Recovering cutting tool modal parameters from randomly sampled signals using compressed sensing

Abstract

A change in the modal parameters of cutting tools could signal tool wear, tool breakage, or other instabilities. The cutting process must be continuously monitored using vibration signals to detect such changes. Since tools vibrate with frequencies of up to a few kHz, continuous monitoring requires sampling at rates of tens of kHz to respect the Nyquist limit. Processing and storing such large data for decision making is cumbersome. To address this issue, this paper discusses the use of a compressed sensing framework that enables non-uniform random sampling at rates below the Nyquist limit. For cutting tools, we show for the first time using synthesized data that it is possible to reconstruct original signals from as few as 1% of the original data. We numerically test the method to characterize the influence of damping, noise, and multiple modes. Recovered modal parameters from the reconstructed signal agree with signals sampled properly.