The trend of the first fourth theoretical natural frequencies, calculated from the static ones (measured as shown in Section 3), are reported in Fig. 1 (right). It can be noticed that the parabolic trend, as expected from eq.1, is more marked for the first and third mode. This is explained by the fact that these modes have horizontal Nodal Lines (NL) and therefore they are more influenced by the gyroscopic force, acting to the NL perpendicular direction, unlike it happens for the modes with vertical NL. Fig. 1 Blade layout (left) and theoretical dependence of the natural frequencies on the rotation speed (right) It has been demonstrated in [5] that the in-plane (tensile or compression) load acting on a beam has no significant effect on the mode shapes and this stands also for isotropic and orthotropic plates. On the other hands, if the structure is made of composite material, this assessment does not go anymore [6]. In this case the possibility of measuring and monitoring the ODSs of the blade during different rotation speeds is an important issue. In this paper the blade under test has been characterized, first, in static condition using modal analysis of impact test data and, secondly, in rotation by measuring on a grid of points over its surface with LDV synchronous with the rotation, i.e. TLDV, [7], [8] and [9]. This technique is based on the use of the Scanning Laser Doppler Vibrometer (SLDV) for Lagrangian measurements. The goal is to lock the laser beam to a single point as that point moves and vibrates with the structure. This enables structural vibrations to be measured in operating conditions. The TLDV [10] is basically a SLDV system modified into a controlled tracking system for rotational motions by driving the two moving mirrors via clock signals generated by an angular position transducer (encoder) linked to the shaft of the rotating device. This strategy has been applied in several kinds of rotating machinery, as helicopter rotors [11] and fans [12]. Therefore, an optimized methodology to recover the ODSs of rotating structures has been applied to the blade during constant regime and also coast-down. The method is based on Continuous Scanning Laser Doppler Vibrometry (CSLDV) synchronous with the structure rotation, i.e. operating in tracking fashion and hence called Tracking CSLDV (TCSLDV). Laser Doppler Vibrometry (LDV) is a non contact techniques allowing to perform remote measurements of structural vibration velocities that is a prerequisite in rotating machinery tests [13], [14]. Based on LDV, the CSLDV is able to reconstruct ODSs with a single shot measurement, because the LDV output is modulated by the ODS itself, the laser beam being scanning over the whole surface of the structure, [15]. This technique has been usually applied in controlled excitation conditions and mostly in resonance lock-in, this allowing a higher Signal to Noise Ratio (SNR) and a better reconstruction of the ODS by demodulation. For structures with well separated mode shapes it has been also used in impact testing [16]. For rotating structures, as bladed discs, the CSLDV has been applied in the asynchronous fashion in [17] and synchronously with rotation in [18], but it has never been applied in coast-down. In the case of rotating structure characterization, the CSLDV has been always employed with controlled excitation. In rotating conditions the coupling of the excitation source and the moving structure is a challenging task since the contact techniques must be obviously avoided. Typical exciters used in the state of the art are electromagnetic or pulsed laser. This latter has been deeply studied in [19], where the force induced by the laser pulse has been simulated via FEM and quantified in [20]. In this work, instead, the excitation is due uniquely by the forces acting in operating conditions (engine order, friction, aerodynamic loads, motor torque oscillation). For this reason together with the well-known CSLDV drawback, i.e. the speckle noise, an optimization between laser beam scanning frequencies in dependence to the actual excitation must be performed as suggested in [21]. 2. Method and instrumentation 2.1 Test bench The experimental item is a two blade rotating structure built-up with the aim to fine-tune the TCSLDV methodology to be applied in operating excitation conditions. Each blade is made of aluminum and has dimensions of 0.270×0.180×0.025 m. The motor drive of the fan in clamped to a rigid and massive concrete block, see Fig. 2. The fan is put into rotation by an in- Y X x y Rotation center Fg ω 5 10 15 20 25 0 20 40 60 80 100 120 140 160 180 Speed [RPS] Resonance frequency [Hz] 526
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