In this paper, a novel controller is developed for control of turning and milling dynamics. The controller design benefits from the use of time-delays in controlling a dynamic system. The gains of the controller are determined by using the discrete optimal control method. Numerical simulations are carried out in order to verify the efficiency of the controller. The findings show that the designed controller can be effective in suppressing chatter in both turning and milling processes as well as improve the stability of the cutting processes with the introduced time-delay. The authors discuss the influence of designed time-delay on control performance and robustness, and point out the advantages of using a time-delayed controller for controlling cutting dynamics.

References

References
1.
Altintaş
,
Y.
, and
Budak
,
E.
,
1995
, “
Analytical Prediction of Stability Lobes in Milling
,”
CIRP Ann.-Manuf. Technol.
,
44
(
1
), pp.
357
362
.
2.
Insperger
,
T.
, and
Stépán
,
G.
,
2002
, “
Semi-Discretization Method for Delayed Systems
,”
Int. J. Numer. Methods Eng.
,
55
(
5
), pp.
503
518
.
3.
Insperger
,
T.
, and
Stépán
,
G.
,
2011
,
Semi-Discretization for Time-Delay Systems
,
Springer
,
New York
.
4.
Long
,
X.-H.
, and
Balachandran
,
B.
,
2007
, “
Stability Analysis for Milling Process
,”
Nonlinear Dyn.
,
49
(
3
), pp.
349
359
.
5.
Ding
,
Y.
,
Zhu
,
L.-M.
, and
Zhang
,
X. J.
,
2011
, “
Numerical Integration Method for Prediction of Milling Stability
,”
ASME J. Manuf. Sci. Eng.
,
133
(
3
), p.
031005
.
6.
Tarng
,
Y.
, and
Lee
,
E.
,
1997
, “
A Critical Investigation of the Phase Shift Between the Inner and Outer Modulation for the Control of Machine Tool Chatter
,”
Int. J. Mach. Tools Manuf.
,
37
(
12
), pp.
1661
1672
.
7.
Schmitz
,
T.
,
Davies
,
M.
,
Medicus
,
K.
, and
Snyder
,
J.
,
2001
, “
Improving High-Speed Machining Material Removal Rates by Rapid Dynamic Analysis
,”
CIRP Ann.-Manuf. Technol.
,
50
(
1
), pp.
263
268
.
8.
Ding
,
H.
,
Ding
,
Y.
, and
Zhu
,
L.
,
2012
, “
On Time-Domain Methods for Milling Stability Analysis
,”
Chin. Sci. Bull.
,
57
(
33
), pp.
4336
4345
.
9.
Rashid
,
A.
, and
Nicolescu
,
C. M.
,
2006
, “
Active Vibration Control in Palletised Work-Holding System for Milling
,”
Int. J. Mach. Tools Manuf.
,
46
(12–13), pp.
1626
1636
.
10.
Rojas
,
J.
,
Liang
,
C.
, and
Geng
,
Z. J.
,
1996
, “
Experimental Investigation of Active Machine Tool Vibration Control
,”
Proc. SPIE
,
2721
, pp.
373
384
.
11.
Long
,
X.
,
Jiang
,
H.
, and
Meng
,
G.
,
2013
, “
Active Vibration Control for Peripheral Milling Processes
,”
J. Mater. Process. Technol.
,
213
(
5
), pp.
660
670
.
12.
Tewani
,
S. G.
,
Rouch
,
K. E.
, and
Walcott
,
B. L.
,
1995
, “
A Study of Cutting Process Stability of a Boring Bar With Active Dynamic Absorber
,”
Int. J. Mach. Tools Manuf.
,
35
(
1
), pp.
91
108
.
13.
Moradi
,
H.
,
Bakhtiari-Nejad
,
F.
, and
Movahhedy
,
M.
,
2008
, “
Tuneable Vibration Absorber Design to Suppress Vibrations: An Application in Boring Manufacturing Process
,”
J. Sound Vib.
,
318
(1–2), pp.
93
108
.
14.
Nagaya
,
K.
,
Yamazaki
,
H.
, and
Kashimoto
,
H.
,
1997
, “
Control of Micro-Vibrations of a Machine Head by Using Piezoelectric Actuators
,”
Int. J. Appl. Electromagn. Mech.
,
8
(
4
), pp.
315
328
.
15.
Parus
,
A.
,
Pajor
,
M.
, and
Hoffmann
,
M.
,
2009
, “
Suppression of Self-Excited Vibration in Cutting Process Using Piezoelectric and Electromagnetic Actuators
,”
Adv. Manuf. Sci. Technol.
,
33
(
4
), pp.
35
50
.
16.
Weremczuka
,
A.
,
Rusineka
,
R.
, and
Warminskia
,
J.
,
2015
, “
The Concept of Active Elimination of Vibrations in Milling Process
,”
Procedia CIRP
,
31
, pp.
82
87
.
17.
Ma
,
H.
,
Deshmukh
,
V.
,
Butcher
,
E.
, and
Averina
,
V.
,
2005
, “
Delayed State Feedback and Chaos Control for Time-Periodic Systems Via a Symbolic Approach
,”
Commun. Nonlinear Sci. Numer. Simul.
,
10
(
5
), pp.
479
497
.
18.
Nazari
,
M.
,
Butcher
,
E.
, and
Bobrenkov
,
O.
,
2014
, “
Optimal Feedback Control Strategies for Periodic Delayed Systems
,”
Int. J. Dyn. Control
,
2
(
1
), pp.
102
118
.
19.
Abdel-Rohman
,
M.
,
1987
, “
Time-Delay Effects on Actively Damped Structures
,”
J. Eng. Mech.
,
113
(
11
), pp.
1709
1719
.
20.
Abdel-Mooty
,
M.
, and
Roorda
,
J.
,
1991
, “
Time-Delay Compensation in Active Damping of Structures
,”
J. Eng. Mech.
,
117
(
11
), pp.
2549
2570
.
21.
Cai
,
G. P.
, and
Hong
,
J. Z.
,
2002
, “
Optimal Control Method for Seismically Excited Building Structures With Time-Delay in Control
,”
J. Eng. Mech.
,
128
(6), pp.
602
612
.
22.
Sipahi
,
R.
, and
Olgac
,
N.
,
2007
, “
Active Vibration Suppression With Time Delayed Feedback
,”
ASME J. Vib. Acoust.
,
125
(3), pp.
384
388
.
23.
Sipahi
,
R.
, and
Olgac
,
N.
,
2005
, “
Complete Stability Robustness of Third-Order LTI Multiple Time-Delay Systems
,”
Automatica
,
41
(
8
), pp.
1413
1422
.
24.
Ulsoy
,
A. G.
,
2013
, “
Improving Stability Margins Via Time Delay Control
,”
ASME
Paper No. DETC2013-12076.
25.
Udwadia
,
F. E.
, and
Phohomsiri
,
P.
,
2006
, “
Active Control of Structures Using Time Delayed Positive Feedback Proportional Control Designs
,”
Struct. Control Health Monit.
,
13
(
1
), pp.
536
552
.
26.
Udwadia
,
F. E.
,
Von Bremen
,
H.
, and
Phohomsiri
,
P.
,
2007
, “
Time-Delayed Control Design for Active Control of Structures: Principles and Applications
,”
Struct. Control Health Monit.
,
14
(
1
), pp.
27
61
.
27.
Chen
,
L.
,
Pan
,
J.
, and
Cai
,
G.
,
2008
, “
Active Control of a Flexible Cantilever Plate With Multiple Time Delays
,”
Acta Mech. Solida Sin.
,
21
(
3
), pp.
257
266
.
28.
Elbeyli
,
O.
, and
Sun
,
J. Q.
,
2004
, “
On the Semi-Discretization Method for Feedback Control Design of Linear Systems With Time Delay
,”
J. Sound Vib.
,
273
(1–2), pp.
429
440
.
29.
Huang
,
R.
,
Chen
,
L.
, and
Sun
,
J.
,
2015
, “
Multi-Objective Optimal Design of Active Vibration Absorber With Delayed Feedback
,”
J. Sound Vib.
,
339
, pp.
56
64
.
30.
Sun
,
Y.
, and
Xu
,
J.
,
2015
, “
Experiments and Analysis for a Controlled Mechanical Absorber Considering Delay Effect
,”
J. Sound Vib.
,
339
, pp.
25
37
.
31.
Nayfeh
,
A. H.
, and
Nayfeh
,
N. A.
,
2012
, “
Time-Delay Feedback Control of Lathe Cutting Tools
,”
J. Vib. Control
,
18
(
8
), pp.
1106
1115
.
32.
Long
,
X.-H.
, and
Balachandran
,
B.
,
2010
, “
Stability of Up-Milling and Down-Milling Operations With Variable Spindle Speed
,”
J. Vib. Control
,
16
, pp.
1151
1168
.
33.
Budak
,
E.
,
2003
, “
An Analytical Design Method for Milling Cutters With Nonconstant Pitch to Increase Stability—Part I: Theory
,”
ASME J. Manuf. Sci. Eng.
,
125
(
1
), pp.
29
34
.
34.
Michiels
,
W.
, and
Niculescu
,
S. I.
,
2007
,
Stability and Stabilization of Time-Delay Systems
,
SIAM
,
Philadelphia, PA
.
35.
Balachandran
,
B.
, and
Zhao
,
M. X.
,
2000
, “
A Mechanics Based Model for Study of Dynamics of Milling Operations
,”
Meccanica
,
35
(
2
), pp.
89
109
.
36.
Zhao
,
M. X.
, and
Balachandran
,
B.
,
2001
, “
Dynamics and Stability of Milling Process
,”
Int. J. Solids Struct.
,
38
(10–13), pp.
2233
2248
.
37.
Varga
,
A.
,
2005
, “
On Solving Discrete-Time Periodic Riccati Equations
,”
IFAC Proc. Vol.
,
38
(
1
), pp.
354
359
.
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