47 Identification of Breathing Cracked Shaft Models from Measurements 541 0 20 40 60 80 100 120 140 10-10 10-5 100 Response (μm) Uncracked 0 20 40 60 80 100 120 140 10-10 10-5 100 Response (μm) Open 0 20 40 60 80 100 120 140 10-10 10-5 100 Response (μm) Mayes 0 20 40 60 80 100 120 140 Frequency (Hz) 10-10 10-5 100 Response (μm) Hinge Fig. 47.2 Spectra of the vertical displacement at node 7 for the simulated rotor Figure 47.5 shows the spectra when the machine is run at a constant speed of approximately 1500 rev/min (25 Hz) for four different cases. This speed is well below the critical speed for this system. The crack is simulated by loosening three bolts. The test runs involve both cracked and uncracked rotors, and both with and without the belt to introduce the lateral load. Without the belt the spectra are similar, with some response at the second and third harmonic, although the amplitude is relatively low. The harmonics indicate the presence of nonlinearities other than the breathing crack and some asymmetry in the rotor. The cracked shaft without any side load from the belt does not breathe because the curvature of the operational deflection shape on the overhung part of the shaft is very low. Adding the belt to the uncracked shaft produces extra frequencies due to the belt resonances but does not significantly affect the response at the fundamental and harmonics of the rotor spin speed. Note that the diameters of the belt pulleys mean that the system is also excited at half the rotor spin speed. When the belt is used for the cracked rotor the response at the second harmonic is increased, and the response at the fundamental is reduced. The third harmonic changes very little. This significant change in the ratio of the response at the second harmonic to the fundamental is vital to identify the presence of a crack.
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