摘要：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.
其他摘要：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.
