Research Papers

Analytical Chatter Stability of Milling With Rotating Cutter Dynamics at Process Damping Speeds

[+] Author and Article Information
M. Eynian, Y. Altintas

Department of Mechanical Engineering, Manufacturing Automation Laboratory, University of British Columbia, Vancouver, BC V6T1Z4, Canada

J. Manuf. Sci. Eng 132(2), 021012 (Apr 21, 2010) (14 pages) doi:10.1115/1.4001251 History: Received August 18, 2009; Revised January 30, 2010; Published April 21, 2010; Online April 21, 2010

This paper presents a chatter stability prediction method for milling flexible workpiece with end mills having asymmetric structural dynamics. The dynamic chip thickness regenerated by the vibrations of the rotating cutter and the fixed workpiece is transformed into the principle modal directions of the rotating tool. The process damping is modeled as a linear function of vibration velocity. The dynamics of the milling system is modeled by a time delay matrix differential equation with time varying directional factors and speed dependent elements. The periodic directional factors are averaged over a spindle period, and the stability of the resulting time invariant but speed dependent characteristic equation of the system is investigated using the Nyquist stability criterion. The stability model is verified with time domain numerical simulations and milling experiments.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Milling of a flexible workpiece with a rotating and vibrating cutter

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Figure 2

Setup for the milling stability test

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Figure 3

Predicted and measured milling forces in slot milling of AISI1045 steel. The cutting conditions are as follows: spindle speed: 4297 rev/min, depth of cut: 0.25 mm, feed rate: 0.1 mm/flute, number of inserts: 2. The cutting coefficients are given in Table 1.

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Figure 4

Predicted and measured chatter stability results in slot milling of AISI 1045 steel with a two teeth cutter. The cutting conditions and parameters are given in Table 1.

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Figure 5

Time domain verification of analytical stability for slot milling with two inserts (cutting coefficients: Kr=1978 MPa, Kt=3242 MPa, Cr=0.61 N/μm, and Ct=0.18 N/μm; modal parameters: ku=15.7 N/μm, ωnu=1152 Hz, ζu=0.023, kv=5.22 N/μm, ωnv=665 Hz, and ζv=0.023)

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Figure 6

Sensitivity of the stability charts to the structural dynamic parameters of the system. Simulation conditions are same as in Fig. 5 except the following modal parameters are used: k=5.22 N/μm, ω=655 Hz, and ζ=0.023.

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Figure 7

gj(ϕ) functions for a five flute cutter with ϕc=0, ϕst=(15/180)π, and ϕex=(80/180)π



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