Characterization of Rotating Structures in Coast-down by means of Continuous Tracking Laser Doppler Vibrometer M. Martarelli1, C.Santolini2, P. Castellini2 1Università degli Studi e-Campus - Via Isimbardi 10 - 22060 Novedrate (CO), Italy 2Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona, Italy ABSTRACT In rotating machinery variations of modal parameters with rotation speed may be extremely important in particular if very light and undamped structures are taken into account, like helicopters rotors or wind turbines. The relation between natural frequencies and rotation speed is expressed in the form of Campbell diagrams. However it could be required to know also the deviation of operational or mode shapes. In several cases it is not possible to fully control the rotating speed of the machine and only coast-down tests can be performed. Such kind of tests is often fast due to the reduced inertia of rotors: for this reason, an experimental technique able to determine Operational Deflection Shapes (ODSs) in short time and with sufficient accuracy, appears very promising. Moreover coast-down processes are very difficult to be controlled, they causing unsteady vibrations. The need to obtain ODSs from coast-down experiments requires the measurement over a large number of points and therefore a very efficient approach for the rotation control and synchronous acquisition must be developed. In this paper a continuous scanning system operating on rotating structures has been developed, that allows to measure ODS and natural frequencies excited in rotating conditions at different rotation speed during a coast down. This techniques has been tested on a laboratory test bench and compared with traditional Experimental Modal Analysis (EMA) results obtained in non-rotating conditions and with data from Tracking Laser Doppler Vibrometry (TLDV) operating in coast down and at consecutive constant rotation speeds (i.e. each measurement was performed in steady conditions). EMA and TLDV have been performed over a grid of points in order to have ODSs with adequate spatial resolution, it requiring long measurement time. However these data has been used as reference to validate the continuous scanning approach. 1. Introduction The dynamic characterization of rotating structures is an important task for understanding their structural behavior in operating conditions and in relation to the operation speed. The theory behind the variation of the modal parameters with the rotation speed has been deeply studied, see [1], [2] and [3]. This theory has been applied in the past to rotating machinery, in particular, turbine engines, turbofan and helicopter rotors. Nowadays the topic becomes very interesting for the understating of wind turbines dynamics and the work carried out in this paper can be applied in this context. Typical excitations of wind turbines, inducing vibrations, are: (i) aerodynamic, (ii) mass (tuned at the engine orders), (iii) gyroscopic and friction (acting at the rolling surfaces) forces, (iv) oscillating torque of the motor. It is well known that the natural frequencies of rotating structures increases depending to the speed because rotation introduces a gyroscopic force acting as tensile axial load inducing stiffness raising. The relation between natural frequencies of a uniform rectangular plate (as it can be seen a single blade of the rotating structure studied in this paper, see Fig. 2), subject to normal in-plane load (fLi,j) and the natural frequencies of the unloaded plate (fi,j) is given by the following equation [4]: (1) where Fg is the normal load, X, Y and m the plate dimensions and mass, see scheme in Fig. 1, and h a tabulated coefficient depending on mode shapes and boundary conditions (clamped-free in this case). The normal load is the centrifugal force, mω 2Y, ω being the rotational speed. T. Proulx (ed.), Modal Analysis Topics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series 6, 525 DOI 10.1007/978-1-4419-9299-4_44, © The Society for Experimental Mechanics, Inc. 2011
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