Modal Complexity Factors as indexes for modal parameter identification in operational modal analysis of coupled dynamic systems

Vibration analysis seeks to extract the modal parameters of a mechanical system by means of experimental measurements. Natural frequencies, damping ratios and mode shapes are identified from the measurements data from experimental or operational modal analysis. Modal shapes can show real or complex values. The degree of complexity of a modal shape can be measured by the Modal Complexity Factors (MCF). Among others, modal complexity can be due to non-uniformly distributed damping. In complex mechanical systems like a robot, complex modes are expected due to its active and non distributed damping. In turn, in a metallic workpiece real modes are expected. In the robotic machining of thin workpieces, both the robot and the workpiece constitute a coupled dynamic system, operating within the same frequency range. This work proposes the use of MCFs as indexes to determine if each mode corresponds to the workpiece or the robot. Experimental results of an operational modal analysis show a lower mode complexity for the workpiece modes and a higher complexity for the robot frequencies. MCFs show a good performance in separating modes of such coupled systems due to the different damping nature of the robot and the workpiece.