The dynamic characteristics of a microdrill in the drilling process were investigated in this study. The trend toward higher density printed circuit boards requires smaller holes, down to 0.3 mm in diameter, to be drilled through the board layers. To improve quality, produce a higher production rate, and avoid drill breakage, the dynamic characteristics of the microdrilling process must be studied. A stepped pretwisted beam is used to simulate the microdrill. A moving Winkler-Type elastic foundation is used to approximate the drilling process. A time-dependent vibration model for drilling is presented. The rotating speed, pretwisted angle, and thrust force effects of the microdrill are considered. The numerical analysis indicates that the natural frequency is reduced suddenly as the microdrill moves into a workpiece.

1.
Shaw, M., 1989, Metal Cutting Principles, Clarendon Press, Oxford.
2.
Rosard
,
D. D.
,
1953
, “
Natural Frequency of Twisted Cantilever Beams
,”
ASME J. Appl. Mech.
,
20
, pp.
241
248
.
3.
Jarrett
,
G. W.
, and
Warner
,
P. C.
,
1953
, “
The Vibration of Rotating Tapered Twisted Beam
,”
ASME J. Appl. Mech.
,
20
, pp.
381
389
.
4.
Tekinalp
,
O.
, and
Ulsoy
,
A. G.
,
1989
, “
Modeling and Finite Element Analysis of Drill Bit Vibration
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
,
111
, pp.
148
155
.
5.
Tekinalp
,
O.
, and
Ulsoy
,
A. G.
,
1990
, “
Effect of Geometric and Process Parameters in Drill Transverse Vibration
,”
ASME J. Eng. Ind.
,
112
, pp.
189
194
.
6.
Liao
,
C. L.
, and
Dang
,
Y. H.
,
1992
, “
Structural Characteristics of Spinning Pretwisted Orthotropic Beams
,”
Comput. Struct.
,
45
(
4
), pp.
715
731
.
7.
Liao
,
C. L.
, and
Huang
,
B. W.
,
1995
, “
Parametric Instability of a Pretwisted Beam Under Periodic Axial Force
,”
Int. J. Mech. Sci.
,
37
(
4
), pp.
423
439
.
8.
Magrab
,
E.
, and
Gilsinn
,
D. E.
,
1984
, “
Bucking Loads and Natural Frequency of Twist Drills
,”
Trans. ASME
,
106
, pp.
196
204
.
9.
Ulsoy
,
A. G.
,
1989
, “
A Lumped Parameter Model for the Transverse Vibration of Drill Bit
,”
Control Manuf. Process. Robotic Sys.
,
pp.
15
25
.
10.
Fuji
,
H.
,
Marui
,
E.
, and
Ema
,
S.
,
1988
, “
Whirling Vibration in Drilling Part 3: Vibration Analysis in Drilling Workpiece With a Pilot Hole
,”
ASME J. Eng. Ind.
,
110
, pp.
315
321
.
11.
Nishimae
,
J.
,
Satoh
,
Y.
,
Kojima
,
T.
, and
Fukushima
,
T.
,
2000
, “
Laser Processing System for Micro Drilling of Printed Circuit Boards
,”
Proc. SPIE
,
4088
, pp.
209
211
.
12.
Okada
,
T.
,
2000
, “
Laser via-Hole Drilling of Printed Wiring Board
,”
Proc. SPIE
,
4088
, pp.
148
153
.
13.
Hinds
,
B. K.
, and
Tyreanor
,
G. M.
,
2000
, “
Analysis of Stress in Micro-Drills Using the Finite Element Method
,”
Int. J. Mach. Tool Manufact.
,
40
, pp.
1443
1456
.
14.
Yang
,
Z.
,
Li
,
W.
,
Chen
,
Y.
, and
Wang
,
L.
,
1998
, “
Study for Increasing Micro-Drill Reliability by Vibrating Drilling
,”
Reliability Eng. Sys. Safety
,
61
, pp.
229
233
.
15.
Chyan
,
H. C.
, and
Ehmann
,
K. F.
,
1998
, “
Development of Curved Helical Micro-Drill Point Technology for Micro-Hole Drilling
,”
Mechatronics
,
8
, pp.
337
358
.
16.
Yang
,
Z.
,
Tan
,
Q.
, and
Wang
,
L.
,
2002
, “
Principle of Precision Micro-Drilling With Axial Vibration of Low Frequency
,”
Int. J. Prod. Res.
,
40
(
6
), pp.
1421
1427
.
17.
Rincon
,
D. M.
, and
Ulsoy
,
A. G.
,
1995
, “
Complex Geometry, Rotary Inertia and Gyroscopic Moment Effects on Drill Vibrations
,”
J. Sound Vib.
,
188
(
5
), pp.
701
715
.
18.
Iwastsubo
,
T.
,
Sugiyama
,
Y.
, and
Ishihara
,
K.
,
1972
, “
Stability and Stationary Vibrations of Columns Under Periodic Loads
,”
J. Sound Vib.
,
23
, pp.
245
257
.
19.
Lee
,
H. P.
,
1994
, “
Buckling and Dynamic Stability of Spinning Pre-Twisted Beams Under Compressive Axial Loads
,”
Int. J. Mech. Sci.
,
36
(
11
), pp.
1011
1026
.
20.
Lee
,
H. P.
,
1996
, “
Dynamic Response of a Beam With a Moving Mass
,”
J. Sound Vib.
,
192
(
2
), pp.
289
294
.
21.
Ram
,
Y. M.
, and
Caldwell
,
J.
,
1996
, “
Free Vibration of a String With Moving Boundary Conditions by the Method of Distorted Images
,”
J. Sound Vib.
,
194
(
1
), pp.
35
47
.
22.
Fung
,
R. F.
,
Huang
,
J. S.
, and
Chu
,
J. J.
,
1998
, “
Dynamic Stability of an Axially Travelling String/Slider Coupling System With Moving Boundary
,”
J. Sound Vib.
,
211
(
4
), pp.
689
701
.
23.
Law
,
S. S.
, and
Zhu
,
X. Q.
,
2000
, “
Study on Different Beam Models in Moving Force Identification
,”
J. Sound Vib.
,
234
(
4
), pp.
661
679
.
24.
Wu
,
J. S.
, and
Chen
,
D. W.
,
2000
, “
Dynamic Analysis of a Uniform Cantilever Beam Carrying a Number of Elastically Mounted Point Masses With Dampers
,”
J. Sound Vib.
,
229
(
3
), pp.
549
578
.
25.
Lee
,
H. P.
,
1996
, “
Dynamic Stability of a Tapered Cantilever Beam on an Elastic Foundation Subjected to a Follower Force
,”
Int. J. Solids Struct.
,
33
(
10
), pp.
1409
1424
.
26.
Daikoh
,
Y.
,
Terabayahshi
,
T.
, and
Masuda
,
M.
,
1994
, “
Micro Drilling of Printed Circuit Boards Cutting Force and Chip Flow Mechanism
,”
J. Jpn. Soc. Precis. Eng.
,
60
(
12
), pp.
1796
1800
(in Japanese).
You do not currently have access to this content.