Using the Eigenvalues of multivariate spectral matrices to monitor equipment

There is a strong need in industry for monitoring techniques that are capable of tracking the health of cutting tools under varying conditions. Unfortunately, most monitoring techniques that are currently available are dependent on the cutting direction and/or the sensor orientation, limiting their effectiveness in the typical industrial environment. With this in mind, this research focuses on developing a monitoring technique that is independent of both of these factors. This is accomplished by using multivariate autoregressive models that are fit to the output from a tri-axial accelerometer. The work shows that the eigenvalues of multivariate spectral matrices, calculated at the machining frequencies, are sensitive to the condition of the tool. Furthermore, it is theoretically demonstrated that these eigenvalues are independent of the direction of cutting and the orientation of the sensor. This independence is verified experimentally through tests conducted under a variety of cutting directions and sensor orientations.