Abstract
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.
Issue Section:
Research Papers
Keywords:
cutting tools,
damping,
differential equations,
machine tool spindles,
machining chatter,
milling,
Nyquist stability,
thickness measurement,
time-domain analysis,
vibrations
Topics:
Chatter,
Cutting,
Damping,
Dynamics (Mechanics),
Milling,
Stability,
Structural dynamics,
Vibration
1.
Tobias
, S. A.
, and Fishwick
, W.
, 1958, A Theory of Regenerative Chatter
, The Engineer
, London
.2.
Tlusty
, J.
, 1970, Machine Tool Structures: The Theory of Chatter and Stability Analysis
, F.
Koenigsberger
and J.
Tlusty
, eds., Pergamon
, Oxford
, pp. 115
–274
.3.
Das
, M. K.
, and Tobias
, S. A.
, 1967, “The Relation Between the Static and the Dynamic Cutting of Metals
,” Int. J. Mach. Tool Des. Res.
0020-7357, 7
, pp. 63
–89
.4.
Tlusty
, J.
, 1978, “Analysis of State of Research in Cutting Dynamics
,” CIRP Ann.
0007-8506, 27
, pp. 583
–589
.5.
Smith
, S.
, and Tlusty
, J.
, 1997, “Current Trends in High-Speed Machining
,” ASME J. Manuf. Sci. Eng.
1087-1357, 119
, pp. 664
–666
.6.
Sridhar
, R.
, Hohn
, R. E.
, and Long
, G. W.
, 1968, “A Stability Algorithm for the General Milling Process—Contribution to Machine Tool Chatter Research—7
,” ASME J. Eng. Ind.
0022-0817, 90
, pp. 330
–334
.7.
Minis
, I.
, and Yanushevsky
, R.
, 1993, “A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling
,” ASME J. Eng. Ind.
0022-0817, 115
, pp. 1
–8
.8.
Budak
, E.
, and Altintas
, Y.
, 1998, “Analytical Prediction of Chatter Stability in Milling—Part I: General Formulation
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 120
, pp. 22
–30
.9.
Insperger
, T.
, Mann
, B. P.
, Stépán
, G.
, and Bayly
, P. V.
, 2003, “Stability of Up-Milling and Down-Milling, Part 1: Alternative Analytical Methods
,” Int. J. Mach. Tools Manuf.
0890-6955, 43
, pp. 25
–34
.10.
Altintas
, Y.
, and Weck
, M.
, 2004, “Chatter Stability in Metal Cutting and Grinding
,” CIRP Ann.
0007-8506, 53
(2
), pp. 619
–642
.11.
Li
, C. J.
, Ulsoy
, A. G.
, and Endres
, W. J.
, 2003, “The Effect of Flexible-Tool Rotation on Regenerative Instability in Machining
,” ASME J. Manuf. Sci. Eng.
1087-1357, 125
, pp. 39
–47
.12.
Schmitz
, T. L.
, Ziegert
, J.
, and Stanislaus
, C.
, 2004, “A Method for Predicting Chatter Stability for Systems With Speed-Dependent Spindle Dynamics
,” Trans. NAMRI/SME
1047-3025, 32
, pp. 17
–24
.13.
Cheng
, C.-H.
, Schmitz
, T. L.
, and Duncan
, G. S.
, 2007, “Rotating Tool Point Frequency Response Prediction Using RCSA
,” Mach. Sci. Technol.
1091-0344, 11
, pp. 433
–446
.14.
Cao
, Y. Z.
, and Altintas
, Y.
, 2004, “A General Method for the Modeling of Spindle-Bearing Systems
,” ASME J. Mach. Des.
, 126
, pp. 1089
–1104
.15.
Altintas
, Y.
, Eynian
, M.
, and Onozuka
, H.
, 2008, “Identification of Dynamic Cutting Force Coefficients and Chatter Stability With Process Damping
,” CIRP Ann.
0007-8506, 57
, pp. 371
–374
.16.
Huang
, C. Y.
, and Wang
, J. J. J.
, 2007, “Mechanistic Modeling of Process Damping in Peripheral Milling
,” ASME J. Manuf. Sci. Eng.
1087-1357, 129
, pp. 12
–20
.17.
Eynian
, M.
, and Altintas
, Y.
, 2009, “Chatter Stability of General Turning Operations With Process Damping
,” ASME J. Manuf. Sci. Eng.
1087-1357, 131
, p. 041005
.18.
Wallace
, P. W.
, and Andrew
, C.
, 1965, “Machining Forces: Some Effects of Tool Vibration
,” J. Mech. Eng. Sci.
0022-2542, 7
, pp. 152
–162
.19.
Chiou
, R. Y.
, and Liang
, S. Y.
, 1998, “Chatter Stability of a Slender Cutting Tool in Turning With Wear Effect
,” Int. J. Mach. Tools Manuf.
0890-6955, 38
, pp. 315
–327
.20.
Clancy
, B. E.
, and Shin
, Y. C.
, 2002, “A Comprehensive Chatter Prediction Model for Face Turning Operation Including the Tool Wear Effect
,” Int. J. Mach. Tools Manuf.
0890-6955, 42
(9
), pp. 1035
–1044
.21.
Altintas
, Y.
, Stepan
, G.
, Merdol
, D.
, and Dombavari
, Z.
, 2008, “Chatter Stability of Milling in Frequency and Discrete Time Domain
,” CIRP J. Manuf. Sci. Technol.
, 1
, pp. 35
–44
.22.
Altintas
, Y.
, 2000, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design
, Cambridge University Press
, Cambridge, England
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
