CRACK DETECTION IN A SPINNING BEAM

Abstract

This paper deals with the detection of a crack in a spinning beam (rotor) by means
of the measured frequencies method. This technique as a crack detection criterion has been
extensively applied in the last decade meanly due to the fact that frequencies are, among other
dynamical parameters, easily measured. However the inverse problem of determination of the
crack parameters (location and depth) for a given set of measured frequencies is not simple. An
efficient numerical technique has to been employed so as to obtain acceptable results. In this
study the effect of the crack is modeled through the introduction of intermediate flexional springs
in a spinning beam of circular cross section and rotating around its longitudinal axis with constant
angular velocity. The beam-springs analytical model is first stated and the power series
method is employed to obtain the solution for a given set of data, say the springs constants, the
crack location or the frequency. It should be noted that the springs and the crack depth may be
related by some expression from Fracture Mechanics. Here a systematization of the series gives
rise to an efficient numerical method. An algorithm is then written and prepared to solve the
inverse problem. Then experimental frequencies are measured in a cracked spinning beam. At
this stage, this experiment is performed numerically, with a spinning beam with a notch. The
flexural frequencies are obtained. These are the input for the previous numerical algorithm to
find the solution of the inverse problem: i.e. predict the crack depth and location resp., given
the measured frequencies. Numerical examples are included with an evaluation of the errors
in the results. The methodology has been tested previously in an non spinning Euler-Bernoulli
beam with very promising results.