ALARM LAB
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1 OPTIMUM CONDITIONS OPTIMUM CONDITIONS FOR FOR VARIABLE PITCH MILLING VARIABLE PITCH MILLING Hassan Fazelinia • • Nejat Olgac Department of Mechanical Engineering Department of Mechanical Engineering University of Connecticut University of Connecticut
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ALARM LAB. OPTIMUM CONDITIONS FOR VARIABLE PITCH MILLING. Hassan Fazelinia • Nejat Olgac Department of Mechanical Engineering University of Connecticut. ALARM LAB. Outline. The Problem and Motivation Process Dynamics Review of CTCR Paradigm - PowerPoint PPT Presentation
Transcript of ALARM LAB
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OPTIMUM CONDITIONSOPTIMUM CONDITIONS FOR FOR
VARIABLE PITCH MILLINGVARIABLE PITCH MILLING
Hassan Fazelinia • • Nejat Olgac
Department of Mechanical Engineering Department of Mechanical Engineering University of ConnecticutUniversity of Connecticut
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• The Problem and Motivation• Process Dynamics• Review of CTCR Paradigm
(A unique process for Multiple Time Delayed Systems)• Measure of Chatter Rejection• Optimization problem
Outline
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Variable vs. Uniform Pitch Cutter
Uniform Pitch end mill
1= 902= 90
Variable Pitch end mill
1= 702= 110
Notable earlier work:[1] Slavicek, J., 1965, “The Effect of Irregular Tooth Pitch on Stability of Milling.” 6th MTDR Conference, London, Pergamon Press.
[2] Minis, I. and Yanushevsky, R. , 1993, "A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling." ASME Journal of Engineering for Industry 115(1), 1-8.
[3] Altintas, Y. and Budak, E., 1995, "Analytical Prediction of Stability Lobes in Milling." Annals of the CIRP 44(1), 357-362.
a
4
+ Feed
Process Dynamics
•Olgac, N. and Sipahi, R., “A Unique Methodology for Chatter Stability Mapping in Simultaneous Machining”. ASME, Journal of Manufacturing Science and Engineering, 2005. 127(4).
•Sipahi, R. and Olgac, N. , Stability in Variable-Pitch Milling Regarding Regenerative Chatter, IMECE 2006
Cutter force formation chip loads
(process / material specific)
Cutter dynamics ID(setup specific)
y
x
y
x
yyyx
xyxx
FF
DFF
DGDGDGDG
yx
TF G)()()()(
:2
5
System Characteristic Equation
• four-flute-two-pitch cutter :
)]())(24(41[det 0
21 seeaKCE sst ΦI
][60
360[deg][sec] 1
1 RPMN
11
22
0)()102690101260104450101060101614247()105380102530108890
1021201013.284943())(10756010572010180109240101270103240102660(
10166010150010565010385010686010027.313761083.35068808750625),,(
21
21
21
222925222
318410)(2925222
318493026
22431941751269
3228225321418
59667821
sτsτ
sττ
sτsτ
ee.+s.+s.+s.+s.e .+s .+s .+
s .+ see .s . s . s .s . s . s .
.+s .+ s .+ s .+ s .+ s+s+ s+ ssCE
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CTCR reveals the stability regions *
Stability outlook for 4 mm axial depth-of-cut (stable zones: shaded)
* [R. Sipahi: PhD Thesis 2005]
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Comparison of CTCR results
Comparison of CTCR result (red) and, [Y. Altintas, 1999] (black)
a
a
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Measure of chatter rejection:
E1
E3
E2
E5
E4
mma 4
domse
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• Finding the real part of rightmost characteristic roots (still an open problem in mathematics)
• Status-quo: Numerical approximations: Infinitesimal Generator Approx. [D. Breda 2005]DDE-BIFTOOL [K. Engelborghs 2000]…..
? domse
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Optimization Problem
• Objective: Maximizing the metal removal rate
while avoiding the onset of chatter
• The pitch angle selection on the tool.• Optimum depth of cut and the spindle speed?
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Objective function:
• Measure of chatter rejection:
21 aseJ dom
a 2130][ rpmN
domse
• Axial depth of cut:• Spindle speed:
0,
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Preliminary results:
JJ
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Optimum points for different depth of cut
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• On going studies:– Experimental validation– Optimization for different number of flutes
• Acknowledgment:– NSF, DoE, Pratt & Whitney
Conclusion
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Thank You!Thank You!Questions?Questions?
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dtdD
y
x
FF
yxis 2D transfer function between)(DG
[4] Olgac, N. and Sipahi, R., “A Unique Methodology for Chatter Stability Mapping in Simultaneous Machining”. ASME, Journal of Manufacturing Science and Engineering, 2005. 127(4).
vi
uii F
F
0
00F is the nominal cutting force under rigid tool assumption.
: cutting force constantsvu KK ,
when tooth i is in the cut when tooth i is out of the cut
01
ig
yx
ii
iii CosSin
SinCosL
i
i
vu rotation matrix transforming
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: axial depth of cut: the number of teeth: the tooth passing period between the i th and i + 1st teeth
an
iDie : delay operator
to , periodic in
and
Feed
Regenerative Effect / Delays
TF 1
Dynamic Depth of Cut
Tool DisplacementTF 2
Cutting Forces+
- ++
y
x
FF
yx
Cutter dynamics ID(setup specific)
Cutter force formation chip loads
(process / material specific)
y
x
y
x
yyyx
xyxx
FF
DFF
DGDGDGDG
yx
TF G)()()()(
:2
n
iiii
n
ii
D
v
uii
y
x gyx
eKK
gaFF
TF i
10
1
1
1 )1(00
:1 FLLL
