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Recent Developments of Electrical Drives - Part 13

Recent Developments of Electrical Drives - Part 13. The book stating the recent developments of electrical drives, can be useful for engineers and researchers investigating and designing electrical and electronic devices as well as for students and young researchers dealing with electrical and electronic engineering, computer sciences (advanced computer modelling, sophisticated control systems with artificial intelligence tools applied, optimal design bye use of classical and genetic algorithms employed), applied mathematics and all the topics where electromagnetic, thermal, mechanical phenomena occur | I-10. Permanent Magnet Synchronous Machine 107 Acoustic model Acoustic intensity I x can be written as a function of the frequency the amplitude of vibrations the mode order and the stator surface 5 9 . I x 8200f2Ym dSe 4n x 2 2m 1 The coefficient a is called factor of radiation. It represents the capacity of a machine to be a good sound generator and can be calculated through two different ways according to whether one assumes the machine to be a sphere or a cylinder a is a factor which varies with X wavelength and the diameter of the machine. It also depends on the mode shape 3 D c f Tl 1 7 c Traveling speed of sound 344 m s fr Vibration frequency. It appears that I x is inversely proportional to the order of the mode in addition the acoustic intensity is proportional to the square of the vibration amplitude. In general we define I and W in decibels. We thus define the levels of acoustic pressure acoustic intensity and sound power as follows Lp 20 log a- Lt 10 log a a with P0 20 pPa I0 10-12 W m2 W0 10-12 W The spectrum of the total noise obtained by our analytical model is presented below Fig. 7 . Figure 7. Spectrum of the noise of the simulated PMSM. 108 Vivier et al. Figure 8. Spectrum of the noise of PMSM measured with 3 555 rpm 1 12 octave . Fig. 8 presents the measured acoustic noise spectrum at the same speed 3 555 rpm . Lines are located at the same frequencies as in the vibration spectrum. The first line determined by measurements is located at 2 900 Hz 12 f . In theory the harmonic of teeth 12f is located at 2 844 Hz. The lines at low frequencies between 24 and 459 Hz are not found in theory because they are mainly related to the background noise. They are not generated by the PMSM but by the driving motor and the ventilator Fig. 9 . Figure 9. Spectrum of the noise of driving motor and ventilator measured with 3 555 rpm 1 12 octave . I-10. Permanent Magnet Synchronous Machine 109 Frequency Hz Figure 10. Level of the 12th harmonic vs. rotation speed. .