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Research Papers

Modeling of Dynamic Instability Via Segmented Cutting Coefficients and Chatter Onset Detection in High-Speed Micromilling of Ti6Al4V

[+] Author and Article Information
Kundan K. Singh

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

V. Kartik

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

Ramesh Singh

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

1Corresponding author.

Manuscript received June 5, 2016; final manuscript received September 13, 2016; published online November 10, 2016. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 139(5), 051005 (Nov 10, 2016) (13 pages) Paper No: MANU-16-1319; doi: 10.1115/1.4034897 History: Received June 05, 2016; Revised September 13, 2016

Miniature components with complex shape can be created by micromilling with excellent form and finish. However, for difficult-to-machine materials, such as Ti-alloys, failure of low-flexural stiffness microtools is a big limitation. High spindle speeds (20,000–100,000 rpm) can be used to reduce the undeformed chip thickness and the cutting forces to reduce the catastrophic failure of the tool. This reduced uncut chip thicknesses, in some cases lower than the cutting edge radius, can result in intermittent chip formation which can lead to dynamic variation in cutting forces. In addition, the run-out and the misalignment effects are amplified at higher rotational speeds which can induce dynamic force variation. These dynamic force variations coupled with low-flexural rigidity of micro end mill can render the process unstable. Consequently, accurate prediction of forces and stability is essential in high-speed micromilling. Most of the previous studies reported in the literature use constant cutting coefficients in the mechanistic cutting force model which does not yield accurate results. Recent work has shown significant improvement in the prediction of cutting forces with velocity–chip load dependent coefficients but a single-function velocity–chip model fails to predict the forces accurately at very high speeds (>80,000 rpm). This inaccurate force prediction affects the predicted stability boundary at those speeds. Hence, this paper presents a segmented approach, wherein a function is fit for a given range of speeds to determine the chip load dependent cutting coefficients. The segmented velocity–chip load dependent cutting coefficient improves the cutting force prediction at high speeds, which yields much accurate stability boundary. This paper employs two degrees-of-freedom (2DOF) model with forcing functions based on segmented velocity–chip load dependent cutting coefficients. Stability lobe diagram based on 2DOF model has been created for different speed ranges using Nyquist stability criterion. Chatter onset has been identified experimentally via accelerometer data and the power spectral density (PSD) analysis of the machined surface topography. Critical spatial chatter frequencies and magnitudes of PSD corresponding to onset of instability have also been determined for different conditions.

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Figures

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Fig. 1

Flow chart of the present work

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Fig. 2

Micromilling process modeling

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Fig. 3

Closed-loop block diagram for micromilling process

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Fig. 4

Nyquist stability criterion: (a) stable and (b) chatter

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Fig. 5

Experimental setup with displacement and acceleration sensors

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Fig. 6

(a) Tangential coefficient fitment and (b) radial coefficient fitment

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Fig. 7

Speed bin for cutting coefficient

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Fig. 8

Experimental and fitted curve for (a) tangential cutting coefficient and (b) radial cutting coefficient

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Fig. 9

Cutting force comparison at constant 30 μm depth of cut and 5 μm/flute, feed and at varying speed: (a) X-direction force at 20,000 rpm, (b) Y-direction force at 20,000 rpm, (c) FFT for X-direction force at 20,000 rpm, (d) FFT for Y-direction force at 20,000 rpm, (e) X-direction force at 60,000 rpm, (f) Y-direction force at 60,000 rpm, (g) FFT for X-direction force at 60,000 rpm, (h) FFT for Y-direction force at 60,000 rpm, (i) X-direction force at 100,000 rpm, (j)Y-direction force at 100,000 rpm, (k) FFT for X-direction force at 100,000 rpm, (l) FFT for Y-direction force at 100,000 rpm, (m) X-direction force at 85,000 rpm, (n) Y-direction force at 85,000 rpm, (o) FFT for X-direction force at 85,000 rpm, and (p) FFT for Y-direction force at 85,000 rpm

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Fig. 10

Experimental and predicted cutting forces at different speeds at constant depth of cut 30 μm and at feed of 5 μm/flute: (a) x-direction forces and (b) y-direction forces

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Fig. 11

Position for tool-tip dynamics

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Fig. 12

Frequency response function at tool tip: (a) imaginary part and (b) real part

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Fig. 13

Flow chart for stability lobe diagram

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Fig. 14

Experimentally validated stability lobe diagram at 3 μm/flute feed

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Fig. 15

Acceleration spectrum at (a) spindle speed 50,000 rpm, depth of cut 100 μm, and 3 μm/flute chip load, stable and (b) spindle speed 80,000 rpm, depth of cut 100 μm, and 3 μm/flute chip load, chatter

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Fig. 16

Plot of power spectral density versus ε

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Fig. 17

Surface topography of (a) 50,000 rpm, 100 μm depth of cut, and at feed of 3 μm/flute (stable) and (b) 80,000 rpm, 100 μm depth of cut, and at feed of 3 μm/flute (chatter); PSD plot with spatial frequency: (c) 50,000 rpm, 100 μm depth of cut, and at chip load of 3 μm/flute (stable) and (d) 80,000 rpm, 100 μm depth of cut, and at chip load of 3 μm/flute (chatter)

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Fig. 18

(a) Chatter frequency selection point and (b) chatter frequency at chatter onset depth of cut

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