Turn-milling machines are widely used in industry because of their multifunctional capabilities in producing complex parts in one setup. Both milling cutter and workpiece rotate simultaneously while the machine travels in three Cartesian directions leading to five axis kinematics with complex chip generation mechanism. This paper presents a general mathematical model to predict the chip thickness, cutting force, and chatter stability of turn milling operations. The dynamic chip thickness is modeled by considering the rigid body motion, relative vibrations between the tool and workpiece, and cutter-workpiece engagement geometry. The dynamics of the process are governed by delayed differential equations by time periodic coefficients with a time varying delay contributed by two simultaneously rotating spindles and kinematics of the machine. The stability of the system has been solved in semidiscrete time domain as a function of depth of cut, feed, tool spindle speed, and workpiece speed. The stability model has been experimentally verified in turn milling of Aluminum alloy cut with a helical cylindrical end mill.

References

References
1.
Comak
,
A.
, and
Altintas
,
Y.
,
2017
, “
Mechanics of Turn-Milling Operations
,”
Int. J. Mach. Tools Manuf.
,
121
, pp.
2
9
.
2.
Tobias
,
S. A.
, and
Fishwick
,
W.
,
1958
, “
Theory of Regenerative Machine Tool Chatter
,”
The Engineer
,
205
(
7
), pp.
199
203
.
3.
Tlusty
,
J.
, and
Polacek
,
M.
,
1963
, “
The Stability of Machine Tools Against Self-Excited Vibrations in Machining
,”
ASME Int. Res. In Prod.
,
1
, pp.
465
474
.
4.
Merritt
,
H. E.
,
1965
, “
Theory of Self-Excited Machine-Tool Chatter-1
,”
Mech. Eng.
,
87
(
4
), p.
86
.
5.
Tlusty
,
J.
, and
Ismail
,
F.
,
1981
, “
Basic Non-Linearity in Machining Chatter
,”
CIRP Ann.-Manuf. Technol.
,
30
(
1
), pp.
299
304
.
6.
Shi
,
H. M.
, and
Tobias
,
S. A.
,
1984
, “
Theory of Finite-Amplitude Machine-Tool Instability
,”
Int. J. Mach. Tools Manuf.
,
24
(
1
), pp.
45
69
.
7.
Minis
,
I.
,
Yanushevsky
,
R.
,
Tembo
,
A.
, and
Hocken
,
R.
,
1990
, “
Analysis of Linear and Nonlinear Chatter in Milling
,”
CIRP Ann.-Manuf. Technol.
,
39
(
1
), pp.
459
462
.
8.
Altintaş
,
Y.
, and
Budak
,
E.
,
1995
, “
Analytical Prediction of Stability Lobes in Milling
,”
CIRP Ann.-Manuf. Technol.
,
44
(
1
), pp.
357
362
.
9.
Altintas
,
Y.
, and
Budak
,
E.
,
1998
, “
Analytical Prediction of Chatter Stability in Milling—Part I: General Formulation
,”
ASME J. Dyn. Syst. Meas. Control
,
120
(
1
), pp.
22
30
.
10.
Merdol
,
S. D.
, and
Altintas
,
Y.
,
2004
, “
Multi Frequency Solution of Chatter Stability for Low Immersion Milling
,”
ASME J. Manuf. Sci. Eng.
,
126
(
3
), pp.
459
466
.
11.
Insperger
,
T.
, and
Stépán
,
G.
,
2000
, “
Stability of High-Speed Milling
,”
ASME Appl. Mech. Div.-Publ.-Amd
,
241
, pp.
119
124
.
12.
Davies
,
M. A.
,
Pratt
,
J. R.
,
Dutterer
,
B.
, and
Burns
,
T. J.
,
2002
, “
Stability Prediction for Low Radial Immersion Milling
,”
ASME J. Manuf. Sci. Eng.
,
124
(
2
), pp.
217
225
.
13.
Insperger
,
T.
,
Stepan
,
G.
,
Bayly
,
P. V.
, and
Mann
,
B. P.
,
2003
, “
Multiple Chatter Frequencies in Milling Processes
,”
J. Sound Vib.
,
262
(
2
), pp.
333
345
.
14.
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
.
15.
Altıntas
,
Y.
,
Engin
,
S.
, and
Budak
,
E.
,
1999
, “
Analytical Stability Prediction and Design of Variable Pitch Cutters
,”
ASME J. Manuf. Sci. Eng.
,
121
(
2
), pp.
173
178
.
16.
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
.
17.
Insperger
,
T.
, and
Stepan
,
G.
,
2004
, “
Stability Analysis of Turning With Periodic Spindle Speed Modulation Via Semidiscretization
,”
J. Vib. Control
,
10
(
12
), pp.
1835
1855
.
18.
Altintas
,
Y.
,
2012
,
Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design
,
Cambridge University Press
, New York.
19.
Eksioglu
,
C.
,
Kilic
,
Z. M.
, and
Altintas
,
Y.
,
2012
, “
Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems
,”
ASME J. Manuf. Sci. Eng.
,
134
(
6
), p.
061006
.
20.
Öztürk
,
E.
, and
Budak
,
E.
,
2009
, “
Dynamics and Stability of Five Axis Ball-End Milling Using Single and Multi Frequency Solutions
,”
ASME J. Manuf. Sci. Technol.
,
132
(
2
), p.
021003
.
21.
Montgomery
,
D.
, and
Altintas
,
Y.
,
1991
, “
Mechanism of Cutting Force and Surface Generation in Dynamic Milling
,”
ASME J. Eng. Ind.
,
113
(
2
), pp.
160
168
.
22.
Dombovari
,
Z.
,
Iglesias
,
A.
,
Zatarain
,
M.
, and
Insperger
,
T.
,
2011
, “
Prediction of Multiple Dominant Chatter Frequencies in Milling Processes
,”
Int. J. Mach. Tools Manuf.
,
51
(
6
), pp.
457
464
.
23.
Gradišek
,
J.
,
Kalveram
,
M.
,
Insperger
,
T.
,
Weinert
,
K.
,
Stépán
,
G.
,
Govekar
,
E.
, and
Grabec
,
I.
,
2005
, “
On Stability Prediction for Milling
,”
Int. J. Mach. Tools Manuf.
,
45
(
1
), pp.
769
781
.
You do not currently have access to this content.