29 Experimental Evaluation of Veering Crossing and Lock-In Occurring in Parameter Varying Systems 317 120 110 100 a b 105 115 0 0.5 |H1| 1 1.5 -1 0 |H1| 1 2 90 95 85 80 120 110 100 105 115 90 95 85 80 frequency(Hz) frequency(Hz) mass(g) mass(g) 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 40 45 Fig. 29.10 Series of FRF for the experimental evaluation of the crossing in the set-up (a); excitation on beam2 and response on beam2 (b) excitation on beam1 and response on beam1 15 10 5 0 8 6 4 2 0 -2 -4 -6 0 5 10 15 mass(g) real(H1) imag(H1) 20 25 30 35 40 Fig. 29.11 Series of FRFs for the experimental evaluation of the crossing in the set-up: real part vs imaginary part of the FRF as the added mass changes The Beam-on-Disc consists of a cantilever beam and a rotating disc pressed against each other using a dead weight. Figure 29.13 shows a photograph and a scheme of the set-up: the disc and the cantilever beam are both made of steel. Using this set-up, an experimental parametric analysis was conducted by adding small masses to the beam, allowing to change the natural frequencies of the beam with the aim of measuring the lock-in plot. The results are presented in Fig. 29.14 for the coupling between the second mode of the beam and the (0,4)1 mode of the rotor. The experiment is conducted by adding step by step mass to the beam and, at each step, measuring the natural frequencies of the system (Fig. 29.14b). Reached a certain distance between the natural frequency of the beam and that of the disc the system becomes unstable and squeal starts. During squeal, only one frequency can be measured: the squeal frequency (Fig. 29.14b) moreover, it is possible to measure with a laser scanner vibrometer the unstable deformed shape that is presented in Fig. 29.13d, e, confirming the fact that, in the instable range, a strongly-coupled modal shape is present, while before and after lock-in, two different natural frequencies, each associated with the mode of either the beam or the disc, are measured. 1The disc modes are denoted as (n,m) where n is the number of nodal circumference, and m is the number of nodal diameters. Because of the axial symmetry of the disc, all the modes are double modes. The contact between disc and pad brakes the symmetry of the system causing the two double disc mode to split; in this case, (n,mC) mode denote the one that has an antinode at the pad position that is usually the higher frequency one.
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