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Technical Brief

Dynamic Force Identification in Peripheral Milling Based on CGLS Using Filtered Acceleration Signals and Averaged Transfer Functions

[+] Author and Article Information
Chenxi Wang

State Key Laboratory for Manufacturing System Engineering,
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: wangchenxi@stu.xjtu.edu.cn

Xingwu Zhang

Associate Professor
State Key Laboratory for Manufacturing System Engineering,
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: xwzhang@xjtu.edu.cn

Baijie Qiao

State Key Laboratory for Manufacturing System Engineering,
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: qiao1224@xjtu.edu.cn

Hongrui Cao

Associate Professor
State Key Laboratory for Manufacturing System Engineering,
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: chr@mail.xjtu.edu.cn

Xuefeng Chen

Professor
State Key Laboratory for Manufacturing System Engineering,
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: chenxf@mail.xjtu.edu.cn

1Corresponding author.

Manuscript received December 24, 2017; final manuscript received March 29, 2019; published online April 12, 2019. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 141(6), 064501 (Apr 12, 2019) (8 pages) Paper No: MANU-17-1805; doi: 10.1115/1.4043362 History: Received December 24, 2017; Accepted April 01, 2019

Dynamic milling forces have been widely used to monitor the condition of the milling process. However, it is very difficult to measure milling forces directly in operation, particularly in the industrial scene. In this paper, a dynamic force identification method in time domain, conjugate gradient least square (CGLS), is employed for reconstructing the time history of milling forces using acceleration signals in the peripheral milling process. CGLS is adopted for force identification because of its high accuracy and efficiency, which handles the ill-conditioned matrix well. In the milling process, the tool with high-speed rotation has different transfer functions between tool nose and accelerometers at different angular positions. Based on this fact, the averaged transfer functions are employed to reduce the error amplification of regularization processing for milling force identification. Moreover, in order to eliminate the effect of idling and high-frequency components on identification accuracy, the Butterworth band-pass filter is adopted for acceleration signals preprocessing. Finally, the proposed method is validated by milling tests under different cutting parameters. Experimental results demonstrate that the identified and measured milling forces are in good agreement on the whole time domain, which verifies the effectiveness and generalization of the indirect method for milling force measuring. In addition, the Tikhonov regularization method is also implemented for comparison, which shows that CGLS has higher accuracy and efficiency.

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Figures

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Fig. 1

Schematic representation of the milling process

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Fig. 2

The transfer function measuring setup

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Fig. 3

The measured and averaged transfer functions: (a) xx direction, (b) yx direction, (c) xy direction, and (d) yy direction

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Fig. 4

The measured milling force signals in the frequency domain

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Fig. 5

The measured acceleration signals in the frequency domain: (a) idling and (b) milling

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Fig. 6

The characteristics of the Butterworth band-pass filter: (a) amplitude-frequency characteristic and (b) phase-frequency characteristic

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Fig. 8

The measured and identified milling forces with radical cutting depth 2 mm in the feed direction, solid line: measured milling forces, dashed line: CGLS identified milling forces with filtering, dotted line: Tikhonov identified milling forces with filtering, dash-dotted line: CGLS identified milling forces without filtering. (a) Whole comparison, (b) magnified view for 0.05 s–0.1 s, (c) magnified view for 0.175 s–0.225 s, and (d) magnified view for 0.3 s–0.35 s.

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Fig. 9

The measured and identified milling forces with radical cutting depth 2 mm in the cross-feed direction, solid line: measured milling forces, dashed line: CGLS identified milling forces with filtering, dotted line: Tikhonov identified milling forces with filtering. (a) Whole comparison, (b) magnified view for 0.05 s–0.1 s, (c) magnified view for 0.175 s–0.225 s, and (d) magnified view for 0.3 s–0.35 s.

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Fig. 10

The measured and identified milling forces with radical cutting depth 1 mm in the feed direction, solid line: measured milling forces, dashed line: CGLS identified milling forces with filtering, dotted line: Tikhonov identified milling forces with filtering. (a) Whole comparison, (b) magnified view for 0.05 s–0.1 s, (c) magnified view for 0.175 s–0.225 s, and (d) magnified view for 0.3 s–0.35 s.

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Fig. 11

The measured and identified milling forces with radical cutting depth 1 mm in the cross-feed direction, solid line: measured milling forces, dashed line: CGLS identified milling forces with filtering, dotted line: Tikhonov identified milling forces with filtering. (a) Whole comparison, (b) magnified view for 0.05 s–0.1 s, (c) magnified view for 0.175 s–0.225 s, and (d) magnified view for 0.3 s–0.35 s.

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Fig. 12

The absolute errors between measured and identified milling forces with radical cutting depth 1 mm in the cross-feed direction

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