Causes and control of electrical machine vibration

November 13th, 2015, Published in Articles: EE Publishers, Articles: Energize, Articles: Vector


This article examines the causes of electrical machine vibration, the effects of vibration, and means taken to mitigate vibration.

All rotating machines, no matter how well designed and manufactured, exhibit vibration of some form when operating. Excessive vibration can cause damage to the machine or reduce its lifetime, as well as damage to other items.

The rotating machines concerned are electric motors and alternator-turbine combinations. Fixed speed machines such as alternators and synchronous motors lend themselves to relatively simple analysis and problem solution. The problem becomes more complex with variable speed drives (VSDs) and with machines interconnected with other mechanically and electrically complex equipment.

A machine which runs smoothly on its own may develop damaging vibration patterns when interconnected to other equipment. In addition to vibrations which could damage the machine itself, large machines can also transmit vibrations through their mountings to building structures and other machinery, which can cause unpleasant working environments or structural damage.

Causes of vibration

We are dealing here with rotating machines, primarily with vibrations due to the rotor of the machine and will be confined to motors and rotary driven systems. Piston driven machinery has its own set of issues. Rotor vibration has two main causes – out of balance vibration, and torsional vibration.

Out of balance vibration

Out of balance condition is the uneven distribution of mass around the axis of rotation of a shaft, resulting in the mass centre axis being displaced from the rotational axis (see Fig. 1). The rotors of electric motors and alternators consist of a large number of components distributed along the length of the rotor, and variations in mass and mounting of these components result in unbalance. In addition, the relative positions of these components can change with temperature, making the balancing process more difficult.

When the shaft of the machine rotates, the unbalance causes a rotating force on the shaft which is transmitted to the bearings and therefore to the machine casing and mounting as well as other items as shown in Fig. 1.

Fig. 1: In an unbalanced condition the mass centre axis is displaced from the rotational axis.

Fig. 1: In an unbalanced condition, the mass centre axis is displaced from the rotational axis.

Out of balance conditions on rotating machines such as motors and alternators cause vibration which can damage the machine as well as components such as bearings and set up vibrations in attached items. In addition to reducing the life of machines, the operation may also be placed in danger. The rotors of large alternators and motors consist of complex assemblies of different parts and balancing is a complex process.

In the past, balancing had to be done at a central factory but modern equipment has made it possible to do on-site balancing on very large machines.

Out of balance conditions cause vibrations which have the following effects:

  • Noise, mostly in the audible range, can be very disturbing.
  • Bearing wear and damage.
  • Damage to welded joints and couplings in pipe systems feeding turbines.

Types of imbalance

Fig. 2: Static unbalance.

Fig. 2: Static imbalance.

Static imbalance

Static imbalance (see Fig. 2) normally occurs in disk-type rotors where the rotor’s diameter is much larger than the rotor’s length. This is characterised by a single mass imbalance on one side of the shaft causing the mass centre axis to be displaced from the rotational axis. Under static free rotation conditions, the rotor will come to rest with the mass centre axis below the rotational axis.

Fig. 3: Couple unbalance.

Fig. 3: Couple imbalance.

Couple imbalance

A couple imbalance consists of two equal masses diametrically opposed at equal distance from the rotational centre but displaced along the axis of the rotor (see Fig. 3). Although the rotor will be statically balanced, the axial displacement of the masses will result in vibration.

Fig. 4: Dynamic unbalance.

Fig. 4: Dynamic imbalance.

Dynamic imbalance

In this case, there are several mass imbalances which are displaced from one another diametrically, angularly and axially , as well as being of different values (see Fig. 4). In this case, the mass centre axis may be displaced angularly with relation to the rotational axis. This becomes a problem at higher speed where the rotor will tend to rotate around the mass axis rather than the rotational axis.

Most large machines, where the rotor consists of a number of different assemblies of different material, will be faced with a dynamic imbalance problem. Alternators are characterised by a rotor where the length is greater than the diameter and the placement of equipment along the length of the rotor is not uniform. The problem can be complicated further when the rotor is flexible and not rigid.

Fig. 5: Residual imbalance limits. (ISO 1940/1 [4]).

Fig. 5: Residual imbalance limits. (ISO 1940/1 [4]).

Measurement of imbalance

Imbalance is measured in terms of the force caused on the rotor by the imbalance mass. The force is given by:
F = mr•ω2    (1)
F = force in Newtons
m = unbalance mass in grams
r = the eccentricity in mm
ω = the angular speed in radians/s

Imbalance (U) is measured in terms of the mass and eccentricity.
U = mr (gm x mm)    (2)

Specific imbalance is the term used in standards and is defined as the imbalance per unit mass of the rotor:
e = U/M = (m•r )/M gm x mm/kg    (3)


M is the mass of the rotor.

Rotor resonance

Fig. 6: The basic measurement chain [1].

Fig. 6: The basic measurement chain [1].

Vibration due to imbalance can be amplified at the natural resonant frequency of the rotor. This is generally only a problem in variable speed machines, as fixed speed devices are designed to have natural resonant frequency removed from the excitation frequency.

Standards for imbalance (imbalance limits and residual imbalance)

A commonly used standard for residual imbalance is the ISO 1040/1: Balance quality requirements of rigid rotors, although there are others used by military and specific industries.

The standard specifies residual imbalance limits in terms of specific imbalance for a range of speeds and a range of applications.

Balance quality grade Product of the relationship
(eper w) mm/s
Rotor types general examples
G6,3 6,3

Medium and large electric armatures (of electric motors having at least 80 mm shaft height) without special requirements.

Small electric armatures, often mass produced, in vibration insensitive applications and/or with vibration-isolating mountings.

G2,5 2,5

Gas and steam turbines, including marine main turbines (merchant service).

Rigid turbo-generator rotors.

Medium and large electric armatures with special requirements.

Small electric armatures not qualifying for one or both of the conditions specified for small electric armatures of balance quality grade G 6,3.

G1 1 Small electric armatures with special requirements.

The range that is applicable to large electrical machines would be G6,3 to G1 as shown in Table 1 [4].

Correcting unbalance

Imbalance is corrected by adding mass to or removing mass from the rotor. In an electrical machine, it will be impractical to remove mass, so balance is generally achieved by adding mass to the rotor.  A rotor is balanced by placing a correction mass of a certain size in a position where it counteracts the imbalance in the rotor. The size and position of the correction mass must be determined by measurement.

Fig. 7: Elastic distortion of shaft due to applied torque or excitation [4].

Fig. 7: Elastic distortion of shaft due to applied torque or excitation [4].

The principle of performing field balancing is to make (usually temporary) alterations to the mass distribution of the rotor, by adding trial masses, and to measure the resulting phase and magnitude of bearing vibration. The effects of these trial corrections enable the amount and position of the required correction mass to be determined. The values are usually calculated manually.

Any fixed point on the bearing experiences the centrifugal force due to the imbalance, once per revolution of the rotor. Therefore, in a frequency spectrum of the vibration signal, imbalance is seen as an increase in the vibration at the frequency of rotation. The vibration due to the unbalance is measured by means of an accelerometer mounted on the bearing housing (see Fig. 6). The vibration signal is passed through a filter tuned to the rotational frequency of the rotor so that only the component of the vibration at the rotational frequency is measured. The filtered signal is passed to a vibration meter, which displays the magnitude.

The indicated vibration level is directly proportional to the force produced by the imbalanced mass. The phase meter measures and displays the phase between the signal from the tachometer probe (the reference signal) and the filtered vibration signal. The angle displayed by the meter enables location of the angular position on the rotor of the imbalance, relative to the datum position [1].

The imbalance procedure may involve numerous calculation and measurement steps and is usually carried out on several different planes [2].

Torsional vibration

Torsional vibration (TV) results from the application of a fluctuating torque or excitation to a machine shaft. If a varying torque with a constant frequency is applied to the shaft, the shaft will vibrate at the frequency of the applied torque.

When the torque is applied to the shaft, angular elastic distortion occurs along the axis of rotation, as shown in Fig. 1. When the torque is removed, the shaft moves back to its original alignment and may also exhibit an oscillatory recovery in the opposite direction. If the torque is removed suddenly, the shaft distortion will oscillate around its rest position at its natural resonant frequency. Any equipment mounted on or connected to the shaft will be affected by this vibration.

Torsional vibration does not normally result in vibration of the machine itself, but can be transferred to couplings and attached equipment. Failures are normally in the rotor shaft itself or couplings to other items of equipment. TV is apparent on drives connected to gearboxes where vibration of the gears causes wear and is audible.

TV has become a problem with wind turbines, as the drive train can be subjected to a rapidly varying torque, and many of the turbines in current use make use of gearboxes in the drive train. Numerous mechanical and electrical solutions have been developed to reduce this effect.

In the case of alternators, torsional excitation can result from phase imbalances, faults on the grid, minor load imbalances and others. In the case of direct on line (DOL)  motors, torsional excitation can be caused by phase voltage imbalance, sags and dips in supply, faults on the line and within the machine and other imbalance issues. VFD systems remove most of these supply quality problems but bring a host of torsional excitation problems of their own.

Torsional resonance

Torsional vibration can be excessive at frequencies close to and at the natural resonant frequency of the rotor. For DOL motors, the frequency of the supply is the main source of torsional excitation and, for this reason, machines are designed to have rotor resonant frequencies that are spaced apart from both the fundamental supply frequency and its harmonics. The moments of inertia and the torsional stiffness of the system define the torsional resonances of the drive train [3].

In most industrial cases, each drive train element is designed and produced by a different manufacturer, and often without due consideration of the other elements. This poses a challenge to the system integrator as a characteristic feature of drivetrain vibration is the interaction of these elements, which requires the system torsional vibrations to be analysed as a whole. It is common practice for the system integrator to prepare a torsional model based on the data provided by the individual component manufacturers. Using this model, the system integrator, together with the manufacturers, tunes the drive train design to fulfil the torsional vibration requirements [3].

Variable frequency drives

VFDs can be problematic because the output not only varies in frequency but can contain additional harmonic and inter-harmonic components resulting from the conversion process. These can provide excitation at the fundamental and harmonic resonant frequencies of the motor, which can result in torsional vibration at frequencies above the supply frequency.

Certain types of VFD can be used to reduce torsional vibration by making use of inherent feedback functions to control the motor speed to avoid resonant points [4].

Vibrational mitigation

Drive train damping

Torsional vibration is damped out by the use of damping materials in the drive train, particularly at coupling points.

Machine mounting damping

Machine vibration is most often damped out by the use of anti-vibration mountings, which prevent the vibration from being transmitted to building and mounting structures.  Other methods must be used for very large machines.

Sand bed vibration mitigation

Sand beds are often used as a damping medium for larger machines. Turbines at Medupi Power Station are mounted on a reinforced concrete “raft” which rests on a bed of compressed sand. The raft is mechanically isolated from the rest of the turbine hall structure.


[1] M Macamhoil: “Static and dynamic balancing of rigid rotors”, Brüel and Kjaer application notes, BO-0276-12,
[2] T Feese: “Balance this: case histories from difficult balance jobs”, Engineering Dynamics incorporated,!_-_peg&tdf.pdf
[3] TP Halopeinen et al:  “Electric motors and drives in torsional analysis and design”, Proceedings of the 42nd Turbomachinery Symposium, October, 2013, Houston, Texas.
[4] N Nakenen: “A quick refresher on converting coupling torsional stiffness”,

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