Robot Assisted Modal Analysis on a Stationary Bladed Wheel

This paper shows an automated procedure to experimentally find the eigenmodes of a bladed wheel with highly three-dimensional geometry. The stationary wheel is supported in free-free conditions, neglecting stress-stiffening effects. The single input / multiple output approach was followed. The vibration speed was measured by means of a laser-Doppler vibrometer, and an anthropomorphic robot was used for accurate orientation and positioning of the measuring laser beam, allowing multiple measurements during a limited testing time. The vibration at corresponding points on each blade was measured and the data elaborated in order to find the initial (lower frequency) modes. These modal shapes were then compared to finite element simulations and accurate frequency matching and exact number of nodal diameters obtained. Being the modes cyclically harmonic, the complex formulation could be attractive, being not affected by the angular phase of the mode representation. Nevertheless, stationary modes were experimentally detected, rather than rotating, and then the real representation was necessary. The discrete Fourier transform of the blade displacements easily allowed to find both the angular phase and the correct number of nodal diameters. Successful MAC experimental to analytical comparison was finally obtained with the real representation after introducing the proper angular phase for each mode.