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Research Papers

Dynamics and Stability of Turn-Milling Operations With Varying Time Delay in Discrete Time Domain

[+] Author and Article Information
Alptunc Comak

Manufacturing Automation Laboratory (MAL),
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: alptunc@alumni.ubc.ca

Yusuf Altintas

Fellow ASME
Professor
Manufacturing Automation Laboratory (MAL),
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: altintas@mech.ubc.ca

1Corresponding author.

Manuscript received November 28, 2017; final manuscript received June 21, 2018; published online July 27, 2018. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 140(10), 101013 (Jul 27, 2018) (14 pages) Paper No: MANU-17-1741; doi: 10.1115/1.4040726 History: Received November 28, 2017; Revised June 21, 2018

Turn-milling machines are widely used in industry because of their multifunctional capabilities in producing complex parts in one setup. Both milling cutter and workpiece rotate simultaneously while the machine travels in three Cartesian directions leading to five axis kinematics with complex chip generation mechanism. This paper presents a general mathematical model to predict the chip thickness, cutting force, and chatter stability of turn milling operations. The dynamic chip thickness is modeled by considering the rigid body motion, relative vibrations between the tool and workpiece, and cutter-workpiece engagement geometry. The dynamics of the process are governed by delayed differential equations by time periodic coefficients with a time varying delay contributed by two simultaneously rotating spindles and kinematics of the machine. The stability of the system has been solved in semidiscrete time domain as a function of depth of cut, feed, tool spindle speed, and workpiece speed. The stability model has been experimentally verified in turn milling of Aluminum alloy cut with a helical cylindrical end mill.

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References

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Figures

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Fig. 1

Structural flexibilities in a turn-milling machine tool (a). Dynamic displacements at tool and workpiece (b).

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Fig. 2

Machine and TCSs in the turn-milling process and total feed vector representation

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Fig. 3

The geometry of helical flute on a ball end mill

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Fig. 4

Geometrical representations of discrete chip geometry and axial depth

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Fig. 5

Delay mechanism in turn-milling

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Fig. 6

Representation of full discrete tool motion in Cartesian coordinates

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Fig. 7

Discretization of workpiece motion and resulted time delay

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Fig. 8

Variation of phase difference as a result of workpiece rotation

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Fig. 9

Comparison of discrete time delays in turn milling and regular milling operations. Tool diameter Dt=12 mm with four teeth, tool speed Ωt=6000 (rev/min), workpiece speed ΩC=600 (rev/min), workpiece Dw=36 mm, a=1 mm, immersion range =0−π, discrete time interval Δt=2.6×10−5 s.

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Fig. 10

Time delay variation amplitude with different speed and diameter ratios of tool and workpiece

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Fig. 11

Approximation of delayed states by time-varying weights [14] (a) and variation of discrete weights within one period of the system (b)

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Fig. 12

3D stability diagram

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Fig. 13

Experimental setup for turn-milling cutting tests

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Fig. 14

Stability diagram for case 1. See Table 1 for the dynamic parameters of the turn milling system. Experimental results at Ωc=6 (rev/min) (b) and Ωc=21 (rev/min) (e); the fast Fourier Transformation of sound data at point A (c) and point B (f); tool motion in feed and normal directions for Hopf bifurcation (d) and stable cutting points (g).

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Fig. 15

Stability diagram for case 2. Stability verifications for Ωc=6 (rev/min) (a), Ωc=12 (rev/min) (b), Ωc=40 (rev/min) (c), Ωc=100 (rev/min) and the fast Fourier Transformation of sound data at point A (e) and point B (f).

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Fig. 16

Stable and unstable regions of cutting with their corresponding stability properties based on the eigenvalue analysis. A—stable, B—Hopf type chatter, C—primary flip type chatter, and D—Secondary flip type chatter.

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Fig. 17

Stability properties at high speed and low immersion of turn-milling

Tables

Errata

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