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Recent Developments of Electrical Drives - Part 25

Recent Developments of Electrical Drives - Part 25. 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 | II-8. To Determine Natural Frequencies of Electrical Machines 233 Figure 9. Vertical current jM N response impact excitation . Fixed structure Figure 13 presents the mode shapes and the natural frequencies of the statoric ring first in free condition and then when it is attached. Figure 10. FFT. 234 Lecointe et al. Figure 11. Suspended stator and meshing. Figure 12. Experimental results modes 2-2D 3-2D 4-2D and modes 2-3D 3-3D 4-3D. Table 4. Results for the sleek cylinders Natural frequencies Hz Mode Analytical laws FE Software Analogies Hammer test Cyl 1 2-2D 2 244 2 232 2 095 2 280 2-3D x 2 808 x 2 740 3-2D 6 208 6 169 6 395 6 280 3-3D x 7 155 x 6 930 Cyl 2 2-2D 756 824 799 742.6 2-3D x 1 454 x 1 350 3-2D 2 102 2 295 1 899 2 060 3-3D x 3 752 x 3 470 4-2D 3 940 4 301 3 700 3 860 4-3D x 6 278 x 5 810 5-2D 6 200 6 761 6 318 6 060 5-3D x 8 976 x 8 230 II-8. To Determine Natural Frequencies of Electrical Machines 235 Figure 13. Mode shapes and natural frequencies. In free mode the three first modes are perfectly identified. However some modes are not as perfectly defined as for the sleek cylinders. For example the shape of the mode 2 in two dimensions is undoubtedly deformed by the welded feet. When the stator yoke is fixed to the chassis the natural frequencies are increased but the maximal relative variation is equal to 5.2 . This evolution is attributed to the fixation of the structure. If the natural frequencies are not modified a lot the mode shapes differ from the shapes observed in free mode. For example the modes 3-2D and 3-3D in free mode become almost modes 4-2D and 4-3D when the structure is fixed. The fixation prevents the structure from moving. It is clearly visible at presented .