必需且充分的條件。這兩個配重，既能補償力偶不平衡所產生的力矩，也能補償質量相對轉子軸線不對稱（即靜態不平衡）所產生的離心力。通常來說，力偶不平衡是長轉子（例如各類軸）的典型特徵，而靜態不平衡則是窄轉子的典型特徵。但需注意，如果窄轉子相對軸線發生歪斜，或出現變形（俗稱「8字形」），那麼力偶不平衡就會變得難以消除（見圖4），原因就在於，在這種情況下，很難安裝能夠產生所需補償力矩的校正配重。
The forces F1 and F2 do not lie on the same line and do not compensate each other.
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 也同樣存在：葉片幾何形狀不一致會導致葉片受力不均，從而產生一個淨徑向力。這個力與校正重塊產生的離心力一樣，都按速度的平方增長，但它還取決於運行工況——空氣密度、風門位置、管道阻力——因此在某一工況下調好平衡的校正重塊，到另一工況下就未必最優。所以氣動分量必須透過恢復葉片幾何形狀來修正，而不是靠增加質量。
電磁力 在電動機中（由偏心氣隙引起的不平衡磁拉力、斷條、短路疊片）的表現又有所不同：它們受氣隙磁通支配，而不是受轉速支配，且主要在電網頻率的兩倍以及極通過邊帶處激發機器振動，而不是在1×處。由於它們是在旋轉頻率以外的頻率上起作用的，平衡校正對它們完全無法補償。簡而言之，平衡校正只能消除與質量相關的1×激振——它無法消除機器中所有的振動來源。
Vibration of mechanisms
Vibration is the reaction of the mechanism design to the effects of a cyclic excitatory force. This force can be of different nature.
The centrifugal force resulting from the unbalanced rotor is an uncompensated force acting on the "heavy point". It is this force and the vibration caused by it that can be eliminated by balancing the rotor.
由配合零件的製造與裝配誤差所引起的“幾何性”交互作用力。例如，這些力可能源於軸頸的不圓度、齒輪齒形的誤差、軸承滾道的波紋度、配合軸的不對中等。在軸頸不圓的情況下，軸線會隨轉子轉動角度的不同而發生位移。雖然這種振動同樣發生在轉子轉速上，但幾乎不可能透過平衡來消除它。
Aerodynamic forces resulting from the rotation of the impellers of fans and other vane mechanisms. Hydrodynamic forces resulting from the rotation of impellers of hydraulic pumps, turbines, etc.
Electromagnetic forces resulting from the operation of electrical machines, e.g. asymmetric rotor windings, short-circuited windings, etc.
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.
可使用多種類型的感測器來測量振動並對機構進行動平衡校正，包括：
- 用於測量振動加速度的絕對振動感測器（加速規）以及振動速度感測器；
- 相對振動感測器——渦流式或電容式，用於測量振動位移；
- 在某些情況下（當機構設計允許時），力感測器也可用於評估其振動負荷；特別是，它們被廣泛用於測量硬支承動平衡機支承的振動負荷。
因此，振動是機器對外力作用的反應。振動的大小不僅取決於作用在機構上的力的大小，也取決於機構結構的剛度。同一個力可能引起不同的振動。在硬支承機器中，即使振動很小，軸承仍可能承受相當大的動載荷。這正是為什麼在對硬支承機器進行平衡時，使用的是力感測器，而不是振動感測器（振動加速度計）。
Vibration sensors are used on mechanisms with relatively pliable supports, when the action of unbalanced centrifugal forces leads to a noticeable deformation of supports and vibration. Force sensors are used for rigid supports, when even significant forces due to unbalance do not lead to significant vibration.
Resonance is a factor that prevents balancing
前面我們提到，轉子分為剛性和柔性兩種。轉子的剛性或柔性，不應與安裝轉子所用的支承（基礎）的剛度或可動性相混淆。當轉子在離心力作用下的變形（彎曲）可以忽略不計時，該轉子被視為剛性轉子。柔性轉子的變形相對較大，不能被忽略。
在本文中，我們只討論剛性轉子的平衡。剛性（不可變形）轉子又可以安裝在剛性支承或可動（柔順）支承上。顯然，支承的這種剛性／可動性同樣是相對的，取決於轉子轉速以及由此產生的離心力大小。一個約定的分界線，就是轉子支承的固有振動頻率。
對於機械系統而言，固有振動的振型與頻率，是由構成該機械系統的各個元件的質量以及彈性，共同決定出來的。也就是說，固有振動的頻率，是機械系統本身所具有的一種內部特性，並不依賴於外力的作用。當支承部分由於彈性的作用，而偏離了原本的平衡狀態時，它就會趨向於回到平衡位置上去。但是，由於轉子本身質量龐大，因而具有相當程度的慣性，所以這一回復的過程，就帶有阻尼振動的性質。而這些振動，正是轉子—支承這一系統本身的固有振動。它們的頻率，取決於轉子的質量，與支承彈性之間的比值，正如下面的公式（2）所顯示的那樣。
When the rotor begins to rotate and the frequency of its rotation approaches the frequency of natural vibrations, the amplitude of vibration increases sharply, which can lead to the destruction of the structure.
由此產生機械共振現象。在共振附近，響應會被品質因數Q = 1/(2ζ)放大，機械結構的Q值通常為3~17，且峰值可能非常尖銳：轉速僅變化百分之幾，振動水準就可能成倍變化。經過共振區時，相位滯後會擺動180°，在峰值處經過90°。
如果機構設計不合理，轉子的工作頻率接近固有振動頻率，那麼振動會高到無法接受，機構也就無法正常運行。這種情況下常規方法已無法進行平衡，因為哪怕轉速有微小變化，振動參數也會劇烈改變。要在共振區域內進行平衡，需要使用本文未涉及的專門方法。
It is possible to determine the frequency of natural vibrations of the mechanism at coasting (at switching off the rotor rotation) or by the shock method with the subsequent spectral analysis of the system response to the shock.
對於工作轉速高於共振頻率、即工作在超臨界（共振後）狀態的機構，其支承被視為可動的，測量時使用振動感測器，主要是振動加速度計，測量結構部件的加速度。對於工作在共振前狀態的機構，其支承被視為剛性的，此時使用力感測器。
Linear and nonlinear models of a mechanical system. Non-linearity is a factor that prevents balancing
在對剛性轉子進行平衡時，平衡計算所採用的數學模型稱為線性模型。所謂線性模型，是指在這種模型中，一個量與另一個量成正比（線性）關係。例如，如果轉子上未補償的質量增加一倍，那麼振動值也會相應增加一倍。對於剛性轉子，可以使用線性模型，因為它們不會發生變形。
對於柔性轉子，線性模型已不再適用。對於柔性轉子而言，如果重點的質量在旋轉過程中增大，就會產生額外的變形，除了質量之外，重點所在位置的半徑也會隨之增大。因此，對於柔性轉子，振動的增大幅度會超過兩倍，常規的計算方法將不再適用。
此外，支承的彈性，在其發生較大變形時也同樣會出現變化——舉例來說，當支承的變形較小時，是由某一部分的結構元件在承擔負荷；而當變形較大時，則會有另外一些結構元件參與進來，共同分擔負荷。這正是為什麼，無法對那些沒有固定於基礎之上、而只是簡單放置在地面上的機構，進行動平衡校正的原因所在。當振動變得較為明顯的時候，不平衡所產生的作用力，有可能會把整個機構從地面上掀起來，從而顯著地改變系統本身的剛度特性。因此，馬達的機腳必須牢固地固定住，螺栓連接的部位必須確實鎖緊，墊圈的厚度也必須能夠提供足夠的安裝剛度，諸如此類的措施都不可或缺。如果軸承本身已經損壞，那麼就有可能出現明顯的軸不對中現象，以及各種衝擊，而這同樣會導致線性度變差，從而無法實現高品質的動平衡校正效果。
Balancing devices and balancing machines
Recall that balancing is the process of aligning the main central axis of inertia with the rotor's axis of rotation.
This process can be performed by two methods.
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.
The second (most common) method involves moving, installing or removing correction weights on the rotor, which are placed so that the axis of inertia of the rotor is as close to its axis of rotation as possible.
Moving, adding or removing correction weights during balancing may be accomplished by various technological operations including: drilling, milling, surfacing, welding, screwing or unscrewing, laser or electron beam burning, electrolysis, electromagnetic surfacing, etc.
The balancing process can be accomplished in two ways:
- 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.
對於在自身軸承中運行的轉子進行平衡，通常使用專用的平衡裝置（套件），這類裝置能以向量形式測量被平衡轉子在其旋轉頻率下的振動，也就是同時測量振動的振幅和相位。目前，上述裝置均採用微處理器技術製造，除了振動測量和分析之外，還能自動計算需要安裝在轉子上、用以補償其不平衡的校正重塊參數。
These devices include:
- a measuring and computing unit based on a computer or industrial controller;
- 兩個（或更多）振動感測器；
- a phase angle sensor;
- accessories for mounting the sensors on the site;
- specialized software, designed to perform a full cycle of rotor vibration parameters measurement in one, two or more correction planes.
Two types of balancing machines are currently the most common:
- Soft-bearing machines (with pliable supports);
- Hard-bearing machines (with rigid supports).
Soft-bearing (above-resonance) machines 具有相對柔順的支承，例如基於平板彈簧的結構。這些支承的固有振動頻率通常比安裝其上的被平衡轉子的旋轉頻率低2~3倍，因此機器工作在共振點以上。對於這類超共振機器，通常使用振動感測器（加速度計、振動速度感測器等）來測量支承的運動。
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.
Balancing rigid rotors
Important!
- Balancing only eliminates vibration caused by asymmetrical distribution of the rotor mass relative to its rotational axis. Other types of vibration are not eliminated by balancing!
- Technical mechanisms, whose design ensures the absence of resonances at the operating frequency of rotation, reliably fixed on the foundation, installed in serviceable bearings, are subject to balancing.
- Defective machinery must be repaired before balancing. Otherwise, quality balancing is not possible.
Balancing is no substitute for repair!
動平衡校正的主要任務是找出抵消離心力的配重質量及其位置。
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.
How dynamic balancing is performed (three-run method)
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 校正平面. 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).
第一次啟動時測量初始振動（在Balanset軟體中即為Run 0）。接著，在轉子上靠近其中一個軸承的位置安裝一個已知質量的試重。進行第二次啟動（Run 1）並測量振動參數，該參數應因安裝試重而發生變化。然後將第一平面的試重拆下，安裝到第二平面。進行第三次測試運轉（Run 2）並測量振動參數。拆除試重後，軟體會自動計算出平衡重塊的質量和安裝角度。
計算出的校正重塊隨後被安裝到各自的平面上，並進行一次檢驗運轉——在Balanset軟體中這就是Run T（Trim，修正）。將殘餘振動與公差進行比較。如果結果仍高於目標值，軟體會重新利用已經確定的影響係數，因此不需要再做新的試重運轉——只需計算並安裝一次小的額外修正即可。
安裝測試重塊的目的是確定系統對不平衡變化的響應方式。由於測試重塊的質量和安裝位置都是已知的，軟體便可以計算出所謂的影響係數，反映引入已知不平衡量後振動參數的變化情況。影響係數是機械系統本身固有的特性，取決於支承的剛度以及轉子—支承系統的質量（慣量）。
對於同一設計、同一類型的機構，其影響係數會非常接近。可以將這些係數保存在電腦記憶體中，並用於同類機構的平衡，而無需再做試運轉，這大幅提高了平衡作業的效率。請注意，測試重塊的質量應選擇適當，使安裝後振動參數能有明顯變化。否則，影響係數的計算誤差會增大，平衡品質也會隨之下降。
從圖 1 可以看出，離心力作用於徑向，即垂直於轉子軸。因此，振動感測器必須安裝得使其靈敏度軸也指向徑向。通常，基礎在水平方向的剛性較低，因此水平方向的振動較高。因此，為了提高靈敏度，感測器應安裝得使其靈敏度軸也指向水平方向。儘管這沒有根本性的區別。除了徑向振動外，還必須監測沿轉子旋轉軸的軸向振動。這種振動通常不是由不平衡引起的，而是由其他原因引起的，主要與通過聯軸器連接的軸不對心有關。
這種振動無法透過平衡消除，此時需要進行對中。實際上，這類機器通常同時存在轉子不平衡和軸不對中，這使得消除振動的工作困難得多。在這種情況下，必須先對中機器，然後再進行平衡。（不過，當力偶不平衡較強時，由於基礎結構發生“扭轉”，軸向也會出現振動。）
相關文章（動平衡支架範例）
評估機構動平衡品質之準則
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 e每 and the service angular velocity ω, expressed in mm/s:
- ω = 2π·n / 60 [rad/s], where n is the service speed in rpm;
- e每 = G · 1000 / ω [g·mm/kg] (numerically equal to µm of center-of-mass offset) — equivalently e每 = 9549 · G / n;
- U每 = e每 · 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; e每 = 6.3 · 1000 / 314.2 = 20.1 g·mm/kg (cross-check: 9549 · 6.3 / 3000 ≈ 20.1); U每 = 20.1 · 50 ≈ 1000 g·mm for the whole rotor.
Splitting the tolerance between two planes. 對於質心位於兩個校正平面之間的轉子，總公差按質心到各平面距離的反比分配；對於對稱轉子，這就意味著每個平面各分一半——在上面的例子中約為每個平面500 g·mm。任何一個平面所分配的比例都不應超過U每.
Typical grades: G 0.4 — 陀螺儀、精密磨床主軸 · G 1 — 磨床主軸、精密電樞 · G 2.5 — 渦輪機、渦輪發電機、工具機傳動裝置 · G 6.3 — 通用機械：風機、幫浦葉輪、飛輪、標準電動機 · G 16 — 有特殊要求的萬向軸、農業機械、破碎機 · G 40 — 汽車車輪、傳動軸（萬向軸）· G 100 — 高速柴油機曲軸傳動裝置。
然而，即便完全符合了規定當中的所有公差要求，也仍然並不能完全保證機構本身的運作可靠性，這一點，是與達到最低振動水準這一目標相互關聯的。之所以如此，是因為機構振動的大小，並不僅僅取決於與其轉子殘餘不平衡相關聯的那個力的大小，同時還取決於其他好幾項不同的參數，其中包括：機構結構元件本身的剛度k、其質量m、阻尼係數，以及旋轉頻率等等這些因素在內。因此，為了評估機構的動態品質——其中自然也包括其動平衡校正的品質——在許多實際情況下，都會建議進一步評估機構的殘餘振動水準，而這一水準，正是受到多項相關的行業標準所共同加以規範和約束的。
工業機械許用振動水準最廣泛採用的標準是ISO 20816-3（原ISO 10816-3）。該標準涵蓋功率高於15 kW、轉速在120–15,000 rpm之間的機械，並依兩個維度進行分類：依功率分組（第1組——高於300 kW；第2組——15至300 kW），以及依支承型式（剛性或撓性）。每一種組合各有其以mm/s RMS表示的A/B、B/C和C/D區間邊界。不在此範圍內的機械，則適用該系列中的其他專門部分（渦輪機組——ISO 20816-2、液壓機械、往復式機械、幫浦），或適用產品標準，例如針對工業風機的ISO 14694。
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:
| 級別 | 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.
Standards and references
- ISO 21940-11:2016 — Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors with rigid behaviour. （取代已廢止的 ISO 1940-1。） 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.
常見問題
Does balancing remove all vibration?
No. Balancing removes vibration caused by the asymmetrical distribution of rotor mass relative to its rotational axis. Vibration from misalignment, bearing defects, aerodynamic/hydrodynamic forces, electromagnetic forces, and other causes requires separate diagnostics and corrective actions.
Why can balancing fail near resonance?
Near resonance, small speed changes can cause large changes in vibration amplitude and a 180° phase shift. In such conditions the measurement results become unstable, and conventional balancing procedures may not converge without special methods.
When do you need one-plane vs. two-plane balancing?
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.
雙平面 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.
What should be done before balancing?
Ensure the machine is serviceable: reliable mounting to the foundation, healthy bearings, no severe looseness, and no obvious sources of non-linearity. Balancing is not a substitute for repair.
重點摘要
- 動平衡校正修正與質量相關（離心力）的激振；它無法解決不對心、軸承損壞或電磁/空氣動力學來源的問題。
- 共振和非線性可能使常規動平衡校正失效或不安全。
- For rigid rotors, two-plane balancing is the general solution for dynamic unbalance (the combination of static + couple).
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
