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Technical Brief

Non-normal Dynamic Analysis for Predicting Transient Milling Stability

[+] Author and Article Information
Qingzhen Bi

State Key Laboratory of Mechanical, System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240 P.R. China
biqz@sjtu.edu.cn

XinZhi Wang

State Key Laboratory of Mechanical, System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240 P.R. China
1130209030@sjtu.edu.cn

Hua Chen

Dalian Maritime University, Dalian 116026, P.R. China
huachen204887@163.com

Li-Min Zhu

State Key Laboratory of Mechanical, System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240 P.R. China
zhulm@sjtu.edu.cn

Han Ding

State Key Laboratory of Mechanical, System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240 P.R. China
hding@sjtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4039033 History: Received July 19, 2017; Revised December 19, 2017

Abstract

A transient milling stability analysis method is presented based on linear dynamics. Milling stability is usually analyzed based on asymptotic stability methods, such as the Floquet theory and the Nyquist stability criterion. These theories define stability that can return to equilibrium in an infinite time horizon under any initial condition. However, as a matter of fact, most dynamic processes in milling operations occur on a finite time scale. The transient vibration can be caused by some disturbance in practical milling process. Heavy transient vibrations were observed in existing works, though the machining parameters were selected in the stability zone determined by the asymptotic stability method. The strong transient vibrations will severely decrease the machining surface quality, especially for small workpieces in which the majority of machining process is executed in a short period of time. The analysis method of the transient milling stability is seldom studied, and only some experiments and conjectures can be found. Here the transient milling stability is defined as transient energy growth in transition matrix are all used to predict the transient milling stability, while only eigenvalues are employed in the traditional asymptotic stability analysis method. The transient stability is finally analyzed by taking the maximum vibration energy growth and the maximum duration time of transient energy growth in a finite time for optimal selection of processing paramters.

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