An investigation of modeling of the machiningdatabase in turning operations

B.Y. Leea, Y.S. Tarngb,*, H.R. Liic

aDepartment of Mechanical Manufacture Engineering, National Huwei Institute of Technology, Yunlin 632, Taiwan, ROCbDepartment of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan, ROC

cAeronautical Research Laboratory, Aeronautical Industrial Development Center, Chung Shan Institute of Science and Technology,

Taichung, Taiwan, ROC

Received 15 November 1998

Abstract

Modeling of the machining database in turning operations has been investigated in this paper. The machining database is constructed

based on polynomial networks. The polynomial networks can learn the relationships between cutting parameters (cutting speed, feed rate,

and depth of cut) and cutting performance (tool life, surface roughness, and cutting force) through a self-organizing adaptive modeling

technique. Experimental results have been shown that the machining database in turning operations can be modeled well through this

approach. # 2000 Elsevier Science S.A. All rights reserved.

Keywords: Modeling; Machining database; Turning; Polynomial networks

1. Introduction

Turning is a commonly used machining operation in the

manufacturing processes. Therefore, modeling of the

machining database to associate cutting parameters with

cutting performance is very important for the industry. In the

past, several mathematical models have been formulated to

establish the machining database [1±6]. In reality, reliable

mathematical models are not easy to obtain and the applica-

tion of the developed models in machining is still limited

due to the insuf®cient interpolation ability for different

machining conditions. In recent years, the use of adaptive

learning tools to construct the machining database for

associating the cutting parameters with cutting performance

has gradually been accepted as a reliable, effective modeling

technique [7±11]. This is because adaptive learning tools

have an excellent ability to learn and to interpolate the

complicated relationships between cutting parameters and

cutting performance.

In this paper, a polynomial network [12] is used to

construct the relationships between the cutting parameters

(cutting speed, feed rate, and depth of cut) and cutting

performance (tool life, surface roughness, and cutting force).

The polynomial network is a self-organizing adaptive mod-

eling tool for constructing the mathematical relationships

between input and output variables. It has been shown that

the polynomial network has a great representational power

for dealing with highly nonlinear, strongly coupled, multi-

variable systems [13]. A comparison between the polyno-

mial network and back-propagation network has shown that

the polynomial network has higher prediction accuracy and

fewer internal network connections [14]. The best network

structure, number of layers, and functional node types can be

determined by using an algorithm for synthesis of polyno-

mial networks (ASPN) [15].

The paper is organized in the following manner. Poly-

nomial networks are introduced ®rst. The use of polynomial

networks to construct a machining database is given next.

Finally, experimental veri®cation of the machining database

is shown.

2. Polynomial networks

The polynomial networks proposed by Ivakhnenko [12]

are a group method of data handling (GMDH) techniques

[16]. In a polynomial network, complex systems are decom-

posed into smaller, simpler subsystems and grouped into

several layers by using polynomial functional nodes. Inputs

Journal of Materials Processing Technology 105 (2000) 1±6

* Corresponding author. Tel.: �886-2-2737-6456;

fax: �886-2-2737-6460.

E-mail address: ystarng@mail.ntust.edu.tw (Y.S. Tarng).

0924-0136/00/$ ± see front matter # 2000 Elsevier Science S.A. All rights reserved.

PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 5 3 5 - 5

of the network are subdivided into groups, then transmitted

into individual functional nodes. These nodes evaluate the

limited number of inputs by a polynomial function and

generate an output to serve as an input to subsequent nodes

of the next layer. The general methodology of dealing with a

limited number of inputs at a time, then summarizing the

input information, and then passing the summarized infor-

mation to a higher reasoning level is directly related to

human behavior observed by Miller [17]. Therefore, poly-

nomial networks can be recognized as a special class of

biologically inspired networks with machine intelligence

and can be used effectively as a predictor for estimating the

outputs of complex systems.

2.1. Polynomial functional nodes

The general polynomial function known as the Ivakh-

nenko polynomial in a polynomial functional node can be

expressed as

y0 � w0 �Xm

i�1

wixi �Xm

i�1

Xm

j�1

wijxixj

�Xm

i�1

Xm

j�1

Xm

k�1

wijkxixjxk � � � � (1)

where xi, xj, xk are the inputs, y0 the output, and

w0;wi;wij;wijk are the coef®cients of the polynomial func-

tional node.

In the present study, several speci®c types of polynomial

functional nodes (Fig. 1) are used in the polynomial network

for the modeling of cutting performance in turning opera-

tions. An explanation of these polynomial functional nodes

is given as follows.

2.1.1. Normalizer

A normalizer transforms the original input into the nor-

malized input and the corresponding polynomial function

can be expressed as

y1 � w0 � w1x1 (2)

where x1 is the original input, y1 the normalized input, and

w0;w1 are the coef®cients of the normalizer.

During this normalization process, the normalized input

y1 is adjusted to have a mean of zero and a variance of one.

2.1.2. Unitizer

On the other hand, a unitizer converts the output of the

network to the real output. The polynomial equation of the

unitizer can be expressed as

y1 � w0 � w1x1 (3)

where x1 is the output of the network, y1 the real output, and

w0;w1 are the coef®cients of the unitizer.

The mean and variance of the real output must be equal to

those of the output used to synthesize the network.

2.1.3. Single node

The single node only has one input and the polynomial

equation is limited to the third degree, that is

y1 � w0 � w1x1 � w2x21 � w3x3

1 (4)

where x1 is the input to the node, y1 the output of the

node, and w0;w1;w2 and w3 are the coef®cients of the single

node.

2.1.4. Double node

The double node takes two inputs at a time and the third-

degree polynomial equation has the cross-term so as to

consider the interaction between the two inputs, that is

y1 � w0 � w1x1 � w2x2 � w3x21 � w4x2

2 � w5x1x2

� w6x31 � w7x3

2 (5)

where x1, x2 are the inputs to the node, y1 the output of the

node, and w0;w1;w2; . . . ;w7 are the coef®cients of the

double node.

2.1.5. Triple node

Similar to the single and double nodes, the triple node

with three inputs has more complicated polynomial equation

Fig. 1. Various polynomial functional nodes.

2 B.Y. Lee et al. / Journal of Materials Processing Technology 105 (2000) 1±6

allowing the interaction among these inputs, that is

y1 � w0 � w1x1 � w2x2 � w3x3 � w4x21 � w5x2

2

� w6x23 � w7x1x2 � w8x1x3 � w9x2x3

� w10x1x2x3 � w11x31 � w12x3

2 � w13x33 (6)

where x1, x2, x3 are the inputs to the node, y1 the output of the

node, and w0;w1;w2; . . . ;w13 are the coef®cients of the

triple node.

2.1.6. White node

The white node is used to summarize all linear weighted

inputs plus a constant, that is

y1 � w0 � w1x1 � w2x2 � w3x3 � � � � � wnxn (7)

where x1; x2; x3; . . . ; xn are the inputs to the node, y1 the

output of the node, and w0;w1;w2; . . . ;wn are the coef®-

cients of the triple node.

Since the functions of various polynomial functional

nodes are explained, the next step is to construct a poly-

nomial network based on these functional nodes.

2.2. Synthesis of polynomial networks

To build a polynomial network, training samples with the

information of inputs and outputs are required ®rst. Then,

ASPN is used to determine an optimal network structure

with the minimum value of the predicted squared error

(PSE) of the training samples. The PSE of the training

samples is composed of two terms, that is

PSE � FSE� KP (8)

where FSE is the average squared error of the network for

®tting the training data and KP is the complex penalty of the

network.

The average squared error of the network FSE can be

expressed as

FSE � 1

N

XN

i�1

�yi ÿ yi�2 (9)

where N is the number of training data, yi the desired value in

the training set, and yi is the predicted value from the

network.

The complex penalty of the network KP can be expressed

as

KP � CPM2s2

PK

N(10)

where CPM is the complex penalty multiplier, K the number

of coef®cients in the network, and s2P is a prior estimate of the

model error variance, also equal to a prior estimate of FSE.

As shown by Eq. (8), a trade-off between model accuracy

and complexity is performed in the ASPN criterion. This is

because the principle of the ASPN criterion is to select a

network as accurate but as less complex as possible. In

addition, the coef®cient of CPM (Eq. (10)) can be used to

adjust the trade-off. A complex network will be penalized

more in the ASPN criterion as CPM is increased. On the

contrary, a complex network will be selected if CPM is

decreased.

3. Modeling of the machining database usingpolynomial networks

In this section, turning experiments and cutting perfor-

mance are discussed ®rst. Experimental data with regard to

different cutting parameters (cutting speed, feed rate, and

depth of cut) and cutting performance (tool life, surface

roughness, and cutting force) are performed. Then, the

polynomial networks are trained by the experimental data

to construct the machining database in turning operations.

3.1. Turning experiments and cutting performance measure

A number of turning experiments were carried out on an

engine lathe using tungsten carbides with the grade of P-10

for machining of S45C steel bars. The feasible space of the

cutting parameters were selected by varying cutting speed

in the range of 135±285 m/min, feed rate in the range of

0.08±0.32 mm per revolution, depth of cut in the range of

0.6±1.6 mm. Each of these cutting parameters was set at

three levels that are listed in Table 1. Hence, 27 turning

Table 1

Experimental cutting parameters and cutting performance

S. no. V

(m/min)

f (mm per

revolution)

d

(mm)

T

(mm)

Ra

(mm)

F (N)

1 135 0.08 0.6 2645 1.2 263

2 135 0.20 0.6 2379 5.3 403

3 135 0.32 0.6 2233 9.5 550

4 135 0.08 1.1 2604 1.7 454

5 135 0.20 1.1 2060 1.9 704

6 135 0.32 1.1 1870 4.1 889

7 135 0.08 1.6 2563 1.9 628

8 135 0.20 1.6 2032 4.1 924

9 135 0.32 1.6 1733 9.4 1198

10 210 0.08 0.6 1605 2.6 212

11 210 0.20 0.6 1198 4.5 389

12 210 0.32 0.6 802 11.0 502

13 210 0.08 1.1 1350 1.0 377

14 210 0.20 1.1 1059 2.8 622

15 210 0.32 1.1 734 7.5 854

16 210 0.08 1.6 1310 2.6 593

17 210 0.20 1.6 1031 6.1 952

18 210 0.32 1.6 602 14.4 1170

19 285 0.08 0.6 860 0.6 203

20 285 0.20 0.6 847 2.8 364

21 285 0.32 0.6 216 9.7 464

22 285 0.08 1.1 854 0.9 335

23 285 0.20 1.1 846 2.7 573

24 285 0.32 1.1 212 6.1 813

25 285 0.08 1.6 840 1.2 443

26 285 0.20 1.6 765 4.2 857

27 285 0.32 1.6 203 10.2 1099

B.Y. Lee et al. / Journal of Materials Processing Technology 105 (2000) 1±6 3

experiments were performed based on the cutting parameter

combinations.

Tool life T is de®ned as the period of cutting time that the

average ¯ank wear land VB of the tool is equal to 0.3 mm or

the maximum ¯ank wear land VBmax is equal to 0.6 mm [18].

In the experiments, the ¯ank wear land was measured by

using an optical tool microscope (Isoma). The machined

surface roughness was measured by a pro®le meter (3D-

Hommelewerk). The average surface roughness Ra that is

the most widely used surface ®nish parameter in industry is

selected in this study. It is the arithmetic average of the

absolute value of the heights of roughness irregularities from

the mean value measured within the sampling length of

8 mm. The cutting force acting on the cutting tool in the X, Y,

and Z directions was measured by a three-component piezo-

electric dynamometer (Kistler 5257A) under the tool holder.

The resultant cutting force F is then calculated to evaluate

machining performance in this study. The cutting perfor-

mance (tool life, surface roughness, and cutting force)

corresponding to 27 turning experiments is summarized

and also listed in Table 1.

3.2. Machining database for turning operations

Based on the experimental data listed in Table 1, poly-

nomial networks for predicting tool life, surface roughness,

and cutting force are constructed. The best network struc-

ture, number of layers, and functional node types can be

determined by using ASPN (Eqs. (8)±(10)). Fig. 2 shows the

developed polynomial network for predicting tool life. A

comparison of the estimated tool life and measured tool life

is shown in Fig. 3. It is shown that the estimated tool life is

very close to the measured tool life. Fig. 4 shows the

developed polynomial network for predicting surface rough-

Fig. 2. Polynomial network for predicting tool life.

Fig. 3. Comparison between the estimated tool life and measured tool life.

Fig. 4. Polynomial network for predicting surface roughness.

4 B.Y. Lee et al. / Journal of Materials Processing Technology 105 (2000) 1±6

ness. The estimated surface roughness consistent with the

measured surface roughness is shown in Fig. 5. Fig. 6 shows

the developed polynomial network for predicting cutting

force. Good agreement between the estimated cutting force

and measured cutting force is shown in Fig. 7. All of the

polynomial equations using in the networks (Figs. 2, 4 and 6)

are listed in Appendix A. Based on the experimental results,

it has been demonstrated clearly that the polynomial net-

works (Figs. 2, 4 and 6) can be used to predict cutting

performance (tool life, surface roughness, and cutting force)

with a high accuracy. In other words, the machining database

can be constructed by the developed polynomial networks

(Figs. 2, 4 and 6).

4. Conclusions

The paper has described the use of polynomial networks

to construct the machining database in turning operations. It

is shown that the polynomial networks have a self-organized

adaptive learning ability that can correctly model highly

nonlinear, strongly coupled, multivariable turning opera-

tions. As a result, the complicated relationships between

the cutting parameters (cutting speed, feed rate, and depth of

cut) and cutting performance (tool life, surface roughness,

and cutting force) can accurately be correlated in the

machining database. Experimental results have shown that

the machining database has a high accuracy in the prediction

of cutting performance in turning operations.

Acknowledgements

Financial supported from the National Science Council of

the Republic of China, Taiwan under grant number NSC87-

2216-E011-025 is acknowledged with gratitude.

Appendix A.

1. Normalizer:

1.1. y1 � ÿ3:37� 0:016x1

1.2. y1 � ÿ2� 10x1

1.3. y1 � ÿ2:64� 2:4x1

2. Unitizer:

2.1. y1 � 4:82� 3:72x1

2.2. y2 � 623� 289x1

2.3. y3 � 1310� 757x1

Fig. 5. Comparison between the estimated surface roughness and

measured surface roughness.

Fig. 6. Polynomial network for predicting cutting force.

Fig. 7. Comparison between the estimated cutting force and measured

cutting force.

B.Y. Lee et al. / Journal of Materials Processing Technology 105 (2000) 1±6 5

3. Single node:

3.1. y1 � 0:0586ÿ 0:368x1 ÿ 0:0608x21

4. Double node:

4.1. y1 � ÿ0:166� 0:0839x2 ÿ 0:282x21 � 0:455x2

2

�0:0488x1x2

4.2. y1 � 0:846x2 ÿ 0:28x21 � 0:278x2

2 � 0:0783x1x2

4.3. y1 � 0:0904ÿ 0:138x1 � 0:644x2 ÿ 0:0236x21

ÿ0:0703x22 � 0:0206x1x2

5. Triple node:

5.1. y1 � ÿ0:485� 0:445x1 � 0:808x2 � 0:635x21

�0:276x22 � 0:149x2

3 � 0:611x1x2

ÿ0:116x2x3 � 0:467x1x2x3 � 1:33x31

5.2. y1 � ÿ0:0565� 0:89x1 ÿ 0:0777x2 ÿ 0:0695x3

ÿ0:133x21 ÿ 0:23x2

2 � 0:044x23 � 0:346x1x2

ÿ0:313x1x3 � 0:32x2x3 � 0:0937x1x2x3

�0:00794x31 � 0:146x3

2

5.3. y1 � 0:953x1 � 0:727x3 � 0:297x1x3

�0:042x1x2x3 � 0:0679x31

5.4. y1 � ÿ0:258� 0:975x1 � 0:102x2 � 0:0564x3

�0:408x21 ÿ 1:54x1x2 ÿ 0:274x1x3

ÿ0:26x1x2x3 ÿ 0:0427x31

5.5. y1 � ÿ0:0293� x1 ÿ 0:0188x3 � 0:0304x23

ÿ0:0253x2x3 ÿ 0:0395x1x2x3

6. White node:

6.1. y1 � ÿ0:883x1 ÿ 0:368x2 ÿ 0:104x3

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