15 Modal Excitation of Circular Rotating Structures Using an Innovative Electromagnetic Device 161 flux density has to be smaller. The noise on the signals (for example dominant on the first peak of the yellow curve) is mainly introduced by the inverter of the driving motor and can be reduced through averaging. It can already be seen that the shape of the curves are of harmonic nature with k = 5 periods per turn. Also, a harmonic content withk = 1 period per turn can be seen especially in the larger curve. This is due to alignment imperfections of the measurement beams rotation axis relative to the exciter normal axis. With better alignment this harmonic content vanishes. For this reason, the excited wavenumber of the profile rings has to be chosen as k = 5 to not be impacted by the alignment imperfections with k = 1. The amplitude of around 10 mT agrees well with conducted magnet field simulations which will be published in future. For further insights, the power spectra are analysed. Figure 15.9c shows WELCHs power spectrum estimate (reference 1· 10−3 mT) of the angleseries of the magnetic flux density for 10 A excitation current shown in Fig. 15.9a (yellow and purple plot, plot colours are corresponding). From now on, the spectral lines will be denoted by their wavenumber which, from the point of view of the circular structure to be excited equals to the nodal diameter. For spectrum averaging to reduce noise, 20 revolutions of the beam are measured. The main harmonic content comes with wavenumber k = 5, as expected. Alsok = 1 is notable as it is caused by misalignment of the beam as discussed above. Furthermore, due to the calculated waveform of the magnetic flux density which is proportional to the inverse square root of a sine Eq. (15.9), notable harmonic content with wavenumbers k = 10 and k = 15 is also present (also compare to the spectrum of Fig. 15.5). It is expected that this spectrum of the magnetic flux density causes a force spectrum which is purely monoharmonic due to Eq. (15.3). The signal peaks (k = 5 and k = 10) do have a signal to noise ratio of about 20 dBm which equals to 1 100 and the next signal peak (k = 15) has a signal to noise ratio of 15 dBm. This value can be improved by proper shielding of the electronic equipment as it is only caused by interfering electric fields of the test setup. The power spectrum estimate for an excitation current of 1 A is depicted in Fig. 15.9d. As the useful signal decreases, the signal to noise ratio also declines so the higher wavenumber k = 15 is not visible any more. For k = 10 the signal to noise ratio is 5 dBm and for k = 10 it remains 20 dBm. But again, this is due to the electronic equipment and is not a flaw in the concept of the device. For clarity only the spectra for excitation currents of 1 and 10 A are shown. The behaviour of all other excitation levels can be seen in Fig. 15.9b where the peak power levels for each excitation level for wavenumber k = 5 is depicted. Except for I = 1 A, I = 9 A and I = 10 A the peak values of the outer ring are always lower than the inner ring. This is the expected behaviour as the magnetic flux density should be higher at the ring with smaller surface. For the lowest excitation current the misbehaviour is due to a low signal to noise ratio, for the higher excitation currents it is most likely caused by a feedback effect of the beams stronger magnetisation. Fitted functions of order 2 are plotted revealing a quadratic behaviour between the power of the magnetic flux density and the excitation current. This equals a linear dependency between the magnetic flux density and the current which is in accordance with Eq. (15.4). 15.4 Conclusions A electromagnetic device for the excitation of travelling wave modes of rotating structures has been presented. With this device it is for the first time possible to excite a rotating structure like circular blades or turbine discs exactly in the desired modeshapes and nodal diameters without disturbances. The disadvantage of existing excitation concepts explained above, the occurrence of higher harmonic, interfering excitation frequencies, can be completely avoided with the device. It has been shown that the measured magnetic flux density distribution fulfils the predictions. In particular the spectra of the magnetic flux densities promise to achieve the desired properties of the excitation force. It is both possible to create purely monoharmonic excitation forces and any other arbitrary excitation force functions. It is for the first time possible to resemble nodal diameter excitations for rotating structures which are typically used in simulation tools like finite element programs. Therefore, the device can play an important part in validating simulation tools and improve the process of simulation-heavy design chains like for gas turbines. Acknowledgements The investigations were conducted as part of the joint research programme COOREFlex-turbo in the frame of AG Turbo. The work was supported by the Bundesministerium für Wirtschaft und Technologie (BMWi) as per resolution of the German Federal Parliament under grant number 03ET7041L. The responsibility for the content lies solely with its authors. References 1. Hoffmann, T., Jahn, M., Panning-von Scheidt, L., Wallaschek, J.: Ein Elektromagnetischer Mechanismus Zur Anregung von Schaufelschwingungen, Patent DE 102017114153.7, vol. 26.07.2017, July 2017 2. Rao, S.S.: Vibration of Continuous Systems. Wiley, Hoboken (2007), oCLC: ocm65301593
RkJQdWJsaXNoZXIy MTMzNzEzMQ==