M. Barkova, A. Shablinsky, VibroAcoustical Systems and Technologies, Inc.


In field balancing machines with high vibrations, the use of common methods of determining balance weights often does not yield satisfactory results. An analysis of the reasons for this shows that there are two main groups of constraints on the balancing efficiency: the forces of different nature from simple unbalance that excite vibration at the rotation frequency and the existence of certain defects in the machine that can change the mechanical properties of the machine. The nature of these forces and the methods for the detection of defects of machine units and its base supports that can be used by experts in balancing are discussed.


Consideration of the reliability and service life of a machine suggests that low frequency vibrations present the greatest source of danger to a machine. For machines with rotating parts (rotors), this is typically a vibration at the rotation frequency. This vibration may significantly increase during the machine operation. Usually, when the vibration level exceeds certain limits, the users conduct maintenance of the machine. The inertial forces due to the unbalance of the rotating parts relative to the rotation axis are typically considered to be the reasons for the vibration increase. That's why the users try field balancing the machine when possible. Unfortunately, attempting to balance the machine may not always produce acceptable results. The main reasons for this are other problems of the machine or of its supports. To eliminate additional expenses and delays, the customer should have the information about the various possible defects of the machine that can be responsible for the machine vibration at the rotation frequency and this information should be available before or at least during the balancing.


The machine vibration at rotation speed depends not only on the amount of rotor unbalance, but also on the existence and development stage of a number of possible defects as well as the deviations from the technical specifications in the following units:

An analysis of the most frequent defects that result in the vibration increase on the rotation frequency shows numerous possibilities:


The vibration of the machine at the rotation frequency is defined by the sum of all the oscillation forces, including the centrifugal ones excited by unbalanced rotor combined with the mechanical properties of the machine and its base supports. As both the forces and mechanic properties depend on the existing defects of machine or its base supports and their types and severity, it is necessary to define how efficient the procedure of balancing may be in presence of particular types of defects.

Rotor unbalance during rotation excites centrifugal rotation (i.e. tracing out a circle during one revolution) synchronously with the radial (directed with the radius to the rotation axis) forces applied directly to the rotor. Similar rotating forces occur with defects of flexible couplings or jointed shafts. The magnitude of centrifugal forces depend on the unbalance of the rotor and rotation speed, but the forces synchronously rotating with the rotor that originated in the defects of couplings depend on the defect severity and momentum transferred, i.e. machine load, and are not so dependent on the rotation speed. For this reason, if you attempt to balance a machine with a coupling defect at one load or rotation speed, you may receive a significant increase of the vibration on the rotation frequency on another load or at the rotation speed for the same machine.

Another reason for the appearance of the rotating radial forces is a defect of dynamic eccentricity of air gap in the AC electric machines which coincide in the direction of the inertial forces in only one of two machine parts (rotor or stator). In the other machine part, they are applied in the opposite direction. This is why, when they are compensated by mounting additional weights of the rotor, they cause an increase in the vibration of another machine part. Also, these forces are not really dependent on the rotation speed and the change in the rotation speed of AC machine with dynamic eccentricity of the air gap will lead to the increase of its vibration if it was balanced on another speed.

The third practical case when radial rotating forces appear is bending of the shaft line that has more than two distant rotation supports. In this case, the forces applied on the supports do not depend on the rotation speed, but are fully dependent on the degree of bend and the rigidity of the shaft. The amplitudes of the oscillating displacement of the bearing housings also depend on the bend degree and the rigidity of the housings. To decrease vibration in this case, it is necessary to decrease the shaft bend which is nearly impossible to achieve with centrifugal forces produced by the balancing weights as the shaft is straightened with the forces applied to the bearings on which the centrifugal forces are applied in their turn.

The last of the most frequent practical cases of the appearance of rotating radial forces applied on the supports with the rotation frequency is connected with the appearance of incipient self-sustained oscillation processes. These self-sustained oscillations are the full or partial revolution of the stationary friction surface of the bearing with the rotating friction surface of the rotor. Most frequently, such cases are observed in vertical machines with journal bearings. The appearance and increase of oscillations, as a rule, is nearly independent on the magnitude and angle position of the rotor unbalance. That's why it is impossible to predict whether it is possible to decrease them in the process of balancing.

A number of friction surface defects in a machine may cause oscillation forces at the rotation frequency, but in this case, the direction of the force vector does not change with rotation. These are the defects of bearing or mechanical transmission wear. So, vertical oscillation forces appear due to non-uniform wear of friction surfaces on rotor in the machines with horizontal rotor and horizontal forces when there is wear of the stationary race in the bearings of vertical machines. Also, similar forces occur with the gears or pulleys wobbling or wear in gear or belt transmissions. These forces are applied in the direction between the shaft axes. None of the above forces can be fully compensated by the centrifugal forces produced by mounting balancing weights.

The most difficult case in rotor balancing occurs when pulsating torque affects the rotor at the rotation frequency. In practice, this case may be observed in multi-bearing rotors and AC electric machines. In multi-bearing rotors, pulsating torque occurs because of combined defects of misalignment of the bearings and bend in the shaft line. In this case, the friction forces depend on the rotation angle and once per revolution the shaft sticks in the bearings, thus producing significant pulsating torque. To decrease this torque, you should either correct misalignment or the shaft bend. It is evident that straightening a shaft with high rigidity by mounting balancing weights is practically impossible.

In electric machines, the pulsating torque at the rotation frequency appears with a combined defect of both static and dynamic eccentricities of the air gap. The magnitude of the pulsating torque is proportional to the constant torque of the machine and the product of relative magnitude of each of the eccentricities. It can reach very high values, especially in the case of induction motors with small air gaps which produce high relative eccentricities normalized to the normal clearance value. As a rule, pulsating torque in electric machines can be corrected only by repair of the machine or replacement of its bearings.

The forces excited by the rotation of machine parts with hydrodynamic unbalance influence the machine in the same way as a mechanic unbalance. The main peculiarity of these forces is the unknown dependence of hydrodynamic unbalance on the rotation speed of impeller, pressure difference on the inlet and outlet of pump and other factors. This means that changes in operating mode of a well balanced pump may result in the significant increase of its vibration on the rotation frequency.


Many of the defects leading to the increase of vibration on the rotation frequency can be detected prior to balancing by the analysis of machine vibration measured on the bearing housings and on the machine body. Some of the defects are best detected during balancing by the analysis of machine vibration reactions produced by the installation of the trial weights.

Defects that preferably should be detected before the start of balancing include shaft or coupling wobbling, wear of bearings, self-sustained oscillations of rotor in the bearings, eccentricity of air gaps in electric machines, transmission defects, collisions between stationary and rotating parts of the machine. When balancing pumps, it is worth detecting the presence or absence of the hydrodynamic unbalance.

To detect such defects as shaft or coupling wobbling, defects of mechanic transmissions, bearings wear, self-sustained oscillations of the rotor in the bearings, and contact between stationary and rotating parts of the machine, it is necessary to measure an autospectrum of the low frequency vibration and envelope spectrum of high frequency vibration at each of the bearing housings. The presence of a series of rotation speed harmonics with similar amplitudes in the autospectrum as well as in the envelope spectrum is a symptom for shaft wobbling, bearing wear or transmission defects (see figure 1). Consider correcting these defects before balancing, especially if their severity is significant.

Figure 1 (above). Envelope spectrum of shaft or coupling wobbling. Frot is the rotation frequency of the rotor.

The defect severity can be estimated by the amplitude of the bearing housing oscillations in two different directions orthogonal to each other and to the rotation axis. The defect severity should be considered very high if the amplitude of any of the harmonics with the exception of the first one exceeds the specified level for the vibration at the rotation speed.

Self-sustained oscillations of the shaft in journal bearings can be detected by the appearance of harmonic series with the frequencies k*Frot/2 or k*Frot/3 in the autospectrum or the envelope spectrum of the bearing vibration (see figure 2 below). Appearance of such spectrum components in even one bearing should tell you that there is a high probability for the self-sustained oscillations of the shaft in the other bearings also.

Figure 2 (above). Envelope spectrum of machine with self-sustained oscillations.

In AC electric machines, it is much more important to detect possible dynamic eccentricity of the air gap. It can be detected by the index of slot frequency vibration component modulation by the rotation frequency harmonics. The sidebands Fz + Frot of the slot frequency component Fz=z*Frot (where z equals the number of slots) and Fz - 2Fm + Frot (where Fm is the mains supply frequency) can be observed in the vibration spectrum in this case.

Figure 3 (above). Autospectrum of AC machine with dynamic eccentricity of the air gap. Here:

 is frot is fz-2fm ƒ is fz
  is fz-2fm-frot is fz-frot
  is fz-2fm+frot is fz+frot

Hydrodynamic unbalance of a pump impeller can also be detected prior to balancing by the envelope spectrum of the high frequency vibration of the pipeline at a significant (up to 3-10 meters) distance from the pump. The cavitation symptoms (k*Fb = k*n*Frot where n equals the number of blades) should be absent in the envelope spectrum. Only components at the rotation frequency of the impeller should be present.

Two more defect types can be detected prior to balancing. These are a soft-foot (fastening looseness between bearings and machine case or machine and the base supports) and the appearance of machine body or base support resonance close to the rotation speed of the machine. To detect these defects, you should compare the levels of rotation frequency components in the spectra measured in two orthogonal directions that are orthogonal to the rotation axis as well. For the horizontal machine these are typically horizontal and vertical directions. If the vibration level on the rotation speed in one direction is 3-4 times greater than in another direction it should be considered as a symptom for a defect. Note that for machines with belt, gear or other mechanical transmissions, this difference can be natural in the direction connecting the axes of driver and driven shafts in presence of transmission defects. It is defined by the significant differences not of rigidity, but of oscillation forces in different directions. This symptom can not be applied to the machines with considerably different rigidity in different directions as well. To distinguish these two defects you can analyze the amplitude and phase-frequency parameters of the machine during run-out. The influence of resonance is limited to a narrow band of frequencies close to its central frequency, but a soft-foot produces the same symptoms in a very wide band of frequencies.

Once you found any defect in the shaft line or bearings of the machine during diagnostics, before balancing you should make a full diagnosis of the machine to determine the volume of maintenance or repair work needed for the machine. This allows not only increasing the efficiency of balancing and completing it in a short time, but also increasing the time intervals between periodic balancing as well.

A number of the machine defects that increase the vibration on the rotation speed of the machine can not be reliably detected during preliminary machine diagnostics. Pulsating torque is very hard to detect. Similarly, self-sustained rotor oscillations due to severe bearing wear cannot always be detected prior to balancing. For this very reason, it is worthwhile to conduct diagnostics during the balancing process as well. This includes looking for possible self-sustained oscillations in all bearings.


Some of the defects considered above can be missed during the diagnostics of a machine prior to balancing or can appear during balancing during partial disassembly of the machine for trial and balancing weight mounting. These are the main defects that hamper balancing. First of all, there is shaft bending or wobbling. The symptom for this defect is the absence of the reaction (changes in vibration within the measurement error) on test actions, i.e. trial weights mounting and resulting centrifugal forces. This absence of reaction is usually observed at all measurement points and remains with increased of test action (increase of trial weights size). These measurements can not distinguish between shaft bend and wobbling.

The second defect group consists of those detected by the results of balancing weight calculation. By comparison of balancing weights calculated by measurements conducted in different directions including two radial and one tangential directions (tangential to the machine body and orthogonal to the rotation axis), it is possible to detect the presence of significant pulsating torque at the rotation frequency of the machine. In this case, the values of the balancing weights calculated by the two radial measurements are very close to each other, but they are very different from the ones calculated by the results of tangential measurements.


The analysis of possibilities for detection and identification of the defects hampering the efficiency of rotor field balancing shows that:


  1. Barkov, A., Barkova, M., Shablinsky, A. "Rotor balancing for multi-condition machines." Proceedings of the transport and noise conference., ed. Kovinskaya S., Saint Petersburg, Russia , October 4-6, 1994, 53-56.

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