Experimental construction of reduced mathematical models of rotating equipments in operation

An experimental method is proposed to obtain simplified mathematical models of rotating equipment systems. The Instrumental Variable Filter (IVF) method is applied to estimate mass, damping and stiffness force coefficients within a frequency range, through experimental measurements. This method is based on the least squares approximation technique and it uses analytical weight functions to reduce the effect of noise in the measurements. The experimental data is obtained for different configurations of rotating equipments, which consist of rigid wheels, a flexible shaft supported by bushing bearings, an electrical motor, a base-plate, and a concrete foundation. Frequency response functions (FRF) were obtained by impact excitation techniques. In the tests, the unbalanced response measurements were compared with the ones predicted by the IVF model. The method allows the study of mass, damping and stiffness force coefficients as a function of excitation frequency. Linearities and non-linearities of phenomena are identified, and the method sums up all the individual components into a definition for the system. The tests were conducted by operating, or not, the motor, in order to evaluate the IVF method in both cases. The high correlation between the IVF (FRF, and unbalance responses) and the actual measurements of the FRF and unbalance responses, shows that the method generates useful mathematical models of dynamic systems, that can have industrial applications. Modal analysis methods were used to compare the natural frequencies and the damping ratios, obtained by dynamic coefficients estimation.