Research Papers

Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems

[+] Author and Article Information
Z. M. Kilic

Ph.D. Candidate

Y. Altintas

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

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received April 12, 2012; final manuscript received September 7, 2012; published online November 1, 2012. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 134(6), 061006 (Nov 12, 2012) (13 pages) doi:10.1115/1.4007622 History: Received April 12, 2012; Revised September 07, 2012

This paper presents a discrete-time modeling of dynamic milling systems. End mills with arbitrary geometry are divided into differential elements along the cutter axis. Variable pitch and helix angles, as well as run-outs can be assigned to cutting edges. The structural dynamics of the slender end mills and thin-walled parts are also considered at each differential element at the tool-part contact zone. The cutting forces include static chip removal, ploughing, regenerative vibrations, and process damping components. The dynamic milling system is modeled by a matrix of delay differential equations with periodic coefficients, and solved with an improved semidiscrete-time domain method in modal space. The chatter stability of the system is predicted by checking the eigenvalues of the time-dependent transition matrix which covers the tooth period for regular or spindle periods for variable pitch cutters, respectively. The same equation is also used to predict the process states such as cutting forces, vibrations, and dimensional surface errors at discrete-time domain intervals analytically. The proposed model is experimentally validated in down milling of a workpiece with 5% radial immersion and 30 mm axial depth of cut with a four fluted helical end mill.

Copyright © 2012 by ASME
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Fig. 1

Peripheral milling with varying geometry and structural dynamics along the axial depth of cut

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Fig. 2

Process damping mechanism

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Fig. 3

Structural dynamic model of a flexible cutter milling a flexible part

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Fig. 4

SLE on the workpiece

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Fig. 5

Measured FRF along the slender end mill axis: (a) measurement points; (b) measured FRF in feed (x) direction; (c) measured FRF in normal (y) direction. (Note: Impact location is kept constant at Point 3 to avoid hammer bounces; the vibrations are measured with laser at points 1 to 4.)

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Fig. 6

Experimental validation of stability models. (a) Unstable cut at 10,500 rev/min spindle speed with 30 mm depth of cut. (b) Stable cut at 12,700 rev/min spindle speed with 25 mm depth of cut.

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Fig. 7

Comparison of predicted and measured cutting forces. Prediction includes run-out parameters. Cutting conditions: spindle speed = 12,700 rev/min; axial depth of cut = 25 mm; radial depth of cut = 0.9525 mm down milling. See Table 1 for dynamic parameters.

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Fig. 8

SLE measurement: (a) setup and (b) comparison of experimental and simulated SLE results. See Fig. 7 for cutting conditions.



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