Phase Coupling in Orthogonal Cutting

Bispectral Analysis of the Cutting Process

“…The frequency f+205 Hz corresponds to a natural frequency of the work-piece that is shifted because of the work-piece}tool coupling. The characteristic chatter frequencies found in the literature are in the same frequency range as ours [8,10], although they can be either much higher, when the chatter is in#uenced by a slender tool holder [13], or lower, when it is in#uenced by some other machine part. For the bispectral analysis, a vector time series F was recorded in each of the three cutting regimes.…”

“…Furthermore, the measured data contained noise, thus reducing the reliability of the estimates. One method of "ltering out noise levels is to display only the estimators' values above a certain level [10]. However, by doing so, the variance of the estimator remains the same.…”

“…Recently, bicoherence [10] and singular values of a Toeplitz matrix of third-order cumulants [11] have been used for detecting quadratic phase coupling and cutting state identi"cation. It is our aim to use the bicoherence estimator when looking for a representative process variable.…”

Auto-Regressive SVD Algorithms and Cutting State Identification

“…The R matrix determined the coe$cients in an auto-regressive (AR) approximation of the bispectrum based on the third order recursion method (TOR) [20]. A bispectral and bicoherency analysis of the cutting tool acceleration measurements showed that the cutting process is quadratically phase coupled [15]. Reference [19] shows the ratio of the sum of the largest pair of singular values of R to the sum of the second largest pair, the R-ratio, di!erentiated between light cutting, medium cutting, pre-chatter and chatter states.…”

“…Time}frequency plots based on Gaussian wavelet transforms were used to detect and characterize non-stationary phenomena such as built up edge breakage. Wavelet analysis indicates that the non-regenerative cutting process is probably quadratically non-linear [15]. Cutting states, associated with the orthogonal cutting of sti!…”