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Chatter Analysis and Stability Prediction of Milling Tool Based on Zero-Order and Envelope Methods for Real-Time Monitoring and Compensation


The artificial intelligence means that it can autonomously determine the cutting situations regardless any cutting states and change them automatically as required. Regenerative chatter is an instability occurrence during CNC machining operation that must be avoided for high accuracy and greater surface manufactures. In this paper, an artificial intelligence based on zero-order and enveloped method is use for the chatter analysis and stability prediction of milling tool in real-time and on-line compensations. In order to measure the phase shift of harmonic frequency for real-time in cutting process, two three-axis accelerometers are installed at the bottom of the workpiece and at the above of the spindle to collect the vibration signal. Experimental results showed that the phase shift of regenerative chatter is higher than unchartered. The stable chatter signals of time domain vibration according to stability lobe diagram have low amplitude of vibration. This was confirmed that characteristic marks of chatter vibrations have higher amplitude level signal in the experimental test. In addition, this study developed a chatter prediction system for on-line calculation and real-time monitoring and compensation. The modal parameters of the chatter analysis and stability prediction system like natural frequencies, damping, and residues must also be identified automatically.

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\( v_{j} \left( {t - T} \right) \) :

Vibration vector in present period

\( v_{j} \left( t \right) \) :

Vibration vector in previous period

g(ϕj), A(t):

Unit step function and periodic vector over a tooth period

\( \emptyset_{j} \) :

Rotational angle of jth tooth measured CW from normal y axis

\( S_{f} \) :

Feed rate per tooth


Milling tooth period

dFtj, dFrj :

Tangential and radial cutting forces

\( \phi_{st} , \phi_{ex} \) :

Start and exit immersion angles of milling tooth

Kt, Kr :

Cutting coefficients along tangential and radial directions

ϕp, N:

Cutter pitch angle and number of milling teeth

Ps, Pw :

Spindle phase and workpiece phase


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This work was partially supported by the Ministry of Science and Technology, under Grant Nos. MOST 106-2221-E-150-020, MOST 107-2221-E-150-019, 106-AF-090, 107AF036, and 107B1034.

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Correspondence to Wen-Yang Chang.

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Chang, WY., Chen, CC. & Wu, SJ. Chatter Analysis and Stability Prediction of Milling Tool Based on Zero-Order and Envelope Methods for Real-Time Monitoring and Compensation. Int. J. Precis. Eng. Manuf. 20, 693–700 (2019).

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