Multi-modal method for chatter stability prediction and control in milling of thin-walled workpiece

• Published in: Applied Mathematical Modelling Vol. 80; pp. 602 - 624
• Main Authors: Dun, Yichao, Zhu, Lida, Wang, Shuhao
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.04.2020; Elsevier BV
• Subjects: Chatter; Computational efficiency; Computational time; Computing time; Control stability; Mathematical analysis; Methods; Milling; Numerical analysis; Numerical methods; Numerical prediction; Stability analysis; Stability analysis in frequency domain; Stability analysis in time domain; Thin-walled workpiece; Workpieces; Thin-walled workpiece; Computational time; Stability analysis in frequency domain; Stability analysis in time domain; Milling
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.12.003

•A numerical difference method for predicting stability in milling.•Time- and position- dependent change of workpiece modal parameters, and its effect on stability prediction.•A multi-modal scheme of numerical methods.•Comparison between analytical methods and numerical methods.•Time complexity of analytical methods and numerical methods. Chatter stability in milling can be predicted by analytical methods or numerical methods. The system should be considered as multi-modal in milling of thin-walled workpiece. This paper proposes a numerical difference method based on Adams-Bashforth scheme. Moreover, multi-modal scheme of numerical methods is proposed. Analytical methods and numerical methods are verified by performing a series of milling trials. The experimental results are consistent with the predicted critical stability boundaries. Moreover, a new method for analyzing the computational time of analytical methods and numerical methods, which is based on the time complexity modeling, is presented. Computational time can be expressed as exact mathematical expression. By using the expression, the rate of increase of computational time can be derived.