Chen, Joseph C. "Neural Networks and Neural-Fuzzy Approaches in an In-Process Surface
Roughness Recognition System for End Milling Operations"
Computational Intelligence in Manufacturing Handbook
Edited by Jun Wang et al
Boca Raton: CRC Press LLC,2001

©2001 CRC Press LLC

16

Neural Networks and
Neural-Fuzzy
Approaches in an
In-Process Surface
Roughness Recognition
System for End

Milling Operations

16.1 Introduction

16.2 Methodologies

16.3 Experimental Setup and Design

16.4 The In-Process Surface Roughness Recognition
Systems

16.5 Testing Results and Conclusions

16.1 Introduction

predicting the two- or three-dimensional shape of a milled surface under ideal and non-ideal conditions.
Kline et. al. [1982] demonstrated the effects of cutter runout on surface errors, and surface errors or
dimensional inaccuracies were predicted using the cantilever beam theory for cutter runout. Another
study by Babin et al. [1985] applied the cantilever beam theory to predict the topography of wall surfaces
produced by end milling. Armarego and Deshpande [1989] presented one more milling process geometry
model that incorporates cutter runout to predict cutting forces.
Sutherland and Babin [1985] demonstrated a two-dimensional worst-case analysis of the slot floor
surface. However, the model for the slot floor surface significantly underpredicted surface roughness
values. Research by Kolarits and DeVries [1989] extended the previous model to account for varying cut
geometries and feed rates. This extended floor surface generation model improved prediction capabilities
considerably. However, the roughness parameter predictions for some of the tests were found to deviate
greatly from measured values.
You and Ehmann [1989] developed a comprehensive model to predict the three-dimensional surface
texture generated by ball end mills. They also presented an algorithm for three-dimensional representa-
tions of the machined surface; however, the effect of flexibility of the cutter-workpiece system was not
considered in this model. Montgomery and Altintas [1991] presented the effects of the cutter-workpiece
system flexibility in their force and surface prediction model in order to analyze the surface generation
mechanism in peripheral milling under dynamic cutting conditions.
All models previously discussed represent only deterministic cutting models, but most machined
surfaces exhibit interrelated characteristics of both random and deterministic components. Zhang and
Kapoor [1991] demonstrated the effect of random vibrations on surface roughness in the turning process.
These vibrations were shown to occur due to random variations in the microhardness of the workpiece
material. Ismail and others presented a surface generation model in milling that included both cutter
vibrations and the effects of tool wear [Ismail et al., 1993]. Melkote and Thangaraj [1994] presented
another enhanced end milling surface texture model including the effects of radial rake and primary
relief angles. These three models, limited to laboratory usage or based on theoretical analysis, could not
be implemented as an in-process monitoring system.
The findings of this literature review, in addition to communication with leading private industrial
research and development laboratories in the state of Iowa (including Winnebago Co. in Forest City;
Delavan Inc. in Des Moines; Sauer-Sundstrand Inc. in Ames), point to the feasibility of in-process surface

additionally, it has been consistently successful when used in practical applications [Das et al., 1996;
Huang and Chiou, 1996].
The backpropagation algorithm can be divided into two main processes, the process of

learning

and
the process of

recalling

.

16.2.1.1 The Learning Process

Step 1. Given network parameters:
Set all the necessary parameters, such as the number of input neurons (

i

), the number of
hidden layers and the number of neurons included in each hidden layer (

h

), the number of
output neurons (

j


Equation (16.4)
Step 5: Calculate the error term.
(a) The error term of the output layer:
Equation (16.5)
(b) The error term of the hidden layer: Equation (16.6)
net W xh X h
hih
i
ih
=•
∑
_–_
θ
H f net
hh
net
h
=
()
=
+
1
1 exp
–
net W hy H y
jh hj h j
=〈−__
θ
Y f net
jj


Step 6: Calculate the revised weight of the weight matrix and the revised bias of the bias vector.
(a) For the output layer:
Equation (16.7)
(b) For the hidden layer: Equation (16.8)
Step 7: Adjust and renew the weight matrix and the bias vector.
(a) For the output layer:

W_hy

hj

= W_hy

hj
+

∆

W_hy

hj

,

θ



ih

= W_xh

ih
+

∆

W_xh

ih

,

θ

_h

h

=

θ

_h

θ_

h

and

θ_

y

.
Step 3: Load the input vector

X

of a testing example.
Step 4: Calculate and infer the actual output Y.
(a) Calculate the output vector

H

of hidden layers.
Equation (16.11)
Equation (16.12)
(b) Infer the actual output vector

Y

.
Equation (16.13)

+

]. Each domain interval can be divided into 2

N

+ 1 regions. The value of

N

is dynamic for different variables, and the lengths of each region can be equal or unequal. Each
region is denoted by
∆∆
Why H y
hj j h j j
_,_–==
ηδ θ ηδ

∆∆
Wxh X h
ih h i h h
_,_–==
ηδ θ ηδ

net W xh X h
hih
i
ih
=•
∑

1 exp
–
xx
ii
–
,
+
[]

©2001 CRC Press LLC

SN (Small N), S(N-1) (Small N-1), …, MD (Medium), … , LN (Large N),

Equation
(16.15)
and then assigned a fuzzy membership function. The divisions of the input and output spaces are shown
in Figure 16.1, where

N

is 2 for

x


). The output variable is the surface roughness average value,

R

a

. A triangular
membership function specified by three parameters {

a

,

b

,

c

} is employed as follows:
Equation (16.16)

FIGURE 16.1

The domain intervals of the input–output variables and triangular membership function.
MDS1S2S3 L1 L2 L3
0
1
x
2

xa
xa
ba
axb
cx
cb
bxc
cx
;,,
–
–
–
–
()
=
≤
≤≤
≤≤
≤









0
0

X

i

.
The center points of each linguistic variable are
Equation (16.18)
Equations 16.17 and 16.18 are also used for the output variable

y.

16.2.2.2 Step 2. Generate Fuzzy Rules from Given Data Pairs through Experimentation

Three steps are used for generating fuzzy rules:
1. Determine the degree of input–output data obtained from the successful experiment.
2. Assign the input–output pairs to the region with the maximum degree.
3. Obtain one rule from one pair of designated input–output data.
In this study, the experimental input–output pairs were
Equation (16.19)
where

i

denotes the number of input–output pairs.
1. A human expert examined these rules to ensure their usefulness and correctness.
2. The degrees of each data pair were determined by the function
Equation (16.20)
where

x

S

1

,

F

1

,

D

1

,

V

1

,

R

a

1


,, ,, ,
[]
µ
x
xx
x
xxxx
xx
x
xxxx
i
ic
s
iccs
ci
s
icsc
()
=
∈+
[]
∈
[]








and

F

1

is

L

3 and

D

1

is

L

2 and

V

1

is

S


(F
i
) = the degree of the feed rate variable,
µ
(D
i
) = the degree of the depth of cut variable,
µ
(V
i
) = the degree of the vibration variable,
µ
(R
a
i
) = the degree of the surface roughness variable,
µ
(E
i
) = the degree assigned by the human expert to determine the importance of this rule.
The following function resolved the conflict between rules:
Equation (16.25)
where R
k
and R
l
are two conflicting rules, d(R
k
) and d(R
l

03 07 1
()
=∈ ∈
{}
()
=∈ ∈
{}
()
=∈ ∈
{}
()
=∈ ∈
{}
()
=∈ ∈
{}.,.MD, S
L, L
LL
MD, S
S2, S
SMDFLDLVSRS
a
1 1111
3211∈ ∈∈∈∈,, ,,.

i
= the center value of the region, and y = the output
for a given input datum. This is the most widely adopted defuzzification strategy today, and it is
reminiscent of the calculation of expected values of probability distributions.
16.3 Experimental Setup and Design
Figure 16.3 shows the complete experimental setup in this research. A computer numerical control (CNC)
program was written to perform the end milling cutting processes. The electromagnetic proximity sensor
was fixed at a close distance to the spindle, as shown in Figure 16.4, and the accelerometer sensor was
mounted on the vise beneath the workpiece (Figure 16.5).
Rotation and vibration data were collected simultaneously by the proximity sensor and the acceler-
ometer sensor, respectively, when the cutter had cut the workpiece at a distance of 0.35 in. The main
concern was to avoid the impact of initially unstable or significant vibration. Figure 16.6 illustrates the
two types of signals (i.e., rotation data and vibration data). These two types of data were connected to
an analog-to-digital (A/D) board (the vibration data from the accelerometer sensor had to be amplified
by the PCB battery power unit beforehand) and then transmitted to a 486 personal computer for further
data recording, processing, and analysis.
FIGURE 16.2 Illustration of a combined fuzzy rule base.
F
L2
L1
MD
S1
S2
S2
S1 MD
L1
L2
S
L1
S1

between cutting vibrations and surface roughness in end milling.
With the experimental setup complete, the next step was to develop the ISRR-ANN and -FN models.
In this study, identifying the parameters of the training and testing data sets was a very important factor
in establishing the experimental runs. These runs could not exceed the suggested cutting parameters,
which were based on machine capabilities and the nature of the material composition of both the
workpiece and end mill.
FIGURE 16.3 Experimental setup.
VM
DESIGNER:
Wei-Liang
DESIGNER:
Wei-Liang
Proximity Sensor
CNC
Machine
Center
Accelerometer
Sensor
A/D Board
486 Personal Computer
Workpiece
Vise
PCB Battery
Power Unit
©2001 CRC Press LLC
16.3.1 Training and Testing Experiments
A total of 48 specimens were cut based on the following combination of cutting parameters: four levels
of spindle speed (S = 750, 1000, 1250, and 1500 rpm); four levels of feed rate (F = 6, 12, 18, and 24
in./min); and three levels of depth of cut (D = 0.01, 0.03, and 0.05 in.).
After these cuts were made, all specimens were measured off-line with a stylus profilometer to obtain

flexible testing data set (Table 16.1). Therefore, a total of 128 pieces of data were used to evaluate the
accuracy of ISRR systems. The evaluation criteria are summarized in the next section.
16.3.2 Test Criteria
Criteria used in this experiment to judge the predictive capabilities of the ISRR–ANN and FN systems
included the percentage deviation (
φ
i
) of each testing sample, given as:
Equation (16.28)
where
φ
i
= percentage deviation of single sample data
= actual R
a
measured by a profilometer
= predicted R
a
generated by the ISRR systems; M indicates the predicted value using ISRR-
ANN or ISRR-FN models, respectively.
Additionally, the overall average percentage deviation (
φ
) of all 128 samples is given as
Equation (16.29)
where
–
φ
= average percentage deviation of all sample data
m = the size of testing samples; in this study m = 128.
16.4 The In-Process Surface Roughness Recognition Systems

590
621
652
683
714
745
776
807
Data poipnts
Vibration data
Revolution data
Voltage
φ
i
iiM
i
Ra Ra
Ra
=
′
′
×
–
%,
,
~
100
Ra
i
′

1 750 6 0.01 65.40
2 750 6 0.03 62.75
3 750 6 0.05 72.40
4 750 12 0.01 143.85
5 750 12 0.03 101.90
6 750 12 0.05 94.05
7 750 18 0.01 184.80
8 750 18 0.03 146.60
9 750 18 0.05 121.05
10 750 24 0.01 186.55
11 750 24 0.03 170.40
12 750 24 0.05 172.40
13 1000 6 0.01 58.40
14 1000 6 0.03 78.30
15 1000 6 0.05 62.20
16 1000 12 0.01 129.90
17 1000 12 0.03 83.60
18 1000 12 0.05 92.05
19 1000 18 0.01 137.50
20 1000 18 0.03 124.15
21 1000 18 0.05 85.75
22 1000 24 0.01 163.15
23 1000 24 0.03 153.30
24 1000 24 0.05 142.30
25 1250 6 0.01 49.95
26 1250 6 0.03 63.30
27 1250 6 0.05 70.85
28 1250 12 0.01 101.30
29 1250 12 0.03 98.75
30 1250 12 0.05 84.95

parameters, and ISRR-FN. In this sensing system, an accelerometer sensor was used to measure the real-
time vibration of the workpiece, a proximity sensor was used to measure the real-time rotation of the
spindle of the CNC machine center, and an A/D board and interface program were applied for analog-
to-digital conversion with 12-bit resolution. Machining parameters, such as spindle speed, feed rate, and
depth of cut, were transmitted to the ISRR-FN before or during machining.
The primary objective was to train the fuzzy system by generating fuzzy rules from input–output pairs,
and combining these generated and linguistic rules into a common fuzzy rule base. After input vectors
were fuzzified by the fuzzification interface, the fuzzy inference engine generated output values by
inferencing these fuzzified input values based on the fuzzy rule bank. Finally, the defuzzification interface
determined the final prediction of R
a
values based on input variables. Through training, the ISRR-FN
learned to detect different conditions for individual machines, build the fuzzy rule base, and infer the
surface roughness, R
a
. All of these processes were based on the experimental data.
Before the fuzzy-nets training takes up the experimental data, some parameters need to be preset based
on the limitations of the machine and the machining processes. They are summarized as follows:
1. The domain intervals of the input–output data pairs were assigned as follows:
• Spindle speed: [500, 2000] rpm
• Feed rate: [6, 42] inches per minute
• Depth of cut: [0.01, 0.07] inches
• Vibration: [780, 2460] microvolts
•R
a
: [38, 168] micro inches
FIGURE 16.7 Structure of the ISRR-ANN.
ISRR-ANN
Ra
Input Output

in Section 3.1 were used for testing the accuracy of these two systems.
Using the same four variables (spindle speed, feed rate, depth of cut, and the VAPR) as independent
variables or input neurons, predicted roughness R
a
values (response variable or output neuron) were
generated for either the ANN or FN model. Tables 16.2 and 16.3 contain the measured R
a
values and
their predicted R
a
values, as well as the percentage deviation of both ISRR systems with the 92-item
testing set and the 36-item flexible testing set, respectively. Considering the percentage deviation, both
models performed well in their ability to predict the roughness of machined surfaces. In summary, the
prediction accuracy of ISRR-FN, ISRR-ANN 4-5-1, and ISRR-ANN 4-7-7-1 models are 95.78%, 95.87%,
and 99.27%, respectively.
16.5.2 Conclusions
The fuzzy logic and neural-networks-based ISRR models demonstrated that learning and reasoning
capabilities could be used for an in-process surface roughness recognition system. With better than 95%
FIGURE 16.8 Structure of the ISRR-FN.
Fuzzy Rule Bank
Fuzzifier
Deffuzzifier
Fuzzy Inference
Engine
ISRR-FN
Ra
Machining
Process
Machining
Parameters

1500 12 5 0.1225 94 91 94
750 12 3 0.1509 102 104 100
1500 12 1 0.1249 88 83 87
1000 24 5 0.1859 142 146 142
1000 6 3 0.1013 78 73 76
1250 6 1 0.8855 50 44 49
1250 12 1 0.1418 100 104 101
750 6 3 .01045 63 68 64
1500 18 5 0.1509 104 102 104
1000 18 5 0.1647 86 105 86
1500 12 5 0.1180 94 92 94
1250 6 5 0.0974 71 67 71
1500 12 3 0.1232 82 85 82
1000 18 3 0.1691 124 108 124
750 18 5 0.1656 121 128 121
1250 18 1 0.1252 115 116 116
1500 12 1 0.1203 88 84 84
1250 18 1 0.1266 115 117 116
1500 6 3 0.1119 56 57 55
1000 12 3 0.1391 84 91 84
1250 18 5 0.2122 95 102 94
1500 24 3 0.2164 103 106 103
1000 6 5 0.0989 62 69 63
1250 12 5 0.1253 85 93 85
1250 18 3 0.1700 92 100 92
1500 24 1 0.1372 120 125 118
1000 18 3 0.1592 124 109 124
1500 12 1 0.1151 88 85 84
750 18 5 0.1699 121 126 121
750 6 1 0.0899 66 63 64

the machine table. Thus, a study of interface techniques between the ISRR system and the CNC
machining center is also necessary.
TABLE 16.2 (continued) Testing Data Set—92 Samples
Spindle
Speed Feed Rate Depth of cut Vibration R
a
R
a
ANN 4-5-1
R
a
ANN 4-7-7-1
1500 12 3 0.1101 82 84 82
1500 18 5 0.1500 104 102 105
1250 12 1 0.1288 100 106 101
1500 6 3 0.1084 56 57 55
1250 12 5 0.1253 85 93 85
1500 6 1 0.0647 37 39 36
1500 18 3 0.1359 87 96 87
1000 24 1 0.1187 163 166 163
1500 12 3 0.1151 82 84 82
750 6 3 0.1028 63 68 65
1500 24 1 0.1394 120 125 118
1500 12 3 0.1233 82 85 82
1250 24 1 0.1316 156 153 155
1000 12 5 0.1832 92 92 92
1500 24 1 0.1339 120 126 118
1500 24 1 0.1374 120 125 118
1000 18 1 0.1011 138 139 137
750 18 3 0.1734 147 145 147

Das, S., Roy, R., and Chaptopadhyay, A. B., 1996. Evaluation of wear of turning carbide inserts using
neural networks, Int. J. Mach. Tools Manuf., 36(7), pp. 789-797.
TABLE 16.3 Flexible Testing Data — 36 Samples
Sample No.
Spindle
Speed (rpm)
Feed Rate
(ipm)
Depth of Cut
(in.) VAPR
Measured R
a

(
µ
in.)
ISRR-FN R
a
ISRR-FN
1 1500 9 0.01 0.0883 53 53
2 1500 9 0.03 0.1110 74 74
3 1500 9 0.05 0.1056 70 70
4 1500 15 0.01 0.1464 110 110
5 1500 15 0.03 0.1256 84 84
6 1500 15 0.05 0.1638 99 99
7 1500 21 0.01 0.1473 119 119
8 1500 21 0.03 0.1787 102 102
9 1500 21 0.05 0.1980 113 113
10 1250 9 0.01 0.1197 80 80
11 1250 9 0.03 0.1381 82 82

Kline, W. A., DeVor, R. E., and Shareef, I. A., 1982, The prediction of surface accuracy in end milling,
ASME J. Eng. Ind., 104, pp. 272-278.
Kolarits, F. M. and DeVries, W., 1989, A model of the geometry of the surface generated in end milling
with variable process inputs, in Mechanics of Deburring and Surface Finishing Processes, J. R. Stango,
and P. R. Fitzpatrick, Eds., ASME, PED, vol. 38, pp. 63-78.
Martellotti, M. E., 1941, An analysis of the milling process, Trans. ASME. 12:677-700.
Martellotti, M. E., 1945, An analysis of the milling process, part II — Down milling, Trans. ASME, 67,
pp. 233-251.
Melkote, S. N. and Thangaraj, A. R., 1994, An enhanced end milling surface texture model including the
effects of radial rake and primary relief angles, ASME J. Eng. Ind., 116, pp. 166-174.
Montgomery, D. and Altintas, Y., 1991, Machanism of cutting force and surface generation in dynamic
milling, ASME J. Eng. Ind., 113 (1), pp. 160-168.
Sutherland and Babin 1985,
You, S. J. and Ehmann, K. F., 1989, Scallop removal in die milling by tertiary cutter motion, ASME J.
Eng. Ind., 111, pp. 213-219.
Zhang, G. M. and Kapoor, S. G., 1991, Dynamic generation of machined surface, part 1: Description of
a random excitation system, ASME J. Eng. Ind., 113(3), pp. 137-144.
Zhang, G. M. and Kapoor, S. G., 1991b, Dynamic generation of machined surface, part 2: Construction
of surface topography, ASME J. Eng. Ind., 113(3), pp. 145-153.