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Research Papers

A Free Interface Component Mode Synthesis Approach for Determining the Micro-End Mill Dynamics

[+] Author and Article Information
Kundan K. Singh

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai 400076, Mumbai, India
e-mail: kundansingh@iitb.ac.in

Salil S. Kulkarni

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai 400076, Mumbai, India
e-mail: salil.kulkarni@iitb.ac.in

V. Kartik

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai 400076, Mumbai, India
e-mail: vkartik@iitb.ac.in

Ramesh Singh

Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai 400076, Mumbai, India
e-mail: rameshksingh@gmail.com

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MICRO-AND NANO-MANUFACTURING. Manuscript received January 11, 2018; final manuscript received May 29, 2018; published online June 22, 2018. Assoc. Editor: Takashi Matsumura.

J. Micro Nano-Manuf 6(3), 031005 (Jun 22, 2018) (11 pages) Paper No: JMNM-18-1002; doi: 10.1115/1.4040468 History: Received January 11, 2018; Revised May 29, 2018

The prediction accuracy of the stability boundary in the machining process depends upon accurate estimation of cutting tool-tip dynamics. Note that the experimental modal analysis using direct impact at miniature end mill (typically 50–500 μm in diameter) is not feasible as it can result in tool failure. Consequently, alternative techniques such as experimental modal analysis using reciprocity theory and frequency-based receptance coupling substructure analysis (RCSA) have been used extensively for determining tool-tip dynamics. The experimental approach based on reciprocity theory assumes that the structure is symmetric (cross frequency response functions (FRFs) are same between two points of interest in a structure). RCSA requires a very fine frequency resolution and matrix inversion, which can lead to computational complexities. In addition, RCSA takes into account the FRFs only at the interface and free end, which can induce errors. Owing to these issues with existing approaches, this paper proposes a free-interface component mode synthesis (CMS) approach for estimation of micro-end mill dynamics. The effect of machine tool compliance including the collet–tool interface has been included for estimation of micro-end mill dynamics via a free-interface CMS approach wherein the experimental and analytical mode shapes are coupled. The predicted micro-end mill dynamics have been compared with RCSA and experimental modal analysis using reciprocity theory. Finally, the stability lobe diagrams for high-speed micromilling of Ti6Al4V has been made using the tool-tip dynamics from CMS, RCSA, and experimental technique using reciprocity theory and validated against experimental measurements for onset of instability.

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Figures

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Fig. 1

Substructures for CMS: (a) idealized micro-end mill and (b) micro-end mill with machine tool compliance

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Fig. 2

Methodology for CMS: (a) idealized micro-end mill (Case 1) and (b) micro-end mill with machine tool compliance (Case 2)

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Fig. 3

(a) Micro-end mill and (b) equivalent area measurement

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Fig. 4

Substructures with machine tool compliance

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Fig. 5

Nodes for substructure for experimental modal analysis

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Fig. 6

Experimental setup for modal analysis

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Fig. 7

Flowchart for estimation of modes shape

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Fig. 8

(a) Mode frequency comparison for perfectly cantilever end mill and (b) NRFD for modes frequency

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Fig. 9

Experimental and fitted FRF, H33 (a) imaginary part and (b) real part

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Fig. 10

Experimental and fitted FRF, P33 (a) imaginary part and (b) real part

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Fig. 11

Experimental and fitted FRF, H44 (a) imaginary part and (b) real part

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Fig. 12

Experimental and fitted FRF, P44 (a) imaginary part and (b) real part

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Fig. 13

Tool-tip FRF predicted from CMS: (a) imaginary part and (b) real part

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Fig. 14

Effect of element on FRF for higher and order modes (second and third): (a) imaginary part and (b) real part

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Fig. 15

Frequency response function comparison: (a) imaginary part and (b) real part

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Fig. 16

Stability lobe diagram

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Fig. 17

Frequency response functions for different lengths of the tapered portion for a 500 μm diameter micro-end mill: (a) imaginary part and (b) real part

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Fig. 18

Frequency response functions for 1 mm, 500 μm, 300 μm, and 100 μm diameter micro-end mill: (a) imaginary part and (b) real part

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