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Portable field balancer "Balanset-1"
Portable dynamic balancer "Balanset-4"
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Introduction to rotor balancing


The rotor is a body that rotates around a certain axis and is held by its bearing surfaces in the supports. Bearing surfaces of the rotor transmit loads to the supports through rolling or sliding bearings. While using the term of "bearing surface" we simply refer to the Zapfen* or Zapfen-replacing surfaces.


*Zapfen (german for "journal", "pin") - is a part of an shaft or an axis, that is being carried by a holder (bearing box).

Dynamic balancing. Rotor and centrifugal forces.

fig.1 Rotor and centrifugal forces.



In a perfectly balanced rotor, its mass is distributed symmetrically regarding the axis of the rotation. This means that any element of the rotor can correspond to another element located symmetrically in a relation to the axis of the rotation. During rotation, each rotor element acts upon by a centrifugal force directed in the radial direction (perpendicular to the axis of the rotor rotation). In a balanced rotor, the centrifugal force influencing any element of the rotor is balanced by the centrifugal force that influences the symmetrical element. For example, elements 1 and 2 (shown in fig.1 and coloured in green) are influenced by centrifugal forces F1 and F2: equal in value and absolutely opposite in directions. This is true for all symmetrical elements of the rotor and thus the total centrifugal force influencing the rotor is equal to 0 the rotor is balanced. But if the symmetry of the rotor is broken (in Figure 1, the asymmetric element is marked in red), then the unbalanced centrifugal force F3 begins to act on the rotor.


When rotating, this force changes the direction together with the rotation of the rotor. The dynamic load resulting from this force is transferred to the bearings, which leads to their accelerated wear. In addition, under the influence of this variable towards the force, there is a cyclic deformation of the supports and of the foundation on which the rotor is fixed, which lets out a vibration. To eliminate the imbalance of the rotor and the accompanying vibration, it is necessary to set balancing masses, that will restore the symmetry of the rotor.

Rotor balancing is an operation to eliminate imbalance by adding balancing masses.

The task of balancing is to find the value and places (angle) of the installation of one or more balancing masses.


The types of rotors and imbalance.

Considering the strength of the rotor material and the magnitude of the centrifugal forces influencing it, the rotors can be divided into two types: rigid and flexible.

Rigid rotors at operating conditions under the influence of centrifugal force may get slightly deformed and the influence of this deformation in the calculations may therefore be neglected.


Deformation of flexible rotors on the other hand should never be neglected. The deformation of flexible rotors complicates the solution for the balancing problem and requires the use of some other mathematical models in comparison with the task of balancing rigid rotors. It is important to mention that the same rotor at low speeds of rotation can behave like rigid one and at high speeds it will behave like flexible one. Further on we will consider the balancing of rigid rotors only.

Depending on the distribution of imbalanced masses along the length of the rotor, two types of imbalance can be distinguished - static and dynamic (quick, instant). It works correspondingly same with the static and the dynamic rotor balancing.

The static imbalance of the rotor occurs without the rotation of the rotor. In other words, it is quiescent when the rotor is under the influence of gravity and in addition it turns the "heavy point" down. An example of a rotor with the static imbalance is presented in Fig.2

Static imbalance of rotor


Fig.2


The dynamic imbalance occurs only when the rotor spins.

An example of a rotor with the dynamic imbalance is presented in Fig.3.


Dynamic imbalance of rotor - couple of the centrifugal forces

Fig.3. Dynamic imbalance of rotor - couple of the centrifugal forces


In this case, imbalanced equal masses M1 and M2 are located in different surfaces - in different places along the length of the rotor. In the static position, i.e. when the rotor does not spin, the rotor may only be influenced by gravity and the masses therefore will balance each other. In dynamics when the rotor is spinning, the masses M1 and M2 start to be influenced by centrifugal forces FЎ1 and FЎ2. These forces are equal in value and are opposite in the direction. However, since they are located in different places along the length of the shaft and are not on the same line, the forces do not compensate each other. The forces of FЎ1 and FЎ2 create a moment impacted to the rotor. That is why this imbalance has another name "momentary". Accordingly, non-compensated centrifugal forces influence the bearing supports, which can significantly exceed the forces that we relied on and also reduce the service life for the bearings.

Since this type of imbalance occurs only in dynamics during the rotor spinning, thus it is called dynamic. It can not be eliminated in the static balancing (or so called "on the knives") or in any other similar ways. To eliminate the dynamic imbalance, it is necessary to set two compensating weghts that will create a moment equal in value and opposite in direction to the moment arising from the masses of M1 and M2. Compensating masses do not necessarily have to be installed opposite to the masses M1 and M2 and be equal to them in value. The most important thing is that they create a moment that fully compensates right at the moment of imbalance.

In general, the masses M1 and M2 may not be equal to each other, so there will be a combination of static and dynamic imbalance. It is theoretically proved that for a rigid rotor to eliminate its imbalance it is necessary and sufficient to install two weghts spaced along the length of the rotor. These weghts will compensate both the moment resulting from the dynamic imbalance and the centrifugal force resulting from the asymmetry of the mass relative to the rotor axis (static imbalance). As usual the dynamic imbalance is typical for long rotors, such as shafts, and static - for narrow. However, if the narrow rotor is mounted skewed in reference to the axis, or worse, deformed (the so-called "wheel wobbles"), in this case it will be difficult to eliminate the dynamic imbalance (see Fig.4), due to the fact that it is difficult to set correcting weghts, that create the right compensating moment.


Dynamic balancing of the wobbling wheel

Fig.4 Dynamic balancing of the wobbling wheel



Since the narrow rotor shoulder creates a short moment, it may require correcting weghts of a large mass. But at the same time there is an additional so-called "induced imbalance" associated with the deformation of the narrow rotor under the influence of centrifugal forces from the correcting masses.

See the example:

" Methodical instructions on rigid rotors balancing" ISO 1940-1:2003 Mechanical vibration - Balance quality requirements for rotors in a constant (rigid) state - Part 1: Specification and verification of balance tolerances


This is visible for narrow fan wheels, which, in addition to the power imbalance, also influences an aerodynamic imbalance. And it is important to bear in mind that the aerodynamic imbalance, in fact the aerodynamic force, is directly proportional to the angular velocity of the rotor, and to compensate it, the centrifugal force of the correcting mass is used, which is proportional to the square of the angular velocity. Therefore, the balancing effect may only occur at a specific balancing frequency. At other speeds there would be an additional gap. The same can be said about electromagnetic forces in an electromagnetic motor, which are also proportional to the angular velocity. In other words it is impossible to eliminate all causes of vibration of the mechanism by any means of balancing.

Fundamentals of Vibration.

Vibration is a reaction of the mechanism design to the effect of cyclic excitation force. This force can may a different nature.

  • The centrifugal force arising due to the imbalance of the rotor is an uncompensated force influencing the "heavy point". Particularly this force and also the vibration caused by it are eliminated by the rotor balancing.

  • Interacting forces, that have a "geometric" nature and arise out of errors in the manufacture and installation of mating parts. These forces can occur, for instance, due to the non-roundness of the shaft journal, errors in the tooth profiles in gears, the waviness of the bearing treadmills, misalignment of the mating shafts, etc.in case of non-roundness of the necks, the shaft axis will shift depending on the angle of rotation of the shaft. Although this vibration is manifested at the rotor speed, it is almost impossible to eliminate it with the balancing.

  • Aerodynamic forces arising from the rotation of the impeller fans and other blade mechanisms. Hydrodynamic forces arising from the rotation of hydraulic pump impellers, turbines, etc.

  • Electromagnetic forces arising from the operation of electric machines as a result, for example, due to the asymmetry of the rotor windings, the presence of short-circuited turns, etc.reasons.


    The magnitude of vibration (for example, its amplitude AB) depends not only on the magnitude of the excitation force Fт acting on the mechanism with the circular frequency ω, but also on the stiffness k of the structure of the mechanism, its mass m , and damping coefficient C.



    Various types of sensors can be used to measure vibration and balance mechanisms, including:

    - absolute vibration sensors designed to measure vibration acceleration (accelerometers) and vibration velocity sensors;

    - relative vibration sensors eddy-current or capacitive, designed to measure vibration.

    In some cases (when the structure of the mechanism allows it) sensors of force can also be used to examine its vibration load.

    Particularly, they are widely used to measure the vibration load of the supports of pre-resonance balancing machines.


    Therefore vibration is the reaction of the mechanism to the influence of external forces. The amount of vibration depends not only on the magnitude of the force acting on the mechanism, but also on the rigidity of the mechanism. Two forces with the same magnitude can lead to different vibrations. In mechanisms with a rigid support structure, even with the small vibration, the bearing units can be significantly influenced by dynamic loads. Therefore, when balancing mechanisms with stiff legs apply the force sensors, and vibration (vibroaccelerometers). Vibration sensors are only used on mechanisms with relatively pliable supports, right when the action of unbalanced centrifugal forces leads to a noticeable deformation of the supports and vibration. Force sensors are used in rigid supports even when significant forces arising from imbalance do not lead to significant vibration.

    The resonance of the structure.

    We have previously mentioned that rotors are divided into rigid and flexible. The rigidity or flexibility of the rotor should not be confused with the stiffness or mobility of the supports (foundation) on which the rotor is located. The rotor is considered rigid when its deformation (bending) under the action of centrifugal forces can be neglected. The deformation of the flexible rotor is relatively large: it cannot be neglected.

    In this article we only study the balancing of rigid rotors. The rigid (non-deformable) rotor in its turn can be located on rigid or movable (malleable) supports. It is clear that this stiffness/mobility of the supports is relative depending on the speed of rotation of the rotor and the magnitude of the resulting centrifugal forces. The conventional border is the frequency of free oscillations of the rotor supports/foundation. For mechanical systems, the shape and frequency of the free oscillations are determined by the mass and elasticity of the elements of the mechanical system. That is, the frequency of natural oscillations is an internal characteristic of the mechanical system and does not depend on external forces. Being deflected from the equilibrium state, supports tend to return to its equilibrium position due to the elasticity. But due to the inertia of the massive rotor, this process is in the nature of damped oscillations. These oscillations are their own oscillations of the rotor-support system. Their frequency depends on the ratio of the rotor mass and the elasticity of the supports.





    When the rotor begins to rotate and the frequency of its rotation approaches the frequency of its own oscillations, the vibration amplitude increases sharply, which can even lead to the destruction of the structure.

    There is a phenomenon of mechanical resonance. In the resonance region, a change in the speed of rotation by 100 rpm can lead to an increase in a vibration tenfold. In this case (in the resonance region) the vibration phase changes by 180°.

    If the design of the mechanism is calculated unsuccessfully, and the operating speed of the rotor is close to the natural frequency of oscillations, the operation of the mechanism becomes impossible due to unacceptably high vibration. Usual balancing way is also impossible, as parameters change dramatically even with a slight change in the speed of vibration. Special methods in the field of resonance balancing are used but they are not well-described in this article. You can determine the frequency of natural oscillations of the mechanism on the run-out (when the rotor is turned off) or by impact with subsequent spectral analysis of the system response to the shock. The device "Balcom-1" provides the ability to determine the natural frequencies of mechanical structures by these methods.

    For mechanisms whose operating speed is higher than the resonance frequency, that is, operating in the resonant mode, supports are considered as mobile ones and vibration sensors are used to measure, mainly vibration accelerometers that measure the acceleration of structural elements. For mechanisms operating in pre-resonance mode, supports are considered as rigid. In this case, force sensors are used.

    Linear and nonlinear models of the mechanical system.

    Mathematical models (linear) are used for calculations when balancing rigid rotors. The linearity of the model means that one model is directly proportionally (linearly) dependent on the other. For example, if the uncompensated mass on the rotor is doubled, then the vibration value will be doubled correspondingly. For rigid rotors you can use a linear model because such rotors are not deformed. It is no longer possible to use a linear model for flexible rotors. For a flexible rotor, with an increase of the mass of a heavy point during rotation, an additional deformation will occur, and in addition to the mass, the radius of the heavy point will also increase. Therefore, for a flexible rotor, the vibration will more than double, and the usual calculation methods will not work. Also, a violation of the linearity of the model can lead to a change in the elasticity of the supports at their large deformations, for example, when small deformations of the supports work some structural elements, and when large in the work include other structural elements. Therefore it is impossible to balance the mechanisms that are not fixed at the base, and, for example, are simply established on a floor. With significant vibrations, the unbalance force can detach the mechanism from the floor, thereby significantly changing the stiffness characteristics of the system. The engine legs must be securely fastened, bolted fasteners tightened, the thickness of the washers must provide sufficient rigidity, etc. With broken bearings, a significant displacement of the shaft and its impacts is possible, which will also lead to a violation of linearity and the impossibility of carrying out high-quality balancing.


    Methods and devices for balancing

    As mentioned above, balancing is the process of combining the main Central axis of inertia with the axis of rotation of the rotor.

    The specified process can be executed in two ways.

    The first method involves the processing of the rotor axles, which is performed in such a way that the axis passing through the centers of the section of the axles with the main Central axis of inertia of the rotor. This 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 corrective masses on the rotor, which are placed in such a way that the axis of inertia of the rotor is as close as possible to the axis of its rotation.

    Moving, adding or removing corrective masses during balancing can be done using a variety of technological operations, including: drilling, milling, surfacing, welding, screwing or unscrewing screws, burning with a laser beam or electron beam, electrolysis, electromagnetic welding, etc.

    The balancing process can be performed in two ways:

    - balanced rotors Assembly (in its own bearings);

    - balancing of rotors on balancing machines.

    To balance the rotors in their own bearings we usually use specialized balancing devices (kits), which allows us to measure the vibration of the balanced rotor at the speed of its rotation in a vector form, i.e. to measure both the amplitude and phase of vibration.

    Currently, these devices are manufactured on the basis of microprocessor technology and (in addition to the measurement and analysis of vibration) provide automated calculation of the parameters of corrective weghts that must be installed on the rotor to compensate its imbalance.

    These devices include:

    - measuring and computing unit, made on the basis of a computer or industrial controller;

    - two (or more) vibration sensors;

    - phase angle sensor;

    - equipment for installation of sensors at the facility;

    - specialized software designed to perform a full cycle of measurement of rotor unbalance parameters in one, two or more planes of correction.

    For balancing rotors on balancing machines in addition to a specialized balancing device (measuring system of the machine) it is required to have an "unwinding mechanism" designed to install the rotor on the supports and ensure its rotation at a fixed speed.

    Currently, the most common balancing machines exist in two types:

    - over-resonant (with supple supports);

    - pre-resonant (with stiff supports).

    Over-resonant machines have a relatively pliable supports, made, for example, on the basis of the flat springs.

    The natural oscillation frequency of these supports is usually 2-3 times lower than the speed of the balanced rotor, which is mounted on them.

    Vibration sensors (accelerometers, vibration velocity sensors, etc.) are usually used to measure the vibration of the supports of a resonant machine.

    In the pre-resonant balancing machines are used relatively-rigid supports, natural oscillation frequencies of which should be 2-3 times higher than the speed of the balanced rotor.

    Force sensors are usually used to measure the vibration load on the supports of the machine.

    The advantage of the pre-resonant balancing machines is that they can be balanced at relatively low rotor speeds (up to 400-500 rpm), which greatly simplifies the design of the machine and its foundation, as well as increases the productivity and safety of balancing.


    Balancing technique

    Balancing eliminates only the vibration which is caused by the asymmetry of the rotor mass distribution relative to its axis of rotation. Other types of the vibration cannot be eliminated with the help of the balancing!

    Balancing is the subject to technically serviceable mechanisms, the design of which ensures the absence of resonances at the operating speed, securely fixed on the foundation, installed in serviceable bearings.

    The faulty mechanism is the subject to a repair, and only then - to a balancing. Otherwise, qualitative balancing impossible.

    Balancing cannot be a substitute for repair!


    The main task of balancing is to find the mass and the place (angle) of installation of compensating weghts, which are balanced by centrifugal forces.

    As mentioned above, for rigid rotors it is generally necessary and sufficient to install two compensating weghts. This will eliminate both the static and dynamic rotor imbalance. A general scheme of the vibration measurement during balancing looks like the following:


    Rigid rotor dynamic balancing - corection planes 
and measure points


    fig.5 Dynamic balancing - corection planes and measure points


    Vibration sensors are installed on the bearing supports at points 1 and 2. The speed mark is fixed right on the rotor, a reflective tape is glued usually. The speed mark is used by the laser tachometer to determine the speed of the rotor and the phase of the vibration signal.





    fig. 6. Installation of sensors during balancing in two planes? using Balanset-1 1.2-vibration sensors, 3-phase, 4-measuring unit, 5-laptop



    In most cases, dynamic balancing is carried out by the method of three starts. This method is based on the fact that test weghts of an already-known mass are installed on the rotor in series in 1 and 2 planes; so the masses and the place of installation of balancing weghts are calculated based on the results of changing the vibration parameters.

    The place of installation of the load is called the correction plane. Usually, the correction planes are selected in the area of the bearing supports on which the rotor is mounted.

    The initial vibration is measured at the first start. Then, a test weight of a known mass is installed on the rotor closer to one of the supports. Then the second start is performed, and we measure the vibration parameters, that should change because of the installation of the test load. Then the test load in the first plane is removed and installed in the second plane. The third start-up is performed and the vibration parameters are measured. When the test load is removed, the program automatically calculates the mass and the place (angles) of the installation of balancing weghts.

    The point in setting up test weghts is to determine how the system responds to the imbalance change. When we know the masses and the location of the sample weghts, the program can calculate the so-called influence factors, showing how the introduction of a known imbalance affects the vibration parameters. The coefficients of influence are the characteristics of the mechanical system itself and depend on the stiffness of the supports and the mass (inertia) of the rotor-support system.

    For the same type of mechanisms of the same design, the coefficients of influence will be similar. You can save them in your computer memory and use them afterwards for balancing the same type of mechanisms without carrying out test runs, which greatly improves the performance of the balancing. We should also note that the mass of test weghts should be chosen as such so that the vibration parameters vary markedly when installing test weghts. Otherwise, the error in calculating the coefficients of the affect increases and the quality of balancing deteriorates.

    1111 A guide to the device Balcom-1 provides a formula by which you can approximately determine the mass of the test load, depending on the mass and the speed of the rotation of the balanced rotor. As you can understand from Fig. 1 the centrifugal force acts in the radial direction, i.e. perpendicular to the rotor axis. Therefore, vibration sensors should be installed so that their sensitivity axis is also directed in the radial direction. Usually the rigidity of the foundation in the horizontal direction is less, so the vibration in the horizontal direction is higher. Therefore, to increase the sensitivity of the sensors should be installed so that their axis of sensitivity could also be directed horizontally. Although there is no fundamental difference. In addition to the vibration in the radial direction, it is necessary to control the vibration in the axial direction, along the axis of rotation of the rotor. This vibration is usually caused not by imbalance, but by other reasons, mainly due to misalignments and misalignments of shafts connected through the coupling. This vibration is not eliminated by balancing, in this case alignment is required. In practice, usually in such mechanisms there is an imbalance of the rotor and misalignment of the shafts, which greatly complicates the task of eliminating the vibration. In such cases, you must first align and then balance the mechanism. (Although with a strong torque imbalance, vibration also occurs in the axial direction due to the" twisting " of the foundation structure).


    Criteria for assessing the quality of balancing mechanisms.


    Quality of rotor (mechanisms) balancing can be estimated in two ways. The first method involves comparing the value of the residual imbalance determined during the balancing with the tolerance for the residual imbalance. The specified tolerances for various classes of rotors installed in the standard ISO 1940-1-2007. «Vibration. Requirements for the balancing quality of rigid rotors. Part 1. Determination of permissible imbalance".
    However, the implementation of these tolerances can not fully guarantee the operational reliability of the mechanism associated with the achievement of a minimum level of vibration. This is due to the fact that the vibration of the mechanism is determined not only by the amount of force associated with the residual imbalance of its rotor, but also depends on a number of other parameters, including: the rigidity K of the structural elements of the mechanism, its mass M, damping coefficient, and the speed. Therefore, to assess the dynamic qualities of the mechanism (including the quality of its balance) in some cases, it is recommended to assess the level of residual vibration of the mechanism, which is regulated by a number of standards.
    The most common standard regulating permissible vibration levels of mechanisms is ISO 10816-3:2009 Preview Mechanical vibration -- Evaluation of machine vibration by measurements on non-rotating parts -- Part 3: Industrial machines with nominal power above 15 kW and nominal speeds between 120 r/min and 15 000 r/min when measured in situ.»
    With its help, you can set the tolerance on all types of machines, taking into account the power of their electric drive.
    In addition to this universal standard, there are a number of specialized standards developed for specific types of mechanisms. For example,
    ISO 14694:2003 "Industrial fans - Specifications for balance quality and vibration levels",
    ISO 7919-1-2002 "Vibration of machines without reciprocating motion. Measurements on rotating shafts and evaluation criteria. General guidance.»