Milling chatters caused by the regenerative effect is one of the major limitations in increasing the machining efficiency and accuracy of milling operations. This paper studies robust active chatter control for milling processes with variable pitch cutters whose dynamics are governed by multidelay nonlinear differential equations. We propose a state feedback controller based on linear matrix inequality (LMI) approach that can enlarge multiple stability domains in the stability lobe diagram (SLD) while the controller gain is minimized. Numerical simulations of active magnetic bearing systems demonstrate the effectiveness of the proposed method.
Issue Section:
Research Papers
References
1.
Budak
, E.
, and Tekeli
, A.
, 2005
, “Maximizing Chatter Free Material Removal Rate in Milling Through Optimal Selection of Axial and Radial Depth of Cut Pairs
,” CIRP Ann.—Manuf. Technol.
, 54
(1
), pp. 353
–356
.2.
Moradi
, H.
, Movahhedy
, M. R.
, and Vossoughi
, G.
, 2012
, “Dynamics of Regenerative Chatter and Internal Resonance in Milling Process With Structural and Cutting Force Nonlinearities
,” J. Sound Vib.
, 331
(16
), pp. 3844
–3865
.3.
Moradi
, H.
, Vossoughi
, G.
, Movahhedy
, M. R.
, and Salarieh
, H.
, 2013
, “Suppression of Nonlinear Regenerative Chatter in Milling Process Via Robust Optimal Control
,” J. Process Control
, 23
(5
), pp. 631
–648
.4.
Chen
, Z.
, Zhang
, H.
, Zhang
, X.
, and Ding
, H.
, 2014
, “Adaptive Active Chatter Control in Milling Processes
,” ASME J. Dyn. Syst., Meas., Control
, 136
(2
), p. 021007
.5.
Insperger
, T.
, Wahi
, P.
, Colombo
, A.
, Stepan
, G.
, Di Bernardo
, M.
, and Hogan
, S.
, 2010
, “Full Characterization of Act-and-Wait Control for First-Order Unstable Lag Processes
,” J. Vib. Control
, 16
(7–8
), pp. 1209
–1233
.6.
Rashid
, A.
, and Nicolescu
, C. M.
, 2006
, “Active Vibration Control in Palletised Workholding System for Milling
,” Int. J. Mach. Tools Manuf.
, 46
(12–13
), pp. 1626
–1636
.7.
Sallese
, L.
, Innocenti
, G.
, Grossi
, N.
, Scippa
, A.
, Flores
, R.
, Basso
, M.
, and Campatelli
, G.
, 2017
, “Mitigation of Chatter Instabilities in Milling Using an Active Fixture With a Novel Control Strategy
,” Int. J. Adv. Manuf. Technol.
, 89
(9–12
), pp. 2771
–2787
.8.
Ford
, D.
, Myers
, A.
, Haase
, F.
, Lockwood
, S.
, and Longstaff
, A.
, 2013
, “Active Vibration Control for a CNC Milling Machine
,” Proc. Inst. Mech. Eng., Part C
, 228
(2
), pp. 230
–245
.9.
Dohner
, J. L.
, Lauffer
, J. P.
, Hinnerichs
, T. D.
, Shankar
, N.
, Regelbrugge
, M.
, Kwan
, C.
, Xu
, R.
, Winterbauer
, B.
, and Bridger
, K.
, 2004
, “Mitigation of Chatter Instabilities in Milling by Active Structural Control
,” J. Sound Vib.
, 269
(1–2
), pp. 197
–211
.10.
Monnin
, J.
, Kuster
, F.
, and Wegener
, K.
, 2014
, “Optimal Control for Chatter Mitigation in Milling—Part 1: Modeling and Control Design
,” Control Eng. Pract.
, 24
(1
), pp. 156
–166
.11.
Denkena
, B.
, and Gümmer
, O.
, 2012
, “Process Stabilization With an Adaptronic Spindle System
,” Prod. Eng.
, 6
(4–5
), pp. 485
–492
.12.
Bleuler
, H.
, Cole
, M.
, Keogh
, P.
, Larsonneur
, R.
, Maslen
, E.
, Okada
, Y.
, Schweitzer
, G.
, and Traxler
, A.
, 2009
, Magnetic Bearings: Theory, Design, and Application to Rotating Machinery
, G.
Schweitzer
, and E. H.
Maslen
, eds., Springer Science and Business Media
, Berlin, Germany
.13.
Huang
, T.
, Chen
, Z.
, Zhang
, H.
, and Ding
, H.
, 2015
, “Active Control of an Active Magnetic Bearings Supported Spindle for Chatter Suppression in Milling Process
,” ASME J. Dyn. Syst., Meas., Control
, 137
(11
), p. 111003
.14.
Munoa
, J.
, Beudaert
, X.
, Dombovari
, Z.
, Altintas
, Y.
, Budak
, E.
, Brecher
, C.
, and Stepan
, G.
, 2016
, “Chatter Suppression Techniques in Metal Cutting
,” CIRP Ann.—Manuf. Technol.
, 65
(2
), pp. 785
–808
.15.
Uriarte
, L.
, Etxaniz
, I.
, Iturbe
, I.
, Zatarain
, M.
, and Munoa
, J.
, 2014
, “Chatter Suppression in a High Speed Magnetic Spindle by Adding Damping
,” J. Mach. Eng.
, 14
(4
), pp. 65
–74
.16.
Van de Wouw
, N.
, Van Dijk
, N.
, Schiffler
, A.
, Nijmeijer
, H.
, and Abele
, E.
, 2017
, “Experimental Validation of Robust Chatter Control for High-Speed Milling Processes
,” Time Delay Systems
, Springer
, Cham, Switzerland
, pp. 315
–331
.17.
Gourc
, E.
, Seguy
, S.
, and Arnaud
, L.
, 2011
, “Chatter Milling Modeling of Active Magnetic Bearing Spindle in High-Speed Domain
,” Int. J. Mach. Tools Manuf.
, 51
(12
), pp. 928
–936
.18.
Kline
, W.
, and DeVor
, R.
, 1983
, “The Effect of Runout on Cutting Geometry and Forces in End Milling
,” Int. J. Mach. Tool Des. Res.
, 23
(2–3
), pp. 123
–140
.19.
Insperger
, T.
, Mann
, B. P.
, Surmann
, T.
, and Stépán
, G.
, 2008
, “On the Chatter Frequencies of Milling Processes With Runout
,” Int. J. Mach. Tools Manuf.
, 48
(10
), pp. 1081
–1089
.20.
Zhang
, X.
, Xiong
, C.
, Ding
, Y.
, and Xiong
, Y.
, 2011
, “Variable-Step Integration Method for Milling Chatter Stability Prediction With Multiple Delays
,” Sci. China Technol. Sci.
, 54
(12
), pp. 3137
–3154
.21.
Sims
, N.
, Mann
, B.
, and Huyanan
, S.
, 2008
, “Analytical Prediction of Chatter Stability for Variable Pitch and Variable Helix Milling Tools
,” J. Sound Vib.
, 317
(3–5
), pp. 664
–686
.22.
Khasawneh
, F. A.
, and Mann
, B. P.
, 2013
, “A Spectral Element Approach for the Stability Analysis of Time-Periodic Delay Equations With Multiple Delays
,” Commun. Nonlinear Sci. Numer. Simul.
, 18
(8
), pp. 2129
–2141
.23.
Comak
, A.
, and Budak
, E.
, 2017
, “Modeling Dynamics and Stability of Variable Pitch and Helix Milling Tools for Development of a Design Method to Maximize Chatter Stability
,” Precis. Eng.
, 47
, pp. 459
–468
.24.
Hayasaka
, T.
, Ito
, A.
, and Shamoto
, E.
, 2017
, “Generalized Design Method of Highly-Varied-Helix End Mills for Suppression of Regenerative Chatter in Peripheral Milling
,” Precis. Eng.
, 48
, pp. 45
–59
.25.
Gu
, K.
, and Niculescu
, S.
, 2003
, “Survey on Recent Results in the Stability and Control of Time-Delay Systems
,” ASME J. Dyn. Syst., Meas., Control
, 125
(2
), pp. 158
–165
.26.
Altintas
, Y.
, 2000
, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design
, Cambridge University Press
, New York
.27.
Altintas
, Y.
, Shamoto
, E.
, Lee
, P.
, and Budak
, E.
, 1999
, “Analytical Prediction of Stability Lobes in Ball-End-Milling
,” ASME J. Manuf. Sci. Eng.
, 121
(4
), pp. 586
–592
.28.
Insperger
, T.
, and Stépán
, G.
, 2004
, “Updated Semi-Discretization Method for Periodic Delay-Differential Equations With Discrete Delay
,” Int. J. Numer. Methods Eng.
, 61
(1
), pp. 117
–141
.29.
Huang
, T.
, Zhang
, X.
, Zhang
, X.
, and Ding
, H.
, 2013
, “An Efficient Linear Approximation of Acceleration Method for Milling Stability Prediction
,” Int. J. Mach. Tools Manuf.
, 74
(8
), pp. 56
–64
.30.
Khalil
, H.
, 2002
, Nonlinear Systems
, Vol. 3
, Prentice Hall
, Upper Saddle River, NJ
.31.
Gu
, K.
, Chen
, J.
, and Kharitonov
, V.
, 2003
, Stability of Time-Delay Systems
, Springer Science and Business Media
, Basel, Switzerland
.32.
Schweitzer
, G.
, Bleuler
, H.
, and Traxler
, A.
, 1994
, Active Magnetic Bearings
, Verlag der Fachvereine
, Zurich, Switzerland
.33.
van Dijk
, N.
, van de Wouw
, N.
, Doppenberg
, E.
, Oosterling
, H.
, and Nijmeijer
, H.
, 2012
, “Robust Active Chatter Control in the High-Speed Milling Process
,” IEEE Trans. Control Syst. Technol.
, 20
(4
), pp. 901
–917
.34.
Huang
, T.
, Zhang
, X.
, and Ding
, H.
, 2017
, “A Novel Approach With Smallest Transition Matrix for Milling Stability Prediction
,” Nonlinear Dyn.
, 90
(1
), pp. 1
–10
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