540 M.I. Friswell et al. Long Bearing Short Bearing Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Fig. 47.1 The simulated rotor Figure 47.1 shows the model used for the simulations, which approximates an experimental test rig at Texas A&M at Qatar. The rotor is modeled by nine shaft finite elements in MATLAB [14]. The system comprised of a long shaft with diameter 20 mm and length 502 mm, coupled to a short flange of 14 mm diameter and 85 mm of length. The assembly of the disk and the flange have been modeled as one disc at node 7, with 14 mm thickness and 90 mm diameter. The small pulley has been modeled as a disk at node 9 with 27 mm thickness and 66 mm diameter. The left bearing at node 3 is modeled as a long rigid bearing (i.e. displacements and rotations fixed) and the right bearing at node 6 is modeled as a short rigid bearing (i.e. only displacements fixed). To reduce the time needed to simulate the transient response, damping in both lateral directions with value 100 Ns/m has been added at disk 1 (node 7). The rotor is made of steel with modulus of elasticity ED200 GPa, Poisson’s ratio D0.24 and mass density¡D7840kg/m3. The shaft crack is modeled as a stiffness reduction in element 7. An unbalance of magnitude 10 3 Nm was added at disk 2 (small pulley, node 9). The flange on the overhung part of the rotor has six bolts which may be loosened to simulate a crack. The first critical speed of the undamaged machine is 7700 rev/min. The rotor is simulated at 1500 rev/min; this is well below the critical speed but does allow the parametric excitation to be demonstrated without the risk of exciting any resonances. Figure 47.2 shows the spectra of the response at the flange when a crack is modeled as a fully open crack and also a breathing crack using the Mayes model and the hinge model. The open crack is modeled by a 20 % reduction in the lateral stiffness of element 7 in one plane in the rotating frame. The spectrum for the uncracked rotor is also shown, and highlights that the harmonics of the rotor spin speed are not excited in this case. The harmonics are excited in the cracked cases, and the amplitude of the harmonics increases from the fully open crack to the Mayes model to the hinge model. For the open crack the rotor is asymmetric, although no harmonics in the response will be excited because the bearing and support model is isotropic. The hinge model also gives responses at other frequencies because resonances of the machine have been excited which give combination frequency responses at many different frequencies. 47.4 Experimental Test Rig and Results The experimental test rig is manufactured by GUNT and incorporates a flange with bolts that may be loosened to simulate a crack. Since the size and weight of the rotor is too small to give weight dominance to the breathing crack behavior, a belt is used to provide a lateral (horizontal) load that is approximately constant in amplitude and direction in the stationary frame. If this force is sufficiently large then the crack will exhibit breathing behavior. Figure 47.3 shows the test rig and Fig. 47.4 shows the belt system used to apply the lateral load. The response is measured by accelerometers in the vertical and horizontal directions at the outer bearing support.
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