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Related Experiment Video

Updated: May 7, 2025

Operation of the Collaborative Composite Manufacturing CCM System

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

Newton-Simpson-based predictor-corrector methods for milling chatter stability prediction.

Yongjian Ji^1,2, Xiaokang Xu³, Yulin Yang³

¹Key Laboratory of Modern Measurement & Control Technology Ministry of Education, Beijing Information Science & Technology University, No.12 East Qinghexiaoying Road, Beijing, 100192, China. jiyongjian@bistu.edu.cn.

Scientific Reports

|January 2, 2025

Summary

This summary is machine-generated.

This study introduces novel Newton-Simpson predictor-corrector methods to accurately predict milling stability lobes, effectively mitigating chatter in machining. These advanced techniques offer faster convergence and higher precision for chatter-free milling parameter selection.

Keywords:

Chatter stability Milling Predictor–corrector Semi-discretization Stability lobe diagrams

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Area of Science:

Mechanical Engineering
Manufacturing Processes
Vibrational Analysis

Background:

Milling chatter, a self-excited vibration, significantly damages manufactured parts.
Selecting optimal milling parameters is crucial for mitigating chatter without reducing efficiency.

Purpose of the Study:

To introduce Newton-Simpson-based predictor-corrector methods for computing milling stability lobe diagrams.
To enhance the accuracy and efficiency of milling stability prediction.

Main Methods:

Transforming the milling delay differential equation into a state-space form.
Approximating time-delayed terms and periodic coefficient matrices using Newton interpolation and Simpson's formula.
Constructing the state transition matrix via a predictor-corrector scheme and applying Floquet theory.

Main Results:

The proposed Newton-Simpson methods exhibit a faster convergence rate compared to existing techniques.
Achieved significantly lower arithmetic mean of relative error (AMRE), mean squared error (MSE), and sum of absolute error (SAE).
Demonstrated superior calculation accuracy for local stability lobe diagrams.

Conclusions:

The developed methods provide a highly accurate and efficient approach for milling stability prediction.
Offers broad application prospects for precision machining and selecting chatter-free milling parameters.