Exploring Once-Per-Revolution Audio Signal Variance as a Chatter Indicator

Abstract

The purpose of this study is an evaluation of the statistical variance in the once-per-revolution sampled audio signal during milling as a chatter indicator. It is shown that, due to the synchronous and asynchronous nature of stable and unstable cuts, respectively, once-per-revolution sampling leads to a tight distribution of values for stable cuts, with a corresponding low variance, and a wider sample distribution for unstable cuts, with an associated high variance. A comparison of stability maps developed using: 1) analytic techniques, and 2) the variance from once-per-revolution sampled timedomain simulations is provided and good agreement is shown. Experimental agreement between the well-known Fast Fourier Transform (FFT) chatter detection method, that analyzes the content of the FFT spectrum for chatter frequencies, and the new variance-based technique is also demonstrated.

Stability of linear time‐periodic delay‐differential equations via Chebyshev polynomials

“…Recently, however, a few numerical methods have been proposed to study the stability of this kind of system. These include time finite element analysis [3], numerical simulation [10], statistical signal variance [14], harmonic balance and infinite determinants [4,7,9,15], approximation of the delay by weighted integrals [6] and the semi-discretization method [16]. In each of these papers, the traditional stability charts related to different dynamic models are given.…”

Efficient determination of stability lobe diagrams by in-process varying of spindle speed and cutting depth

“…This idea has been used as an indicator for process stability for time domain simulation models of milling process in Refs. [8][9][10] as well as for milling experiments in Refs. [11][12][13].…”

Numerical Computation of Characteristic Multipliers for Linear Time Periodic Coefficients Delay Differential Equations

“…In the last decade, a few numerical methods have been proposed to address the study of the asymptotic stability of time periodic delay systems including time finite element analysis (Bayly et al , 2001), numerical simulation (Zhao and Balachandran, 2001), statistical signal variance (Schmitz et al , 2002), harmonic balance and infinite determinants (Budak and Altintas, 1998), approximation of the delay by weighted integrals and semi-discretization method (Insperger and Stepan, 2004). Other interesting papers are (Szalai et al , 2006;Verheyden et al , 2005).…”