High powered industrial applications
The main aims of this study are to develop a magnetic bimorph concept and individually controlled conductors which will together reduce the tonal noise radiated from a large electrical machine and improve the efficiency of the machine. Relevant applications for these machines include military marine vessels, cruise liners and LNG carriers, wind turbines, petroleum and chemical pumps, cooling towers and process machinery.
Vibrations of the Stator
A stator is a cyclically symmetric structure, and this property occurs because a stator can be divided into subsections, with every one of the subsections being identical to every other subsection. Incidently, each subsection includes one tooth, a section of the windings and the corresponding segment of the back of core.
Cyclically symmetric structures exhibit unique vibration characteristics and these characteristics are described briefly here.
The mode shapes of a cyclically symmetric structure can be described by a mode number n, the mode number describes the number of complete deformation waves around the circumference that the structure deforms into. At most resonant frequencies of a cyclically symmetric structure there are two corresponding, orthogonal mode shapes with the same mode number.
The majority of noise producing forces within an electrical machine are periodic forces with respect to time and space. These can be decomposed in space into families which correspond to integer mode numbers. The applied forcing is usually made up of travelling waves around the air gap between the rotor and stator.
However, radial standing waves are often formed around the circumference of the stator from the interaction of two radial force waves with equal frequency rotating in opposite directions.
At a resonant frequency of the stator, there is a corresponding stator mode shape which dominates the response of the stator. If some forcing is applied to the stator at that resonant frequency, and the force wave has a spatial distribution with the same mode number as that stator mode shape, the stator will resonate.
The amplitude of vibration will be large and will depend on the damping in the structure. If the frequency of the force matches the resonant frequency of the stator but the mode number of the force does not match the mode number of the stator there will be zero net modal excitation at that frequency and the resonance will not be excited.
In electrical machines resonance must be avoided if noise and vibration is to be avoided and therefore knowledge of the vibrational response of the stator is required. The vibration of a structure in a narrow frequency band that is within the range of acoustic interest directly causes tonal acoustic noise to be radiated from the surface of the structure.
The different oscillating shapes of the stator produce different levels of noise.
The radial vibration of the back of the stator core is the most dominant source of airborne noise. From the point of view of noise emission, the most important force waves are those which have mode numbers between 1 and 10. This is because the flexural rigidity of the stator increases with mode number and so for higher mode numbers the deflections decrease.
The surface vibrations from deflected shapes which are described by a high mode number also have low noise radiation efficiency. The natural frequencies of the stator for an n=0 mode number are usually higher than the frequencies of interest.
In the range of acoustic interest, a large electrical machine can have thousands of resonant frequencies, whereas a small machine will have only a low number. In a large machine there are also many components of force present at frequencies that are related to noise production.
The frequencies and spatial distribution of these force components are likely to coincide with the resonances and mode shapes of the stator and cause high levels of vibration and tonal noise to be emitted.
Title: | Improving the efficiency and reducing the vibrations of large electrical machines – Annabel Shahaj, BEng(Hons), PhD thesis, University of Nottingham |
Format: | |
Size: | 11.5 MB |
Pages: | 452 |
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