Using the eigenvalues of multivariate spectral matrices to achieve cutting direction and sensor orientation independence

There in a strong need for monitoring techniques capable of tracking the health of cutting tools under varying conditions. Unfortunately, most monitoring techniques 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 develops 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 triaxial accelerometer. The work shows that the eigenvalues of multivariate spectral matrices, calculated at the machining frequencies, are not only sensitive to the condition of the tool but are also 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.