"Grey Box" Model Based Visualisation of Vibrations in Mechanical Systems

High-speed machining increases the need for accurate characterisation of machine tool dynamics. The most comprehensive approach to define these dynamics involves either analytical or numerical models. Regardless of the method by which these models are developed, they require validation. Visualisation of machine vibrations under controlled (e.g. harmonic) or ambient excitations is an important element of this validation. Visualisation is also a powerful tool in the monitoring and diagnosis of production equipment. The most representative example of this is experimental modal analysis (EMA) which facilitates displaying mode shapes of the investigated systems. It employs non-parametric or transfer functions (“black-box”) models to extract mode shapes from the signals recorded on the tested objects. This approach is conceptually straightforward and computationally efficient, but its disadvantage is high sensitivity to disturbances. A new approach proposed in this paper postulates using constitutive models of machine tools. The structure of these models (“grey box”) is derived on the basis of physical phenomena and first principles that govern the dynamic behaviour of tested machines. Model coefficients are next estimated from the operational and test data.