Letter to the Editor
Chatter recognition by a statistical evaluation of the synchronously sampled audio signal

https://doi.org/10.1016/S0022-460X(03)00119-6Get rights and content

Introduction

Milling is a complex dynamic process that includes periodic impacts of the cutting teeth with the workpiece, corresponding vibrations of the cutter and workpiece that define the machined surface, and overcutting of the surface left by previous teeth by the current tooth. The removal of the undulating surface produced by the preceding tooth with the current tooth is referred to as regeneration of waviness and is a primary source of instability in milling [1]. Regeneration of waviness leads to a variable chip thickness and, therefore, variable cutting force which causes, in turn, vibrations of the tool and workpiece. This closed-loop feedback of force and vibration provides the mechanism for self-excited vibration, or chatter. Depending on the selected chip width (for a particular dynamic system, cutter geometry, and workpiece material), the subsequent vibrations of the cutter can diminish for stable cutting, or increase to some bounded limit for chatter. A schematic representation of a 50% radial immersion down-milling operation is shown in Fig. 1.

Because the variable cutting force can become large and the machined surface quality is poor, it is desirable to avoid unstable milling conditions. An important analytic tool that has been developed to aid in the selection of stable cutting parameters is the stability lobe diagram [2], [3], [4], [5], [6]. These diagrams allow the user to select appropriate combinations of the control parameters, chip width and spindle speed, by separating stable from unstable regions with the analytic ‘lobes’; see Fig. 2. The construction of these diagrams requires pre-process knowledge including the tool point frequency response function, expected radial immersion, and specific cutting energy coefficients that depend on the workpiece material, tool geometry, and cut parameters.

In many instances, the calculation of optimum milling conditions using stability lobes diagrams for each tool/holder/spindle/machine/material combination on the shop floor is not possible due to inadequate engineering support. In these situations, the need to rapidly identify stability behavior using methods that do not require an extensive background in vibration theory increases. One available pre-process option is the Harmonizer™ system [7] that calculates the fast fourier transform (FFT) of the time-based audio signal collected during unstable milling.1 The resulting spectrum is comb filtered to remove the tooth passing frequency and higher harmonics. The dominant chatter frequency, fc (in Hz), can then be identified from the filtered spectrum and the most stable spindle speeds selected according to Eq. (1), where Ωj is the spindle speed (in revolutions/min or r.p.m.) corresponding to the jth lobe, j is the integer lobe number, and Nf is the number of flutes on the cutter:Ωj=60fcjNf,j=1,2,3….

Although the in-process method described here does not offer the diagnostic capability of identifying alternate stable spindle speeds without additional signal processing, it does sense chatter using a much less computationally intensive procedure, i.e., a simple statistical interrogation of the time-based signal versus the frequency-domain FFT and subsequent filtering, and operates on a much smaller data set. Specifically, only one sample per spindle revolution is required versus the tens of kiloHertz sampling rates necessary to avoid aliasing in the FFT analysis. Additionally, it is not necessary to analyze the entire frequency spectrum within the selected bandwidth to search for and identify any offending chatter frequencies; it is only required that a single scalar quantity, the variance in the synchronously sampled cutting data, be considered. These benefits make it a prime candidate for real-time, remote condition-based monitoring of milling process stability. Other efforts in the general area of condition-based monitoring of machines and structures include both time and frequency domain techniques. Example references are included for further reading [8], [9], [10], [11], [12], [13], [14], [15], [16].

Section snippets

Theory

The notion of a statistical evaluation of the once-per-revolution milling audio signal to detect chatter is based on Poincaré mapping techniques, where a local description of transient behavior is constructed from the Poincaré map and the system stability may be established [17]. For milling, the stability can be evaluated by plotting the x direction versus y direction tool motions and identifying the once-per-revolution sampled data points [18]. For stable cutting, the synchronously sampled

Experimental results

In this section, a description of the experiment set-up and cutting tests parameters is provided. This is followed by the analysis methods applied to the milling audio signal. The methods include recording the once-per-revolution audio signal using: (1) an infrared emitter/detector pair, (2) the actual spindle speed, and (3) the commanded spindle speed. The latter two were explored in an effort to simplify the test set-up.

Conclusions

A chatter detection technique for condition-based monitoring of milling process stability, based on the statistical variance in the once-per-revolution milling audio signal, is described. This method uses the synchronous and asynchronous nature of stable and unstable cuts, respectively, to identify regenerative chatter. Specifically, it relies on the fact that stable cuts generate content synchronous with spindle rotation and, therefore, the once-per-revolution milling signal is characterized

Acknowledgements

The author would like to acknowledge Kate Medicus (University of North Carolina at Charlotte, Charlotte, NC) and Brian Dutterer (NIST, Gaithersburg, MD) for help in collecting the data for this study.

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