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Research Papers

Patterns of Regenerative Milling Chatter Under Joint Influences of Cutting Parameters, Tool Geometries, and Runout

[+] Author and Article Information
Jinbo Niu, Han Ding

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

Ye Ding

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: y.ding@sjtu.edu.cn

Zunmin Geng

Advanced Manufacturing Research Centre,
University of Sheffield,
Rotherham S60 5TZ, UK

LiMin Zhu

State Key Laboratory of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zhulm@sjtu.edu.cn

1Corresponding authors.

Manuscript received June 21, 2018; final manuscript received August 13, 2018; published online September 17, 2018. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 140(12), 121004 (Sep 17, 2018) (19 pages) Paper No: MANU-18-1467; doi: 10.1115/1.4041250 History: Received June 21, 2018; Revised August 13, 2018

The regenerative milling chatter is usually regarded as some kind of bifurcation or chaos behaviors of the machining system. Although several chatter patterns such as the secondary Hopf, the period doubling, and the cyclic fold bifurcations were once reported, their relationships with cutting conditions remain undiscovered. This paper aims to uncover the dynamic mechanism of distinct chatter behaviors in general milling scenarios. First, two complementary methods, i.e., the generalized Runge–Kutta method and the time-domain simulation technique, are presented to jointly study the distribution rule of chatter patterns in stability lobe diagrams for milling processes with general flute-spacing tools considering runout. The theoretical predictions are validated by one published example and two cutting experiments under three different cutting conditions. Furthermore, the cutting signal characteristics and cutting surface topography of distinct chatter patterns are analyzed and compared in detail. On this basis, this paper studies the joint influences of cutting parameters, tool geometries, and runout on regenerative chatter behaviors with the proposed methods.

Copyright © 2018 by ASME
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Figures

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Fig. 1

Schematic of milling processes with general flute-spacing tools considering runout: (a) down-milling processes and (b) up-milling processes

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Fig. 2

Bifurcation lobe diagram with the GRK method. Period-2 (red circle), period-3 (blue triangle), period-4 (cyan square), period-5 (green plus), period-6 (magenta diamond), period-7 (red cross), and quasi-periodic (black dot) bifurcations are identified based on the values of p/q as labeled at the top. (Color version online).

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Fig. 3

Bifurcation lobe diagram drawn with the TDS technique. The period-n bifurcation types are labeled on the top based on the subharmonic sampling.

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Fig. 4

Period-n bifurcations: (a)–(c) period-3 bifurcation (3800 rpm, 5 mm), (d)–(f) period-4 bifurcation (3650 rpm, 6 mm), (a) and (d) vibration displacement with stroboscopic points, (b) and (e) frequency components of the vibration displacement, and (c) and (f) phase portrait with Poincare section

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Fig. 5

Experimental setup for milling operations with CPCH tool and VPVH tool

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Fig. 6

Bifurcation lobe diagrams drawn with the GRK method (a) and the TDS technique (b). The black box indicates the process parameters that were chosen for the cutting test in Fig. 7.

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Fig. 7

Cutting test with increasing axial depth of cut at 2800 rpm spindle speed. (a) Surface topography. (b) Experimental acceleration signal with stroboscopic points. The black boxes from I to IV indicate the period-2, beat vibration, period-7, and period-5 chatter patterns that will be analyzed in Fig. 8. (c) Short-time Fourier transform of the acceleration signal.

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Fig. 8

Frequency components of the chatter patterns that indicated as I–IV in Fig. 7. The green circles (○) indicate the spindle rotation frequency and its harmonics. The red crosses (×) indicate chatter frequencies. (Color version online).

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Fig. 9

Stability and bifurcation analysis with the GRK method. (a) SLD divided by spindle speeds 60fn/k(k=1,2,3,4). Circles (○), squares (◻), and crosses (×) represent the experimentally stable, uncertain, and unstable cutting conditions. (b) Bifurcation lobe diagram of zone A. (c) Bifurcation lobe diagram of zone B.

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Fig. 10

Stability and bifurcation analysis with the TDS technique: (a) peak-to-peak force diagram, (b) bifurcation lobe diagram of zone A, and (c) bifurcation lobe diagram of zone B

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Fig. 11

Chatter frequencies obtained with the GRK method (red lines), the TDS technique (blue star markers), and the experimental signals (magenta circles). (a) The axial depth of cut is 2 mm, and (b) the axial depth of cut is 3 mm. The spindle rotation frequency and its harmonics (black lines) as well as the damped natural frequency (dashed lines) are also illustrated. (Color version online).

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Fig. 12

Cutting test with CPCH tool (2800 rpm, 2 mm): (a) surface topography, (b) experimental acceleration with red circles denoting the once-per-revolution sampled points, and (c) and (d) frequency components with the red crosses (×) denoting the chatter frequencies and the green circles (○) denoting the spindle rotation frequency and its harmonics. (Color version online).

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Fig. 13

Cutting test for period-n chatter using VPVH tool (3000 rpm, 4 mm): (a) surface topography, (b) chatter marks in enlarged scale, (c) experimental acceleration, (d) experimental acceleration on 100 spindle revolution periods (2 s), (e) TDS-based simulated acceleration on 100 spindle revolution periods (2 s), (f) frequency components of the experimental signals, (g) frequency components of the simulated signals, (h) experimental acceleration on two spindle revolution periods, and (i) TDS-based simulated acceleration on two spindle revolution periods

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Fig. 14

Cutting test for quasi-periodic chatter using VPVH tool (2600 rpm, 2 mm): (a) surface topography, (b) chatter marks in enlarged scale, (c) experimental acceleration, (d) experimental acceleration on 100 spindle revolution periods (2.3077 s), (e) TDS-based simulated acceleration on 100 spindle revolution periods (2.3077 s), (f) frequency components of the experimental signals, (g) frequency components of the simulated signals, (h) experimental acceleration on two spindle revolution periods, and (i) TDS-based simulated acceleration on two spindle revolution periods

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Fig. 15

Cutting test for beat vibrations using VPVH tool (2350 rpm, 2 mm): (a) surface topography, (b) experimental acceleration, (c) TDS-based simulated acceleration, (d) frequency components of the experimental signals, and (e) frequency components of the simulated signals

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Fig. 16

Influences of the radial depth of cut: (a)–(c) ae=2 mm, (d)–(f) ae=4 mm, (a) and (d) frequency components obtained with the GRK method, (b) and (e) bifurcation lobe diagrams drawn with the GRK method, and (c) and (f) bifurcation lobe diagrams drawn with the TDS technique

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Fig. 17

Influences of the feed per tooth: (a)–(c) ft=0.1 mm and (d)–(f) ft=0.2 mm

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Fig. 18

Influences of the runout values: (a)–(c) ρ=1.83 μm and (d)–(f) ρ=0

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Fig. 19

Influences of the pitch angles with considering runout: (a)–(c) 90 deg−90 deg−90 deg−90 deg and (d)–(f) 80 deg−100 deg−80 deg−100 deg

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Fig. 20

Influences of the pitch angles without considering runout: (a)–(c) 90 deg−90 deg−90 deg−90 deg and (d)–(f): 80 deg−100 deg−80 deg−100 deg

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Fig. 21

Influences of the helix angles without considering runout: (a)–(c) 15 deg−15 deg−15 deg−15 deg and (d)–(f) 55 deg−55 deg−55 deg−55 deg

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Fig. 22

Illustration of the principal frequency: (a)–(c) without runout, (d)–(f) with runout, (a) and (d) CPCH tool, (b) and (e) symmetric VPVH tool, and (c) and (f) asymmetric VPVH tool

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