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Technical Briefs

# On a Numerical Method for Simultaneous Prediction of Stability and Surface Location Error in Low Radial Immersion Milling

[+] Author and Article Information
Ye Ding, LiMin Zhu

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

XiaoJian Zhang

State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Han Ding1

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

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(2), 024503 (Feb 28, 2011) (8 pages) doi:10.1115/1.4003374 History: Received January 02, 2010; Revised October 05, 2010; Published February 28, 2011; Online February 28, 2011

## Abstract

This brief proposes a numerical approach for simultaneous prediction of stability lobe diagrams and surface location error in low radial immersion milling based on the direct integration scheme and the precise time-integration method. First, the mathematical model of the milling dynamics considering the regenerative effect is presented in a state space form. With the cutter tooth passing period being divided equally into a finite number of elements, the response of the system is formulated on the basis of the direct integration scheme. Then, the four involved time-variant items, i.e., the time-periodic coefficient item, system state item, time delay item, and static force item in the integration terms of the response, are discretized via linear approximations, respectively. The corresponding matrix exponential related functions are all calculated by using the precise time-integration method. After the state transition expression on one small time interval being constructed, an explicit form for the discrete dynamic map of the system on one tooth passing period is established. Thereafter, the milling stability is predicted via Floquet theory and the surface location error is calculated from the fixed point of the dynamic map. The proposed method is verified by the benchmark theoretical and experimental results in published literature. The high efficiency of the algorithm is also demonstrated.

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## Figures

Figure 1

Schematic diagram of the dynamic milling process

Figure 2

Discretization of the helical-edged tool along its axial direction

Figure 3

Stability charts with 2% radial immersion considering the helical-angle effect. The presented results are for (a) the first mode only of Table 2 and (b) two modes of Table 2.

Figure 4

Comparison of the proposed method with the TFEA method for SLE (5% immersion down-milling)

Figure 5

Simultaneous prediction of stability and SLE for 10% immersion down-milling

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