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Research Papers

Output-Only Modal Analysis of Micromilling Systems

[+] Author and Article Information
K. Ahmadi

Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: kvahmadi@uvic.ca

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received July 31, 2017; final manuscript received November 1, 2017; published online December 14, 2017. Assoc. Editor: Martin Jun.

J. Micro Nano-Manuf 6(1), 011006 (Dec 14, 2017) (9 pages) Paper No: JMNM-17-1044; doi: 10.1115/1.4038434 History: Received July 31, 2017; Revised November 01, 2017

An output-only modal analysis (OMA) approach is presented to obtain the direct frequency response function (FRF) at the tip of the tool in micromilling setups. White noise input is provided using acoustic excitation and the resulting vibrations are measured using a laser Doppler vibrometer (LDV). Autoregressive (AR) identification is used to extract the natural frequencies and damping ratios of the structural modes of the milling setup, and mass-sensitivity analysis is used to obtain modal stiffness values. The accuracy of the tool tip FRFs that are constructed using OMA is verified by comparing them against the FRFs that are measured using impulse hammer tests. The direct FRF at the tool tip is an essential component in predicting and avoiding excessive and unstable vibrations in milling operations, and the presented approach provides a practical method for the direct measurement of the tool tip FRF in micromilling where the application of traditional hammer tests is not possible.

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Figures

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Fig. 1

Schematic of the micromill structure

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Fig. 2

Micromilling setup with (a) 13 mm overhang, (b) 30 mm overhang, and (c) 30 mm overhang after adding 70 mg mass atP1

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Fig. 3

Modal analysis at P1 on the tool with 30 mm overhang. (a)–(c) PSD of the filtered signals in frequency ranges I, II, and III, and the stabilization diagram of the AR identification; (d)–(f) modal damping ratios before and after adding 70 mg mass at P1; (g)–(i) modal participation factors before and after adding 70 mg mass at P1.

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Fig. 4

Modal analysis at P2 on the tool with 30 mm overhang. (a)–(c) PSD of the filtered signals in frequency ranges I, II, and III, and the stabilization diagram of the AR identification; (d)–(f) modal damping ratios before and after adding 70 mg mass at P2; (g)–(i) modal participation factors before and after adding 70 mg mass at P2.

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Fig. 5

PSD of the filtered and unfiltered velocities measured at P1 on the tool with 30 mm overhang

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Fig. 6

CFs of the vibrations measured at P1, without added mass, and filtered in frequency range III. Computed using direct method (dashed line) and (solid line) reconstructed using the identified modal frequencies and damping ratios shown in Fig. 4.

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Fig. 7

Direct FRFs measured using impulse hammer (dashed line) and synthesized using OMA results (solid line) at point P1 ((a) and (b)) and point P2 ((c) and (d)). OMA results are shown in Figs. 3 and 4.

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Fig. 8

Modal analysis at P3 on the tool with 13 mm overhang. (a)–(c) PSD of the filtered signals in frequency ranges I, II, and III, and the stabilization diagram of the AR identification; (d)–(f) modal damping ratios before and after adding 100 mg mass at P3; (g)–(i) modal participation factors before and after adding 100 mg mass at P3.

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Fig. 9

Modal analysis at P4 on the tool with 13 mm overhang. (a)–(c) PSD of the filtered signals in frequency ranges I, II, and III, and the stabilization diagram of the AR identification; (d)–(f) modal damping ratios before and after adding 35 mg mass at P4; (g)–(i) modal participation factors of stable modes before and after adding 30 mg mass at P4.

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Fig. 10

Direct FRF at the flute of the tool with 13 mm overhang

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