Tool cutting force modeling and wear estimation of micro-end

Tool cutting force modeling and wear estimation of micro-end
Florida International University
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FIU Electronic Theses and Dissertations
University Graduate School
3-30-1999
Tool cutting force modeling and wear estimation of
micro-end-milling operations
Wei-yu Bao
Florida International University
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FLORIDA INTERNATIONAL UNIVERSITY
Miami, Florida
TOOL CUTTING FORCE MODELING AND WEAR ESTIMATION OF
MICRO-END-MILLING OPERATIONS
A dissertation submitted in partial fulfillment of the
requirements for the degree of
DOCTOR OF PHILOSOPHY
in
MECHANICAL ENGINEERING
by
Wei-Yu Bao
1999
To: Dean Gordon Hopkins
College of Engineering
This dissertation, written by Wei-Yu Bao, and entitled Tool Cutting Force Modeling and
Wear Estimation of Micro End-Milling Operations, having been approved in respect to
style and intellectual content, is referred to you for judgment.
We have read this dissertation and recommend that it be approved.
A
Sabri Tosunoglu
Tachung C
ih
Ibrahim N. Tansel, Major Professor
Data of Defense: March 30, 1999
The dissertation of Wei-Yu Bao is approved.
Dean Gor n Hopkins
Colleg of Engineering
II
Dean Richard L. Camp ll
Division of Graduate Studies
Florida International University, 1999
ACKNOWLEDGMENTS
I would like to thank the members of the committee for their patience and
constructive comments. I especially thank my major professor Dr. Ibrahim N. Tansel for
introducing me to neural networks and genetic algorithms and showing me the beauty and
joy that lie beyond the neuron and gene.
The majority of the experimental data was collected at Engineering Prototype
Center of Radio Technology Division of Motorola Inc. I thank Mr. Bob Shisler, Chris
Nelson, Derek Smith and Michael McCool of Motorola Inc. for their technical supports
and recommendations. I also thank my colleagues Mr. Tacku T. Arkan and Mahendrakar
Naudeshwar for their assistance and help. It would impossible to complete this research
without their cooperation.
iii
ABSTRACT OF THE DISSERTATION
TOOL CUTTING FORCE MODELING AND WEAR ESTIMATION
OF MICRO END-MILLING OPERATIONS
by
Wei-Yu Bao
Florida International University, 1999
Miami, Florida
Professor Ibrahim N. Tansel, Major Professor
The applications of micro-end-milling operations have increased recently. A
Micro-End-Milling Operation Guide and Research Tool (MOGART) package has been
developed for the study and monitoring of micro-end-milling operations. It includes an
analytical cutting force model, neural network based data mapping and forecasting
processes, and genetic algorithms based optimization routines. MOGART uses neural
networks to estimate tool machinability and forecast tool wear from the experimental
cutting force data, and genetic algorithms with the analytical model to monitor tool wear,
breakage, run-out, cutting conditions from the cutting force profiles.
The performance of MOGART has been tested on the experimental data of over
800 experimental cases and very good agreement has been observed between the
theoretical and experimental results. The MOGART package has been applied to the
micro-end-milling operation study of Engineering Prototype Center of Radio Technology
Division of Motorola Inc.
iv
TABLE OF CONTENTS
CHAPTER
PAGE
Chapter I Introduction
1
Chapter I Theoretical Background
4
2.1 Modeling of End Milling Operations
4
2.2 Neural Networks
10
2.3 Genetic Algorithms
19
2.4 Machinability and Monitoring of End Milling Operations
27
Chapter III Analytical Cutting Force Model of Micro-End-Milling Operations
29
3.1 Cutting Force Model without Tool Run-out
29
3.2 Cutting Force Model with Tool Run-out
39
3.3 Cutting Force Model of Conventional End Milling Operations
53
Chapter IV Model Based Cutting Force Characteristics and Surface Finish
55
4.1 Cutting Force Profiles
55
4.2 Cutting Force Characteristics
60
4.3 Work-piece Surface Roughness and Precision
82
Chapter V Model Based Monitoring of Micro-End-Milling Operations
87
87
5.1 Tool Breakage Detection
5.2 Tool Wear Estimation
101
5.3 Tool Run-out Estimation
110
5.4 Cutting Angle Monitoring
115
V
5.5 Cutting Condition Monitoring
119
5.6 Optimal Working Condition Selection
121
Chapter VI Experimental Setup
123
Chapter VII Results And Discussion
133
7.1 Validity of the Analytical Cutting Force Model
133
7.2 Representation of the Cutting Force Characteristics
139
7.3 Performance of Monitoring in Micro-End-Milling Operations
150
159
Chapter VIII Introduction of MOGART Package
8.1 Structure of MOGART Package
160
8.2 Analytical Cutting Force Model
164
8.3 Neural Network Research Tool
168
8.4 Genetic Algorithm Research Tool
175
8.5 Applications of Operation Guide in Micro-End-Milling Operations
178
Chapter IX Conclusion and Recommendations
-
188
List of References
191
Vita
198
vi
LIST OF TABLES
TABLE
PAGE
Table 5.1 Results of the tool wear estimation model
109
Table 5.2 Results of the tool cutting angle identification
118
Table 6.1 Experimental contents
124
Table 6.2 Experimental equipment
124
Table 7.1 Maximum cutting force error of the analytical cutting force model
136
Table 7.2 Experimental data of 0.020" diameter end mill machinability testing
140
Table 7.3 Experimental data of 0.0625" diameter end mill machinability testing
140
Table 7.4 Results of the tool wear forecasting model testing
153
Table 7.5 Run-out experimental results of collet end mill holder
156
Table 7.6 Run-out experimental results of conventional end mill holder
156
Table 7.7 Results of the tool run-out estimation
158
Table 7.8 Results of the tool cutting condition monitoring
158
vii
LIST OF FIGURES
FIGURE
PAGE
Figure 2.1 Construction of neural networks
10
Figure 2.2 Construction of the three-layer neural networks
12
Figure 2.3 A research area map with the ground-water contamination data
15
Figure 2.4 Estimation of the ground-water contamination distributions
15
Figure 2.5 Computational results of a mapping study
16
Figure 2.6 Estimated results of a mapping study
16
Figure 2.7 Results of square wave forecasting
17
Figure 2.8 Results of function forecasting
18
Figure 2.9 A data chromosome with 16 genes presented three DNA
19
Figure 2.10 Biological evolution cycle of species
20
Figure 2.11 A mating procedure of genetic algorithms
21
Figure 2.12 Fixed-point crossover genetic procedure
22
Figure 2.13 Uniform crossover genetic procedure
22
Figure 2.14 Jumping mutation genetic procedure
23
Figure 2.15 Genetic evolution procedure of the tool cutting angle monitoring
25
Figure 2.16 Function of an optimization case
26
Figure 2.17 Genetic evolution procedure of the function optimization
26
Figure 3.1 Tool cutting edge profiles of micro-end-milling operations
30
Figure 3.2 Tool cutting edge profiles of Tlusty's cutting force model
30
viii
Figure 4.1 Cutting force of two-flute tool, climbing milling without tool run-out
57
Figure 4.2 Cutting force of two-flute tool, conventional milling without tool run-out
57
Figure 4.3 Cutting force of two-flute tool, climbing milling with tool run-out
58
Figure 4.4 Cutting force of two-flute tool, conventional milling with tool run-out
58
Figure 4.5 Cutting force of four-flute tool, climbing milling without tool run-out
59
Figure 4.6 Cutting force of four-flute tool, conventional milling without tool run-out
59
Figure 4.7 Cutting force characteristics with spindle speed
62
Figure 4.8 Cutting force characteristics with spindle speed
62
Figure 4.9 Cutting force characteristics with feed rate
63
Figure 4.10 Cutting force characteristics with depth of cut
64
Figure 4.11 2-D cutting force characteristics with spindle speed and feed rate
65
Figure 4.12 3-D cutting force characteristics with spindle speed and feed rate
65
Figure 4.13 2-D cutting force characteristics with spindle speed and depth of cut
66
Figure 4.14 3-D cutting force characteristics with spindle speed and depth of cut
66
Figure 4.15 2-D cutting force characteristics with feed rate and depth of cut
67
Figure 4.16 3-D cutting force characteristics with feed rate and depth of cut
67
Figure 4.17 Cutting force characteristics with tool run-out
68
Figure 4.18 Cutting force characteristics with tool run-out angle
70
Figure 4.19 2-D cutting force characteristics with tool run-out and its angle
71
Figure 4.20 3-D cutting force characteristics with tool run-out and its angle
71
Figure 4.21 Cutting force characteristics with entry cutting angle
72
Figure 4.22 Cutting force characteristics with tool exit cutting angle
73
ix
Figure 4.23 Cutting force characteristics with tool diameter and spindle speed
74
Figure 4.24 Cutting force characteristics with tool diameter and feed rate
75
Figure 4.25 Cutting force characteristics with tool diameter and depth of cut
76
Figure 4.26 2-D cutting force characteristics with tool diameter and spindle speed
77
Figure 4.27 3-D cutting force characteristics with tool diameter and spindle speed
77
Figure 4.28 2-D cutting force characteristics with tool diameter and feed rate
78
Figure 4.29 3-D cutting force characteristics with tool diameter and feed rate
78
Figure 4.30 2-D cutting force characteristics with tool diameter and depth of cut
79
Figure 4.31 3-D cutting force characteristics with tool diameter and depth of cut
79
Figure 4.32 Cutting force characteristics with toot flute numbers
80
Figure 4.33 Cutting force characteristics with toot helix angle
81
Figure 4.34 Work-piece surface roughness by considering the tool cutting edge tip
profiles
82
Figure 4.35 Work-piece surface precision by considering the tool run-out
85
Figure 5.1 AE activity of micro-end-milling experiment I, case 1
89
Figure 5.2 AE activity of micro-end-milling experiment I, case 2
89
Figure 5.3 AE activity of micro-end-milling experiment II, case 1
90
Figure 5.4 AE activity of micro-end-milling experiment II, case 2
90
Figure 5.5 Tool cutting force of micro-end-milling experiment I
93
Figure 5.6 Tool cutting force of micro-end-milling experiment II
93
Figure 5.7 New tool cutting force average of experiment I
97
Figure 5.8 Tool cutting force average before breakage of experiment I
97
x
Figure 5.9 New tool cutting force variation of experiment I
98
Figure 5.10 Tool cutting force variation before breakage of experiment I
98
Figure 5.11 New tool cutting force average of experiment II
99
Figure 5.12 Tool cutting force average before breakage of experiment II
99
Figure 5.13 New tool cutting force variation of experiment II
100
Figure 5.14 Tool cutting force variation before breakage of experiment II
100
Figure 5.15 Monitoring of tool wear by the thrust direction cutting force
103
Figure 5.16 Monitoring of tool wear by the feed direction cutting force
103
Figure 5.17 Indirect monitoring of tool wear by the cutting forces
104
Figure 5.18 Genetic evolution procedure of the tool wear model
107
Figure 5.19 An empirical tool wear model
107
Figure 5.20 Comparison of the tool wear model
109
Figure 5.21 Tool run-out estimation procedure
112
Figure 5.22 Cutting force of climbing milling with tool run-out
113
Figure 5.23 Genetic evolution procedure of tool run-out estimation
114
Figure 5.24 Tool cutting angles of end milling operations
115
Figure 5.25 Tool cutting angle identification procedure
117
Figure 5.26 Spindle speed identification
119
Figure 5.27 Tool cutting condition identification procedure
120
Figure 5.28 Tool optimal working condition estimation procedure
122
Figure 6.1 Experimental setup
123
Figure 6.2 Machine tool
125
xi
Figure 6.3 Cutting force measurement
126
Figure 6.4 Data acquisition
127
Figure 6.5 Hardness measurement
128
Figure 6.6 Image processing system
129
Figure 6.7 The computer screen showing the software used for Image processing
130
Figure 6.8 The cutting edges of a new tool
131
Figure 6.9 The cutting edges of a worn tool
131
Figure 6.10 Work-piece surface cut by a new tool
132
Figure 6.11 Work-piece surface cut by a worn tool
132
Figure 7.1 Experimental cutting forces of micro-end-milling without run-out
137
Figure 7.2 Analytical model based cutting forces of micro-end-milling without run-out137
Figure 7.3 Experimental cutting forces of micro-end-milling with run-out
138
Figure 7.4 Analytical model based cutting forces of micro-end-milling with run-out
138
Figure 7.5 Thrust direction maximum cutting force of 0.020" diameter end mills
142
Figure 7.6 Feed direction maximum cutting force of 0.020" diameter end mills
142
Figure 7.7 Thrust direction maximum cutting force of 0.0625" diameter end mills
143
Figure 7.8 Feed direction maximum cutting force of 0.0625" diameter end mills
143
Figure 7.9 Feed direction maximum cutting force of 0.020" diameter end mills
144
Figure 7.10 Feed direction maximum cutting force of 0.030" diameter end mills
144
Figure 7.11 Feed direction maximum cutting force of 0.050" diameter end mills
145
Figure 7.12 Feed direction maximum cutting force of 0.0625" diameter end mills
145
Figure 7.13 Model based thrust direction maximum cutting force of micro-end-milling 147
xii
Figure 7.14 Model based feed direction maximum cutting force of micro-end-milling
147
Figure 7.15 Difference between micro and conventional end milling operations
148
Figure 7.16 Tool breakage monitoring by AE activity of experiment II, case 1
151
Figure 7.17 Tool breakage monitoring by AE activity of experiment II, case 2
151
Figure 7.18 Performance of the tool wear forecast model
153
Figure 7.19 Thrust direction cutting force of the new tool
155
Figure 7.20 Thrust direction cutting force of the tool before breakage
155
Figure 8.1 MOGART program
159
Figure 8.2 Diagram of MOGAT program
161
Figure 8.3 Menu of MOGART program
163
Figure 8.4 Cutting force estimation
165
Figure 8.5 Cutting force report
165
Figure 8.6 Cutting force profile
167
Figure 8.7 Tool cutter profile
167
Figure 8.8 Neural network project
169
Figure 8.9 Neural network setup
169
Figure 8.10 Training data input
170
Figure 8.11 Neural network running
172
Figure 8.12 Import the project
172
Figure 8.13 Neural network testing report
173
Figure 8.14 Graphics of neural network testing results
174
Figure 8.15 GATool setup step 1
176
xiii
Figure 8.16 GATool setup step 2
176
Figure 8.17 GATool results
178
Figure 8.18 Characteristics of maximum cutting forces
179
Figure 8.19 Three-dimensional cutting force graphic
181
Figure 8.20 Work-piece surface precision estimation
182
Figure 8.21 Work-piece surface roughness estimation
183
Figure 8.22 Tool run-out estimation
185
Figure 8.23 Tool life estimation
186
Figure 8.24 Optimal working condition selection
187
xiv
LIST OF SYMBOLS
r
= tool radius (inch)
Z
= the numbers of tool teeth
z
= the ordinal number of tool teeth
p
= tooth helix angle (rad)
n
= spindle speed (rpm)
Co
= spindle circle speed(1/sec.)
f
= feed rate (ipm)
ft
= feed per tooth (inch)
t
= time (sec.)
a
= depth of thrust (inch)
b
= depth of cut (inch)
o
= tool cutting angle (rad)
X
= leading angle (rad)
a
= engagement angle (rad)
(P
= cutting angle of work piece (rad)
= tool cutter angle per tooth (rad)
6
= computing angle (rad)
fC
= computing feed (inch)
h
= cutting chip thickness (inch)
xv
H
= not working cutter edge length (inch)
p
= proportional factor
Km
= material coefficient (N/cm2 )
KW
= wear coefficient
F~
= unit force (N)
Ft
= tangential cutting force (N)
Fr
= radial cutting force (N)
Fx
= feed direction cutting force (N)
Fy
= thrust direction cutting force (N)
ro
= run-out length (inch)
y
= run-out angle (rad)
69
= integrating start angle (rad)
9e
= integrating end angle (rad)
Sr
= work-piece surface roughness (inch)
S,
= work-piece surface precision (inch)
xVI
Chapter I
Introduction
Micro-end-milling operations were first used for manufacturing of special purpose
equipment in biomedical and aerospace applications. However, miniaturization of many
consumer products and esthetic goals drastically increased micro-end-milling operations in
the
conventional
shop
floor.
Currently,
many state-of-the-art
consumer
product
manufacturers widely use micro-tools with less than 2 mm diameter to prepare the plastic
injection molds of their parts.
At the first glance, micro-end-milling operations look like conventional end-milling
operations with only dimensional difference. However, it was found that cutting force
characteristics of micro-end-milling operations were different from those of conventional
end milling operations after their machinability tests had been done. Micro-tools have very
short tool life compare to the conventional tools. If the cutting conditions are not selected
properly, micro-tools will be broken in a few seconds. Depending on the hardness of
work-pieces, even in the identical cutting conditions micro-tools may have less than 10" of
tool life. Operators have to carefully select the cutting conditions with the small margin of
errors and monitor the machining operations since those tools will create unnoticeable
sound and vibration. Because of their tiny size, it is very different to detect their breakage.
Many hours of machining time could be wasted if the tool failure is not detected on time.
In addition, the ratio of the tool run-out to tool diameter becomes very big compare to
I
conventional tools. In many cases, micro-tools are subjected to larger cutting forces since
only half of the cutting edges remove the material from the work-piece.
Even though the need for a concentrated study on micro-machining is known, very
limited studies had been completed. In this dissertation, a new analytical model was
developed for micro-end-milling operations, and a series of techniques were developed to
use this model for machinability study, cutting condition monitoring, run-out estimation,
tool wear modeling and breakage detection.
All the developed tools were integrated in a single software package. The package
effectively uses neural networks and genetic algorithms together with the analytical model.
In this work, the following studies are integrated:
- A new analytical cutting force model for micro-end-milling with or without tool
run-out.
- Tool cutting force variation estimators based on the analytical model and neural
networks mapping.
- Tool wear estimation by using the genetic algorithms and neural networks.
- Tool breakage detection method.
- Tool cutting condition monitoring method by using the analytical model and
genetic algorithms.
- Run-out estimation by detecting the cutting force profiles.
- The analytical model based surface finish calculation.
The developed package is capable to help engineers to select the optimal cutting
conditions with minimal experiments, to evaluate the performance of their operations and
2
to monitor the tool condition. The cost of micro-machining operations, setup time and
number of inspections could be reduced by using the package effectively.
To verify the analytical cutting force model and get the necessary data, more than
800 experiments have been performed for the cooperation of Mechatronics Lab of
Mechanical Engineering Department of Florida International University and Engineering
Prototype Center of Radio Technology Division of Motorola Inc.
The theoretical background of the studies is introduced in Chapter II, which
includes the tool cutting force modeling of conventional end milling operations, neural
networks and genetic algorithms. The derivation of the developed analytical cutting force
model of the micro-end-milling operations is presented in Chapter III. The analytical
model based cutting force characteristics of the micro-end-milling operations are discussed
in Chapter IV. The analytical model based the monitoring methods of the micro-endmilling operations are proposed in Chapter V, which include tool breakage, wear, run-out
and cutting conditions. The Chapter VI presents the experiment setup and coverage. The
results of the studies are discussed in Chapter VII. Chapter VIII is a user guide of the
Micro-End-Milling Operation Guide and Research Tools (MOGART) program. The
conclusion of the researches and recommended future work are presented in Chapter IX.
3
Chapter II
Theoretical Background
In this chapter, the theoretical background of the existed modeling and processing
techniques that were used in the dissertation are outlined. First the modeling of end milling
operations is discussed. This model will be modified for micro-end-milling operations in
the next chapter. For data processing, neural networks and genetic algorithms are
presented. The neural networks are used for mapping, classification and forecasting. The
genetic algorithms are used for optimization, modeling and monitoring.
2.1 Modeling of End Milling Operations
1. Tlusty's Cutting Force Model of End Milling Operations
In 1975, J. Tlusty developed an analytical cutting force model of the end milling
operations to calculate the cutting force variations.1] Tlusty's cutting force model was
developed based on the following three assumptions:
Assumption 1: The tangential cutting force is proportional to the cutting areas:
(2.1.1)
Ft = Km b h
Assumption 2: The radial cutting force is proportional to the tangential cutting force:
Fr
=
(2.1.2)
p Ft
Assumption 3: The chip thickness can be expressed with the following expression:
h= ft sine
(2.1.3)
4
In the first assumption, the cutting chip thickness h is not a constant, but a function
of z because of tool helix angle. The formula 2.1.1 can be rewritten as:
dFt = Km h(z) dz
Because of z = z(8) and dz
r dO, it becomes:
tan P
dFt = 2 ( Fu / ft) h(0) d9
(2.1.4)
dFr = p dFt= 2 ( Fu / ft ) p h() d0
(2.1.5)
where: F =2tan/
" 2tanp)
The tool cutting forces of the feed direction x and the thrust direction y are
calculated.
dFx= -dFt cos 0 - dFr sin 0 = -2 ( F / ft ) h(0) ( cos 0 d0 + p sin 0 d0)
(2.1.6)
dFy= dFt sin 0 - dFr cos 0 = 2 ( F / ft ) h(0) ( sin 0 d0 - p cos 0 d0)
(2.1.7)
Considering the third assumption, the formulas 2.1.6 and 2.1.7 become:
dF.
=
-2 Fu (sin 0 cos 0 dO + p sin2 0 d0)
(2.1.8)
dFy = 2 F~ ( sin2 0 dO - p sin e cos O d0)
(2.1.9)
After integration, the analytical cutting force model has been derived.
6e -
F, = -Ffu
Fy=F
(e-
0, )+ (
s in0 --in0 2
) - 0.5 p ( sin 2e - sin 20)
s)- p(sin Oe-sin
) -0.5 (sin2O
-sin 20,
(2.1.10)
(2.1.11)
The resultant cutting force on the x-y plant is:
Fr 2 = FY+
Fy
(2.1.12)
5
To calculate the tool cutting force using the formulas 2.1.10 and 2.1.11, three
parameters have to be considered.
The first parameter is the tool cutter angle per tooth y.
y/ =
2r
(2.1.13)
Z
The second parameter is the cutting angle of the work-piece p.
(2.1.14)
rp = arccos (r - a)
r
The third parameter is the engagement angle a.
(2.1.15)
a =tan
r
Three different machining operations have been discussed in Tlusty's model.
Case 1: a(p and a +
py
For conventional milling operations:
section 1:
[ 0, a ]
Os = 0
Oe= 0
section 2:
[ a, p ]
6,= 0 - a
Oe= 0
section 3:
[
Os =
Oe= Q
, ( +a ]
0- a
For climbing milling operations:
section 1:
[7E -(p,7x-9p+
section 2:
[71 -(p+a,7t]
section 3:
[7,
Case 2: a>9 and a +
7+a
a]
]
03 =71 - cp
Oe=
0 3 =0-a
Oe=O
0 3= 0 - a
Oe=
(p< y
For conventional milling operations:
6
n
section 1:
[ 0, p ]
Os = 0
Oee=
section 2:
[ (, a ]
O =0
Oe= (p
section 3:
[a,(p+cL ]
0,=0-a
Oe=qp
03=i - p
Oe=0
Os =
8=
e ep
For climbing milling operations:
section 1:
[7r -(p, 7t]
section 2:
[ n,
section 3:
[a,
a]
+a]
-
es = e - a
n
ee= n
Case 3: a + (p >
Because of overlapping, the tool cutting force of the overlapped part is equal to
the sum of the cutting forces of both cutting edges.
Tlusty's cutting force model has been widely used. It has reasonable assumptions,
straightforward derivation and can be easily applied to most of conventional end milling
operations without tool run-out.
In micro-end-milling operations, the tool diameter is very small. The micro-tools
are easily worn and suddenly broken. The influence of the tool run-out becomes significant
to the cutting force variation because of their tiny sizes. Tlusty's model didn't consider the
tool run-out and wear. It also didn't explain the difference between the conventional and
climbing milling operations. In micro-end-milling operations the ratio of the feed per tooth
to the tool radius (ft/r) usually can not be neglected. In this case the third assumption of
Tlusty's model is not valid. A new analytical cutting force model of micro-end-milling has
been looked for since the micro-end-mills were applied to the manufacturing.
2. Improvements of the Analytical Cutting Force Model.
To include tool run-out into the model, researchers used two approaches. The first
approach was development of a new analytical model. Gygas. improved Trusty's cutting
force modal by considering different total cutting angle, climbing and conventional milling,
symmetric and asymmetric cut in 1979.21 Based on Tlusty's three assumptions and
experimental data, another empirical cutting force modal was developed by Yucesan et al.,
in 1990.E33 The different cutting conditions were investigated and analyzed by statistical
methods and plasticity theory. The empirical model considered the cutting force
coefficients of Tlusty's first assumption as a function of the chip thickness and also gave
the limitations of integration angles. Investigating the tool vibration in three-dimension
cutting, Jemielniak derived a formula from steady state cutting to determine the dynamic
cutting coefficients in 1992.41 To improve Tlusty's cutting force model with tools run-out
and keep the analysis simplicity, Wang et al. developed a cutting force model in frequency
domain in 1994.51 The model was derived as the convolution of three component
functions, and the effect of cutter run-out was taken into consideration in forming revised
chip thickness and average chip thickness expressions. Another milling operation with runout model was developed by Gu et al. in 1991.E63 The run-out were considered as two new
items into Tlusty's third assumption and estimated by cutting force signal.
The second approach was to develop a computational cutting force model.
Sutherland and DeVor developed a computational model in which the chip load and runout were considered in 1986.''3 Armarego and Deshpande focused on the eccentricity and
8
deflection of the cutter, developed three-component based cutting models for end-milling
force, torque and power predictions. These model can be used to predict the average and
fluctuating force components and torque in 1991.E'l The deflection of the end-mill and the
work-piece, and surface error were predicted by using the model rather than the rigid endmilling system. Kim and Ehmann described a procedure for the three-dimensional static
and dynamic cutting force simulation in face milling in 1993.91 The cutting forces created
by machine tool vibrations was simulated in the model.
Tlusty's model has been improved in many different ways. Most developed models
depended on the tlusty's three assumptions. None of the previous studies discussed or
proved the tlusty's third assumption in theory and derived a model with tool run-out by
directly considering the cutting chip thickness. In this dissertation, a new analytical cutting
force model is derived from the tool cutting edges and their tip profiles equations. The
model represents micro-end-milling and conventional end milling operations without or
with tool run-out. It also considers tool wear. The model proves the existence of the
Tlusty's third assumptions in theory and explains the difference between micro-end-milling
and conventional end milling operations. The derivation and discussion of the new model
will be presented in the next chapter.
9
2.2
1.
Neural Networks
Basic Theory of Neural Networks
Neural networks are a class of dynamic computational models that mimic the
constructions and operations of a biological brain to react the real world problems. The
first successful neural network was developed during 1957 and 1958 by Frank Rosenblatt,
Charles Wightman and others 1O]. The basic idea was to construct a network by using
some nodes (neurons) connected together by some connection channels (nerves), which
was able to carry and process the information through its input and output interfaces (see
Figure 2.1). For different problems, only the connection weights between the nodes of the
network had to be adjusted by a training procedure.
Brain
Sensor
Neuron
Nerve
Reaction
Figure 2.1 Construction of neural networks
10
A basic theory of neural networks was contributed by mathematician Andrei
Kolmogorov in 1957.111 He not only proved the existence of the neural networks, but also
commented that they could be trained.
Theorem 1:
(Kolmogorov's Neural Network Existence Theorem) Given any continuous
function f : [0,1]" -> R", f(x) = y, f can be implemented exactly by a three-layer feedforward neural network having n fan-out processing elements in the first (x - input) layer,
(2n+1) processing elements in the middle layer, and m processing elements in the top (y output) layer.
Theorem 2:
Given any
F > 0 and
any L 2 function f : [0,1]" -> R", there exists a three-
layer back-propagation neural network that can approximate f to within c mean squared
error accuracy.
The Kolmogorov's existence theorem proved that neural networks with three
layers were able to implement an arbitrary function. The Kolmogorov's second theorem
proved that neural networks were able to implement the function in any accuracy by
adjusting the connection weights.
2. Architecture of the Back-propagation Neural Network
The back-propagation neural network is one of the most important historical
developments in the neural networks. It is a powerful tool to solve mapping, classification
and forecasting problems, which has been proved in many applications. In the designs of
the back-propagation neural network, three layers (input layer, hidden layer and output
layer) are constructed according to Kolmogorov's existence theorem. The information of
11
distances and directions between the actual and estimating output data is used to update
the connection weights among the connected nodes layer by layer through a backpropagation. A construction of the back-propagation neural network is presented in
Figure 2.2.
Output
Output layer:
Node
Hidden layer:
Connection
Weight
Input layer:
Input
Figure 2.2 Construction of the three-layer neural networks
The back-propagation neural network could be trained by following three steps.
Step 1: Estimate output data by using forward-propagation calculations.
h =w
Ye
=
W2
(x)
5(h)
where: x, h and ye are the data of the input, hidden and output layers.
6(x) and S(h) are the unitizing transfers of the input and hidden layer data.
w1 and w2 are the connection weights between input and hidden nodes,
hidden and output nodes. In the beginning, they are set randomly.
12
Step 2: Calculate the error (distance) between the actual and estimated data (points).
£= IY - Yel
where: y and ye are the actual and estimated data.
Step 3: Find the direction of the actual point, and update the weights by using the backpropagation calculations.
W2
new
=
~old
W2
- a fl(g, Ye)
new= W olold -
fd , h
where: a is learning rate.
Repeat the three steps until the error s is less than the requested error level.
3. Applications of the Back-propagation Neural Network
The back-propagation neural network can be applied to solve the time independent
problems called mapping and time series problems called forecasting. A Neural Network
Tool program (NNTool) developed in 1995 and modified in 1996.2[3 is an application
of back-propagation neural networks. It has been successfully applied to determine the
underground contamination of New York area
[14
and Miami International Airport area. [ 5 ]
The three-dimensional underground contamination distribution graphics of both areas
were generated by using 131 and 49 sample data sets respectively. In the research of
micro-end-milling operations, it has been used to estimate the maximum cutting force of
the micro-end-milling operations with different selected working conditions and tool
parameters by using a few experimental data
[16]
13
(see Chapter V).
Mapping: The problem addressed by mapping is the approximate implementation of a
function f : A C R" -> R'", from a bounded subset A of n-dimensional Euclidean space to
a bounded subset fA] of m-dimensional Euclidean space, by training on the example cases
(x1, yi),
(x 2 , y2),
Example case 1:
...
,
(xk, yk), where y = f(x).
[141[151
The research of Miami International Airport area ground-water contamination with
three-dimensional coordinates and one contamination parameter has been completed. A
back-propagation model with three layers has been constructed in the study, in which the
three-dimensional coordinates were considered as the input nodes, one contamination
parameter as the output node, and ten hidden nodes were designed. The 49 sample data
sets were used to the neural network training with 0.15 learning rate and 0.075
momentum factor. The average error of the contamination estimations was less than 3%.
The map of the research area and estimation of the contamination distributions are
presented in Figure 2.3 and 2.4.
Example case 2:
171
A function with two input and one output (f = sin x + sin y in [0, 2t; 0, 27t]) has
been studied. A back-propagation neural network model with four layers (one input layer
with 2 nodes, two hidden layers with 15 nodes each and one output layer with 1 node) has
been constructed. In this study, The 169 data sets were used for the neural network
training with 0.6 learning rate and 0.9 momentum factor, and 144 data sets for its test. The
average error of the estimation was less than 2.2%. The actual (computational) and
estimated results are presented in Figure 2.5 and 2.6.
14
--
V
.Hm.
4>'
Ai
AMA
2k82
onp"" td
:h
-
-e to
L--itud-
4>'
W
&.
lAre
n
0- atptudeSectin
Longiude
___J
25.820
I'
25.815
25.010
v
>i
t2'~
=
25.800
30.000 - 40.000
-
--
--
..
20.000 - 30.000
2-.79
1
25.785
.'
25.780
25.775
Longitude :
Section
A0i'Latitude
0.0
I- 10.000
8.000
6.000
4 000
r4Longitude - Depth Section
- 20.000
- 10.000
-.
8.000
000
-
00
-
:tflr;'Ls
Q
20.U
<1 000
aiv?
... J UL 1995
._.
-c
60
_T
100
25.820
25.810
Figure 2.4
25.600
25.790
25.780
-80.320 -80.310 -80 300
Estimation
of 250
'MW
80.280 80.270
of the ground-water contamination distributions
15
.0
1.000 - 2.000
-
40.0
) 40.UOG
3.
-'
25.795
S Laitude-Depth
: na:coa
1405(1*4
f = sin x + sin y
1
*1.5-2
~ 1-1.5
~5.4978
0
-0.5 -4.4506
1
3.4034
-1.5
Y
2.3562
.
-2 A4
.-.
-0.5-0
-1--0.5
p -1.5--1
Q0-2-1.5
1.3090
0.2618
N~
x
Figure 2.5 Computational results of a mapping study
Function Estimation
2
-
1.5~-
f
U1.5-2
1-1.
).5
5.4978
-0.5-0
-1-3.4034
t2.3562
1.5
1.3090
-2
S
0.2618
..
0
o-
N
x
0
0
n
t
a
U,
Figure 2.6 Estimated results of a mapping study
16
9.-
Y
0-1-0.5
0-1.5--1
0-2-1.5
Forecasting: The problem addressed by forecasting is the approximate implementation
of a function f : A c R" -+ Rm , from a bounded subset A of (n-1)-dimensional Euclidean
space and a time series dimension to a bounded subset fIA] of (m-1)-dimensional
Euclidean space and a time series dimension, by training on the time series example cases
(Xi,
yi), (x 2 , Y2), ... , (xk, Yk), where y = f(x).
Example case 1:[151
A square wave function has been studied. A three-layer model with 5 input nodes,
16 hidden nodes and 1 output node was used in the study. The 216 data sets of the threeperiodic time were used for the neural network training with 0.15 learning rate and 0.075
momentum factor, and 72 data sets of the following period for its test. The average error
of the estimation was less than 0.5%. The results are presented in Figure 2.7.
Square Wave Forecasting
2
1.5
1
0.5 --
25
45
65
85
10
125
5
1
165
85
205
225
245
265
285
-0.5
-1
-1.5
- Actual
- Predict
-2
t
Figure 2.7 Results of square wave forecasting
17
Example case 2:[151
A exponential function with a exponential faded sine wave oscillation (f = (1 - ell)
+ 0.5 e~"
sin (27itt) ) has been studied. A three-layer model with 3 input nodes, 10 hidden
nodes and 1 output node was used in the study. The 72 data sets of the one-periodic time
were used for the neural network training with 0.15 learning rate and 0.075 momentum
factor, and 72 data sets of the following period for its test. The average error of the
estimation was less than 2%. The results are presented in Figure 2.8.
Function Forecasting
y = (1- e-20) + 0.5 e-120 sin (t)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-
60
120
180
24
300
360
420
480
540
600
-0.1
t
Figure 2.8 Results of function forecasting
18
660
--
Actual
Forecast
2.3 Genetic Algorithms
1.
Basic Theory of Genetic Algorithms
Genetic algorithms are a class of dynamic computational models that mimic the
natural selection and biological evolution to solve the real world problems. Based on
biological theories, the deoxyribonucleic acid (DNA) molecule, a tiny corkscrew built
from simple chemicals and included a large numbers of genes that define individual parts
of the organism's blueprint, is the most fundamental piece carried life's mystery. The
offspring inherit the characteristics from their parents through the genes. The survivals
depended on natural selection (survival of the fittest) determine the characteristics of the
next generation (the evolution of the species).E"I
The first application to solve problems by using the biological evolution was
proposed in 1975 by John Holland. Based on the biomedical DNA theory, a binary number
was designed as a individual chromosome to carry information of the data set, in which
each bit presents a gene (see Figure 2.9). The individuals followed the biomedical DNA
hereditary processes to mate each other and inherit a new generation through gene
crossover and mutation. The natural selection as a rule determined the survivals of the
next generation. The evolution would continue until one individual of the generation fitted
the requested fitness level (see Figure 2.10).
DNA 1
[DNA 2
DNA 3
Figure 2.9 A data chromosome with 16 genes presented three DNA
19
Better Fitters
7
N
Natural
Selection
Grow Up
New Chromosome
Children
Gene
Inheritance
Reproduction
Figure 2.10 Biological evolution cycle of species
2. Architecture of Genetic Algorithms
In the view of the optimization, the genetic algorithms is a powerful tool to find
the optimal solution of the problems with large data sets by using random search
techniques. The natural selection rule is the key to search the optimal solution through the
genetic evolution. The crossover operation keeps the better information from the last
generation and the mutation operation helps to search the domain completely to avoid its
being tripped in local maximum or minimum. The population size, mating pool size and
the numbers of the children from each couple are decided by the problem study. The first
generation can be randomly created and each following generation will be evolved by the
following six steps:
20
Step 1: Selection of the mating couples (parents).
The mating pools can be selected randomly or following some rules from the
population pool. The mating couples can be picked randomly or following some rules
from the mating pool. The procedure is presented in Figure 2.11.
Mating Pool
Natural
Sp 2eSelection o
Female
Male
Group
Group
Mating
Couple
Figure 2.11 A mating procedure of genetic algorithms
Step 2: Selection of the hereditary chromosome of the next generation.
Three different methods are suggested to select the hereditary chromosomes.
1.
The hereditary chromosome is always duplicated from the stronger one of the
mating couple.
2. The hereditary chromosome is duplicated from the one of the mating couple by
the turn.
3.
The hereditary chromosome is randomly duplicated from the mating couple.
Step 3: Gene crossover.
Crossover is one of the genetic processes, in which the both parents' genes are
21
combined to a new chromosome. There are two different processing theories to be applied
to the operations, which are the fixed-point and uniform crossover.
Fixed-point crossover: Randomly pick a point in the chromosome, inherit all the genes
from the one parent before that point and randomly inherit the genes from the both parents
after the point (see Figure 2.12).
Crossover Point
Parent 1
Parent 2
Child
1 0 1 0 11 10 0 1010 1 1010
10
1 0 0 1 0 00 1 1 1 0 1
1 1 1 001
1O 10
L
10
0 1O 10
From Parent 1
0
Randomly From Parent 1 or 2
Figure 2.12 Fixed-point crossover genetic procedure
Uniform crossover: Randomly inherit the genes from the both parents in the whole
chromosome (see Figure 2.13).
Parent 1
1o 1 0 1 1 11 1
Parent 2
010 110 0111010 011i11101
0
1
Child
010
1o1 1
olo
10
10 1
0
0
0 110 1 o 1 0 0
Randomly From Parent 1 or 2
Figure 2.13 Uniform crossover genetic procedure
22
Step 4: Gene mutation.
Mutation is one of the genetic processes, in which the genes of the new
chromosome are changed randomly according to the rapid evolution theories. There are
two different processing theories to be applied to the operations, which are the jumping
and creeping mutation.
Jumping mutation: Randomly change the genes of the chromosome in the certain
jumping mutation probability lever (see Figure 2.14).
Before Jumping Mutation:
Child
0 0 1 O 1 1
After Jumping Mutation:
Child
oj0
0 1 0 1 0 1 0O
Randomly Mutated Genes
0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0
Figure 2.14 Jumping mutation genetic procedure
Creeping mutation: Randomly change a certain value of the chromosome data in the
certain creeping mutation probability lever through a coding and decoding procedure.
Step 5: Creation of next generation (children).
There are two different theories to create new generations. One is that fittest
individual of the one generation is always inherited to the next generations according to
the elitism theory and the other is that fittest one is not necessary to be duplicated from
one generation to the next one.
23
Step 6: Evolution.
The children of this generation grow up and become the parents of the next one.
Repeat the six steps until the fitness is in the requested fitness level.
3. Applications of Genetic Algorithms
The Genetic algorithms can be applied to search a global optimal objective in high
dimensional Euclidean space with a given function. A genetic algorithm program
(GATool) was developed in 1998. It was successfully applied to monitor the cutting tool
entry and exit angles of the micro-end-milling operations."91 In the research of micro-end-
milling operations, it also has been used to estimate the tool breakage, wear, run-out and
optimal working conditions (see Chapter V).
Example case 1:
[191
An identification program of the cutting tool entry and exit angles was developed
by using genetic algorithms with an analytical cutting force model of micro-end-milling
operations (see Chapter III). In all of the studied cases, the tool entry and exit cutting
angles were estimated by the GATool program in less than 20 generations with less than
3% error. In 120 generations the error was reduced to less than 1%. In the study, the
population size was designed as five, mating pool size as two versus two and one child
was created from each couple. 30 bit binary data was used for the individual coding. The
uniform crossover with 0.5 probability, jumping mutation with 0.04 probability, creeping
mutation with 0.02 probability and elitism were used in the genetic procedures. The results
are presented in the Figure 2.15.
24
Geneic Evolution Procedure
3
a
c 2.5
2
W
1.5
0.5
Cutting Angle
From: 0.785
C
0 -
(45 degree)
20
0
60
80
100
120
140
160
180
To: 2.356
2(0
-0.5
(135 degree)
c
-1L--1
-
-1.5 --
Fitness
Starting Angle
-Ending
Angle
-2
Generation
Figure 2.15 Genetic evolution procedure of the tool cutting angle monitoring
Example case 2:
A function with two parameters (f = e("+Yv( 2n) (sin x + sin y) in [0, 4n; 0, 47c]) has
been studied. It has one global minimum, seven local minimum, eight local maximum and
four stay points. The global minimum (-69.615) of the function was found in less than 20
generations with less than 2.6% error and in 100 generation with less than 0.035% error.
In the case, the population size was designed as five, mating pool size as two versus two
and one child from each couple. 30 bit binary data was used for the individual coding. The
uniform crossover with 0.5 probability, jumping mutation with 0.1 probability, creeping
mutation with 0.05 probability and elitism were considered in the genetic procedures. The
function and results are presented in Figure 2.16 and Figure 2.17.
25
f
ex")
360
(sin x + sinn y)
f
&
30
-
f
220-30
2
10-20
100-10
0
-10.0
-20-10
-t.
-10
U-30720
0
720
JO60
-/
120
F'F
-40
360480*
20-40-30
!
-50-40
-0-50
3 -70-60
24400
444
600
x (degree)
360eg80e0 120ree
720
Figure 2.16 Function of an optimization case
Genetic Evolution Procedure
800
700
600
500
-
400
300
200
100 -
-y
0
0
20
40
60
80
100
120
140
Generation
Figure 2.17 Genetic evolution procedure of the function optimization
26
2.4 Machinability and Monitoring of End Milling Operations
Several researches studied machinability and monitoring of end milling operations.
Machinability studies concerned the characteristics of tool cutting force, torsion,
deflection, vibration, run-out, wear, breakage and work-piece surface quality. To evaluate
machinability, researchers measured tool cutting force, spindle torque, acoustic emission,
tool vibration, tool temperature, optical scanning of tool tip, electrical measurements of
the contact resistance between the tool and work-piece, radio active concentration at the
chip. [8][20-25]
To monitor tool wear and detect tool breakage, various methods were developed.
It was specially interested in the tool wear and breakage monitoring, detection and
control. Principle and Yoon detected the tool breakage by using displacement signals in
1991.[261 Tansel et al. developed an on-line tool breakage detection system for end milling
operations from acoustic emission and cutting force signals, and extend the tool life by
reducing the feed rate in 1997.27311 Liang and Dornfeld estimated tool wear from acoustic
emission signals by using an on line time series model in 1989.[321 Elbestawi et al. developed
an on-line flank wear monitor system by monitoring cutting force signals. The harmonics
of the cutting force spectrum were used for classification. [33
Glass and Colbaugh
estimated tool wear in metal cutting operations by directly using cutting force signals with
neural networks in 1996.[341
To process experimental data, there are many different ways included geometry
analyses, analysis methods, statistics, fuzzy mathematics, wavelet transform, neural
networks and genetic algorithms. Statistical methods mainly used the average and
27
deviation characteristics to avoid irregular information that was usually caused by noises in
machining operations. The simple algorithms were applied to online tool breakage
detection.[ 27-3 t1] 35 ](361 Fuzzy mathematics was used to classify signals. It isolated the most
important components of the objects and avoid unimportant details. It is a good way to
analyze end milling operations because of the different characteristics of cutting force
signals at different operating conditions. 37 1 Wavelet transform, which is more efficient
than Fourier transform when the signal is not a sine type, was used to compress any kinds
of cyclical data to several simple characteristics[ 33 [38][391. Neural networks, a mimic human
brain method, can be used for the data mapping, classification and forecasting. They was
used to estimate tool cutting force and tool wear.3 1 ][34](404 2 Genetic algorithms, a mimic
the natural selection and biological evolution method, were used for the functional
optimization. [191
28
Chapter III
Analytical Cutting Force Model of Micro-End-Milling Operations
The derivation of a new analytical cutting force model of end milling operations is
presented in this chapter. The analytical model is developed for micro-end-milling
operations. It also can be applied to conventional end milling operation. Ten parameters
and two coefficients are considered in the model, which includes tool run-out and wear.
They are three working condition variables (spindle speed, feed rate and depth of cut),
two tool run-out variables (run-out and its angle), two cutting condition variables (tool
cutting entry and exit angle) and three tool geometry variables (tool diameter, helix angle
and the numbers of tool flutes). The material coefficient is related to the tool and workpiece materials. The tool wear coefficient is related to the tool life.
The developed analytical cutting force model has very good agreement with the
experimental data of the micro-end-milling operations. The results are presented in
Chapter VII.
3.1 Cutting Force Model without Tool Run-out
1. Tool Cutting Edge and Its Tip Profile of End Milling Operations
In end milling operations, the tip profile of the cutting edge of the tool (see Figure
3.1) is different from the one used by the third assumption of Tlusty's model (see
Figure3.2). They are close only if the f,/r is small enough to be neglected.
29
Tool Cutting Edge Profiles of End Mill machining Operations
2 flutes
0.010" dia. tool, 15,000 ipm spindle speed, 100 ipm feed rate
Cutting surface
-
1st cutting
-
2nd cuting
Figure 3.1 Tool cutting edge profiles of micro-end-milling operations
Tool Cutting Edge Profiles of End Mill machining Operations
2 flutes 0.010" dia. tool. 15,000 rpm spindle speed, 100 ipm feed rate
-
Cutting siuface
-
ai cutting
2nd cIttiog
Figure 3.2 Tool cutting edge profiles of Tlusty's cutting force model
30
The equations of the tool cutting edge tip profiles are:
x -
)
+rsin(cot60
(31.1)
Z
y = r cos(o t -
2;rz
Z)
(3.1.2)
2; z
where:
co
=
60
Z = 2 and z = 0, 1 for two-flute tools.
Z = 4 and z = 0, 1, 2, 3 for four-flute tools.
The equation of the tool cutting edge is:
y
x
60
(3.1.3)
=1
t-ft
60
tan(cot -
27r
)
Z
or:
ft
60
(x -- ) cos(o t -
2irz
Z
- y sin(o t-
2zzz:
Z
)= 0
(3.1.4)
2. Cutting Chip Thickness
The cutting chip thickness can be derived from the equations of the tool cutting
edge and its tip profile instead of the third assumption of Tlusty's model.
It is considered that the first cutting edge tip at time to with angle 0 reaches a
point on the work-piece, and the second cutting edge at time t1 with angle 01 crosses that
point. The following equations can be used:
31
0
-(4z3
)
(1+
z=
Z
(5=0Z+-
2
~
0,
Cot 1 -cot, =
(3.1.6)
2 z
-
(3.1.7)
Z
where: z = 0, 1 for two-flute tools.
z = 0, 1, 2, 3 for four-flute tools.
The equations3.1.1, 3.1.2 and 3.1.4 can also be rewritten as:
x=
fta
60
y = r cos(O to -
ft1
(x-
27r z
+ r sin(cot 0 -
60
27z
) cos(c t,
)
Z
(3.1.8)
)
(3.1.9)
2rz
1
Z
)
-
y sin(o t,
2z
-
Z
)= 0
(3.1.10)
To solve the cross point, substitute x, y from the equations3.1.8 and 3.1.9 to the
equation 3.1.10.
ft
ft,
( 60 -
60
) cos(
- r cos(w to -
f
t, -
2rz
2r(z+1)
27rz
2<r(z+1)
)
+r
sin(w
to
Z)
cos(w
t,
)
ZZZ
) sin(w t, -
S(co to - co t,) cos(co t,
60co
2r(z+1)
2n(z+1)
-
Z
)= 0
2__
)+ r sin(co to - co t + -) = 0
Z
Considering the equations3.1.5 to 3.1.7, the above equations can be simplified.
f
2r
(-
27rn Z
8)cos(-0
2
,)=rsin8
(3.1.11)
32
Because O
0 and 0 1 are very close, S is a small angle. Let:
sin 6
=
S
and also let:
From the equation 3.1.11, the computing angle 6 can be solved.
S~
.fcosO8
r
(3.1.12)
Z cos 0
27rr
where:
f,
= .f
nZ
The computing feed is:
f = f-(ti
-to)
60
(3.1.13)
Considering the equations3.1.5 to 3.1.7, the equation 3.1.13 can be rewritten as:
f =
_f
f(27
(27*8
2ir n
Z
-S)
The computing feed f, can be solved by substituting equation 3.1.12 to it.
ff
'
(3.1.14)
Z cosO
IC
27cr
Because of
f,
f,
~ f,(1-f,
Z cosO
2cr
Z cosO
2r
<<1,
fE can be approximated as below:
(3.1.15)
)
33
In geometry view, computing feed can be obtained.
sin
_
sin(r-0
r
)
f,
r
sinS
sin(r -
sinS
0)
r(
rcosO
f,
_
1 + fZ
cosO
cos
o
27rr
Also from geometry,
r2 = H 2 +f,
2
- 2Hf, cos(r -O)
(3.1.16)
H can be solved from the above equation,
H = -f, sinO + r 2 -(f, cos)
2
(3.1.17)
The cutting chip thickness is:
r 2 -(f, cos)
h=r - H = r +f, sin' -
Bec
0
2
fcosO
Because of
r
1
h ~f sin O +-(f,
2r
<<1,
cosO)
the cutting chip thickness can be approximated.
2
(3.1.19)
Substituting the equation 3.1.15 to 3.1.19, and also considering f, (
fr (.f ) 3
<«lft
(3.1.18)
the cutting chip thickness
f' sin6 cos+
h~ f, sinO 2rrr
r
)'
<<f
and
becomes:
2r
f,1 cos, 0
34
(3.1.20)
If ft/r << 1, the formula becomes h = ft sin 0, this is the third assumption of
Tlusty's model. It is proved that Tlusty's third assumption is satisfactory when f/r is small,
which is encountered in most conventional end milling cases.
In the micro-end milling operations, ft/r is not small enough to be ignored. For
example, if n = 15,000 rpm, f = 100 ipm, r = 0.01 inch and Z = 2, f,/r = 1/3, so that the
second and third item of the formula 3.1.20 can't be neglected.
Let's look at the physical meaning of the formula 2.2.20.
The first term is major cutting chip thickness. It is considered in Tlusty's model for
the cutting force calculation of conventional end milling operations.
The second term presents the difference between conventional milling and climbing
milling. It is a negative valuable when 0 is changed from 0 to 90 degree and a positive
valuable from 90 to 180 degree. It is said that cutting chip thickness of climbing milling is
thicker than that of conventional milling.
The third term is an additional cutting chip thickness. When 0 = 0, the cutting chip
thickness, which is equal to zero in Tlusty's model, is not equal to zero. It can be clearly
known from Figure 3.1. There is a leading angle when f/r value can't be neglected. It will
be solved in following discussions.
The formula 2.2.20, which is derived from the general tool cutting profiles, do not
have z parameter. It is said that any cutting edge has the same cutting chip thickness in the
same cutting angle. This is satisfactory in the case of conventional end milling operations
without tool run-out.
35
3. Leading Angle
In the formula 3.1.20, let h = 0. It becomes:
1
sin
A
f cos2 A
=_2r
1-
2rr
f,
COSH
or:
sin a ~
' cos2 A (1+fZ
cos).)
2r
2r r
(3.1.21)
Because 0 closes to 0 or 180 degree, assume cos 0 = 1,
A
I f, Z
-- arcsin[f (1+
2r
)]
(3.1.22)
I
for conventional milling
t + IX
for climbing milling
=|
=
2Tr r
For example, if n = 15,000 rpm, f = 100 ipm, r = 0.01 inch and Z = 2,
conventional milling or
k=
188.6
k = -8.6
0
in
in climbing milling.
If ft/r is very small, this is ft/r ~0,
k
~0
in conventional milling or
~ 180
in
climbing milling. That is the results of Tlusty's model.
4. Cutting Force
The cutting forces can be derived by using the formulas 2.1.6 and 2.1.7, and
cutting chip thickness formula 3.1.20 instead of the formula 2.1.3 (The third assumption of
Tlusty's model).
36
dF = -2F,(sin0
f, sin~cosO+
-
-f,
cos2 O)(cos0dO+psin dO)
2r
2rr
+- f, cos 2 O)(sin 0d-- p cos0dO)
2rrr f, sinOcosO 2r
F F(sin
where: F = KwKmrf
(3.1.23)
(3.1.24)
(3.1.25)
2 tan 3
Take the integration, the cutting force formulas can be derived.
F =F[
' (1+ p-)(sin' 6, -sin' O,)+ 1 ft (p - -)(cos'
3r
+-p(sin 2Oe -sin
2
F = F~[
if
J
3r
1r
261)-
Be -cos
- (sin e - sin 8S) - p( 0 r
3
0,)-(sin2 Be - sin O,)
0,)]
(3.1.26)
Z
if
Z
' (p - -)(sin 3 e - sin 3 o,) - --' (1+ p-)(cos3 0, - cos 3 9,)- p(sin 2 0, -sin
-1 (sin20, -sin 20j)- p .
r
2
2
I
3r
3r
(sin B,-sinB,) + (e,-
B,)]
(3.1.27)
or:
F =iF[C
F
= F[C,
r
sin
+C2
sin3 9-Cf
F
r
1
r
cos'
cos'
-FC2
r
-sin
2
e-psin2 9-1sin2e-pf
2
Z
where : C = -(1+p -)
3
C2 = -(p--)
3
+1 psin28-
n3
37
r,
sine- p]|e
r
sine+e]||
(3.1.28)
3..9
(3.1.29)
9,)
Compared the cutting force model (formulas 3.1.28 and 3.1.29) to Tlusty's cutting
force model (formulas 2.1.10 and 2.1.11), it is known that Tlusty's model is a special case
of the model derived above when f,/r is small enough to be neglected.
Three different machining operation cases as same as ones mentioned in Tlusty's
model are discussed.
Case 1: axp + X and a +
+(
For conventional milling:
section 1:
[ -?, a - x ]
O, =-_
Oe= 0
section 2:
[ a - k, ( ]
0,= -(
OeL=
0
section 3:
[
p,(p + a ]
,=0 - a
Oe= (
For climbing milling:
section i:
[C -p,n-p+a]
6,=n-(p
Oe=0
section 2:
[t - p + a,7+X]
0,=0-a
Oe=
section 3:
[,t+,
0$=0-a
Oe=it+X
Case 2: aC
p +Xand
+X, +ca ]
+(+k
y
For conventional milling:
section 1:
[ , p]
0 = -k
Oe= 6
section 2:
[ p, a - k ]
6,= -X
Oe=
section 3:
[a-,±+a]
0,=0-a
Oe=(p
38
For climbing milling:
section i:
[7n-(P,l+X ]
0s=7 -(p
0e=0
section 2:
[CX
+X,i-p+ a]
0s=ic-9
0e=i +X
section 3:
[1 -p+a,++
Case 3: a +<p
a ]0,=0.- a
0e=7 +
+%,!>
Because of overlapping, the tool cutting force of the overlapped part is equal to
the sum of the cutting forces of both cutting edges.
3.2 Cutting Force Model with Tool Run-out
1. Tool Cutting Edge and Its Tip Profile of End Milling Operations
The equations of the tool cutting edge tip profiles are:
x =
60
+rsin(wt
y = r cos(co t
-2z
Z)+r
Z
Z
sin(wt +y)
) + r cos(co t + y)
where: co =2cn
60
Z = 2 and z = 0, 1 for two-flutes tool.
Z = 4 and z = 0, 1, 2, 3 for four-flute tool.
From geometry,
of
r
sinlysin(-
2
+w t)
39
(3.2.1)
(3.2.2)
Af = r
sin?'
(3.2.3)
cos CO t
2
Af 2 = ro
+ Ar
2
- 2roAr cosy
Ar = r(cosy - sin y tan co t)
(3.2.4)
The equation of the tool cutting edge is:
y
x
ft +
60
sin(y
ft
cos CO t
60
= 1
sin7y
cos
(3.2.5)
1
CO t
tan(
tZ
or:
[x - (
ft
60
+ ro
sin y )]cos(w t- 27c z ) - y sin(co t 2ir z ) = 0
coscot
Z
Z
(3.2.6)
2. Cutting Chip Thickness
In the end milling with run-out case, each cutting edge has a different chip
thickness. The two-flute tool is chosen in the following discussions.
(1) The chip thickness of the first cutter
The cutting chip thickness can be derived from the equations of the tool cutting
edge and its tip profiles.
The equations3.2.1, 3.2.2 and 3.2.5 can be rewritten as:
x=
60
+r sin(co-
y = r cos(w to
-
Z
2 7rz)+ro
Z
)+r
sin(c to + y)
cos(w to + y)
40
(3.2.7)
(3.2.8)
[x - (-t
60
-ysin(wt, -
-
siny )]cos(co t
coscot,
+ro
Z
Z
)=0
(3.2.9)
As same as the discussion of the end milling without run-out case, to solve the
cross point, substitute x, y from the equations3.2.7 and 3.2.8 to the equation 3.2.9.
[(A60
siny )]cos(w t, - 2(z+1))
60
coswt,
Z
+rsin(wt o -y Z 2)cos(wt - 2f(z1)Z
+ro
sin(a to
[f
60w
+ y ) cos(ca t, - 27
t) -r
(t
+rsin(wto- wt,+
)-r
z+1)
Z
-y 2_:_.___:+_
Z )sin(t
cos(co
- ro cos(cw to + y ) sin(c) t, - 2T
-
Z
)
z+1)
=0
Z
siny ](t
-
coscot,
2n (z+1))
Z
2x.
-)+rosin(oto -wt,+y
2xz+±1)
Z
Z
+
) =0
Considering the equations3.1.5 to 3.1.7, the above equation can be simplified.
f
{
27c
sin_____
-
(
2rn Z
27c(z+1)
cos[ Z-0
, +
2Z
= r sin S+ ro sin(5 + y +
} cos(
siny
c
2rz
Z
Z
2
- 0)
]
)
(3.2.10)
Because 0o and 01 are very close, 6 is a small angle. Let:
sin6=6
and also let:
0 =
_ 1
2
41
From the equation 3.2.10, the computing angle 6 can be solved.
r°
r
cosO
r
27cz
Z
r° .
sinycosO
r
27r(z+1)
cos[O+
]
(3.2.11)
r o
+ ~ Zcos+
1+f,
+--cosy+
27rr
)
r
Z
where:f,= f
nZ
Let's consider the two-flute end mill case. The equation 3.2.11 can be simplified.
sin y
ft coso - (-1) 2
os Br
1+
f,
cos69
rr
(3.2.12)
r
r
+ (-1)
°o
"
r
COY
where: z = 0, 1
Considering
f
r r
<< 'f , (
r
<<
)
r
r
,' f-<< 1 and
rr
r
<<1,
the equation 3.2.12
can be rewritten as:
r
ft cos - (-1)2-°-sin
y -- 1 (f, cosO )
r
r
7
(3.2.13)
r
The computing feed is:
f
=
1
60
(t, - to)+r° sin y (
1
cos co t,
-
1
cos w to
Considering the equations 3.1.5 to 3.1.7 and 00 ~,
equation 3.2.14 can be rewritten as:
f
f
siny
27rn
cos0
42
(3.2.14)
)
because of
6
small, the
Substituting the equation 3.2.12 to it, the computing feed f, can be solved.
f
~ f,[1+(-1)Z
Because of 0-
2rzr siny]-f,2
01,
cos0 -(-1)Z2ro
zrr
assumed Aro
[r + (-1)Z Ar] 2 = H 2 + f
(3.2.15)
siny
cos0
Ar, = Ar . From geometry,
- 2Hf, cos(zr - 0
)
(3.2.16)
H can be solved from above equation:
0 + [r +(-1)Z Ar]2 -(f
H =-fsin
cos)
2
(3.2.17)
The cutting chip thickness is:
h =[r-(-1)" Ar]- H
[r +(-1)Z
= [r - (-1)Z r]+ f, sin 9 -
Because of
h ~ f, sin0 +
cs
r
Or]2 -
cos )2
«1, the cutting chip thickness can be approximated.
2[r +(-1)Z Ar]
h
r
(3.2.19)
(fY cos0)2 - (-1) 2Ar
Substituting the equation 2.3.15 to 2.3.19, and also considering
f,(
(3.2.18)
f,(
r
)2
<<f,
and
)3 <<f,,the cutting chip thickness becomes:
f,[1 + (-1)Z
2r ° sin y)]sin 9
zzr
-1
f2
.rr
sin Ocos9 + - f,2 cos2 0- (_1)Z2r
cosy
2r
(3.2.20)
43
If f/r
<<
1 and ro = 0, the formula becomes h = f,sin 0, this is the third assumption
of Tlusty's model. It is said that Tlusty's model is a special case of end milling without
run-out.
Comparing the formula 3.2.20 to the formula 3.1.20, The tool run-out is expressed
in the first and forth items of the formula 3.2.20.
The forth term of the formula 3.2.20 is a major run-out factor. It reaches a
maximum value when the tool run-out is parallel to the tool cutting edge (y = 0 degree),
and turns to a minimum value when the tool run-out is perpendicular to the tool cutting
edge (y = 90 degree).
The second part of the first term the formula 3.2.20 is an additional run-out factor.
When y = 90 degree, the tool run-out turns into a minimum level and almost disappear. It
can be neglected in most conventional end milling operations because of ro/r
<<
1,.
For two-flute end-mills, if 2ro cos y is larger than f,, only one cutting edge works in
the machining operations.
The formula 3.2.20, which is derived from the general tool cutting profiles, do
have z parameter. It is said that different cutting edges have the deferent cutting chip
thickness. This is a true in the case of end milling with run-out.
Let z = 0, the chip thickness of the first cutter is:
h ~ ,[1 + 2r" sin y)]sin
r
- 1 f 2 sin B cos 6+ 1 f
2r
rr
44
2 cos
B - 2ro cosy
(3.2.21)
(2) The chip thickness of the second cutter
The second cutter chip thickness calculation can be considered into two sections.
In the first section, the second cutting path of the second cutter cuts on its first cutting
path. In the second section, the second cutting path of the second cutter cuts on the first
cutting path of the first cutter path.
A. In the first section of the cutting operations
The equations3.2.1, 3.2.2 and 3.2.5 can be rewritten as:
x=
+r sin(co to
60
y = r cos(w to
[x-(
ft1
f
60
+ rs
-
2fz ) +r sin(ca to + y)
Z
-
(3.2.22)
2ff z
)+ r, cos(c to + y)
Z
sin y
cosCOt
)]cos(co t,
2ff z
-
2
(3.2.23)
)y
Z
sin( t,
2ff z
-
Z
)
=
(3.2.24)
0
As same as the above discussion, to solve the cross point, substitute x, y from the
equations3.2.22 and 3.2.23 to the equation 3.2.24.
ftl)
60
cos co t 2
+rsin(w to
27cz
y ) cos(
[(fto
60
+r
sin(
siny
to + y )cos(
[
t, -
2;f(z +2))
Z
2c(z+2)
n
t,
(w to-2 )
Z
cos w t,
Z
) - r cos(( to -
2rz
) sin(
]cos(ct t 2
- 2
+ r, sin(c to - co t +7 +
45
t, -
2;
2r- )
-
60w
+r sin(co to - co t2 +-)
-
Z+2)
Z
(z+2)
Z
=0
2 (z+2)
)
zZ +
) =0
Considering the equations 3.1.5 to 3.1.7, the above equation can be simplified.
I
4x
sin________
)
{ f(
2;n Z
o
cos[
2
= r sinS+r sin(S +y +
sin
b =
,)
}cos( if-0
2
Z
~
)
(3.2.25)
Z
e0 and 6 1 are very
Because
2r(+2)
-,+
close, 6 is a small angle. Let:
6
and also let:
2
-
From the equation 2.3.25, the computing angle 6 can be solved.
2f, cos)
Zc~s
1+ f,
where:
f,
r
+ -"- cos(y+
Z
r
2rr
=
(3.2.26)
)
.f
nZ
Let's consider the two-flute end-mill case. The equation 3.2.26 can be simplified.
-~
2f, cosO
r
cosO r
1+f,
+ "cosy
r
rr
Considering
(3.2.27)
r r
<<f, (
r
)
r
<<
,
r rcr
can be rewritten as:
46
<<1
and
r
<< 1,
the equation 3.2.27
(2ftcos0 -~-(,cIs
2 ,
r
r
cf
os0)
coa(3.2.28)
322
r
The computing feed is:
f
f
= f(t,
-t
60
o)
+r0 sin y (
1
cosCt
1
-
)
(3.2.29)
cosCto
2
Considering the equations 3.1.5 to 3.1.7; and
~o02 because of S small, the
equation 3.1.14 can be rewritten as:
f = f
2irn
(2r -8)
Substituting equation 3.2.27 to it, the computing feed f, can be solved.
f,
(3.2.30)
~2f, - 2f,2 cos0
rrr
Substituting the equation 2.3.30 to 2.2.19, and also considering
f,( r )3
f,(t )2 <<ft and
r
<<f,, the cutting chip thickness becomes:
f,2 sin0cos0+-ft2 cos2 9
h _ 2f, sin0
(3.2.31)
2r
rr
B. In the second section of the cutting operations
In the formula 3.2.20, let z = 1. The chip thickness of the second cutter becomes:
2r0
h ~ f,[1- 2
icr
sin y)]sin 9
1
nr
f,2 sin cos0-+
47
1
2r
f,2 cos2
+ 2ra cosy
(3.2.32)
3. Integrating Angle
(1)
The integrating angle of the first cutter
In the formula 3.2.21, let h = 0.
1
2ro cosy -f ,- cos 2 .
=
2r
2r
f,(1+ " sin y)f2 cosA ,
rr
7rr
sin2 1
(3.2.33)
If f/r << 1 and ro/r << 1, it becomes:
A
=
arcsin(-" cosy)
(3.2.34)
f,
(2) The integrating angle of the second cutter
A. The first section
In the formula 2.3.31, let h = 0,
1
-f, cosA
r
sin A 21
1
1-
7rr
f,
2
cosA.,,
or:
A 2 ~ - - cos21A
sink
r
(1+ f, 1 -
(3.2.35)
urr
If 0 close to 0 or 180 degree, assume cos 0 = 1. It becomes:
A 21
~ -arcsin[
r
(1+ f
1 )]
(3.2.36)
/7 r
B. The second section
When the formulas 3.2.31 and 3.2.32 have the same h, that is the boundary of the
two sections.
48
-
2f, sin0
2r
2
= f,[1-
2
sin cos6+ 4f
f
2r
rr
sin y)]sin
1
-
.,
r
r
cos2 0
f--1 sin Ocos 0 +--f cos2 0+ 2r° cos y
2r
Solve the equation,
3
2r3cosy
sin1
=
22
2r
f,(1+
If f,/r
<< 1
cos 2 A 22
f
(3.2.37)
2r
" siny)-
ecr
ft cos 22
icr
and ro/r << 1, it becomes:
2r
A 2= 1
= arcsin(
" cosy)
(3.2.38)
4. Cutting Force
The cutting force can be derived by using the formulas 2.1.6 and 2.1.7, and cutting
chip thickness formula 3.2.20 instead of the formula 2.1.3 (the third assumption of
Tlusty's model).
-"-sin y)sin
dFx = -2F [(1+(-1)
Xrcr
1f,
-
sin
rcr
cos
+--ft cos 2 0 -(-1)
2-"-cosy]
2r
f,
x(cosOdO+ psinOdO)
dF, = 2F [(1+(-1)
x(sin
2r
-- sin y ) sin
icr
(3.2.39)
a
1
1r
)cr
2r
-- f, sin 0 cos0+-
d0- pcos d0)
f, cos2 0 -(-1)
2
cosy ]
ft
(3.2.40)
Take the integration,
49
Fx = F{
't (1 +
3 r
- sin 3
p2)(sin3
r
-[1+(-1)Z 2r° sin y](sin 2 O, -sin
ir
f2
+[(-1)z4 r°cosy
2
,) + !Lt(p - 2)(cos'
)
3 r
0,)+
p[1+-1) 2r siny](sin20, - sin20,)
r
' ](sinO, -sin O,)
-
(-1)24p
fr
ft
2r
- p[1 + (-1)' 2r sin
7r
if
F, =Fu{3 r'
2
(p -)(sin
T
2r0
-p[1 + (-1) 2
err
+[(-1)Z4p
y](O, -
3
(3.2.41)
3
e -sin
,) -)
,
3 r
1
-
sin,)
2r
(-1)
+
i r
s)
+ (-1) 2 sin y](sin2,
ir
2
L](si ne
2
(1 +p-)(cos3 9e-cos 3
- sin20e)
cosy (cos0e -cos0,)
4
fr
+[r+(-1)r
cosy (cos0e - cos0,)
OS)}
siny](sin2 O, - sin 0e) -[1
r° cosy
Oe - cos 3 0,)
ft
sin y](0, - O,)}
(3.2.42)
(1) The cutting force of first cutter
In the formulas 3.2.41 and 3.2.42, let z = 0. The first cutter cutting force is:
FX = F {1 ' (1 + p-)(sin 3 O, - sin' O,)
3r
-[1+
z
2r
2r" sin y](sin 2 0S - sin 2
icr
+[4 r° cosy
0
1
+ 1
3r
2r
' (p -
"
e)+-p[1+
ir
2
' ](sinOe - sin 0s) - 4p
2r
-)(cos3
i
O, - cos 3
O,)
sin y ](sin 20S - sin 20e)
cosy (cos0, - cosO,)
(3.2.43)
- p[1 + 2r sin y](0, - 0,)}
rr
50
F
~)(sin'
= F- {^3rf' (p
r
,
2r
"r°siny](sin-2
-p[+
7cr
r°cosy
+[4p
0,
,
-
1
2
2
7r
sin 6S)+ 4
fr
+[I+
2r
2r
;T r
' (1+
3r
, - sin2 0e) -[1+
t ](sin 0
-
3 0 ,) - sin'
p ~-)(cos' B, - cos'
n
0,)
" sin y](sin2s - sin2,)
cosy (cos 6e - cos 6,)
ft
sin y](e, - B,)}
(3.2.44)
or:
F =JF[C3 f sin 3 0±+C
r
+(C -
F, = F[C4
r
+
-
r
cos'0-(1+C,)sin0+ 1p(1+C)sin28
2
r
r
cos' B- p(1+C
1
2
7c
3
C4 =-(p- 2 )
ir
C5 =2sin
7c r
C6 =
4r
5 )sin2
)sin0+ C6 cos0 + (1 + C)011|
where: C3 = -(1+p-)
3
(3.2.45)
)sin 9-pC6 cosO-p(1+C)]":
sin' 6-C
r
f
y
cos7y
ft
51
9-
2
(1+C
5
)sin 26
(3.2.46)
(2) The cutting force of second cutter
A. The first section
The cutting force can be derided by using formulas 2.1.6 and 2.1.7, and cutting
chip thickness formula 3.2.31.
dFx = -2F (2 sin0
dF, =
2F
7c r
(2 sin6 --
ir r
f, sin 0cos +-f,
cos' 6 )(cos d6+p sin edO )
2r
f, sin dcos+-f, cos' 0)(sin Od2r
p cos~dO)
(3.2.47)
(3.2.48)
Take the integration, the cutter cutting force is:
Fx = F[4-f-(1+
3 r
+p(sin26e
F, = Fu[
(p -
)(sin' Oe - sin 3 O,)+4
(p 3r
.ir
-sin20)-4
r
(sin e -sin6S)
)(sin3 Oe - sin 3 0,) -
-(sin 26e - sin 20,) - p 4'
r
(1+
)(cos' Oe - cos' O,) -2(sin
-
2
p( 0 e -6,)]
)(cos' O, -cos'
(sin e - sin 9S) + 2(e -
2 O,
- sin2 B )
(3.2.49)
O,)
- 2p(sin2 0, - sin2 OS)
0,)]
(3.2.50)
or:
13
Fx = F[C,-fsin3 0+ C
1' cos 3
3 0-C
F = F[Cg f ' sin3
f ' cos 3 0-
r
r
,
r
where : C, = -(1+
3
Cs = 4 (P-
3
4f, sinn 0- 2p6]|+ psin2O-f
(3.2.51)
2psin 2 0-sin20-p 4_
4f' sin0+20]10
(3.2.52)
6-2 sin 2
r
r
r
-)
r
1)
i5
52
B. The second section
The formulas 3.2.45 and 3.2.46 can be used to calculate the cutting force of the
second section by using - C5 and - C6 instead of C5 and C6 .
3.3 Cutting Force Model of Conventional End Milling Operations
That cutting force model has been derived above can be applied to all the cases of
end milling operations. The conventional end milling operations is only a special case of
the model, which can be simply obtained from the model. The cutting force expressions of
the conventional end milling operations are much simpler than then the micro-end-milling
operations.
1. Cutting Force Model of Conventional End Milling Operations without Tool Runout
The conventional tools cutting force model can be simply obtained from the
cutting force model by considering f,/r = 0 and ro/r = 0.
From the formulas 3.1.28 and 3.1.29, the cutting force model becomes:
Fx = F[ -sin'
1
+ 1+-p sin 29- p8]|e'
(3.3.1)
F, =TF[(-psin
1
9--1sin 28*~ +9]|
(3.3.2)
3..2
.,
2
2
This is exact Tlusty's cutting force model.
53
2. Cutting Force Model of Conventional End Milling Operations with Tool Run-out
In the two-flute tool case, the cutting force model can be derived from formulas
3.2.45, 3.2.46, 3.2.51 and 3.2.52 by considering f/r = 0.
For the first cutter,
F, = F[-sin2 9+-psin29+
2
" cosy(sin-pcos9)- p4]r'
(3.3.3)
ft
F, = Fu[-psin0 --
sin 2+
4rcosy(p sinO+cosO)+
]|e
(3.3.4)
For the first section of the second cutter,
F, = F-2sin
F, = F
+psin2 -2p9]
(3.3.5)
(3.3.6)
-[-2p sing 9- sin 2+2]|0,
For the second section of the second cutter,
1
4r
F = F[-sin2 O+-p sin2O- "' cosy(sinO- pcos9) - p]~e
2
f
(3.3.7)
F, = Fu[-psin
(3.3.8)
-1 sin20
2
4r2 cosy(psinO+cosO)+]|'
.f,
The integrating angle can be got from the formula 3.2.34.
=
arcsin(
2r
(3.3.9)
cosy)
f,
54
Chapter IV
Model Based Cutting Force Characteristics and Surface Finish
Model based cutting force characteristics of micro-end-milling operations are
discussed in this chapter. The cutting force performances of ten different variables (spindle
speed, feed rate, depth of cut, tool run-out and its angle, tool diameter, helix angle and the
numbers of flutes) are presented. The calculation formulas of work-piece surface
roughness and precision have been derived from the tool cutting edge tip profile equations
of the analytical model.
4.1 Cutting Force Profiles
The developed analytical cutting force model conventional milling (see Chapter
III) can be used to estimate the cutting force of end milling operations. Six sample cases,
which include two-flute and four-flute tool climbing and conventional milling with and
without tool run-out cases are presented in Figure 4.1 to 4.6. In the sample cases, 0.020"
diameter tool with 45 degree helix angle, 15,000 rpm spindle speed, 70 ipm feed rate,
0.010 inch depth of cut, 50% overlapping and 130,000 N/inch 2 material coefficient are
selected. If the case is a tool run-out case, 0.001" tool run-out with 60-degree run-out
angle are chosen. They are listed as below:
Case 1: Two-flute tool, climbing milling without run-out (Figure 4.1).
Case 2: Two-flute tool, conventional milling without run-out (Figure 4.2).
55
Case 3: Two-flute tool, climbing milling with run-out (Figure 4.3).
Case 4: Two-flute tool, conventional milling with run-out (Figure 4.4).
Case 5: Four-flute tool, climbing milling without run-out (Figure 4.5).
Case 6: Four-flute tool, conventional milling without run-out (Figure 4.6).
In all these sample cases the tool wear is not considered, which will be discussed in
the following chapter.
From the sample cases 1 and 2 (see Figure 4.1 and 4.2), it is known that the
maximum resultant cutting force of climbing milling and conventional milling are almost in
the same level. If the effect of feed rate is not considered, the cutting force of the thrust
direction is larger than the feed direction in the climbing milling, and the cutting force of
the feed and thrust direction are almost the same in the conventional milling.
In the conventional milling, the angle of the maximum resultant cutting force is
always the exit cutting angle, which is independent of the spindle speed, feed rate and
depth of cut. It is 90 degree in the 50% overlapping case. In climbing milling, the angle of
the maximum resultant cutting force only depends on the depth of cut, which is b / (r tan
y) in the case of 50% overlapping. It is 147 (90 + 57) degree in the sample case.
A very little change in run-out would produce a 25% change in the maximum
resultant cutting force (compare Figure 4.3 and 4.4 run-out cases with Figures 4.1 and 4.2
without run-out cases). If the tool run-out is larger than the complete run-out that can be
calculated by the formula 4.2.2 (see next section of the chapter), the maximum resultant
cutting force is no more increased even when the tool run-out is increased. In this case it
becomes a one-flute cutting.
56
Cutting Force of Climbing Milling
without Tool Run-out
3.0
Operation Condition:
0.020 " diameter tool
2.5
with two flutes and
450 helix angle.
15,000 rpm spindle
speed.
2.0
z
70
1.5
ipm feed rate.
L.
0.010" depth of cut.
50% overlapping.
S1.0-
130,000 Nin. 2 material
coefficent.
0.5
0.0
- 0
-60
-30
0
30
60
90
Direction
-Feed
Direction
120 150 180 210 240 270 -Thrust
-Resultant
Tool Turning Angle (degree)
Figure 4.1 Cutting force of two-flute tool, climbing milling without tool run-out
Cutting Force of Conventional Milling
without Tool Run-out
3.0
Operation Condition:
0.020 " diameter tool
with two flutes and
450 helix angle.
2.5
2.0
z
15,000 rpm spindle
1.5
1speed.
70 ipm feed rate.
1.0
0.010" depth of cut.
50% overlapping.
2
130,000 Nin. material
LL 0.5
0.0
-0.5--
coefficent.
U
0
60
90
120
150 180
10 240 270
300 330
30
Direction
-Feed
Direction
-Thrust
- Resultant
-1.5
-2.0
Tool Turning Angle (degree)
Figure 4.2 Cutting force of two-flute tool, conventional milling without tool run-out
57
Cutting Force of Climbing Milling
with Tool Run-out
4.0
Z
3.5
Operation Condition:
0.020 " diameter tool
3.0
with two flutes and
450 helix angle.
15,000 rpm spindle
speed.
70 ipm feed rate.
0.010" depth of cut.
50% overlapping.
130,000 Nuin. 2 material
2.5
2.0
0.
1.5
coefficent.
V
0.001" tool run-out
with 60* angle.
1.0
0.5 - -
-Feed
0.0
- 0
-60
-30
0
30
60
90
Direction
-Thrust
Direction
120 150 180 210 240 2'0 -Resultant
-0.5
Tool Turning Angle (degree)
Figure 4.3 Cutting force of two-flute tool, climbing milling with tool run-out
Cutting Force of Conventional Milling
with Tool Run-out
4.0
Operation Condition:
0.020 " diameter tool
3.0
with two flutes and
450 helix angle.
2.0 -15,000
rpm spindle
z
speed.
) 1.0
0.0
30
c
60
90
12
150 180 210
270
-1.0
-2.0
70 ipm feed rate.
0.010" depth of cut.
50% overlapping.
2
330 3 0 130,000 N/in. material
coefficent.
0.001" tool run-out
with 600 angle.
Direction
-Feed
Thrust Direction
-. 0 --
-
Resultant
-4.0
Tool Turning Angle (degree)
Figure 4.4 Cutting force of two-flute tool, conventional milling with tool run-out
58
Cutting Force of Climbing Milling
without Tool Run-out
3.0
Operation Condition:
0.020 " diameter tool
2.5
with four flutes and
450 helix angle.
15,000 rpm spindle
2.0 -speed.
W
70
UL
.
1.5
ipm feed rate.
0.010" depth of cut.
50% overlapping.
130,000 Nuin.2 material
z 1.0
.coefficent.
'-Feed Direction
- Th ust Direction
Resultant
0.5
-90
-60
-30
0
30
60
90
120 150 180 210 240 270
Tool Turning Angle (degree)
Figure 4.5 Cutting force of four-flute tool, climbing milling without tool run-out
Cutting Force of Conventional Milling
without Tool Run-out
3.0
Operation Condition:
0.020 " diameter tool
with four flutes and
2.5
2.0
helix angle.
15,000 rpm spindle
450
z
speed.
70 ipm feed rate.
a 1.5
LL
0.010" depth of cut.
50% overlapping.
2
130,000 Nin. material
1.0
0.5
_coefficent.
0.0
30
60
90
120
150
180 210 240 270
-0.5
300 330
310 -- Feed Direction
'-Thrust Direction
-Resultant
-1.0
Tool Turning Angle (degree)
Figure 4.6 Cutting force of four-flute tool, conventional milling without tool run-out
59
The feed and thrust direction cutting force can be used to decide the tool run-out
and its angle, which will be discussed in Chapter V.
The maximum resultant cutting force of the four-flute tools (see Figure 4.5 and
4.6) is only half of the two-flute tools (see Figure 4.1 and 4.2). The cutting force
oscillation of the four-flute tools becomes only one forth of the two-flute tools.
4.2 Cutting Force Characteristics
The maximum cutting force of tools is the most important factor in the micro-endmilling operations. It can be used to indicate tool wear because it gradually increases when
the tool is worn, which is the most important reason of the tool breakage. It has been
proved in many experimental cases of the micro-end-milling operations (see Chapter V).
The only cutting force in the thrust direction of the micro-end-milling operations is chosen
for the studies because the cutting force in the feed direction has very similar
characteristics in most cases.
A special case is selected for the studied. All other cases discussed in the chapter is
around this special case with different parameter changes. In the studied case, two-flute
20" diameter tool with a 45 degree helix angle are considered working in 50% overlapped
climbing end milling operations without tool run-out and wear. The working conditions
are selected as 15,000 rpm spindle speed, 70 ipm feed rate and 0.030" depth of cut. The
material coefficient is considered as 130,000 N/inch 2. The conditions will be used in all the
discussed case without other explanations.
60
1.
Cutting Force Characteristics with Working Conditions
Three most interesting working conditions, spindle speed, feed rate and depth of
cut, are studied. The spindle speeds are selected between 5,000 and 45,000 rpm, feed rates
between 20 and 120 ipm, depth of cut between 0.010 and 0.030 inch. The tools used in
the studies are two-flute 0.010", 0.020" and 0.030" micro-end-mills.
"
Cutting force characteristics with spindle speed:
The spindle speeds from 5,000 to 45,000 rpm have been studied. Three different
feed rates (20, 70 and 120 ipm) and tool diameters (0.010", 0.020" and 0.030") are
selected in the study. The cutting force is decreased when spindle speed is increased. It
can be divided into two sections, in which the cutting force is decreased sharply from
5,000 rpm to a certain spindle speed and gently after this speed. This speed called critical
spindle speed depends on the feed rate and tool diameter. In the study case, it can be
approximated that critical spindle speed is around 1,000 rpm in the 20 ipm feed rate case,
2,000 rpm in the 70 ipm case and 3,000 rpm in the 120 ipm case from Figure 4.7. It does
not have much help for micro-end-milling operations to increase the spindle speed after
the critical point. For different tool diameters, the same conclusion can be obtained from
Figure 4.8. The larger tool diameter becomes, the smaller critical spindle speed is got and
the littler cutting force is decreased.
The critical spindle speed obtained from the cutting force model can be used to
select the spindle speed of micro-end-milling operations.
61
Maximum Cutting Force in Thrust Direction
of End Milling Operations
25
20
W 15
Tool Dia.
0.020"
L-
DOC
10 --
0.030 "
Feed Rate
(pm)
5
-+ 20
12010
0
5000
15000
25000
35000
45000
Spindle Speed (rpm)
Figure 4.7 Cutting force characteristics with spindle speed
Maximum Cutting Force in Thrust Direction
of End Milling Operations
16
14
12
10
Feed Rate
o
70 ipm
-
cDOC
0.030 "
6 --
Tool Dia.
(inch)
2 -->-
0
_
5000
_
_
15000
__
_
_
35000
25000
Spindle Speed (rpm)
Figure 4.8 Cutting force characteristics with spindle speed
62
-0.010
0.020
- -0.030
45000
"
Cutting force characteristics with feed rate:
The feed rates from 20 to 120 ipm have been studied. Three different spindle
speeds (15,000, 30,000 and 45,000 rpm) are selected in the study. The cutting force is
increased linearly when feed rate is increased. The increasing slope of the cutting force
depends on the selected spindle speed. When spindle speed is turned to faster, it becomes
smaller and the cutting force increase becomes gentler (see Figure 4.9).
Increasing spindle speed and decreasing feed rate can reduce the cutting force. It is
efficient to reduce the cutting force by increasing spindle speed when it is lower than the
critical spindle speed. Otherwise, it becomes better by reducing feed rate.
The cutting force will be unchanged if the ratio of feed rate to the spindle speed is
a constant (see Figure 4.11 and 4.12).
Maximum Cutting Force in Thrust Direction
of End Milling Operations
6
5
Tool Dia.
0.020"
u
LL
3
DoC
0.030 "
Spindle
Speed
S 2 --
(rpm)
1
-
0
20
45
95
70
Feed Rate (ipm)
Figure 4.9 Cutting force characteristics with feed rate
63
-15000
-o-
30000
-8-
45000
120
*
Cutting force characteristics with depth of cut:
The depths of cut from 0 to 0.050" have been studied. Three different spindle
speeds (15,000, 30,000 and 45,000 rpm) are selected in the study. When depth of cut is
increased, the cutting force is increased up to a certain level then kept there independent
of the depth of cut (see Figure 4.10, 4.13 to 4.16).
The critical depth of cut depends on the cutting angle of the work-piece and tool
helix angle. It can be obtained from the analytical model. If the depth of cut is less then ntr,
which happens in most micro-end-milling, it can be calculated by following formula.
b = re
(4.2.1)
tan y
Maximum Cutting Force in Thrust Direction
of End Milling Operations
5
4.5
4
Spindle
3.5
Speed
3 -0
Lc
15,000 rpm
2.5
Feed Rate
ipm
270
O 1.5
Tool Dia.
(inch)
1
--
0.5
0
0
0
0.013
0.01
--o0.02
---0.03
0.037
0.025
0.05
Depth of Cut (inch)
Figure 4.10 Cutting force characteristics with depth of cut
The three dimensional cutting force graphics are presented in Figure 4.11 to 4.16.
64
Maximum Cutting Force in Thrust Direction
of End Milling Operations
120
A 7_
100
EForce
--
V
Cutting
(N)
80
-
-
-
F-
w
Q00-1
01-2
Q 2-3
03-4
04-5
3 5-6
t
I
60
40
--
--
6-7
-
*
7-8
I
20
10000
18000
26000
34000
42000
Spindle Speed (rpm)
50000
Figure 4.11 2-D cutting force characteristics with spindle speed and feed rate
Maximum Cutting Force in Thrust Direction
of End Milling Operations
Cutting
(N)
6.5 -Force
.
2
'
3-3.5 0 3.5-4
\
5.5-
120
U100
=4.5
)
10 5-5.5 05.5-6
80
4 ,
60
3.5
3
10000 18000 26000
20034000
0 44.5 04.5-5
Feed Rate (ipm)
3 6-6.5
6.5-71
40
0
4200
' 50
40050000
Spindle Speed (rpm)
Figure 4.12 3-D cutting force characteristics with spindle speed and feed rate
65
Maximum Cutting Force in Thrust Direction
of End Milling Operations
-
0.03
0.024
---
Cutting
S.1Force
(N)
4-
Y
-
~
t
4.2-4.8
..
U
-
3.6-4.2
o
3-3.6
0.012L
192.4-3
|1.8-2.4
-}
0
0.006
001.2-1.2
2
0-0.6
0
10000
18000
26000
34000
42000
50000
Spindle Speed (rpm)
Figure 4.13 2-D cutting force characteristics with spindle speed and depth of cut
Maximum Cutting Force in Thrust Direction
of End Milling Operations
4.8
Cutting
4.2
Force (N)
4.2-4.8
3.6
U 3.6-4.2
>
3
U 3-3.6
-2.4
-
1.8
0.03
1&
U 1.2 -.
1
-1-Depth
0.6
0.006
p
10000 18000 26000
20034000
0 2.4-3
01.8-2.4
0 024
420
of Cut
(inch)
El1.2-1.8
Q0.6-1.2
O-0.6
40050000
Spindle Speed (rpm)
Figure 4.14 3-D cutting force characteristics with spindle speed and depth of cut
66
Maximum Cutting Force in Thrust Direction
of End Milling Operations
0.03
--
-- -
0.024
>
vForce
Cutting
(N)
U
3 4.9-5.6
4.2-4.9
o
3.5-4.2
.1
02.8-3.5
M 2.1-2.8
1.4-2.1
S00.7-1.4
0 0-0.7
40
20
80
60
0
120
100
Feed Rate (ipm)
Figure 4.15 2-D cutting force characteristics with feed rate and depth of cut
Maximum Cutting Force in Thrust Direction
of End Milling Operations
5.6 ,Cutting
Force (N)
4.9'
4.9-5.6
4.2 -
4.2-4.9
3.5
S3.5-4.2
u- 2.82
0.03
2.1 -'
o
z
7
-
0.024
0.018
1.4
01
0.7
0.006
0
20
40
60
Depth of Cut
(inch)00.7-1.4
2.8-3.5
p 2.1-2.8
01.4-2.1
0 0-0.7
80
6008020
Feed Rate (ipm)
Figure 4.16 3-D cutting force characteristics with feed rate and depth of cut
67
2.
Cutting Force Characteristics with Tool Run-out
*
Cutting force characteristics with tool run-out:
The tool run-out from 0 to 0.020" has been studied. Three different tool run-out
angles (0, 45 and 90 degree) are selected in the study. The cutting force is increased when
tool run-out is increased. Usually, except the case of 90 degree run-out angle, it can be
divided into two sections, in which the cutting force is increased linearly to a maximum
tool run-out called complete run-out then kept there. When tool with 90-degree run-out
angle, the cutting force is increased very little (see Figure 4.17).
Maximum Cutting Force in Thrust Direction
of End Milling Operations
7
6
Z
0
LL
0,
5
4 -
c3
Run-out
Angle
(degree)
0 2
1
0
-&-
0
-<>-
45
-o-90
0
0.0005
0.001
0.0015
Tool Run-out (inch)
Figure 4.17 Cutting force characteristics with tool run-out
68
0.002
The physical meaning of the complete tool run-out is that only one of the tool
flutes works when the tool run-out is larger than it. For two-flute tool, the complete runout depends on the tool run-out angle and feed per tooth. It can be derived from the
analytical model.
Roc =
f(4.2.2)
2cosy
In the study cases, the complete tool run-out have be calculated, which is 0.0012
inch in the 0 degree run-out angle case and 0.00165 inch in the 45 degree case.
*
Cutting force characteristics with tool run-out angle:
The tool run-out angles from 0 to 90 degree have been studied. The cutting force
is decreased when the tool run-out angle is changed from parallel to the tool cutting edges
(0 degree) to perpendicular to them (90 degree). When the tool run-out angle is closely
perpendicular to the tool cutting edges, the cutting force has a minimum value. When the
tool run-out angle is parallel to the tool cutting edges, the cutting force has a maximum
value that almost double of the minimum value (see Figure 4.18).
From cutting force model, it has been proved that cutting force caused by the tool
run-out can be minimized by setting the tool run-out perpendicular to the tool cutting
edges. For normal tool holders, screwing the tool perpendicularly to the tool cutting edges
can easily do it. In the view of the work-piece precision, the same conclusion can be
obtained from exactly computed results, which will be discussed in the following section
of this chapter.
69
Maximum Cutting Force in Thrust Direction
of End Milling Operations
8
7
6
0
LL
--
4
2
I
0
9
18
27
36
45
54
63
72
81
90
Run-out Angle (degree)
Figure 4.18 Cutting force characteristics with tool run-out angle
The three-dimensional graphics of the cutting force with tool run-out and run-out
angle are presented in Figure 4.19 and 4.20. It can be known that tool run-out and angle
can not be recognized by only one maximum cutting force value because the maximum
cutting force is a multiple value function of the tool run-out and its angle. If it is tried to
estimate the tool run-out and its angle, the maximum cutting force of both feed and thrust
directions have to be considered. The tool run-out and its angle are a single value function
of the maximum cutting force of both feed and thrust directions. The detail will be
discussed in Chapter V.
70
Maximum Cutting Force in Thrust Direction
of End Milling Operations
<r
72
Cutting
Force (N)
Fs
54
36
-
--
0.0004
03-3.5 03.5-4
9
0 4-4.5 ®4.5-5
U 5.5-6
-5-5.5
18 0
I.-6-6.5
-
0
0%
0.0008
0.0016
0.0012
6.5-7
0
0.002
Tool Run-out (inch)
Figure 4.19 2-D cutting force characteristics with tool run-out and its angle
Maximum Cutting Force in Thrust Direction
of End Milling Operations
7-
Cutting
Force (N)
6.5
Z
5.5-
0 3-3.5
0 3.5-4
0 4-4.5
®4.5-5
2f
5
-f
90
72
4.5 -
54
4
3Tool
3.5
18
3 o°
o
o
o0
0
N
0
0
0
T
n
Run-out
Angle (degree)
5-5.5 m5.5-6
U 6-6.5 U 6.5-7
0
0
0c
0
Tool Run-out (inch)
Figure 4.20 3-D cutting force characteristics with tool run-out and its angle
71
3.
Cutting Force Characteristics with Tool Cutting Angles
"
Cutting force characteristics with tool entry cutting angle:
The case of climbing micro-end-milling with different percentage overlapping has
been studied, in which the exit cutting angle is fixed on 180 degree and entry cutting
angles are changed from 0 to 180 degree. The cutting force almost has a linear decrease
with the increasing overlapping percentage except the section between 0 and 15 degree, in
which it almost is kept in the same level (see Figure 4.21).
The cutting force can be reduced linearly by increasing the overlapping percentage
of micro-end-milling.
Maximum Cutting Force in Thrust Direction
of End Milling Operations
6
5
4--
z
4)-0
LL
2
1
0
0
18
36
54
72
108
90
126
144
162
Starting Angle (degree)
Figure 4.21 Cutting force characteristics with entry cutting angle
72
180
"
Cutting force characteristics with tool exit cutting angle:
The case of conventional micro-end-milling with different percentage overlapping
has been studied, in which the entry cutting angle is fixed on 0 degree and exit cutting
angles are changed from 0 to 180 degree. The cutting force almost has a linear increase
with the decreasing overlapping percentage except the section between 0 and 15 degree,
in which it almost is 0 (see Figure 4.22).
The same conclusion can be obtained as above that cutting force can be reduced
linearly by increasing the overlapping percentage of micro-end-milling.
Maximum Cutting Force in Thrust Direction
of End Milling Operations
6
5--
4-2
0
L
2
1-
0
0
18
36
54
72
90
108
126
144
162
Ending Angle (degree)
Figure 4.22 Cutting force characteristics with tool exit cutting angle
73
180
4.
Cutting Force Characteristics with Tool Geometry
Cutting force characteristics with tool diameter:
The tool diameters from 0.010" to 0.125" have been studied. Three different
spindle speeds (15,000, 30,000 and 45,000 rpm), feed rates (20, 70 and 120 ipm) and
depths of cut (0.010", 0.030" and 0.050") are selected in the study.
In all the studied cases, when tool diameter becomes smaller, the cutting force is
decreased more rapidly (see Figure 4.23 to 4.25). For all the tool diameters, the decrease
of the cutting force is almost proportional to the increase of the spindle speed when it is
over the critical spindle speed (see Figure 4.23, 4.26 and 4.27).
Maximum Cutting Force in Thrust Direction
of End Milling Operations
10
9
8
7Feed
2
6
Rate
ipm
.70
L
L5
DOC
rn-
0.030 "
Spindle
U
3
-1Speed
(r pm)
2 --6-15000
1
-0-+
30000
--o- 45000
0
0
0.01
0.033
0.079
0.056
0.102
0.125
Tool Diameter (inch)
Figure 4.23 Cutting force characteristics with tool diameter and spindle speed
74
With different feed rates, the same results can be obtained from the cutting force
model. When tool diameter becomes smaller, the cutting force is decreased more rapidly.
For all the tool diameters, the decrease of the cutting force becomes almost proportional
to the increase of the feed rate (see Figure 4.24, 4.28 and 4.29).
The decreasing slope of the cutting force depends on the tool diameters. The small
tool diameter is, the gentler slope of the cutting force becomes.
Maximum Cutting Force in Thrust Direction
of End Milling Operations
16
14
12
Spindle
Speed
10
15,000 rpm
L
0
U --
CDOC
0.030 "
6
U
Feed Rate
4 -pm)
2
2
0
0.01
0.033
--
20
0.079
0.056
0.102
0.125
Tool Diameter (inch)
Figure 4.24 Cutting force characteristics with tool diameter and feed rate
For different depths of cut, the same results can be obtained from the analytical
cutting force model. When tool diameter becomes smaller, the cutting force is decreased
75
more rapidly. For all the tool diameters, the cutting force becomes a constant when the
tool diameter is over the critical tool diameter (see Figure 4.25, 4.30 and 4.31).
The critical tool diameter depends on the engagement angle. It can be obtained
from the analytical model. In the study case, it can be calculated by following formula.
b tan ;v
=tan(4.2.3)
_
Maximum Cutting Force in Thrust Direction
of End Milling Operations
14
12--
0Spindle
Speed
z
15,000 rpm
cs
Feed Rate
6 --
70 ipm
DOC
4
(inch)
2
a- 0.01
--
-o-
0.03
--- 0.05
0
0.01
0.033
0.079
0.056
0.102
0.125
Tool Diameter (inch)
Figure 4.25 Cutting force characteristics with tool diameter and depth of cut
The three dimensional graphics of the cutting force with tool diameter, spindle
speed, feed rate and depth of cut are presented in Figure 4.26 to 4.31.
76
Maximum Cutting Force in Thrust Direction
of End Milling Operations
50000
-
42000
1!
E
a.
Cutting
Force (N)
3400010.5-12
a.
U
9-10.5
7.5-9
26000
-6-7.5
C 4.5-6
3-4.5
O 1.5-3
f?
0 0-1.5
10000
0.01
0.033
0.079
0.056
0.102
0.125
Tool Diameter (inch)
Figure 4.26 2-D cutting force characteristics with tool diameter and spindle speed
Maximum Cutting Force in Thrust Direction
of End Milling Operations
121
Cutting
Force (N)
10.54.
Z
9
* 10.5-12
-
d*
9-10.5
7.5 - :w
37.5-9
U 6-7.5
4.
42000
03-4.5
34000
CJ 3 l
26000
..0
0.01 0.033 0.056
.18000
.
'"a
0.079 0.102
0 4.5-6
Spindle Speed
(rpm)
01.50 0-1.5
10000
0.125
Tool Diameter (inch)
Figure 4.27 3-D cutting force characteristics with tool diameter and spindle speed
77
Maximum Cutting Force in Thrust Direction
of End Milling Operations
120
100
Cutting
Force (N)
S80
-
314-16
312-14
3 10-12
-
\60
8-10
06-8
--
04-6
02-4
Q00-2
-
0.02
0.041
0.062
0.083
0.104
Tool Diameter (inch)
20
0.125
Figure 4.28 2-D cutting force characteristics with tool diameter and feed rate
Maximum Cutting Force in Thrust Direction
of End Milling Operations
z
Cutting
(N)
rForce
14
14-16
12
S10
O
LL-
8
S
g
-
120
-100
312-14
310-12
8-10
0 8-10
06-8
4 -00
4-6
Feed Rate (ipm)
-60
2
0
.1
0.02
0.041 0.062
__40__
.
.:.3.
0.083 0.104
0.125
02-4
0-2
20
Tool Diameter (inch)
Figure 4.29 3-D cutting force characteristics with tool diameter and feed rate
78
Maximum Cutting Force in Thrust Direction
of End Milling Operations
-
0.05
0.042
-
Cutting
Force (N)
0. 0 3 4
Z
12.25-13.5
U 11-12.25
S09.75-11
* 8.5-9.75
. 7.25-8.5
-.
-
0.018.75-
136-7.25
0 3.5-4.75
0.01
0.02
0.041
0.062
0.083
0.104
0.125
Tool Diameter (inch)
Figure 4.30 2-D cutting force characteristics with tool diameter and depth of cut
Maximum Cutting Force in Thrust Direction
of End Milling Operations
13.5---
Cutting
Force (N)
12.25
z
e
l-
12.25-13.5
11
11-12.25
2 9.75-11
8.5-
.s
7.25
0.0
6
4 Depth of Cut
(inch)
4.75
3.5
0.02
0.05
.0D
0.018
0.041 0.062
0020.083
®8.5-9.75
7.25-8.5
067.25.
° s-7.25
04.75-6
0 3.5-4.75
0.
0.104
0140.125
Tool Diameter (inch)
Figure 4.31 3-D cutting force characteristics with tool diameter and depth of cut
79
*
Cutting force characteristics with tool flute numbers:
Two-flute and four-flute 0.020" diameter tools have been studied. They are
operated in 50% overlapped climbing operations without tool run-out. 15,000 rpm spindle
speed, 70 ipm feed rate and 0.030" depth of cut are selected in the operations.
The profiles of the cutting force of the thrust direction are presented in Figure
4.32. The maximum cutting force of the four-flute tool is almost the half of one of the
two-flute tool. In the study case, the cutting force of the four-flute tool is 1.30 N and the
two-flute tool is 2.63 N. The four-flute tool has much smaller cutting force oscillation than
the two-flute tool, which is 0.65 N difference and 2.63 N difference, or 1:4.
Cutting Force in Thrust Direction
of End Milling Operations
3
2.5
-
Z2
v
LL
DOC
1.5
0.011"
0
Number
1
of Tool
Flutes
0.5
--
-4
0
-90
-60
-30
0
30
60
90
120
150
180
210
Tool Turning Angle (degree)
Figure 4.32 Cutting force characteristics with toot flute numbers
80
240
2
"
Cutting force characteristics with tool helix angle:
The tool helix angles from 25 to 75 degrees are studied. The cutting force almost
has a linear decrease when tool helix angle is increased (see Figure 4.33).
Maximum Cutting Force in Thrust Direction
of End Milling Operations
. 8
7
6
5
Z
40
LL
3
2
1
0
25
30
35
40
45
50
55
60
65
Tool Helix Angle (degree)
Figure 4.33 Cutting force characteristics with toot helix angle
81
70
75
4.3 Work-piece Surface Roughness and Precision
1.
Work-piece Surface Roughness
It is important for the machining operations to obtain the request surface quality of
the work-piece. Work-piece surface roughness is one of the surface quality indicant. It can
be derived from the developed analytical cutting force model by considering the tool
cutting edge tip profiles (see Figure 4.34).
edge
come:ing
{xuI rlmner
rros
of End Ie
P
)00
002
+0]n-y-Afr
hw
Figure 4.34 W orec surface
OptvWns
(p
e Spmad
rughnss
(4. 3.1)
conieigteto
y
utn
detppoie
Substituting t from the equations 3.1.1 to 3.1.2, the equations of the tool cutting
edge tip profiles become:
fx -
f[arccos(-) + 2z] }
2nT
r
Z
+Y,=r
where: z = 0, 1 for two-flute tools.
82
(4.3.1)
z = 0, 1, 2, 3 for four-flute tools.
Two equations can be derived from equation 4.3.1 by considering the
1
" path of
the first flute (z = 0) and the p" path of any flutes (included the first flute itself).
{x -
{x -
2nnr
2nf7r
[Arc cos(y)]}2 +y
r
2
= r2
(4.3.2)
[2(p + 7)r - Arccos( )]}2 + y 2 =r2
Z
r
(4.3.3)
where: p = 0, 1, 2, 3, ...
All the roots of the cutting edge profile can be solved from the equations 4.3.2 and
4.3.3.
y
=
r 1 -{4n[2(p +-)
4nr
Z
-(]}z
or:
y = r 1-[
where:
S
2r
(4.3.4)
(m - 9)]2
= 2 Arc cos(-)
7C
r
m = 1, 2, 3, ... until m < 4nr/f.
Because only working surface profiles are interested, y value is very close to r
value. That 6 = 0 is assumed. The formula becomes:
Y = r 1
(mf )2
2r
The work-piece surface roughness is:
83
S, = r-yI= r[1-
1
- (rf)2]
(4.3.5)
Considering that f,/(2r) is small, the formula can be approximated as:
Sr ~
(mf )2
')
(4.3.6)
4d
When m = 1, the formula 4.3.6 gives an approximate value for both conventional
and climbing milling. Actually, the work-piece surface roughness is a little smaller than
that approximate value in conventional milling and a little larger in climbing milling.
Conservatively, m = 1 can be used for conventional milling and m =4 for climbing
milling.
For conventional milling, the work-piece surface roughness is:
t
S ~
(4.3.7)
'4d
For climbing milling, the work-piece surface roughness is:
j2
S ~ '
(4.3.8)
'2d
The results have a similar form to the formula derived by Martellotti, mentioned in
Milton C. Shaw's "Metal Cutting principles" [431
If request surface roughness is Sr, the working conditions have to be selected as
following formulas.
For conventional milling:
f,
(4.3.9)
2Sr
For climbing milling:
84
f,<
2Sd
(4.3.10)
The work-piece surface roughness is proportional to the square of the feed per
tooth and inverse proportional to the diameter of the tool. The faster spindle speed and the
slower feed rate, the better quality work-piece surfaces would be obtained. In theory, the
work-piece surfaces could be manufactured to an absolutely smooth plane when a tiny
feed rate and fast enough spindle speed were given.
2. Work-piece Surface Precision
Work-piece surface precision is anther important surface quality indicant. It can be
derived from the analytical cutting force model by considering the tool run-out which is
the most important factor of the work-piece geometrical accuracy (see Figure 4.35)
Thol Cutter Profiles of End Mill Ma'ining Operations
TDoi
e diuftc}
f
2
C
d fa
C>W A:
'un
[00
Figure 4.35 Work-piece surface precision by considering the tool run-out
85
Considering the tool run-out cutting edge tip profile equations 3.2.1 and 3.2.2, and
the geometry of the tool run-out, the work-piece surface precision can be derived.
For two-flute tools, the work-piece surface precision is:
S, = Ir2 +r2 -2rro cos(rc -y) -r
(4.3.11)
For four-flute tools, the work-piece surface precision is:
S, =
r 2 +ro - 2rrM -r
(4.3.12)
where: M = Max{ Abs[ cos( n - y)], Abs[ cos(
7r/2 + y)]}
When the tool run-out angle is parallel to the tool cutting edges (y = 0), the workpiece surface has the lowest precision. When the tool run-out angle is perpendicular to the
tool cutting edges (y =
cutting edges (y =
7/2)
7/4)
for two-flute tools or 45 degree to the two adjacent tool
for four-flute tools, the work-piece surface has the highest
precision.
If the request surface roughness is Sp, the tool run-out has to be considered as the
following formulas.
For two-flute tools:
r
r cos(r - y)+ J[r cos(r - y)]2 +(r + S,) 2 -r
2
(4.3.13)
For four-flute:
ro
-rM + (rM)2 + (r + S,) 2 - r 2
(4.3.14)
Usually, the run-out angle can be considered as
7/2 for two-flute
four-flute tools. Conservatively, the run-out angle can be considered as 0.
86
tools or
7/4 for
Chapter V
Model Based Monitoring of Micro-End-Milling Operations
Genetic algorithm based optimization method is proposed for the monitoring of
micro-end-milling operations. It is possible to monitor tool wear, breakage, run-out,
cutting angles and cutting conditions by using this approach. The sum of the difference of
cutting forces obtained from the monitoring signals and the analytical cutting force model
is considered as the objective function. It is optimized by a genetic algorithm program
(GATooI) to search the fittest variables of the analytical cutting force model. It has been
proved that information included in the cutting force signals can be identified by the
proposed method. The tool wear, run-out, cutting angles and cutting conditions of microend-milling operations can be estimated in a few evolution generations with an acceptable
error. The GATool program has a fast reaction and accurate results that can be applied to
the on-line monitoring of micro-end-milling operations. The performance of the genetic
algorithm based monitoring method is presented in this chapter.
5.1 Tool Breakage Detection
In micro-end-milling operations, it is hard to see or heard when the tool is broken
because of its tiny size. Tool breakage monitoring methods can avoid wasting machining
time, tools and work-pieces. It can stop the machining operation immediately and warn the
operator to change the tool or to adjust the tool working conditions to extend the tool life
until the task is completed.
87
The tool breakage could be caused by many different reasons that included
unsuitable working conditions, dulled and damaged tool cutting edges, tool cutting edges
stuck with the milted chips and so forth. To detect the tool breakage and to understand its
reason, two most commonly used signals are acoustic emission (AE) and cutting force. In
this study, acoustic emission (AE) is used to monitor the tool breakage, and the cutting
forces are used to explain the reason of the tool breakage.
1. Detecting tool breakage by monitoring machining acoustic emission
[27.30]
Acoustic emission signal characteristics change with the tool conditions. The signal
characteristics are different when the operation and tool (wear, breakage) conditions are
changed. In this section, a new method is proposed to detect tool breakage without giving
false alarm when the tool leave the work-piece.
In the experiments, the AE sensor was attached on the work-piece directly. For
analog signal processing, the DME Corporation's SWAN 3000 system was used. The AE
signal was filtered at 40 KHz modulated and sampled by a Nicolet 310 digital oscilloscope.
Two-flute high speed steel end mill with 0.015" diameter was used to machine
mild steel work-piece. The cutting conditions were 30,000 rpm spindle speed, 0.24 ipm
feed rate and 0.016" depth of cut in the experiment I, and 3,000 rpm spindle speed, 0.9
ipm feed rate and 0.005" depth of cut in the experiment II. The AE signals at the both
experiments are presented in Figure 5.1 to 5.4.
To distinguish the tool breakage from leaving the work-piece, two algorithms are
developed.
88
ACOUSTIC EMISSION TESTING IN END-MILL
MACHINING OPERATIONS
(experiment I: tool broken case)
0.5
0.4
0.3
0.2
w
0.1
0
-0.1
-
-0.2
-0.3
.
0
0.25
0.5
0.75
1
1.25
1.5
1.75
Time (sec.)
Figure 5.1 AE activity of micro-end-milling experiment I, case 1
ACOUSTIC EMISSION TESTING IN END-MILL
MACHINING OPERATIONS
(experiment I: tool left from workpiece case)
0.5
0.4
0.3
0.2
0.1
0
01
-0.2
0
41
0.25
I
0.5
0.75
1
Time (sec.)
1.25
1.5
1.75
Figure 5.2 AE activity of micro-end-milling experiment I, case 2
89
ACOUSTIC EMISSION TESTING IN END-MILL
MACHINING OPERATIONS
(tool broken case 1)
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
-0.6
w 0.4
-0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Time (sec.)
Figure 5.3 AE activity of micro-end-milling experiment II, case 1
ACOUSTIC EMISSION TESTING IN END-MILL
MACHINING OPERATIONS
(tool left from workpiece case 1)
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
p0.6
-0.4
Q
0.2
-1.0-.
-0.42
-0.6
-1.0
-1.2
-1.4
-1.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Time (sec.)
Figure 5.4 AE activity of micro-end-milling experiment II, case 2
90
Method 1: Tool broken with a very sharp spike signal
Step 1. Calculate the average Xa and variation X~ of the first 150 data.
Step 2. Take the following data X; and compare it with the average Xa. If X; > Xa + X g, the
tool was broken, otherwise update the average Xa and variation X~ by considering X;.
Step 3. If Xv> X
0 7,,
1
the tool is cutting normally, otherwise it is leaving from the work-piece.
If the tool was cutting normally, go back to step 2.
Xf 1.,i
and Xih can be decided by studying the AE data pattern.
Method 2: Tool broken with a non-significant spike signal
Step 1. Calculate the average Xa of the first 150 data.
Step 2. Take the following data X; and compare it with the average Xa. If X; < Xa - Xi0o, go to
step 3, otherwise update the average Xa by considering X; and then repeat step 2.
Step 3. Take the following 150 data. Create 15 sections with 10 data each. For each section j
obtain the linear interpolation between the most-left and most-right points:
=
Xj*10.
X
*10
+
i*
(X 6 .1)* 10 - X
* 10)
/ 10
where: i = 0 ~ 9
j=0- 14
Step 4. Estimate the total error of the 150 data
14
9
E=~
j=0
X.0;
2
~
'.0;2
1=0
Step 5. Compare the error with two reference values EnOrma1 and Eba
ge, which can be decided
by studying the AE data patterns. Make the decision by the following rules:
91
E < Enmni
The tool is cutting normally.
Enosai
E ? Eacge
The tool is leaving the work-piece.
Ex,
<E
The tool was broken.
If the tool was cutting normally, go back to step 2.
In case the tool is broken or
leaving the work-piece, stop the process.
Both the algorithms detected tool breakage in all the tests without any error. The
results will be discussed in Chapter VII (Figure 7.3.1 and 7.3.2).
The AE based tool breakage detection methods can be easily implemented and
require relatively simple instrumentation. They are most of the time reliable, however, if
unexpected noises are created in the system because of friction they may fail.
2. Detecting tool breakage by monitoring cutting force
[31]
The characteristics of the cutting force change with tool wear. When the cutting
force increase beyond a critical value, miniature tools break. The objective of the method
in this section is to identify the tool breakage.
In the experiments, the work-piece was installed on a Kistler 9257B dynamometer
that was attached to the table. Two-dimensional cutting force signals were collected by a
Nicolet 310 digital oscilloscope through a Kistler three channel charge amplifier. The
experiment setup is presented in Chapter VI.
Two-flute high speed steel end mill with 0.015" diameter was used to machine
mild steel and aluminum work-pieces. The working conditions were 30,000 rpm spindle
92
Tool Cutting Force of End-mill Machining Operations
(complete tool life cycle, mild steel workpiece case)
3
2.5
2
1.5
Z 0.5
v 0
-1
-1.5
-2
-2.5
1.0
2.0
3.0
Tool lift (inch)
tool broken
Figure 5.5 Tool cutting force of micro-end-milling experiment I
Tool Cutting Force of End-mill Machining Operations
(complete tool life cycle, aluminum workpiece case)
5.0
4.5 4.0
3.5
0.5
2.5
5.0
7.5
12.5
10.0
15.0
17.5
tool broken
Tool life (inch)
Figure 5.6 Tool cutting force of micro-end-milling experiment II
93
speed, 0.004" depth of cut, 1 ipm feed rate for the mild steel work-piece and 2 ipm feed
rate for the aluminum work-piece. The results are presented in Figure 5.5 and 5.6, in
which the tool life is segmented in 5 and 9 different segments.
A high frequency cutting force signal with a lower frequency vibration can be
observed in the figures. The high frequency signal represents the tool cutting force, whose
frequency depended on the machining spindle speed. The lower frequency variation is
created by the tool vibration. The vibrations are created due to the inconsistency in the
feed rate and the non-homogeneous characteristics of the work-piece.
To detect the tool breakage and estimate its reason, the following five statistical
methods were used to process the cutting force data.
1. Cutting force average
Xa'0 =
1
100
100 i
the first 100 data
X
X, = [(i -1)Xa''
after first 100 data
+ X,)]/i
(5.1.1)
where: X; is the if' cutting force data.
2. Cutting force moving average
X,'
X,
00 =
X, 00
the first 100 data
1
= [(I - 1)Xa -' X
00 +
X)] /100
after first 100 data
(5.1.2)
3. Cutting force variation
1
X
X,'
100 1
100
(X -
X 0 0 )2
the first 100 data
[-1)Xvi +(X - X ) 2 ]/
after first 100 data
94
(5.1.3)
4. Cutting force moving variation
X,, 1 = X, 00
X1 = [(i -1)X,,'
the first 100 data
+(X - X,')
2
]/i
after first 100 data
(5.1.4)
5. Variation of cutting force moving averages
X,
* =0
X,
[(
the first 100 data
-100)Xa.,7 1
+ (X,,' -
X,') 2 ]/(i -100+1)
after first 100 data (5.1.5)
The cutting force variation is the main indictor of the tool breakage. When it
becomes larger than a tool breakage critical value, the tool would create a poor machined
surface and break very soon. The cutting force moving variation is related to the tool wear
level. If it is larger than a tool wear critical value, the tool is really worn and shouldn't be
used any more. The cutting force moving average and its variation provides the tool
vibration information. The vibrations could cause rough surface, short tool life or tool
breakage. If the variation of the cutting force moving average is larger than a tool
vibration critical value and the cutting force moving variation is still less than the tool wear
critical value, the tool life could be extended by reducing the feed rate or cleaning it
immediately.
The test results of two experimental cases are presented in Figure 5.7 to 5.14. The
0.015" diameter tool used with the mild steel work-piece had almost 3.5" tool life. The
0.015" diameter tool cutting the aluminum work-piece had almost 20" tool life.
During the machining of mild steel work-piece, the cutting force average was
remained around 0.2 N (see Figure 5.7 and 5.8) and moving average was remained around
+0.2 N. The tool worked in a good condition with a very little vibration. The cutting force
95
was gradually increased while it was worn. The tool cutting force variation was gradually
increased from 0.2 to 1.0 (see Figure 5.10) until reached the tool breakage critical value.
The reason of the tool breakage was the tool wear.
Compared to the mild steel work-piece, the experiment data of the aluminum
work-pork-piece had very different characteristics.
The cutting force average was
remained around 2.2 N (see Figure 5.11 and 5.12). The cutting force variation remained in
the same level 0.15 N (see Figure 5.13 and 5.14). The tool cutting force changed very
little, but its vibration continuously increased. The moving average changed from a small
vibration ±0.1 N for the new tool (see Figure 5.11) to a large vibration +1.0 N for the
worn tool just before its breakage (see Figure 5.14). The significant change was observed
around 2300
data point (see Figure 5.14). The variation of the cutting force moving
average rapidly increased. This increase caused the cutting force variation to increase over
the tool breakage critical value.
The main reason of the tool breakage during the machining the aluminum workpiece is the vibration, not the tool wear. Since aluminum has a lower milting point, some
melted chips might have stuck on the tool. The cutting edges lost their sharpness and
vibrations were created. Finally tool life could be extended if the cutting edges were
allowed to be cleaned down by reducing the feed rate.
Tool breakage and vibration critical values of the proposed algorithms should be
determined from the experimental study.
96
New Micro-tool Cutting Force Average
(mild steel work-piece)
1
0.8
0.6
z0.4
W0.2-0-average
S0
--
moving
ave.
a)
Q
-0.4
-0.6
-0.8
-1
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.7 New tool cutting force average of experiment I
Micro-tool Cutting Force Average Before Breakage
(mild steel work-piece)
1
0.8
0.6
_
0.4
0.2
0
U
-average
-moving
0
-0.2
-0.6
-0.8
-1
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.8 Tool cutting force average before breakage of experiment I
97
ave.
New Micro-tool Cutting Force Variation
(mild steel work-piece)
1.2
1
0
U_
0.8
--variation
o0.6
- moving var.
-var.of
moving ave.
o
0.4
0.2
0
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.9 New tool cutting force variation of experiment I
Micro-tool Cutting Force Variation Before Breakage
(mild steel work-piece)
1.2
1
2 0.8
0
L-
-variation
r0 0.6
var.
-moving
-var.of
moving ave.
o
> 0.4
0.2
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.10 Tool cutting force variation before breakage of experiment I
98
New Micro-tool Cutting Force Average
(aluminum work-piece)
43.5
3
U
w2.5
2
-average
moving ave.
2
0 1.5
1
0.5
0
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.11 New tool cutting force average of experiment II
Micro-tool Cutting Force Average Before Breakage
(aluminum work-piece)
4
3.5
3
u 2.5
-average
'o
2 ---
moving ave.
ci
c
1.5
1
0.5
0
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.12 Tool cutting force average before breakage of experiment II
99
New Micro-tool Cutting Force Variation
(aluminum work-piece)
0.5
0.45
0.4
a> 0.35
LL
0.3
-variation
o
- moving var.
moving ave.
S-var.of
0.2
Ca
> 0.15
0.1
0.05
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.13 New tool cutting force variation of experiment II
Micro-tool Cutting Force Variation Before Breakage
(aluminum work-piece)
0.5
0.45
0.4
U) 0.35
L.
0.3
o
0.25
o
-variation
moving var.
-var.of
moving ave.
0.2
> 0.15
0.1
0.05
0
101
601
1101
1601
2101
2601
3101
3601
Data
Figure 5.14 Tool cutting force variation before breakage of experiment II
100
5.2 Tool Wear Estimation
Many researchers have studied the characteristics of cutting force to relate them to
tool wear. To simplify the estimation algorithm, to reduce the cost of the instrumentation,
and to increase the reliability of the system, the following assumptions can be made:
Assumption 1: The tool works in an identical cutting condition.
Assumption 2: The tool cutting force depends on the tool wear only.
In this section, the relationship of cutting force and tool wear will be studied and a
tool wear estimation method will be proposed.
1. Relationship of tool wear and cutting force
[421
It has been known that cutting forces of micro-end-milling operations increase
with tool wear. For most of metals, the cutting forces can be measured with conventional
dynamometers. For some non-metal material work-pieces, like POCO-3 and POCO-C3,
the small cutting force is almost at the same level with the noises created by the inertia
force of the dynamometer. To evaluate tool condition, the cutting forces were collected
while an aluminum work-piece was cut periodically.
The experiments were performed on a 3-axis 15,000 rpm Fadal CNC Machine in
Engineering Prototype Center of Radio Technology Division of Motorola Inc. A POCOC3 work-piece was attached onto a Kistler 9257B dynamometer that was installed on the
table of the machine tool. On the top of the work-piece, a small aluminum test work-piece
was attached. The tool cutting force signals were monitored and collected by a Nicolet
310 two-channel digital oscilloscope through a Kistler three channel charge amplifier. To
101
control the experimental machining operation, the CNC machine was programmed by
using Smart CAM Version 10 Production Milling software. The experimental setup will be
presented in Chapter VI.
Two different work-pieces, steel and POCO-C3, were tested. In the machining of
steel work-pieces, cutting force was collected during the machining operations. Two-flute
carbide end mills with 0.030" diameter were used in the experiments. The working
conditions were 30,000 rpm spindle speed, 2.5 ipm feed rate and 0.015" depth of cut for
the experiment I; and 20,000 rpm spindle speed, 1.25 ipm feed rate and 0.0225" depth of
cut for the experiment II. The experimental results are presented in Figure 5.15 and 5.16,
which includes 14 and 10 data points starting from new tools and ending until they were
broken. The tools had around 42" and 33" tool life in the experiment I and II respectively.
To evaluate the cutting force characteristics and tool wear relationship of nonmetal POCO-C3 work-piece, periodic test cuttings were done on the aluminum test workpiece during the machining of POCO-C3. Two-flute carbide end mills with 0.030"
diameter were used. The working conditions of the POCO-C3 machining operations were
15,000 rpm spindle speed, 20 ipm feed rate and 0.030" depth of cut. The working
conditions of the machining of the aluminum test work-piece were 5,000 rpm spindle
speed, 5 ipm feed rate and 0.015" depth of cut. The experimental results are presented in
Figure 5.17, which includes 9 data points starting from a new tool and ending until it was
broken. The tool had around 1350" tool life. That non-metal material work-piece had an
excellent machinability.
102
Monitoring Tool Wear by Cutting Force(thrust direction)
two flute 0.030" diameter carbide end mill, steel work-piece
45
40
Zv
v 35
-Experiment
LL
I
Experiment II
-
30
U
25
20
0
10
20
30
40
50
Tool Lift (inch)
Figure 5.15 Monitoring of tool wear by the thrust direction cutting force
Monitoring Tool Wear by Cutting Force (feed direction)
two flute 0.030" diameter carbide end mill, steel work-piece
35
30
--
25
-Experiment
o20
I
-- Experiment II
c15-
U 10
5
0
0
10
30
20
40
50
Tool Life (inch)
Figure 5.16 Monitoring of tool wear by the feed direction cutting force
103
Monitoring Tool Wear by Cutting Force
40
35
30
25
25 -
-Feed
L. 20
-Thrust
15
10
5
0
0
200
400
800
600
1000
1200
Tool Life (inch)
Figure 5.17 Indirect monitoring of tool wear by the cutting forces
104
direction
direction
2. Estimation of tool wear by using genetic algorithms
Based on the tool wear and cutting force relationship study, the empirical tool
wear model is proposed in the following format.
Fmax
=
C1 + (C
2
* L )c3
(5.2.1)
where: Fmax is tool maximum cutting force (N)
L is tool life (inch)
C 1, C2 and C 3 are coefficients.
In the empirical tool wear model, three coefficients have their physical meaning. C 1
is the basic cutting force level, which depends on the working conditions of micro-endmilling operation. C 2 is the tool wear gradient, which depends on the cutting conditions,
the tool and work-piece materials. A small C 2 indicates slow progress of the wear. C3
presents how fast the tool is broken when the cutting force is above a critical level. The
harder the work-piece material is or the more uncomfortable cutting conditions the tool
has, the larger C 3 is.
From the experimental data of the tool wear, the coefficients of the proposed tool
wear model can be found by using the genetic algorithms (see Chapter II). The program
GATool (Genetic Algorithm Research Tool) used in the research was developed in 1998
and successfully applied to the tool cutting condition monitoring.P[1 GATool is used to
search the optimal fitting coefficients of the tool wear model. The sum of the difference
between the experimental cutting force data and the cutting force obtained from the
developed analytical model is used as the optimal objective function.
105
Objective function:
Min(E) =
F
'" (i)- F " "" (i)I
5.2.2
where: E is the average absolute error.
N is the number of the experimental data.
F""' (i) and Fenmat'ed (i) are the experimental and estimated maximum
cutting forces in the i" tool life.
In the genetic evolution procedures, the 30-bit binary coding is used for three
coefficients by assigning 10 bits for each one. The population size was selected as five.
Mating pool size was two versus two and one child from each couple. The uniform
crossover (with 0.5 probability), jumping mutation (with 0.1 probability), creeping
mutation (with 0.05 probability) and elitism are chosen. The 14 data sets of the tool wear
experiment I (see Figure 5.15, experiment I) were used in the study.
The optimal coefficients of the tool wear model were found in the 5001 generation
with ±1.1 N or 3.3% error.
C 1 = 30.968
C 2 = 0.0423
C 3 = 4.352
The genetic evolution procedure of the tool wear model is presented in Figure
5.18. The empirical tool wear model is presented in Figure 5.19.
106
Genetic Evolution Procedure
40
35
30
25
20
o 15
-
10
0
15
-C1
-C2
-C3
0
-5
x 100
-Fitness
-10
0
50
100
150
200
250
300
350
400
450
500
Generation
Figure 5.18 Genetic evolution procedure of the tool wear model
Tool Wear Empirical Model
2 flute 0.030" diameter carbide end mill, steel work-piece
45
40 -
35
Experimental Data
Tool Wear Model
30
U
25
20
0
5
10
15
20
25
30
Tool Life (inch)
Figure 5.19 An empirical tool wear model
107
35
40
45
3. Tool wear estimation by using neural network forecasting model
[39][44][451
Back-propagation neural network with time series type input (see Chapter II) is
proposed to estimate the tool wear. The program NNTool (Neural Network Research
Tool) used in the studies was developed in 1995 and modified in 1996. Its forecasting
capability has been proved in many cases.[15 '
In this study, the two input and one output back-propagation neural network was
used. The inputs were the present and one-step prior cutting force data and output was the
one-step ahead cutting force data. A three-layer neural network with seven hidden nodes
was designed. The learning rate and momentum factor were selected as 0.15 and 0.9
respectively. Out of the 14 data sets of the tool wear experiment I (see Figure 5.15,
experiment I), The 12 data sets were used for the training of the neural network.
The tool wear estimation neural network model had been generated in 10,000
iterations. Compared to the empirical tool wear model and the experimental data, the tool
wear estimation model had 0.4% and 3.3% error respectively. The results are presented in
Table 5.1 and Figure 5.20. The future cutting force could be forecast by the tool wear
estimation neural network model. By comparing the estimated cutting force to the
maximum allowable cutting force, the tool life could be estimated.
The tool wear coefficient KW of the analytical cutting force model can be obtained
by using the following equation:
(5.2.3)
KW = Fmax / C 1
108
Cutting
Force
Tool Life
Experimental
Empirical
Estimation
(inch)
Data
Model
Model
3
32.200
30.968
6
9
12
15
18
21
24
27
30
33
36
39
42
Average
30.240
32.040
31.640
30.220
30.120
31.520
32.280
31.640
34.400
33.000
41.120
38.320
43.200
33.710
30.971
30.983
31.020
31.106
31.273
31.565
32.036
32.751
33.788
35.238
37.203
39.802
43.164
33.705
Percentage
____________
(N)
Empirical
Estimation
Model Error Model Error
Error between
Both Models
1.232
31.204
31.215
31.252
31.346
31.542
31.907
32.530
33.534
35.061
37.238
40.036
43.107
29.284
-0.731
1.057
0.620
-0.886
-1.153
-0.045
0.244
-1.111
0.612
-2.238
3.917
-1.482
0.036
1.097
0.836
0.425
-1.032
-1.226
-0.022
0.373
-0.890
0.867
-2.061
3.882
-1.716
0.093
1.119
-0.221
-0.195
-0.146
-0.072
0.023
0.129
0.221
0.255
0.176
-0.034
-0.234
0.057
0.147
3.26%
3.32%
0.44%
_____
Table 5.1 Results of the tool wear estimation model
Tool Wear Estimation Model
2 flute 0.030" diameter carbide end mill, steel work-piece
45
40 -
v35
*
Experimental Data
Empirical Model
Model
-Estimation
LI.-
~30O
U
25
20
0
5
10
15
20
25
30
35
Tool Life (inch)
Figure 5.20 Comparison of the tool wear model
109
40
45
5.3 Tool Run-out Estimation
The maximum cutting force of micro-end-milling operations is very different
depending on whether the tool has run-out or not. A small tool run-out could significantly
increase cutting forces and not favor the surface finish.
From the characteristics of the cutting force, existence of run-out can be easily
understood. The maximum cutting forces created by each cutting edge are the main
indicators. If they are the same, there is no run-out. If they are different, the tool is
working with run-out. The run-out of two-flute end-mill can be easily estimated from the
maximum cutting forces of each cutting edge.
Let's consider x-coordinate for the feed direction and y-coordinate for the thrust
direction. The tool run-out ro is the distance between the tool center and tool turning
center, and tool run-out angle y is the angle between the tool run-out and y-axis. In other
words, the tool run-out in the x direction and in the y direction can be calculated by ro sin y
and r0 con y. The maximum cutting force is a function of tool run-out and its angle if the
other machining operation conditions are remained unchanged. It can be expressed as:
Fmax
=
f(ro, y)
According to the discussion of the cutting force characteristics with tool run-out
and angle (see Chapter IV), the tool run-out and angle can not be recognized by only one
maximum cutting force value because the maximum cutting force is a multiple value
function of the tool run-out and its angle. The maximum cutting forces of both feed and
thrust direction are needed for the estimations of tool run-out and its angle by an optimal
objective function.
110
Min (E1)=
(tFi'""'
4
-FFsd'ate''"+ Fa'""'
Xmax m
X max2
axax
-F'"+mated
e
+|Factual
X max 2
Ymax1
-Fes'mated
+|Factual
Y max2
Ymax
-
Fes'mated
Ymax 2
)
(5.3.1)
where: E is an absolute error.
Fmxl, Fma"l
FX""
and F"""2 are the monitoring maximum cutting
forces in feed and thrust directions of both cutting edges. It is assumed that
cutting force value of the first cutting edge is larger than the value of the
second cutting one.
Fe"""ted
,Fe"daed,
Fes'a ted
and Fe'"ted are the
estimating maximum
cutting forces calculated by the analytic cutting force model in feed and
thrust directions of both cutting edges.
The genetic algorithm (see Chapter II) was used to minimize the absolute error of
the optimal objective function. 30-bit binary coding was used for individuals that include
two factors: tool run-out and its angle (15 bits for each ). The population size was selected
as five. Mating pool size was two versus two and one child from each couple. The uniform
crossover (with 0.5 probability), jumping mutation (with 0.1 probability), creeping
mutation (with 0.05 probability) and elitism are chosen.
Tool run-out estimation program is included in the MOGART program (see
Chapter VIII). The tool run-out and its angle are estimated according to the given tool
geometry, cutting conditions, measured feed and thrust direction maximum cutting forces.
The estimated maximum cutting forces can be easily obtained from the analytical cutting
force model (see Chapter III). The program estimates the tool run-out and its angle, and
111
improves their accuracy generation by generation until they reach the optimal one. The
procedure of the tool run-out estimation is presented in Figure 5.21. The program user
interface is presented in Figure 8.21 of Chapter VIII.
Tool Run-out Estimation
Program
Tool Geometry And
Cutting Conditions
Analytical Cutting
Force Model
Simulating Or Experimental
Cutting Force Data
Genetic
Algorithm
Tool Run-out
And Angle
Figure 5.21 Tool run-out estimation procedure
The performance of the tool run-out estimation program was evaluated on a test
case. Simulation data was generated by using a two-flute end-mill with 0.020 inch
diameter and 45 degree helix angle. The working conditions were 15,000 rpm spindle
speed, 120 imp feed rate, 0.010 inch depth of cut, 50% overlapped climbing milling
operations. The material coefficient was considered 80,000 N/inch2 . The tool had a 0.001
inch tool run-out with 30 degree run-out angle. The cutting force variation is presented in
Figure 5.22.
112
The maximum cutting forces in the feed and thrust directions of both cutting edges
are easily obtained from the cutting force profiles. They are:
F"""'
1 = 2.75 N
F,,"
= 4.22 N
F,"""2 = 0.45 N
F""'
= 1.69 N
Cutting Force of Climbing Milling
with Tool Run-Out
5
4 --
3
2
U
L°0
0
r
CI
~
0
0D
C
r-
0
1-
0
W~
0
10
N.
m
)
0
0
0
Cn
N
W
r0
0
CO
0
0
0 O~
Q1
O~
D
W
O
0
I-.
r
0
CD
W
N
-2-
--3
-4
-Feed
Direction
- Thrust Direction
Tool Turning Angle (degree)
Figure 5.22 Cutting force of climbing milling with tool run-out
In the genetic evolution procedures, the absolute error level of the objective
function was selected as 0.005 or 0.5%. The desired error level was reached in the 210"'
generation with less than 0.32% error. The estimated tool run-out and its angle were
0.00099 inch and 29.26 degree. Their errors were less than 1% and 2.5%. The variation of
the tool run-out estimation during the optimization process of the genetic algorithm is
presented in Figure 5.23.
113
Genetic Evolution Procedure
2
a)
1.5
C,
0
0
0
1-
*C 0.5
9
=
0
30
60
90
120
150
180
2 0
0
W -0.5
Run-out
-Run-out
angle
-- Absolute Error
-1
Generation
Figure 5.23 Genetic evolution procedure of tool run-out estimation
The accuracy and efficiency of the genetic algorithms were found satisfactory for
this application. Accuracy and the computational time were related in reverse. It is found
that 0.5% to 1%
absolute error level is enough to obtain the required accuracy in very
short time for most of the cases.
114
5.4 Cutting Angle Monitoring
[19]
The tool cutting angle of micro-end-milling is one of the interesting cutting
conditions to be monitored. It is difficult to evaluate the sensory data to estimate the tool
cutting angle because of the small tool diameter and continuous changed cutting angle in
complicated machining profiles. Considering cutting force characteristics, it is proposed to
compare the profile of the on-line recorded cutting force signals with one of the analytical
estimated cutting force to identify the tool cutting angles. If the tool working conditions
are unchanged in the end milling operations, the cutting force profile is only depended on
the cutting angles.
The tool cutting angles are considered as entry and exit angles, which include all
the cases of the climbing and conventional end milling operations. Two cases, 50%
overlapping conventional and climbing milling, are presented in Figure 5.24.
Work-piece
Feed
Tool
Tool
Feed
Work-piece
Case 1: Entry angle: 0 degree
Case 2: Entry angle: 90 degree
Exit angle: 90 degree
Exit angle: 180 degree
Figure 5.24 Tool cutting angles of end milling operations
115
The profile of tool cutting force in the either feed or thrust direction can be used to
identify the tool cutting angle. In the research, the resultant cutting force profile was
chosen. An optimal objective function was introduced into the identification of tool cutting
force profile. It is:
N
Mn(E))=
(F," ""(a)- Fesmated(0 2
1
5.4.1)
where: E is the square error.
N is the number of computing points in a tool turning cycle (360 degree).
F """'(i) and
F''naed
(i) are the monitoring and estimated resultant
cutting forces in the i' time or tool turning angle.
The genetic algorithm (see Chapter II) was applied to minimize the error of the
optimal objective function. In the genetic evolution procedures, the 30 bits binary coding
was used for individuals that include two factors, tool cutting entry and exit angle, with 15
bits each. The population size was selected as five, mating pool size as two versus two and
one child from each couple. The uniform crossover (with 0.5 probability), jumping
mutation (with 0.02 probability), creeping mutation (with 0.04 probability) and elitism
were chosen.
The procedure of the tool cutting angle identification is presented in Figure 5.25.
The tool cutting angles were estimated automatically according to the given tool
geometry, cutting conditions, actual and estimating cutting force profiles. The actual and
estimated maximum cutting forces were able to be easily obtained from the on-line
recorded data and the analytical cutting force model (see Chapter III). The estimated tool
116
cutting angles were improved generation by generation during the genetic evolution
procedure until reach the optimal one.
Tool Cutting Angle
Identification Program
Tool Geometry And
Cutting Conditions
Analytical Cutting
Force Model
Simulating Or Experimental
Cutting Force Data
Genetic
Algorithm
Tool Cutting
Angle
Figure 5.25 Tool cutting angle identification procedure
Four simulation cases were selected to test the performance of the tool cutting
angle identification program. Two-flutes 0.020" diameter tool with 45 degree helix angle,
15,000 rpm spindle speed, 120 imp feed rate, 0.010 inch depth of cut and 80,000 N/inch 2
material coefficient were selected in the micro-end-milling operations.
Case 1: 0° entry angle and 900 exit angle (50% overlapping conventional milling).
Case 2: 900 entry angle and 1800 exit angle (50% overlapping climbing milling).
Case 3: 1350 entry angle and 180° exit angle (85% overlapping climbing milling).
Case 4: 450 entry angle and 1350 exit angle.
The results of four testing cases are presented in Table 5.2.
117
Actual
Value
Case 1
Case 2
Case 3
Case 4
Estimating
Value in 20th
Error
in 20th
Estimating
Value in 120th
Error
in 120th
Generation
Generation
Generation
Generation
Entry Angle
0
0.170
0.027
0.001
0.000
Exit Angle
1.571
1.592
0.003
1.571
0.000
Fitness
0
-0.036
0.036
0.000
0.000
Entry Angle
1.571
1.404
0.027
1.545
0.004
Exit Angle
3.142
3.129
0.002
3.142
0.000
Fitness
0
-4.732
4.732
0.000
0.000
Entry Angle
2.356
2.377
0.003
2.400
0.007
Exit Angle
3.142
3.129
0.002
3.142
0.000
Fitness
0
0.000
0.000
0.000
0.000
Entry Angle
0.785
0.847
0.010
0.835
0.008
Exit Angle
2.356
2.254
0.016
2.353
0.000
Fitness
0
-0.663
0.663
-0.021
0.021
Table 5.2 Results of the tool cutting angle identification
In all of the studied cases, the tool entry and exit cutting angles were estimated in
less than 20 generations with less than 3% error and in 120 generations with less than 1%
error.
The identification program has a good performance by using genetic algorithm. It
has fast reactions and accurate results for the on-line monitoring. The more high sampling
resolution is selected, the more accuracy results will be obtained. It will take a little more
running time to find a qualified generation. It is found that 72 points per tool turning cycle
are enough to obtain the required accuracy with the fast reaction in many testing cases.
118
5.5 Cutting Condition Monitoring
The most interesting cutting conditions are spindle speed, feed rate and depth of
cut. They can be obtained by monitoring the cutting force signals in micro-end-mill
operations.
The spindle speed of micro-end-mill operations can be directly obtained from the
cutting force signals. The method to monitor the spindle speed is to take a cutting force
value from the cutting force signal and find the same cutting force value after one cutting
cycle (see Figure 5.26). The interval time T between these two points can be used to
calculate the spindle speed by formula 5.5.1.
n = 60
5.5.1
T
Thrust Direction Cutting Force of Climbing EndMilling with Tool Run-out
4
3.5
Operation Condition:
0.020 " diameter tool
with two flutes and
T
450helix angle.
3
15,000 rpm spindle
speed.
2.5 -0
U.
70 ipm feed rate.
0.010" depth of cut.
2
50% overlapping.
130,000 Nuin. 2 material
coefficent.
1.5
O
0.001" tool run-out
1
with 600 angle.
0.5
0
0
1
2
3
5
4
6
7
Time (ms)
Figure 5.26 Spindle speed identification
119
8
The feed rate and depth of cut can be obtained by using the same method as
monitoring cutting angle, which is to compare the profile of the on-line recorded cutting
force with one of the analytical estimated cutting force. The only difference is to use feed
rate and depth of cut instead of entry and exit cutting angles. The genetic algorithm also
can be applied to find the fittest feed rate and depth of cut. The optimal objective function
has the same form as the formula 5.3.1. The procedure of the method is presented in
Figure 5.27. The feed rate and depth of cut can be estimated automatically according to
the given tool geometry, cutting angles, actual and estimating cutting force profiles. The
actual and estimated cutting force profiles can be easily obtained from the on-line cutting
force recording and the analytical cutting force model (see Chapter III).
Tool Cutting Condition
Identification Program
Tool Geometry And
Analytical Cutting
Cutting Angles
Force Model
Simulating Or Experimental
Cutting Force Data
Genetic
Algorithm
Parameters of
Cutting
Condition
Figure 5.27 Tool cutting condition identification procedure
120
5.6 Optimal Working Condition Selection
In micro-end-milling operations, it is important to select the tool optimal working
conditions. Because the tiny tools are very easily broken, the conservative selections of the
tool working conditions would cost longer machining time, otherwise the unsuitable
selections of the tool working conditions would make change the tools frequently that
wastes the machining time too. It is very difficult for operators to select the optimal
working conditions in so many different types of tools, work-pieces and different
machining tasks.
In the research, the tool working conditions were optimized based on the minimum
machining time, that is to find the maximum feed rate that is able to meet the tool life
requirement in the specific machining task. It is known how many cutting inches are
required in the specific machining task. Approximated tool life can be estimated depended
on how many tools will be used in the task. Referred to tool life estimation (5.2), the
maximum feed rate can be determined with the other possible working conditions (for
example, maximum spindle speed of the machine tool) by the analytical cutting force
model.
The genetic algorithms were used to optimize the tool working conditions with the
analytical cutting force model. The maximum cutting forces of the cutting force profiles,
which were got from the analytical model and estimation, were used for the optimal
objective function and conditions as the following.
Objective function:
Min(E)
=
(IFy""
2 FXmax
2
-_ F""oabl
X max
- Fl"owabl)
F+Ies"'mated
Y max
Y max
5.6.1
Conditions:
F7'm'ed
< F""o"le
5.6.2
Fal"wa'"
5.6.3
Fest'm"''d <
where: E is the absolute error.
121
F"''all
and Fm""'ble are the allowable maximum cutting forces in feed
and thrust directions, which can be determined by the tool life estimation.
F '"Vfed
and F/m""""d are the estimated maximum cutting forces in feed
and thrust directions, which can be calculated by the analytical cutting
force model.
The tool working condition optimization program is included in the MOGART
program (see Chapter VIII). In the program, the tool working conditions can be selected
automatically according to the required tool life. The procedure of the tool working
condition optimization is presented in Figure 5.28. The program user interface is presented
in Figure 8.24 of Chapter VIII.
Tool Working Condition
Optimal Program
Tool Geometry And
Working Conditions
Analytical Cutting
Force Model
Simulating Or Experimental
Cutting Force Data
Genetic
Algorithm
Parameters of
Working
Condition
Figure 5.28 Tool optimal working condition estimation procedure
122
CHAPTER VI
Experiment Setup
All the experiments were performed at Mechatronics Lab, Mechanical Engineering
Department, Florida International University and Engineering Prototype Center, Radio
Technology Division, Motorola Inc. More than 800 cutting experiments were performed
and more than 160 megabytes of cutting force data were recorded. The experimental
contents are listed in Table 6.1.
A typical experimental setup is presented in Figure 6.1. Three different milling
machines were used in the experiments. The work-piece to be tested was installed on a
dynamometer, which was clamped on the table of the machine tool. Two components of
the cutting forces were recorded by using a digital oscilloscope through a charge amplifier.
All the experimental equipment is listed in Table 6.2 and shown in Figures 6.2 to 6.7.
Spindle
Tool
Work-piece
Dynamometer
Workbench
Amplifier
Oscilloscope
Figure 6.1 Experimental setup
123
Tool type:
Two-flute and four-flute micro-end-mill
Tool diameter (inch):
15/1000, 20/1000, 30/1000, 1/32, 1/16 and 1/8
Tool material:
High speed steel (HSS) and carbide
Work-piece material:
Aluminum, copper and mild steel
Steel: NAK-55, P-20, 420, Moly, Aged Moly and 3DP
Non-metal: POCO-3 and POCO-C3 graphite.
Cutting conditions:
Slot and 50% overlapped climbing end milling with
different spindle speed, feed rate and depth of cut.
Table 6.1 Experimental contents
Machine tool:
Bridgeport series I 3,000 rpm milling machine
Fadal 3-axis 15,000 rpm CNC machine
Fadal 5-axis 50,000 rpm CNC machine
Nicolet 310 digital oscilloscope
Data acquisition:
Nicolet integra model 10 digital oscilloscope
Cutting force measurement:
Kistler 9257B 3-component piezoelectric dynamometer
Kistler 3-channel charge amplifier
Displacement measurement:
Kaman KD2310-2S measuring systems
Hardness measurement:
Wilson TU220
Image processing system:
Olympus SZH10 microscope and SONY DXC-107A
digital color video camera
Table 6.2 Experimental equipment
124
Figure 6.2 Machine tool
Majority of the experiments was performed on Fadal 5-axis 50,000 rpm CNC
machine. Fadal 3-axis 15,000-rpm CNC machine. Bridgeport series I 3,000 rpm milling
machine was also used in some experiments.
125
§*'>
1261
~
.~
..........
......
'4''
'(N
~i
'(k~ec
N
X
t/
~
Figure
Cutnfremasrmn
~
Kistler
~
3-opnn
~
~
~
9257B4
izeeti
~
4Y
~
6.3
yaomtrwsue
omntrto
dimnsin fee diecionaFigu 6.3 cton C utting forcesurmn
126
k''.P~'
--------
>
u
It
x
*~
Figure 6.4 Data acquisition
Two digital oscilloscopes (Nicolet 310 digital oscilloscope and Nicolet integra
model 10 digital oscilloscope) were used to record the cutting force and acoustic emission
signals, which were amplified by using a Kistler 3-channel charge amplifier.
127
LII
~Z
Figure 6.5 Hardness measurement
The Wilson TU220 hardness measurement machine was used to test the hardness
of the work-pieces.
128
Figure 6.6 Image processing system
The Image processing system used Olympus SZH1O microscope and SONY DXC107A digital color video camera to investigate tool wear.
129
"
Fa.K t rw Weg~YN+"~fMf {ht~S.Y. ¢{4h
C
'
is
y
.>'K'K
<K
.R
Y m o.w4~~~. . ^
KK
.K4
K,~'
K
h
K,<K~~~
K
,h<~
K
Ki
'
KK
K/K;>
:KK
'
''tA<'>
aaCH#Y
NNTwa
4{Jt _______'.
+
K'
Figure 6.7 The computer screen showing the software used for Image processing
Figure 6.8 and 6.9 shows the cutting edges of a new tool and a worn-out tool
respectively and the figure 6.10 and 6.11 shows the work-piece surfaces cut by a new tool
and by a worn-out tool respectively.
130
: : :
:- :F:::::::::::
g:::::
u re:
T:::::::::ged:
:
.,
r
:
.:
:Figure
:33::33:9::3
4%
e::e4:~ox:x-
w r..
: :
::
.:w
6.9 The:cu:in : edes::::
3::3:::33:3::
-o~:2o~
-xx.oz~o-:~c:-e~~e
-4
/3
-3
/:x
/+++3:
: :
'
: :: + :
w:34
::8
..
.-
; :
of a Wor toolx
44//n
-
s
;
%2
/
Figure 6.8 The cutting edges of a New tool
7''
Fig.r
,.:,
.9
h
faW/nt
utigege
131
:;
-:
<'w
A
'A
'A'"
6
x;
x
;
A
>
8A
2
3
>-
>
'A.43
X
A "'A
x;
8
-A''A
'..x
'
",xv"*'>'~~A
'
A8A,~
-.
-
Figure 6 10 Work-piece surface cut by a new tool
-
/
/
/
~~
A;AA>
A;
;A
A
A
;
.n<A
/
~
w
A'',
A>4A
A
<A4~
-A
'A2<>AA
8
Ax~";
~
A:5
8
A
8
AA
A
2 /
'
'>
-
,,
'
-.
"
AA
A
94;
A,4>~
.
-Ax
A;
>AA,,
A'
'x
'
'x
,
A
-
A
-
'4A
A
'A>~«,
A'
AN fr
'
-A;
AA
'>'"n'u'
'A
'4
A'>
A
A
A
'
.
A
''
A
- A,-'
A
2
A
Figure 6.11 Work-piece surface cut by a worn tool
132
A
-
' <4xA
A
-''
A
A
A'
<
-'
;~A
A
A
'A
-
A
A
: ,'A-:
A
A
x
5
-- -
'
A::
'A
'
A
4
.
AA
'-'
A-
;->A
x
4Af
A -s
'A
'A8
'A:
A;
. Ei>
;A'A,
A '
Chapter VII
Results and Discussion
In this chapter, the validity of the proposed analytical model is discussed. The
accuracy of the cutting force estimation of the two approaches (neural networks and
analytical models) has been evaluated on the experimental data. The analytical models of
both micro and conventional end milling have been compared. Also the genetic algorithms
based monitoring techniques has been tested on the simulated and experimental data.
The data from more than 800 experimental cases was used to investigate the
cutting force characteristics and some of the data was used to verify the validity of the
developed techniques.
7.1 Validity of the Analytical Cutting Force Model
[19]
The analytical cutting force model of the micro-end-mill machining operations was
derived in Chapter III, which included the micro and conventional end milling with or
without tool run-out and wear cases. Ten parameters and two coefficients are used in this
model. They are three working condition variables (spindle speed, feed rate and depth of
cut), two tool run-out variables (run-out and its angle), two cutting condition variables
(tool cutting entry and exit angle), three tool geometry variables (tool diameter, helix
angle and the numbers of tool flutes), material and wear coefficients.
The analytical cutting force model of end milling operations can been expressed in
the following formulas:
133
*
The developed cutting force mode of end milling operations
F =F[C3 --13
sin3 9+ C4 1' cos
r
3
6- (1+
1
CS)sin
+-1p(1+
r
+(C 6 - 1
r
)sin-- pC cos-
1
2
3
F, = Fu[C4 -r sin 3 9- C3 -'r cos O- p(1+ C5 ) sin O- -(1+
2
+ p(C6
"
r
(7.1.1)
p(1+C)]I'
f
f,.
CS)sin2O
2
(7.1.2)
CS) sin 2
)sinO+C 6 cos9+(1+C 5 )]I0
Micro-end milling operations without tool run-out
F = F[C
F = F,[C
sin3 9+C
r
r
sin3
r
r
cos3 9-sin2 9+
2
cos3 9- psin2 9-
psin20-
r
sin29- p
sing- p9]
_-C
2
r
J
sin+6l]|e
(7.1.3)
(7.1.4)
" Conventional end milling operations with tool run-out
2 1
4r
F= F[- sin2 O+- psin 2O±
cosy(sinO-.p cosO) - p9]j'
2
f(
1
4r
F = F[-psin2 0- -- sin2± "rocosy(psin
2
f,
"
+ cosO)
+0]1e
(7.1.5)
(7.1.6)
Conventional end milling operations without tool run-out
FX = Fu[-sin0+-p sin20- p9] '
(7.1.7)
F=F,[- psin2 0- -sin 20+0]|~
(7.1.8)
2
K.Krf,
where : F =K
32tan4
134
C, =-(1+P-)
3
7r
C, =-(P--)
1
2
C 3 =-(l+p-)
C
3
.ir
2r
CS= -2-sin
irr
y
3
1
-
n
2
a
3
7
4r
C=±
ocosy
ft
The formulas 7.1.1 and 7.1.2 are the basic formulas of the developed cutting force
model of the end milling operations. The others can be simply derived from them. For
example, formulas 7.1.3 and 7.1.4 can be derived from the formulas 7.1.1 and 7.1.2 by
considering tool run-out ro = 0. In the conventional end milling operation case, formulas
7.1.5, 7.1.6 and 7.1.7, 7.1.8 can be derived from the formulas 7.1.1 and 7.1.2 by
considering f/r = 0, and both ro = 0 and f/r = 0 respectively. In the conventional end
milling without tool run-out, the formulas 7.1.7 and 7.1.8 exactly match Tlusty's model.
The develop analytical cutting force model has been tested on many experimental
cases of the micro-end-milling operations with different tool, work-piece and cutting
condition.
Very good agreement has been observed between the theoretical and
experimental results.
The cutting forces of one experimental case of micro-end-mill operation without
tool run-out are presented in Figure 7.1. Two-flute 1/8" diameter carbide end-mill and
steel work-piece were tested in the experiment. The working conditions were 2,000 rpm
spindle speed, 1 ipm feed rate, 0.0625" depth of cut and 50% overlapped climbing end
milling. At the same cutting conditions, the cutting forces calculated by using the
analytical cutting force model are presented in Figure 7.2. The maximum cutting force
error of both the cutting forces was less than 1%, which is presented in Table 7.1.
135
The cutting forces of one experimental case of micro-end-mill operations with tool
run-out are presented in Figure 7.3. Two-flute 1/16" diameter high speed steel end mill
and POCO-3 graphite work-piece were tested in the experiment. The working conditions
were 15,000 rpm spindle speed, 100 ipm feed rate, 0.0625" depth of cut and 50%
overlapped climbing end milling. The tool run-out was 0.001" with 50 degree angle. At
the same cutting conditions, the cutting forces calculated by using the analytical cutting
force model are presented in Figure 7.4. The maximum cutting force error of both the
cutting forces was with less than 3%, which is presented in Table 7.1.
Flute Direction Maximum cutting force
Without tool Both
run-out case
1st
With tool
run-out case 2nd
Error
Experiment
Model Based
Thrust
Feed
Thrust
Feed
Thrust
87.3
54.6
9.07
43.07
6.25
87.82
54.73
7.99
43.13
6.14
0.60%
0.15%
2.51%
0.14%
0.26%
Feed
17.62
17.54
0.19%
Table 7.1 Maximum cutting force error of the analytical cutting force model
In the above two presented cases, the material coefficients are 68,000,000 and
115,000 N/inch 2 with 1.78 and 5.85 feed rate correction respectively. New tools were
considered in both the cases so that tool wear coefficient is 1.
Since the analytical cutting force model was developed based on two general
assumptions, it could be considered as a theoretical foundation for end milling operations
including both micro and conventional end milling operations.
136
Cutting Forces of Micro-End-Milling Operations
2 flute 1/8" diameter carbide end mill, steel work-piece
100
80
z
60
tJ
0
0.C
Feed direction
Thrust direction
40
0
20
0
0.00
1.00
2.00
3.00
5.00
4.00
6.00
7.00
8.00
9.00
Time (ms)
Figure 7.1 Experimental cutting forces of micro-end-milling without run-out
Cutting Forces of Micro-End-Milling Operations
2 flute 1/8" diameter carbide end mill, steel work-piece
100
80
0
L
60
---
Feed Direction
Thrust Direction
40
0
20
0
90
270
450
630
810
990
1170
Tool Rotation Angle (degree)
Figure 7.2 Analytical model based cutting forces of micro-end-milling without run-out
137
Cutting Forces of Micro-End-Milling Operations
2 flute 1/16" diameter HSS end mill, POCO-3 work-piece
50
40
30 -3C)
direction
-Feed
Thrust direction
o0 20
C
S10
04 ms ! rotation
10
0.00
5.00
10.00
15.00
20.00
25.00
Time (ms)
Figure 7.3 Experimental cutting forces of micro-end-milling with run-out
Cutting Force of Micro-End-Milling Operations
2 flute 1/16" diameter HSS end mill, POCO-3 work-piece
50
40
30 C)
U
20
-Feed
direction
Thrust direction
C
10
0
-10
90
450
810
1170
1530
1890
2250
Tool Rotation Angle (degree)
Figure 7.4 Analytical model based cutting forces of micro-end-milling with run-out
138
7.2 Representation of the Cutting Force Characteristics
1. Representation of the Cutting Force Characteristics by Using Neural Networks
1161
The machinability study requires large number of tests. In this research, neural
networks have been proposed to represent the characteristics of cutting forces. The
objective is to be able to interpolate the maximum cutting force within the considerable
tool parameter range by performing the minimum number of the experiments.
The back-propagation neural network is a well known powerful tool for the
experimental data mapping. The program NNTool (Neural Network Research Tool)
program was developed in 1995 and modified in 1996. The program was successfully used
to determine the underground contamination distributions of New York area [14] and
Miami International Airport area.' 511"46, In this study, the NNTool was used to estimate the
maximum cutting force of micro-end-milling operations at different selected working
conditions and tool diameters.1161 The NNTool can automatically develop a good model of
the research problems by using a few experimental data sets and create a maximum cutting
force chart in the research area.
The experimental cases presented below are the examples of the neural network
based experimental data mapping. In the experimental cases, two-flute 0.020", 0.0625"
diameter end mills and POCO-3 graphite were tested. In the case of 0.020" diameter end
mill, the working conditions were 20, 70, 120 ipm feed rates and 0.010", 0.030", 0.050"
depths of cut. In the case of 0.0625" diameter end mill, the working conditions were 30,
65, 100 ipm feed rates and 0.0625", 0.100", 0.150" depths of cut. 15,000 rpm spindle
speed and 50% overlapped climbing end milling operations were used in the both cases.
139
The cutting forces were found at 16 different working conditions. The experimental
cutting forces of the selected working conditions are presented in Table 7.2 and 7.3.
X (thrust) direction cuffing force (N)
Depth of cut (inch)
0.05
0.03
0.01
Y (feed) direction cutting force (N)
Depth of cut (inch)
0.05
0.03
0.01
Feed rate (rpm)
20
3.750
4.850
4.500
70
6.750
6.500
5.425
120
non
non
5.150
Feed rate (rpm)
20
70
120
8.250
16.500
non
7.500
13.250
non
5.000
8.750
10.000
Table 7.2 Experimental data of 0.020" diameter end mill machinability testing
X (thrust) direction cutting force (N)
Depth of cut (inch)
0.15
0.1
0.062
Y (feed) direction cutting force
Depth of cut (inch)
0.15
0.1
0.062
m
Feed rate
100
30
65
6.800
14.900 28.600
12.700 19.900
6.800
7.900
20.100
6.200
Feed rate (rpm)
65
100
30
23.500 30.000 70.000
16.250 24.500 42.500
14.500 20.000 37.500
Table 7.3 Experimental data of 0.0625" diameter end mill machinability testing
The NNTool was used to develop an empirical model to evaluate the machinability
of the whole selected test range by using the experimental data from very few test cases.
The experimental data were collected at 7 and 9 different working conditions with 0.020"
and 0.0625" end mills respectively. The feed rate and depth of cut were considered as two
inputs of the neural network, and the tool cutting force was the output. A three-layer
140
neural network with 10 hidden nodes was trained. The learning rate and momentum factor
were 0.15 and 0.075 respectively. In the case of 0.020" diameter tools, 13 data sets (6
experimental data and 7 boundary conditions) were used to train the neural network and 1
experimental data was reserved for its testing. In the case of 0.0625" diameter tools, 9
experimental data sets were used to train the neural network. Two-dimensional neural
network based empirical cutting force models of 0.020" and 0.0625" diameter end mills
were developed with 8.4 % and 4.8% average errors respectively when they were tested
on the training cases. The model showed 15.7 % error on the test case that was not used
in the training. The results of 0.020" diameter tools are presented in Figure 7.5 and 7.6
and the results of 0.0625" diameter tool are presented in Figure 7.7 and 7.8.
Considering the tool diameter, another three-dimensional neural network was
developed by using the data of all the 16 experiments. In the study, the three inputs to the
neural network were the feed rate, depth of cut and tool diameter. The output was the tool
cutting force. A ten-hidden-node three-layer neural network was designed. During the
training of the neural network, a learning rate of 0.15 and a momentum factor of 0.075
were selected. Based on the experimental data, 30 data sets (16 experimental data and 14
boundary data) were used for the training of the neural network. The average error was
less than 8.8%. The results are presented in Figures 7.9 through 7.12.
The results confirmed the accuracy of the neural network based experimental data
mapping. The NNTool can be used to estimate the tool cutting forces with acceptable
error in a selected range of parameters.
141
Micro-tool Cutting Force in X Direction
(15,000 rpm spindle speed, 0.020 Inch HS steel tool, graphite workpiece)
.0.05
04
Cutting
force (N)
c
t m7-7.5
m 6.5-7
06-6.5
f
-0.3
©5.5-6
5-5.5
0
t.
a
S
04.5-5
4-4.5
0.02
01
20
45
95
70
120
Feed rate (ipm)
Figure 7.5 Thrust direction maximum cutting force of 0.020" diameter end mills
Micro-tool Cutting Force In Feed Direction
(15,000 rpm spindle speed, 0.020 inch HS steel tool, graphite workpice)
0.05
-
Tool #5
broken with
6 inch life
Cutting
force (N)
0.04
Tools #3,#4
broken with
9 inch life
U 18.520.5
\
t
1651.
®14.5-16.5
B 12.5-14.5
10.5-12.5
3
t t
\00
-
Tool #2
broken with
36 inch life
8.5-10.5
o
.
o
06.5-8.5
0 4.5-6.5
C Tool
survival
Tool #1
broken with
60 inch life
Tool
broken
-
20
45
70
95
120
Feed rate (ipm)
Figure 7.6 Feed direction maximum cutting force of 0.020" diameter end mills
142
Micro-tool Cutting Force in X Direction
(15,000 rpm spindle speed, 0.0625 inch HS steel tool, graphite workpiece)
015
Cutting
02
25force (N)
25-30
20-25 j
©15-20
010-15
01
05-10
00
20
40
60
80
100
Feed rate (ipm)
Figure 7.7 Thrust direction maximum cutting force of 0.0625" diameter end mills
Micro-tool Cutting Force In Feed Direction
(15,000 rpm spindle speed, 0.0625 inch dia. tool, graphite)
Tool #1
broken with
2 inch life
Cutting
force (N)
0.125
Tool #3
survival with
18 inch life
y:m
o
~~0.1
30-35
25-30
20-25
D 15-20
010-15
0 5-10
Tool #2
0.075
survival with
837 inch life
0 Testing
cases
0.05
20
40
60
80
100
Feed rate (1pm)
Figure 7.8 Feed direction maximum cutting force of 0.0625" diameter end mills
143
Micro-tool Cutting Force In Feed Direction
POCO 3 workpiece, 0.020 inch diameter high speed steel end mill
Cutting
-{
Force (N)
350-60
-
-j0.02
1~
~1i
a
®20-30
O
110-20
00-10
0.01
0
20
40
60
80
100
120
Feed rate (ipm)
Figure 7.9 Feed direction maximum cutting force of 0.020" diameter end mill
Micro-tool Cutting Force In Feed Direction
POCO 3 workpiece, 0.030 inch diameter high speed steel end mill
0.60-70
005
3 50-60
40-40
-
fl30-40
\.e
0.3
~20-30
O
10-20
00-10
0015
0
0
20
40
60
80
100
120
Feed rate ((pm)
Figure 7.10 Feed direction maximum cutting force of 0.030" diameter end mill
144
Micro-tool Cutting Force In Feed Direction
POCO 3 workpiece, 0.050 inch diameter high speed steel end mill
......
,.-0.125
-01
Cutting
Force (N)
-0.075
c
60-70
U 50-60
40-60
0 30-40
a 120-30
0 10-20
0 0-10
--
0
20
60
40
100
80
0
120
Feed rate (ipm)
Figure 7.11 Feed direction maximum cutting force of 0.050" diameter end mill
Micro-tool Cutting Force In Feed Direction
POCO 3 workpiece, 0.0625 inch diameter high speed steel end mill
0.15625
-
0.125
-
Cutting
Force (N)
0.09375 c
07
50460
40.60
0.0625
o ®30-0
20-0
t
0
010-20
010-10|
-0.03125
-
0
20
40
60
80
100
0
120
Feed rate (ipm)
Figure 7.12 Feed direction maximum cutting force of 0.0625" diameter end mill
145
2. Representation of the Cutting Force Characteristics by Using Analytical Model
The calculation of the cutting forces by using the analytical model has been
presented in Chapter IV (Figure 4.7 to 4.27). The parameters discussed in the model
includes the spindle speed, feed rate, depth of cut, run-out and it's angle, tool cutting entry
and exit angle, tool diameter, tool helix angle and the numbers of tool flutes.
During the machining of POCO-3 graphite work-piece with high speed tool, the
experimental data of maximum cutting force is listed in Table 7.2 and 7.3. Based on the
empirical neural network cutting force model, the characteristics of the tool maximum
cutting forces are presented in Figure 7.5 to 7.12.
Considering the case of 0.020" diameter end mill and POCO-3 graphite workpiece, the characteristics of the tool maximum cutting forces can be calculated from the
analytical model. The working conditions are 15,000 rpm spindle speed, 20 to 120 ipm
feed rate, 0.01" to 0.05" depth of cut and 50% overlapped climbing milling. The thrust
and feed direction maximum cutting forces are presented in Figures 7.13 and 7.14.
Compared to the experimental cutting forces (see Table 7.2) and estimated cutting
forces by using the neural network based model (Figure 7.5 and 7.6), the cutting forces
calculated by using the analytical cutting force model (Figure 7.13 and 7.14) have a good
agreement with them. The average error of the maximum cutting forces of the analytical
model is less than 38.2%.
146
Thrust Direction Maximum Cutting Force
of Micro-End-milling Operations
(2 flute 20" diameter HSS end mill, POCO-3 graphite work-piece)
-t
0.05
Cutting Force
(N)
-.04 ....
312-14
U 10-12
7
a
®s-10
04-
02-4
.3
-
15,000 rpm
spindle speed
-0.01
20
45
70
95
0 0-2
- 0.02
120
Feed rate (ipm)
Figure 7.13 Model based thrust direction maximum cutting force of micro-end-milling
Feed Direction Maximum Cutting Force
of Micro-End-milling Operations
(2 flute 20" diameter HSS end mill, POCO-3 graphite work-piece)
0.05
," ..-..
##
Cutting
0.04
Force (N)
30-34
326-30
r-0.013.0
II
t
2 2-26
pnl 018-22
pe
14-18
t
0
o
w,
o10-14
0 02
2
--------
0.01
\
20
45
70
95
06-10
Q 2-6
15,000 rpm
s pindle speed
120
Feed rate (ipm)
Figure 7.14 Model based feed direction maximum cutting force of micro-end-milling
147
3. Difference Between Micro and Conventional End Milling Operations
From formulas 7.1.1 to 7.1.8, it can be easily understood that micro-end-milling
operations has the same cutting force values as conventional end milling operations if the
ratio of the feed per tooth to the tool's radius (f/r) is equal to zero. It is suggested that
database of conventional end milling operations could be used for micro-end-milling
operations when ft/r were small enough to be neglected.
Two cases of the simulated cutting force ratio of the both models are presented in
Figure 7.15. In the cases, tool had 0.020" diameter. The cutting conditions were 15,000
rpm spindle speed, 0 to 150 ipm feed rate and 0.010" and 0.020" depth of cut.
Difference Between Micro and Conventional End
Milling Operations
2.0
1.9
1.8
1.6
01.5
1.4
1.2
Depth of cut
--
1.1
0.5 d
-1.0
1.0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Ratio of feed per tooth to tool radius (Ft / r)
Figure 7.15 Difference between micro and conventional end milling operations
148
d
The cutting force calculated by using conventional end milling model (ft/r = 0) is
always smaller than the one calculated by micro-end-milling model (considering ft/r). If ft/r
< 0.1, the difference of maximum cutting force between the both models is less than 10 %.
In other word, the both models have very similar performance when ft/r < 0.1. The
database of conventional end milling operations could be used for micro-end-milling
operations with a 10% difference of the maximum cutting force. If the conclusion could
proved experimentally, it would save a lot of experimental time and money for the
investigation of micro-end-mill machinability.
149
7.3 Performance of Monitoring in Micro-End-Milling Operations
1. Tool Breakage Detection
[27-301
Tool breakage detection methods that use acoustic emission (AE) signal have been
discussed in Chapter V. The procedures of the AE based tool breakage detection are
simple and efficient. Two statistics algorithms of the tool breakage detection have been
developed for two different working conditions. They accurately detected the tool
breakage in all the studied cases with a very fast response capability. Two experimental
cases were presented in Chapter V. Two-flute 0.015" diameter high speed steel end mill
cut on mild steel work-piece were tested. The working conditions were 30,000 rpm
spindle speed, 0.24 ipm feed rate and 0.016" depth of cut in the experiment I, 3,000 rpm
spindle speed, 0.9 ipm feed rate and 0.005" depth of cut in the experiment II.
The data pattern of the experiment I was simple and tool breakage was detected by
the detecting method I (see Chapter V). The data pattern of the experiment II was more
complicated and difficult to distinguish the difference between tool broken and leaving the
work-piece. The method II successfully detected the tool breakage in all of the cases of
the experiment II. The test results are presented in Figure 7.16 (tool broken case) and
Figure 7.17 (tool left from work-piece case), where the test procedures are shown under
the AE signals. The down points of the line were testing points. The line was down to the
level 1 when the tool left the work-piece and the level 2 when it was broken.
The results of monitoring tool breakage by the tool cutting force have been
discussed in Chapter V. It has been proved that tool cutting force can be used not only to
detect but also predict the tool breakage.
150
ACOUSTIC EMISSION TESTING IN END-MILL
MACHINING OPERATIONS
(experiment II: tool broken case)
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
>
-
Data
-Method 1
2
-Method
0.6
0.2
0.0 --
-0.2
-0.4
-0.6
-0.8
i
-1.0
-1.2
-1.4
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Time (sec.)
Figure 7.16 Tool breakage monitoring by AE activity of experiment II, case 1
ACOUSTIC EMISSION TESTING IN END-MILL
MACHINING OPERATIONS
(experiment II: tool left from the work-piece case)
2.4
2.2
2.0 1.8
1.6
1.4
1.2
1.0
p
0.8
0.6
-Data
-Method
0.40-Method
1
2
-0.2
rK
-0.4
-0.6
-0.8
-1.0
-1.2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Time (sec.)
Figure 7.17 Tool breakage monitoring by AE activity of experiment II, case 2
151
2. Tool Wear Monitoring and Estimation
[39][42]
A tool wear estimation model has been developed in Chapter V by using the backpropagation neural network and empirical tool wear model that was based on the data of
the tool wear experiment I (see Chapter V, Figure 5.15). In the tool wear experiment I,
two-flute 0.030" carbide end mill and steel work-piece were tested. The working
conditions were 30,000 rpm spindle speed, 2.5 ipm feed rate and 0.045" depth of cut. The
results of the tool wear estimation by tool cutting force have been presented in Chapter V
(Table 5.1 and Figure 5.20).
To validate the tool wear estimation model, another case, tool wear experiment II
(see Chapter V, Figure 5.15), was tested. The data of the experiment II never be used
when the tool wear estimation model was generated. In the experiment II, two-flute
0.030" carbide end mill and steel work-piece were tested. The working conditions were
20,000 rpm spindle speed, 1.25 ipm feed rate, 0.0225" depth of cut and 50% overlapped
climbing end milling. The experimental results have been presented in Figure 5.15 and
5.16, which included 10 cutting force data begun from a new tool and ended until it was
broken. The tool had around 33" tool life.
Based on the 10 experimental data, 10 data sets were used for the test of the
neural network based tool wear estimation model. In the 10 data sets, the first 7 data sets
were from the first 8 experimental data. The following 3 data sets were estimated by the
tool wear estimation model that was developed in Chapter V. The last 2 experimental data
were reserved for the test purpose. In other word, in the study the tool life was estimated
after the tool had cut a 27"-long work-piece.
152
Cutting Force (N)
Tool Life
(inch)
Experimental
Data
Empirical Estimation
Model
Data
Empirical
Model Error
Estimation
Error
3
6
28.080
27.807
0.273
9
25.360
27.839
-2.479
12
15
18
21
24
27
30
33
25.920
29.320
29.560
28.840
31.240
31.320
33.160
38.200
27.935
28.150
28.566
29.283
30.428
32.154
34.640
38.093
25.234
26.577
28.911
28.699
29.491
31.703
33.051
34.871
36
-2.015
1.170
0.994
-0.443
0.812
-0.834
-1.480
0.107
0.687
2.743
0.649
0.141
1.749
-0.383
0.109
3.329
1.980
7.08%
2.255
8.06%
36.195
39
39.012
Average
Persentage
27.976
Table 7.4 Results of the tool wear forecasting model testing
Tool Wear Estimation Testing
2 flute 0.030" diameter carbide end mill, steel work-piece
45
40
Experimental
W. 35
35 -Data
u
0
-Empirical
Model
-Estimation
Data
-
30
,
25-*
20
0
5
10
15
20
25
30
35
40
Tool Life (inch)
Figure 7.18 Performance of the tool wear forecast model
153
45
The test results of the tool wear estimation model are presented in Table 7.4 and
Figure 7.18. The cutting force was estimated with 1.8 N or 6.45% average error. The
empirical tool wear model shown in Figure 7.18 was developed from the 10 experimental
data after the experiment had been completed. It was very similar to the model developed
in Chapter V. Only the basic cutting force level C1 was different because of the different
working conditions. The coefficients of empirical tool wear model were:
C 1 = 27.800
C 2 = 0.0522
C 3 = 4.287
If the tool breakage critical cutting force was selected as 38 N, the tool life would
be estimated as around 37.5 inch. Compared to the actual tool life, 33 inch, the tool life
estimated by the tool wear estimation model had an acceptable error, 13.6%.
The tool breakage critical cutting force can be determined by the experimental
data. To improve the accuracy of tool wear estimation, the tool wear empirical and
estimation model should be improved further based on experimental observations.
Considering the tool wear coefficient K, in formula 5.2.3, the analytical cutting
force model has been modified to include the tool wear. The cutting forces of two cases,
the new tool case and pre-failure case of the tool wear experiment I (see Chapter V,
Figure 5.15), were presented in Figure 7.19 and 7.20, in which they were compared with
the cutting forces of the analytical model.
154
Cutting Force of Micro-End-Milling Operations
in Tool Wear Experiments
(new tool)
50
40
Z
2 30
Experimental data
model
O0-
-Analytcal
20
-
10
0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Time (ms)
Figure 7.19 Thrust direction cutting force of the new tool
Cutting Force of Micro-End-Milling Operations
in Tool Wear Experiments
(tool before breakage)
50
40
z
o 30
0
-Experimental
data
-Analytical
model
20
10
0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Time (ms)
Figure 7.20 Thrust direction cutting force of the tool before breakage
155
3. Tool Run-out Estimation and Cutting Condition Monitoring
[19]
Tool run-out exists in most of micro-end-milling operations. Because of tiny tool
diameter, the cutting force would be changed significantly if there was only a small tool
run-out. It is important to estimate tool run-out and reduce it to a minimum level.
In the experiments, two different end mill holders, conventional and collet end mill
holder, have been studied. The results are presented in Table 7.5 and 7.6.
X (thrust) direction runout (%)
Feed rate (ipt)
0.00100
0.00075
0.00050
Spinle speed (rpm)
15,000 32,000 50,000
9
9
34
8
9
49
0
0
35
Y (feed) direction runout (%)
Feed rate (ipt)
0.00100
0.00075
0.00050
Spindle speed (rpm)
15,000 32,000 50,000
48
10
20
50
65
47
63
55
23
Table 7.5 Run-out experimental results of collet end mill holder
X (thrust) direction runout (%)
Depth of cut (inch)
0.150
0.100
0.062
30
72
57
56
Feed rate ip)
65
85
54
83
Y (feed) direction runout (%)
Depth of cut (inch)
0.150
0.100
0.062
30
87
40
78
Feed rate (ipm
100
65
87
46
48
63
86
79
100
71
64
60
Table 7.6 Run-out experimental results of conventional end mill holder
In the experimental cases of the end mill holder with a collet, two-flute carbide end
mill with 0.0625" diameter is used to cut aluminum work-piece. The working conditions
were following: 15,000, 32,000 and 50,000 rpm spindle speed, 0.0005, 0.00075 and 0.001
ipm feed rate, 0.020" depth of cut and 50% overlapped climbing milling. In the cases of
156
the conventional end mill holder (holding the tool with set-screw), POCO-3 graphite
work-piece was cut by a high speed end mill with two-flute 0.0625" tool diameter. The
working conditions were 15,000 rpm spindle speed, 30, 65 and 100 ipm feed rate,
0.0625", 0.100" and 0.150" depth of cut, and 50% overlapped climbing milling.
Based on the experimental results, it is known that run-out of micro-tools effect
cutting performance more serious than conventional tools. The tested end mill holder with
a collet had 0% to 65% run-out and the average was around 30% average. The tested end
mill holder with set-screw had 40% to 87% run-out and the average was around 68%. The
collet end mill holder is much better than the conventional one.
Based on the analytical cutting force model, estimated the tool run-out was studied
in Chapter IV. When the tool run-out angle is parallel to the tool cutting edges (y = 0), the
cutting force has a maximum value that almost double of the minimum value (see Chapter
IV, Figure 4.18) and the work-piece surface has the lowest precision. When the tool runout angle is perpendicular to the tool cutting edges (y =
7t/2),
the cutting force has a
minimum value and the work-piece surface has the highest precision.
If end mill holder with a set screw is going to be used, the tool should be screwed
on the holder perpendicular to the cutting edges of the two-flute tool. The same angle
should be 45 degree in the case of the four-flute tool. These adjustments would reduce the
run-out to the minimum level.
It is important to estimate the tool run-out and monitor the tool cutting conditions
of micro-end-milling operations. The method of estimating tool run-out and monitoring
tool cutting conditions by using the genetic algorithm with the analytical cutting force
157
model has been discussed in Chapter V. The main idea is to compare the experimental
cutting forces to the cutting forces calculated by the analytical model, and use the genetic
algorithm to search the optimal fitting variables of the parameters (tool run-out or cutting
conditions) of the analytical model. The method can be used to estimate the tool run-out,
spindle speed, feed rate, depth of cut, entry and exit cutting angles. The details were
discussed in Chapter V.
The genetic evolution procedure of tool run-out estimation had been presented in
Figure 5.23 of Chapter V. The results are presented in Table 7.7. The error is less than
2.5% after 210 generations.
Tool Run-out (inch)
Tool Run-out Angle (degree)
Optimal Function Fitness
Acutal Value
0.001
30
0
Estimating Value
0.00099
29.26
0.0031
Error
1.00%
2.47%
0.0031
Table 7.7 Results of the tool run-out estimation
The results of the tool cutting condition monitoring have been presented in Table
5.2 of Chapter V. The error is reduced to less than 3% in 20 generations and less than 1%
in 120 generations. The average errors of all the studied cases are 1.13% at the 20t
generation and 0.19% at 120t generation, which are presented in Table 7.8.
Tool Cutting Angle
Optimal Function Fitness
Error in 20th Generation Error in 120th Generation
1.13%
0.19%
1.3578
0.0525
Table 7.8 Results of the tool cutting condition monitoring
158
Chapter VIII
Introduction of MOGART Package
Based on the analytical cutting force model and experimental data of micro-endmilling operations, a Micro-End-Milling Operation Guide and Research Tool (MOGART)
package has been developed for the machinability studies, modeling and monitoring of
micro-end-milling operations (see Figure 8.1).
MicrG-End-Milling Operation Guide
And Researh TooL
Figure 8.1 MOGART package
The package is capable to perform the following tasks by using a user friendly
interface:
159
"
The model and neural network based cutting force estimation
"
Cutting force characteristics analysis
"
Investigation of machability
"
Estimation of wear
"
Detection of breakage
"
Estimation of run-out
"
Selection of optimal working conditions
" Estimation of surface roughness and precision
"
Neural network based data mapping, forecasting and classification
"
Genetic algorithm based modeling, monitoring and optimization
As a convenient and efficient research tool, the MOGART has being applied to the
micro-end-milling studies of the Engineering Prototype Center of Radio Technology
Division of Motorola Inc., which include machinability, wear, breakage, run-out and
optimal working conditions. The performance of the MOGART has been tested on the
experimental data of over 800 experimental cases and satisfactory results have been
obtained. This chapter is a basic user guide for introduction of the MOGART program.
8.1 Structure of MOGART Package
The structure diagram of the MOGART program is presented in Figure 8.2
160
Neural Network
Research Tool
Neural Network Based
Cutting Force
Estimation
Analytical Cutting
Force Model
Analytical Model Based
Cutting Force
Genetic Algorithm
Research Tool
Cutting Force
Characteristics
Estimation
Tool Run-out
Estimation
Analysis
Calculation of
Work-piece
Surface Roughness
Calculation of
Work-piece
Surface Precision
Tool Wear
Estimation
Estimation of
Working Condition
Estimation of
Tool Run-out
Selection of
Optimal
Limitation
Limitation
Working Condition
Figure 8.2 Diagram of MOGART program
161
The MOGART includes three main research tools: the analytical cutting force
model,
neural networks and genetic algorithms. Also, it included many research
applications: neural networks-based experimental data processing, analytical cutting force
model-based machinability studies, cutting force estimation, work-piece surface precision
and roughness calculation, genetic algorithms-based tool life, run-out and optimal working
condition estimation.
The MOGART has four sections: the analytical cutting force model, neural
network research tool, genetic algorithm research tool and operation guide applications of
milling operations (see Figure 8.3). In the analytical cutting force model section, a tool to
study the cutting force model of end milling operations is provided. The results of the
studies are stored in the operation guide applications section. The neural network research
tool can be used to generate empirical cutting force estimation models and wear
forecasting models. The genetic algorithm research tool can be used to search the optimal
parameters and coefficients of the analytical cutting force model. The neural network
research tool (NNTool) and genetic algorithm research tool (GATool) are designed for
general research purposes so that they can be used to solve data mapping, forecasting and
optimization problems of other engineering systems.
The MOGART program is developed by using Visual Basic 4.0 version compiler.
It has a friendly user interface that includes the data file import and Microsoft Excel
Worksheet-based data input options, and visualized results that include the graphics of the
tool cutting edge profiles, cutting force profiles and characteristics, and so forth.
162
*
For a new research project
1. From the File menu, choose Project.
2. From the Project sub-menu, select New Project.
3.
In the New Project screen (see Figure 8.3), type the project directory and name, click
Ok button.
...........
(<~~c'~..
.
Figure 8.3 Menu of MOGART program
*
For a matured project
1.
From the File menu, choose Project.
2.
From the Project sub-menu, select Tool Material.
3. From the Tool Material sub-menu, select tool material.
4.
From the Project sub-menu, select Work-piece Material.
5. From the Work-piece Material sub-menu, select work-piece material.
163
8.2 Analytical Cutting Force Model
Based on the analytical cutting force model, the MOGART can be used to
calculate the tool cutting forces of milling operations by the formulas derived in the model.
There are four features, Cutting Force Estimation, Cutting Force Report, Cutting
Force Graphic and Tool Cutter Profile, which are included in the main menu Research
section.
"
To estimate the tool maximum and minimum cutting forces in the feed and thrust
directions
1.
From the Research menu, choose Cutting Force Estimation.
2. In the Cutting Force Estimation screen (see Figure 8.4), there are three tool geometry
parameters, seven tool working condition parameters and two material coefficients.
Select the parameters and coefficients one by one by pointing the cursor at the text
box and click the right mouse button, and type the data depending on the tool
operation conditions. For example, if there is a 50% overlapped climbing milling case,
type 90 in the Cutting Start Angle text box and 180 in the Cutting End Angle text box.
3. One option is the calculation precision angle. 5 degrees is chosen as the default
calculation angle, which means the tool cutting force data are calculated at every 5
degrees of the cutting period. The maximum calculation precision can be selected to 1
degree.
4. Click Ok button.
164
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F
aru
En
[.n
iing
._ln
esiatoDiuction
forceV
Fedt
I I kun. . O~ati
ruttmag
F:pm]
Cacu
8.4~d1 2Cttin
Figure
?t-sh
"'rnha
eed lnch
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9 . *..r:
eo Hots;ne
upoToQ-rimete;
J5
1*Hun t A Pia
2 su
t 1
PtsvstA
C wui1n St Anje...............
uttin9
n
.n
14
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]oo1* j
1Stet
.Tf ((':#£;a a '
i.ad
.pM
Liloe
1
4cEnd
Tcrst
Figrure 8.4 Cutting force estimation
Cutting Force Calculacmon In End-Hilling
Angle
Feed Direction
Thrust Direction
Resultant
-90
-89
-88
-87
-86
-85
-84
-83
-82
-81
-80
-79
-78
-77
-76
0.0000
-0.0154*
-0.0299
-0.0435
-0.0562
-0.0679
-0.0787
-0.0885
-0.0974
-0.1053
-0.1122
-0.1182
-0.1232
-0.1272
-0.1303
0.0000
0.0531
0.1065
0.1603
0.2142
0.2684
0.3229
0.3774
0.4322
0.4870
0.5419
0.5969
0.6519
0.7069
0.7618
0.00
0.26
0.11
0.17
0.22
0.28
0.33
0.39
0.44
0.50
0.55
0.61
40s
4
-N4I t.%s
s-
4/u,,
0.66
0.72
0.77
4
Figure 8.5 Cutting force report
165
__ma
d|
TolC
KU'a5
"
Tool feed direction, thrust direction and resultant cutting force profile estimation data
1.
Follow the steps of Cutting Force Estimation to estimate the cutting force.
2. From the Research menu, choose Cutting Force Report.
3. In the Report screen, point the cursor to the icon with the project name you worked
on, and double-click the icon (see Figure 8.5).
"
Tool feed direction, thrust direction and resultant cutting force graphics
1.
Follow the steps of Cutting Force Estimation to estimate the cutting force.
2. From the Research menu, choose Cutting Force Graphic.
3. In the Cutting Force Graphic screen (see Figure 8.6), point the cursor to the check box
and click the right mouse button to check the force graphic you would like to see.
4. To change the tool turning angle display option to time, point the cursor to the option
button and click the right mouse button.
5.
To change the graphic scale, select the Scale text box, type the scale, which decides
how many periods of data will be displayed on the graphic, and click Ok button.
*
Tool cutter profiles
1.
From the Research menu, choose Tool Cutter Profile.
2. In the Tool Cutter Profile screen (see Figure 8.7), select the parameters one by one by
pointing the cursor at the text box and click the right mouse button, and type the data
depending on the tool operation conditions.
3.
Click Ok button.
166
u
ool CiutI-ng Force ind
lMachining OpetiAlns
Tool Cutting Force (1)
4
2
0
90
-90
270
630
450
-2
4
Tool Twning
G.
Angle
(degree) C
Time (ms]
Scale
Figure 8.6 Cutting force profile
Totl Cu
ter
Poroiles
TuI Cmetneusr tm
1
aumbet
of
1u1e
of
1Ud
-lil
S Std e S etdtso4
Feed R.te7
OpeativOfs
l
%
1
Ru-ut (Ac
0
Fu aut-ogh
17m>
ist tng edge
-
MSic
i r
i . ?
Uo-End
Figure 8.7 Tool cutter profile
167
:
2af CuTTe
'O)sdi
Wrd
-
fi
-e
8.3 Neural Network Research Tool
The back-propagation neural network as a data processing tool is included in the
main menu NNTool section of the MOGART program. The theory of neural networks has
been discussed in Chapter II. The mapping feature of neural networks can be used to
estimate the maximum cutting force in the selected working condition ranges by only a
few experimental data. The forecasting feature of neural networks can be used to estimate
the worn tool cutting force by a tool wear empirical model that has been generated by the
experimental data. The back-propagation neural network program was developed for
general data processing purposes so that it can be used for studies of micro-end-milling
operation and other engineering systems.
The NNTool includes three sections, Training, Testing and Results.
*
To train the neural network
1.
From the NNTool menu, choose NN Project.
2. From the NN Project sub-menu, select New NN Project.
3. In the New NN Project screen (see Figure 8.8), type the project directory and name,
type the number of the input and output nodes, click Ok button.
4. From the NNTool menu, choose Setup.
5. In the Neural Network Setup screen (see Figure 8.9), select parameters one by one
and type data in the text box, click Ok button.
6. From the NNTool menu, choose Training.
168
lit
-
S nt ut naralns,
__
p ,t
t nuf Ge+
a;crf
;'>
yy
a
f
Figure 8.8 Neural network project
Asdcr Nodes ri==d '
f:
L" orl;
Cdrcef
I.
y i.Ar
M[;,ncrlme fia;tq
F
VK
r
MN11f11W11 dad
f
.
M rxunum data (umi
link[
f
4lei lfem Fears
URtaa3f FfegUerMY
l ia1,0
rJ
f
t
Figure 8.9 Neural network setup
169
.:
7. Import a pre-prepared training data file by selecting Import Training File from the
Training sub-menu, or input training data on the Excel Worksheet by selecting Input
Training Data from the Training sub-menu and follow the steps below:
(1)
In the Input Data screen, point the cursor at the upper-right corner and double
click it.
(2) In the Excel Worksheet (see Figure 8.10), type the number of the training data
cases; type the input data then output data one case by one case; type the support
service phone number 3053483304 as a data checking number.
-
---------
5
i.
1
2
3
4
.. 5
3483304
L
~~
2
4
6
8
10
Figure 8.10 Training data input
(3) In the Excel Worksheet, choose Save As from the File menu.
(4) In the Save As screen, select Text (OS/2 or MS-DOS) (*.txt) from Save As type
section. Find the project directory, and click Save button to save the training data
file with name "project name + Trn.txt."
170
(5) Close the Excel Worksheet.
8. From the Training sub-menu, select Setup Start Point.
9.
From the Setup Start Point sub-menu, select Random, Index Random or Constant.
If selecting Random, it will set a random start point. If selecting Index Random, type
a random index number in the Random Start Point screen and click Ok button. It will
set a random start point depending on the given index number so that the running
procedure can be repeated. If selecting Constant, type a constant number in the
Constant Start Point screen and click Ok button. It will set all connection weights as a
given constant at the beginning.
10. From the Training sub-menu, select Start. The neural network will start to be trained
until it reaches the given Error Level or maximum Iteration times. A "project name +
.pj" file will be created after the training, which includes all the neural network data
processing information.
11. If the training procedure is interrupted, it can be continued by selecting Continue
from the Training sub-menu.
12. One option is Show Running Error in the Training sub-menu. If it is checked, the
Data Train Report screen (see Figure 8.11) will be displayed during the training
procedure.
"
To test the neural network
1.
After training, choose NN Project from the NNTool menu.
2. From the NN Project sub-menu, select Import NN Project (see Figure 8.12).
3. In the Import Project screen, find the project directory and name, double click it.
171
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Figure 8.12 Import the project
172
aosdt V sual B as c mytest.pri
25R p
txt
4. From the NNTool menu, choose Testing.
5.
From the Testing sub-menu, select Import Testing File from the Testing sub-menu,
or input testing data on the Excel Worksheet by selecting Input Testing Data from
the Testing sub-menu and follow step 7 of the training section.
6. From the Testing sub-menu, select Start. A "project name + Rpt.txt" file will be
created after the testing.
7T
o.
Data value
Estimate data
Error
Relatiue error
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
5.0000
8.7500
10.0000
7.5000
13.2500
8.2500
16.5000
0.4916
0.9274
4.0812
12.0850
0.9399
1.9366
3.0841
1.4850
0.4916
0.9274
4.0812
12.0850
0.9399
1.9366
3.0841
0.0070
0.0132
0.0583
0.1726
0.0134
0.0277
0.0441
-3.5150
-0.0502
5.0708
-3.6792
3.8603
-4.7724
-5.9685
-4.0881
-6.6619
-4.7844
-2.1928
3.1258
-0.0526
0.0551
-0.0682
-0.0853
-0.0584
-0.0952
-0.0683
-0.0313
0.0000
0.0000
0.0000
13.8603
2.7276
7.2815
4.1619
9.8381
-4.7844
-2.1928
3.1258
I
0.0447
Figure 8.13 Neural network testing report
*
The data of neural network testing results
1.
After testing, choose Results from the NNTool menu.
2. From the Results sub-menu, select Show Report.
3. In the Report screen (see Figure 8.13), point the cursor to the icon that has a project
name you worked on, and double click the icon.
173
*
The graphics of neural network testing results
1.
After testing, choose Results from the NNTool menu.
2. From the Results sub-menu, select Show Graphic.
3. In the 3 Dimension Cutting Force Distribution screen (see Figure 8.14), click the
option button, type the working condition data in the gray area, and click the Redraw
button. It will redraw a given case's graphics.
9&
Micro-tcaD
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00 20.000 - 25.000
0.030
0
0.02 0 04 0-06 O.U8 U
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0
20
40
60
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Figure 8.14 Graphics of neural network testing results
4.
One option is to click the option button, and click Auto-draw button. It will draw the
graphic layer by layer automatically.
5.
Click Stop button to stop the Auto-draw function.
174
8.4 Genetic Algorithm Research Tool
The genetic algorithm as a data analysis tool is included in the main menu GATool
section of the MOGART program. The theory of the genetic algorithms has been
discussed in Chapter II. The optimization feature of genetic algorithms can be used to
monitor the tool wear, run-out, cutting angles and working conditions with the analytical
cutting force model. The genetic algorithm was developed for general optimization
purposes so that it can be used for monitoring micro-end-milling operations and solving
optimization problems of other engineering systems.
The GATool includes two sections, Generator and Results.
"
Genetic evolution
1.
From the GATool menu, choose GA Project.
2. In the New GA Project screen, type the project directory and name, click Ok button.
3. From the GATool menu, choose Setup.
4. In the Genetic Algorithm Setup screen (see Figure 8.15), select parameter and type the
data in the text box one by one, also check the option check box, click Ok button.
5. In another Genetic Algorithm Setup screen (see Figure 8.16), select parameter and
type the data range and the number of chromosomes in the text box one by one, click
Ok button.
6. From the GATool menu, choose Generator.
7. From the Generator sub-menu, select Setup Start Point.
175
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Figure 8.16 GATool setup step 2
176
7' afl
t
8. From the Setup Start Point sub-menu, select Random or Index Random. If you
select Random, it will set a random start point. If selecting Index Random, type a
random index number in the Random Start Point screen and click Ok button. It will
set a random start point depending on the given index number so that the running
procedure can be repeated.
9.
From the Generator sub-menu, select Start. The Generator will start to create one
generation by one generation until it reaches the given Error Level or maximum
Generation Steps. A "project name + Report.txt" file will be created after running,
which includes all the generation data information.
10. If the running process is interrupted, it can be continued by selecting Continue from
the Generator sub-menu.
11. One option is Show Running Fitness in the Generator sub-menu. If it is checked,
the Generation Report screen will be displayed during the running process.
12. Another option is Show End Results in the Generator sub-menu. If it is checked, the
Results screen (see Figure 8.17) will be displayed after the running process. It tells the
best fitness and factor data in the last generation.
"
Genetic evolution results
1.
After testing, choose Results from the GATool menu.
2. In the Report screen, point the cursor to the icon that has a project name you worked
on, and double click the icon.
177
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.
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a
1
Figure 8.17 GATool results
8.5 Applications of Operation Guide in Micro-End-Milling Operations
Based on the analytical cutting force model, six tool operation guide applications
have been done, Cutting Force Estimate, Work-piece Surface Precision Estimation,
Work-piece Surface Roughness Estimation, Tool Run-out Estimation, Tool Life
Estimation and Working Condition Selection, which are included in the main menu
Application section.
*
To estimate the tool feed direction and thrust direction maximum cutting force
characteristics with different parameters
1.
From the Application menu, choose Cutting Force Estimate.
178
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Figure 8.18 Characteristics of maximum cutting forces
2. In the Cutting Force Estimation screen (see Figure 8.18), select one or two parameters
by pointing the cursor at the check box and click the right mouse button, type the data
range in the Maximum and Minimum Data text box, and the data number in the Data
Number text box.
3. Click Ok button.
4.
To know the cutting force data, point the cursor to the Fx (Feed Direction) or Fy
(Thrust Direction) and click the right mouse button.
5. To have a nice hard copy of the graphics, follow steps as below:
(1) In the Cutting Force Estimation screen, double click the graphic.
(2) In the Report screen, point the cursor at the upper-right corner and double click it.
179
(3) In the Excel sample sheet, choose Open from the File menu.
(4) In the Open screen, select All files (*.*) from Files of the type section. Under the
project directory, find the project name + CFx.txt or CFy.txt file, and double click
it to open the file.
(5) In Text Import Wizard - Step 1 screen, click Next button.
(6) In Text Import Wizard - Step 2 screen, check Space check box, and click Finish
button.
(7) In the Excel sample sheet, select the data area, and choose Copy from the Edit
menu.
(8) In the Excel sample sheet, choose ToolCF.xls from the Window menu.
(9) In the Excel sample sheet, if it is one parameter, select the CF2Ddata sheet; or if it
is two parameters, select the CF3Ddata sheet.
(10) In the CF2Ddata sheet or CF3Ddata sheet, select the same data area, and choose
Paste from the Edit menu.
(11) Click CF2Dchart to see maximum cutting force with one parameter graphic or
click CF3Dchart1 and CF3Dchart2 to see the maximum cutting force with two
parameter graphics (see Figure 8.19).
(12) To get a hard copy, choose Print from the File menu.
180
Legend
y
5.6
4.31
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j
Force
3.
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Figure 8.19 Three-dimensional cutting force graphic
"
To estimate the work-piece surface precision depending on the tool run-out
1.
From the Application menu, choose Work-piece Surface Precision Estimation.
2. In the Work-piece Surface Precision Estimation screen (see Figure 8.20), select the
tool geometry parameters by pointing the cursor at the text box and click the right
mouse button, and type the data depended on the tool operation case.
3. In the right section of the screen, check the Working Condition check box, and select
the run-out parameters by pointing the cursor at the text box and click the right mouse
button, and type the data depending on the tool operation case.
4. Click Ok button.
181
*
To estimate the tool run-out depending on the work-piece surface precision
1.
From the Application menu, choose Work-piece Surface Precision Estimation.
2. In the Work-piece Surface Precision Estimation screen (see Figure 8.20), select the
tool geometry parameters, and type the data depending on the tool operation case.
3. In the left section of the screen, check the Requirement check box, and type the
required work-piece precision.
4. To calculate one of the tool run-out parameters, point the cursor to the Maximum
Run-out or Minimum Run-out Angle option button, and click the right mouse button.
5. Type the data in the other tool run-out parameter text box.
6. Click Ok button.
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Figure 8.20 Work-piece surface precision estimation
182
*
To estimate the work-piece surface roughness depending on the tool cutting edge tip
profiles
1.
From the Application menu, choose Work-piece Surface Roughness Estimation.
2. In the Work-piece Surface Roughness Estimation screen (see Figure 8.21), select the
tool geometry parameters, and type the data depending on the tool operation case.
3. Under the Milling Type section, check the Conventional Milling or Climbing Milling
check box.
4. In the right section of the screen, check the Working Condition check box, and select
working condition parameters, and type the data depending on the tool operation case.
5. Click Ok button.
7
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Figure 8.21 Work-piece surface roughness estimation
1R3
*
To estimate the tool working condition depending on the work-piece surface
roughness
1.
From the Application menu, choose Work-piece Surface Roughness Estimation.
2. In the Work-piece Surface Roughness Estimation screen (see Figure 8.21), select the
tool geometry parameters, and type the data depending on the tool operation case.
3. Under the Milling Type section, check the Conventional Milling or Climbing Milling
check box.
4. In the left section of the screen, check the Requirement check box, and type the
required work-piece surface roughness.
5. To calculate one of the working condition parameters, point the cursor to the
Minimum Spindle Speed or Maximum Feed Rate option button, and click the right
mouse button.
6. Type the data in the text box of the other working condition parameters.
7. Click Ok button.
*
To estimate the tool run-out
1.
From the Application menu, choose Tool Run-out Estimation.
2. In the Tool Run-out Estimation screen (see Figure 8.22), select the parameters one by
one, and type the data depending on the tool operation case.
184
3. In the left section of the screen, type the experimental data of the maximum cutting
force in feed direction and thrust direction. The largest one of the two flutes is defined
as the 1 cutting edge.
4. Click Ok button.
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Figure 8.22 Tool run-out estimation
"
To estimate the tool life
1.
From the Application menu, choose Tool Life Estimation.
2. In the Tool Life Estimation screen (see Figure 8.23), select the parameters one by one,
and type the data depending on the tool operation case.
3.
Click Ok button.
185
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Figure 8.23 Tool life estimation
*
To select the optimal working condition
1. From the Application menu, choose Working Condition Selection.
2. In the Working Condition Selection screen (see Figure 8.24), select the parameters
one by one, and type the data depending on the tool operation case.
3. In the left section of the screen, point the cursor at the working condition check box
that you would like to select, and click the right mouse button.
4. Type the data in the text box of the other working condition parameters.
5.
Click Ok button.
186
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Figure 8.24 Optimal working condition selection
187
? ''z>S},c
Chapter IX
Conclusion and Recommendations
A new analytical model was developed for micro-end-milling operations, and
computational tools were customized for analysis of experimental data. All the developed
tools were integrated with the Micro-End-Milling Operation Guide and Research Tools
(MOGART) package.
Studying tool tip trajectory and experimental data developed the analytical cutting
force model of micro-end-milling operations. The analytical model estimates the cutting
force variation of micro and conventional end milling operation with or without tool runout and wear. Ten parameters and two coefficients are considered in the model. They are
three working condition variables (spindle speed, feed rate and depth of cut), two tool
run-out variables (run-out and its angle), two cutting condition variables (tool cutting
entry and exit angle) and three tool geometry variables (tool diameter, helix angle and the
numbers of tool flutes). The material coefficient is related to the tool and work-piece
materials. The wear coefficient is related to the tool life. The estimated cutting forces of
the analytical model were well matched with the experimental cutting force data.
Compared to the numerical procedures, computational time is extremely short. The model
is very convenient to study the characteristics of the cutting forces at various different
conditions and model based monitoring method is introduced for the first time in this
study.
188
The MOGART package developed in this study mainly includes three researches:
a) analytical cutting force model, b) neural network based experimental data processing
module and c) genetic algorithm based optimization routines. Experimental data can be
easily passed to the package through Excel worksheet or through import data file option.
Similarly, the results of any analysis can be transferred to a text document and an Excel
worksheet based chart .
For machinability study, back-propagation neural network was proposed for twodimension and three-dimension interpolation. The empirical maximum cutting force
estimation models and wear forecasting models of the micro-end-milling operations were
generated with acceptable errors by using a back-propagation neural network program
(NNTool). This program is a part of the MOGART package and has been tested on the
experimental data. The tool maximum cutting force and wear characteristics of micro-endmilling operations can be estimated at any cutting condition after the neural network was
trained. The program saved a lot of time in machinability studies. The back-propagation
neural network was found as an excellent interpolation tool for micro-end-milling and
other three-dimension cases.
In the first time, genetic algorithm was used to estimate the parameters of the
analytical model to monitor micro-end-milling operations. Wear, breakage, run-out,
cutting angles and optimal working conditions were estimated instantaneously without
requiring any prior experimental data analysis or training. The proposed approach was
found fast and accurate when it was tested on the simulated and experimental data. A
genetic algorithm program (GATool) is included in the MOGART package. The
189
MOGART was used for the estimation of optimal cutting condition, run-out, wear and
breakage. It minimized the cost of data processing and allowed analysis of identical data
by using different methods to compare the results.
For different micro-end-mills, work-pieces and working conditions of the microend-milling operations, over 800 milling operation experiments were performed and more
than 160 megabytes of cutting force data was collected for this study. The most
representative and reliable data were separated and used in this study.
The NNTool and GATool modules were designed for general purpose data
processing applications. A modified version of NNTool was used for environmental
engineering studies.
The following research work could be done to improve the presented work:
1. Improvement of the analytical model
- Identifying the difference between conventional and micro end milling machining
based on the experimental data.
- Investigation of tool wear at different operating conditions to improve the
empirical tool wear model.
- Addition of dynamic characteristics of the tools to the model.
2. On line monitoring
- Development of a monitoring system, which would estimate the tool wear and
evaluate the cutting conditions to keep the quality of the production at the
desired standards.
190
LIST OF REFERENCES
[1] J. Tlusty, P. Macneil,
"Dynamics of Cutting Forces In End Milling", Annals of the
CIRP, Vol. 24, No. 1, 1975, pp. 21-25.
[2] P. E. Gygax, "Dynamics of Single-Tooth Milling", IWF/ETH Zurich, Annals of the
CIRP, Vol. 28, No. 1, 1979, pp. 65-70.
[3] G. Yucesan, A. E. Bayoumi, L. A. Kendall, "An Analytic Cutting Force Model for
Milling", Transactions of the North American Manufacturing Research Institution of
SME 1990, May 1990, pp. 137-145.
[4] Krzysztof Jemlelniak , "Modelling of Dynamic Cutting Coefficients in ThreeDimensional Cutting", International Journal of Machine Tools & Manufacture, 1992,
Vol. 32, No. 4, pp. 509-519.
[5] J.-J. Junz Wang, S. Y. Liang, W. J. Book, "Convolution Analysis of Milling Force
Pulsatio", Journal of Engineering for Industry, February 1994, Vol. 116, pp. 17-25.
[6] Fangming Gu, S. G. Kapoor, R. E. DeVo, "An Approach to On-line Cutter Runout
Estimation in Face Milling", Transactions of the North American Manufacturing
Research Institution of SME, May 1991, pp. 240-247.
[7] J. W. Sutherland, R. E. DeVor, "An Improved Method for Cutting Force and Surface
Error Prediction in Flexible End Milling Systems", Journal of Engineering for Industry,
November 1986, Vol. 108, pp. 269-279.
191
[8] E. J. A. Armarego, N. P. Deshpande, "Computerized End-Milling Force Predictions
with Cutting Models Allowing for Eccentricity and Cutter Deflection", Annals CIRP,
Vol. 19, No. 1, 1991, pp. 25-29.
[9] H. S. Kim, K. F. Ehmann, "A Cutting Force Model for Face Milling Operatins",
International Journal of Machine Tools & Manufacture, 1993, Vol. 33, No. 5, pp.
651-673.
[10]Rosenblatt, F., "The Perceptron: A Probabilistic Model for Information Storage and
Organization in The Brain", Psychol. Rev., Vol. 65, pp. 386-408, 1958.
[11]Robert Hecht-Nielsen, "Neurocomputing", Addison-Wesley Publishing Company,
Inc., 1990.
[12]Russell C. Eberhart, Roy W. Dobbins, "Neural Network PC Tools: A Practical
Guide", Academic Press, Inc., 1990.
[13]Stephen T. Welstead, "Neural Network and Fuzzy Logic Applications In C/C++",
John Wiley & Sons, Inc., 1997.
[14]W.Y.Bao,
I.N.Tansel,
T.T.Arkan,
B.Tansel,
"Visualization
of Underground
Contamination with A Self Contained Package", Proceedings of the American Society
of Civil Engineers, Florida / South Florida Section Conference, September 18-20,
1997.
[15]I.N.Tansel,
W.Y.Bao,
T.T.Arkan,
B.Tansel,
"Visualization
of
Underground
Contamination by Using Neural Networks", Smart Engineering System: Neural Networks,
Fuzzy Logic, Data Mining, and Evolutionary Programming, Intelligent Engineering
192
Systems Through Artificial Neural Networks, Vol.7, pp. 1007-1012, ASME Press,
1997.
[16]I.N.Tansel, W.Y.Bao, T.T.Arkan, B.Shisler, M.McCool, and D.Smith, "Neural Network
Based Cutting Force Estimators for Micro-End-Milling Operations", Smart Engineering
System: Neural Networks, Fuzzy Logic, Data Mining, and Evolutionary Programming,
Intelligent Engineering Systems Through Artificial Neural Networks, Vol.7, pp. 885890, ASME Press, 1997.
[17]I.N.Tansel, W.Y.Bao, B.Tansel, C.M.Jordahl, "Modeling, Contamination Sites with
Trainable Networks",
Fuzzy Logic and Evolutionary Programming, Intelligent
Engineering Systems Through Artificial Neural Networks, Vol.5, pp.823-828, ASME
Press, 1995.
[18]Scott Robert Ladd, "Genetic Algorithms in C++", M&T Books, 1996.
[19]I.N.Tansel, W.Y.Bao, B.Tansel, B.Shisler, D.Smith and J.Murray, "Identification of
Cutting Conditions by Using an Analytical Model and Genetic Algorithms for MicroEnd-Milling Operations", Smart Engineering System Design: Neural Networks, Fuzzy
Logic, Rough Sets and Evolutionary Programming, Intelligent Engineering Systems
Through Artificial Neural Networks, Vol.8, pp. 779-784, ASME Press, 1998.
[20]S. D. J. A. Arsecularatne, G. Barrow, S. Hinduja, "Prediction of The Radial Force in
Turing Using Feed Force Data",
International
Manufacture, 1993, Vol. 33, No. 6, pp. 827-839.
193
Journal of Machine Tools &
[21]M. Liu, S. Y. Liang, "Monitoring of Peripheral Milling Using Acoustic Emission",
Transactions of the North American Manufacturing Research Institution of SME
1990, May 1990, pp. 120-127.
[22]P. Bandyopadhyay, E. M. Gonzalez, R. Huang, S. M. Wu, "A feasibility Study of on Line
Monitoring of DDS Methodology," International Journal of Machine Tool Design &
Research, 1986, Vol. 26, pp. 245-257.
[23]T. I. Liu, "Automated Visual Inspection of drill wear", ASME Manufacturing International
Conference, Atlanta, Georgia, 1990.
[24]K. Uehara, "New Attempts for Short time tool life testing", Annals of the CIRP, 1973,
Vol. 22, pp. 23.
[25]M. E. Merchant, E. J. Krabacher, "Radioactive Tracers for Rapid Measurements of
Cutting Tool Life", Journal of Applied Physics, 1951, Vol. 22, pp. 1507-1508.
[26]J. C. Principle, T. Yoon, " A New Algorithm for The Detection of Tool Breakage in
Milling", International Journal of Machine Tools & Manufacture, 1991, Vol. 31, No. 4,
pp. 443-454.
[27]I.N.Tansel, M.Trujillo, A.Nedbouyan, C.Velez, W.Y.Bao, T.T.Arkan and B.Tansel,
"Micro-end-milling-III: Wear estimation and tool breakage detection using acoustic
emission signals", Machine Tools & Manufacture, Vol.38, No.12, pp.1449-1466,
December 1998.
[28]I.N.Tansel, M.Trujillo, W.Y.Bao, T.T.Arkan, "Detecting Microtool Failures," Cutting
Tool Engineering, Vol.49, No.6, pp.54-62, September, 1997.
194
[29]I.N.Tansel, M.Trujillo, W.Y.Bao, T.T.Arkan, "Detection of Tool Breakage in MicroEnd-Milling Operations by Monitoring Acoustic Emission", Technical Papers of the
North American Manufacturing Research Institution of Society of Manufacturing
Engineers (NAIMIRI SME 1997), pp. 6 9 - 7 4 , May 20-23, 1997.
[ 3 0]I.N.Tansel, M.E.Trujillo, W.Y.Bao, T.T.Arkan, "Tool Breakage Detection in the
Micro-Machining of Aluminium by Monitoring Acoustic Emission", Proceedings of
the 1997 Florida Conference on Recent Advances in Robotics, pp.230-234, April 1011, 1997.
[31]I.N.Tansel, W.Y.Bao, M.Trujillo, O.Rodriguez, T.T.Arkan, "Detection of Prefailure
Phase in Micro-End-Milling operations", presented at the Industrial Engineering
Research Conference (IERC Solutions'97), May 17-18, 1997.
[32]S. Y. Liang, D. A. Donfeld, "Tool Wear Detection Using Time Series Analysis of
Acoustic Emission", Joural of Engineering for Industry, August 1989, Vol. 111, pp. 199205.
[33]M. A. Elbestawi, T. A. Papazafiriou, R. X. Du, "In-process Monitoring of Tool Wear in
Milling Using Cutting Force Signature", International Journal of Machine Tools &
Manufacture, 1991, Vol. 31, No. 1, pp. 55-73.
[34]K. Glass, R. Colbaugh, "Real-Time Tool Wear Estimation Using Cutting Force
Measurements", Interational Conference on Robotics and Automation, Minneapolis,
Minnesota, April 1996, pp. 3067-3072.
195
[35]M. A. El Baradie, "Statistical Analysis of the Dynamic Cutting Coefficients and Machine
Tool Stability", Transactions of The ASME, Journal of Engineering for Industry, May
1993, Vol. 115, pp. 205-215.
[36]I. N. Tansel, C. McLaughlin, "Detection of Tool Breakage in Milling Operations- Time
Series Approach", International Journal of Machine Tools Manufacture, Vol. 33, No. 4,
1993, pp. 531-544.
[37]T. J. Ko, D. W. Cho, "Tool Wear Monitoring in Diamond Turning by Fuzzy Pattern
Recognition", Transactions of The ASME, Journal of Engineering for Industry, May
1994, Vol. 116, pp. 225-232.
[38]I. N. Tansel, O. Rodriguez, M. Trujillo, E. Paz, W. Li, "Wear Induced Stress (WIS) And
Tool Breakage in Micro-End-Milling", Intelligent Engineering Systems Through Artificial
Neural Networks, November 1995, Vol. 5, pp. 867-872.
[39]I.N.Tansel, W.Y.Bao, T.T.Arkan and B.Shisler, "Wear Estimation in Micro-End
Milling with Wavelet Transformations and Probabilistic Neural Networks", Smart
Engineering System Design: Neural Networks, Fuzzy Logic, Rough Sets and Evolutionary
Programming, Intelligent Engineering Systems Through Artificial Neural Networks,
Vol.8, pp. 755-760, ASME Press, 1998.
[40]I. N. Tansel, C. McLaughlin, "Detection of Tool Breakage in Milling Opeartions - Neural
Network Approach", Int. Journal of Machine Tools Manufact., Vol 33, No. 4, 1993, pp.
545-558.
[41]Y. Chao, Y. D. Hwang, "An Improved Neural Network Model for The Prediction of
Cutting Tool Life", Journal of Intelligent Manufacturing, 1997, Vol. 8, pp. 107-115.
196
[42]I.N.Tansel, W.Y.Bao, T.T.Arkan, B.Shisler, M.McCool, A.Jinks, and D.Smith, "Wear
Estimation for Micro-Machining of Non-Metal Materials", Smart Engineering System:
Neural Networks, Fuzzy Logic, Data Mining, and Evolutionary Programming, Intelligent
Engineering Systems Through Artificial Neural Networks, Vol.7, pp.903-908, ASME
Press, 1997.
[43]Milton C. Shaw, "Metal Cutting Principles", Oxford University Press, New York, 1986.
[44]S. M. Pandit, S. M. Wu, "Time Series and System Analysis with Applications",
John
Wiley and Sons, Inc., 1983.
[45]Timothy Masters, "Advanced Algorithms for Neural Networks", John Wiley & Sons,
Inc., 1995.
[46]B.Tansel, I.N.Tansel, W.Y.Bao, "Neural Network Based performance Estimator for
High Energy Electron Beam Irradiation Process", Smart Engineering System Design:
Neural Networks, Fuzzy Logic, Rough Sets and Evolutionary Programming, Intelligent
Engineering Systems Through Artificial Neural Networks, Vol.8, pp. 839-844, ASME
Press, 1998.
197
VITA
Wei-Yu Bao
1982
B.S., Power Machinery Engineering
Shanghai Jiao Tong University
Shanghai, China
1982-1985
Shanghai Ocean Fishery Company, China
1988
M.S., Power Machinery Engineering
Shanghai Jiao Tong University
Shanghai, China
1988-1990
Shanghai Jiao Tong University, China
PUBLICATIONS AND PRESENTATIONS
Published Journal Papers:
"Micro-end-milling-III: Wear estimation and tool breakage detection using
acoustic emission signals", I.N.Tansel, M.Trujillo, A.Nedbouyan, C.Velez, W.Y.Bao,
T.T.Arkan and B.Tansel, "Machine Tools & Manufacture", Vol.38, No.12, pp. 1449-1466,
December 1998.
2. "Detecting Microtool Failures," I.N.Tansel, M.Trujillo, W.Y.Bao, T.T.Arkan, "Cutting
Tool Engineering", Vol.49, No.6, Vol.8, pp.54-62, September, 1997.
*
1.
Refereed Papers Published in Books:
"Identification of Cutting Conditions by Using an Analytical Model and Genetic
Algorithms for Micro-End-Milling Operations", I.N.Tansel, W.Y.Bao, B.Tansel,
B.Shisler, D.Smith and J.Murray, Vol.8, pp. 779-784, 1998.*
4. "Wear Estimation in Micro-End Milling with Wavelet Transformations and
Probabilistic Neural Networks", I.N.Tansel, W.Y.Bao, T.T.Arkan and B.Shisler,
Vol.8, pp. 755-760, 1998.*
5. "Neural Network Based performance Estimator for High Energy Electron Beam
Irradiation Process", B.Tansel, I.N.Tansel, W.Y.Bao, Vol.8, pp. 839-844, 1998.*
* Presented at the Artificial Neural Networks In Engineering (ANNIE'98) Conference and
published at the Smart Engineering System Design: Neural Networks, Fuzzy Logic, Rough
"
3.
Sets and Evolutionary Programming, Intelligent Engineering Systems Through Artificial
Neural Networks, edited by Drs. Dagli, Akay, Buczak, Ersoy, and Fernandez, ASME
Press, New York, 1998.
198
6. "Neural Network Based Cutting Force Estimators for Micro-End-Milling
Operations", I.N.Tansel, W.Y.Bao, T.T.Arkan, B.Shisler, M.McCool, and D.Smith,
Vol.7, pp.885-890, 1997.**
7. "Wear Estimation for Micro-Machining of Non-Metal Materials", I.N.Tansel,
W.Y.Bao, T.T.Arkan, B.Shisler, M.McCool, A.Jinks, and D.Smith, Vol.7, pp. 9 0 3 - 9 0 8 ,
1997.**
8.
"Visualization of Underground
Contamination
by Using Neural
Networks",
I.N.Tansel, W.Y.Bao, T.T.Arkan, B.Tansel, Vol.7, pp.1007-1012, 1997.**
** Presented at the Artificial Neural Networks In Engineering (ANNIE'97) Conference and
published at the Smart Engineering System: Neural Networks, Fuzzy Logic, Data Mining,
and Evolutionary Programming
Intelligent Engineering Systems Through Artificial
Neural Networks, edited by C.H.Dagli, M.Akay, O.Ersoy, B.R.Fernandez, and A.Smith,
ASME Press, New York, 1997.
9.
"Modeling, Contamination Sites with Trainable Networks", I.N.Tansel, W.Y.Bao,
B.Tansel, C.M.Jordahl, presented at the Artificial Neural Networks in Engineering
(ANNIE'95) Conference and published at the Fuzzy Logic and Evolutionary
Programming, Intelligent Engineering Systems Through Artificial Neural Networks,
Vol.5, pp.823-828, ASME Press, New York, 1995.
" Published Conference Papers:
10. "Visualization of Underground Contamination with A Self Contained Package",
W.Y.Bao, I.N.Tansel, T.T.Arkan, B.Tansel, Proceedings of the American Society of
Civil Engineers, Florida / South Florida Section Conference, September 18-20, 1997.
11. "Detection of Tool Breakage in Micro-End-Milling Operations by Monitoring
Acoustic Emission", I.N.Tansel, M.Trujillo, W.Y.Bao, T.T.Arkan, Technical Papers of
the North American Manufacturing Research Institution of Society of Manufacturing
Engineers (NAMRI SME 1997), pp.69-74, May 20-23, 1997.
12. "Detection of Prefailure Phase in Micro-End-Milling Operations", I.N.Tansel,
W.Y.Bao, M.Trujillo, O.Rodriguez, T.T.Arkan, presented at the Industrial Engineering
Research Conference (IERC Solutions'97), May 17-18, 1997.
13. "Tool Breakage Detection in the Micro-Machining of Aluminium by Monitoring
Acoustic Emission", I.N.Tansel, M.E.Trujillo, W.Y.Bao, T.T.Arkan, Proceedings of
the 1997 Florida Conference on Recent Advances in Robotics, pp.230-234, April 1011, 1997.
14. "Prototyping for High-Tech Consumer Products", B.Shisler, D.Johnson, D.Smith,
I.N.Tansel, W.Y.Bao, T.T.Arkan, Proceedings of the 1997 Florida Conference on
Recent Advances in Robotics, pp. 2 4 - 2 6 , April 10-11, 1997.
15. "Design and Realization of an Automated Log Strip Seperator", I.N.Tansel,
T.T.Arkan, W.Y.Bao, J.Shaw, C.A.Velez, T.C.Yih, S.Tosunoglu, I.Fernandez,
B.Tansel, Proceedings of the 1997 Florida Conference on Recent Advances in
Robotics, pp.8-11, April 10-11, 1997.
16. "Solving industrial Problems in Mechatronics Class",
I.N.Tansel, T.T.Arkan,
W.Y.Bao, J.Show, C.A.Veldez, T.C.Yih, S.Tosunoglu, I.Fernandez, Proceedings of
Mechatronics 96, June 13-15, 1996.
199
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