Stability assessment of machine systems described by receptance

Abstract

The usual approach [1] of finding the stability regions' boundaries is insufficient when the system dynamics is considered in other than the speed or the frequency domain, as it gives no indication on which side, if any, of a boundary stability prevails. This paper presents a method of assessing system stability on the basis of its numerical receptance matrix, obtained from computation or experiment. An approximation approach [2] is adopted to obtain the characteristic equation and its roots that determine the system stability. The numerical procedures presented permit not only assessment of the system stability but also yield an analytical form for the experimentally measured receptances. This processing is usually necessary as a smoothing procedure to eliminate spurious effects, e.g., instabilities related to the measurement errors, when experimental data are used in computational processes. Actual application cases are also presented.