Int. I. Math. Tools Matmftta.Vol.37. No. 9. pp. 1353-1372. 1997
Copyright~ 1997Publish~lby El~vier Scietw,,eLtd.
Printedin Great Britain.All tights reserved
0890--6955/97517.00 + .00
Pergamon
PII: S0890--6955(95)00094- I
A FUZZY LOGIC MODEL FOR MACHINING
DATA SELECTION
M. A. EL BARADIE*
(Original received 3 July 1995)
A l ~ t r a e t - - T h i s paper describes the development stages of a fuzzy logic model for metal cutting. The model is
based on the assumption that the relationship between the hardness of a given material and the recommended
cutting speed is an imprecise relationship, and can be described and evaluated by the theory of fuzzy sets. The
model has been applied to data extracted from the Machining Data Handbook [Metcut Research Associates, 3rd
edn, Vols 1 and 2 (1980)], and a very good correlation was obtained between the handbook data and that
predicted using the fuzzy logic model. The objective of the model is to facilitate the computerization process
of the vast machining information contained in machining d~_ta handbooks. Also, the proposed model suggests
the possibility of developing an expert system for machining data selection based on fuzzy logic. Copyright
© 1997 Published by Elsevier Science Ltd. All rights reserved
1.
INTRODUCTION
Machinability data, which includes the selection of the appropriate cutting tools and the
machining parameters of speed, feed and depth of cut, play an important role in the
efficient utilization of machine tools and thus significantly influences the overall manufacturing costs. The machinability data system has become an important component in the
implementation of computer integrated manufacturing (CIM) systems [ 1, 2].
Computerized machinability data systems have been classified into two general types:
mathematical model and database systems [1]. The mathematical model systems attempt
to predict the optimum cutting conditions for a specific operation. The machining response
data such as tool life, surface roughness, cutting forces, power, etc., are used as the primary
data. Then mathematical models of these machining responses are developed as a function
of the machining variables using a model building module. The model parameters and
other relevant economic factors are used to derive the optimum set of cutting conditions
[2, 31.
The database systems are based on the collection and storage of large quantities of data
from laboratory experiments and workshop experience, which then can simply retrieve
recommended cutting speeds and feedrates for any specific cutting operation [ 1, 2].
The most widely used source of such data is the Machining Data Handbook [4] published by Metcut Research Associates. It is a vast information source that compiles parameter data for different tool-work combinations. Work materials are organised in this
handbook based on hardness data. For each work material and hardness, one may scan
through different possible tool materials. For each work tool combination, based on depth
of cut values, one can ascertain the type of cut (finish or rough), and speeds and feeds
are selected accordingly. These speed and feed values are usually good starting estimates.
Laboratory technicians and academic researchers usually use these nominal values to conduct "bracketing tests", thus reducing the search space for parameter selection [5].
Although the handbook approach is often a logical and effective solution to the requirements of machinability data, it has the following limitations [1]:
( 1) Handbook recommendations represent a "starting" set of cutting conditions and hence
tend to be conservative in order to cope with a worst case machining scenario.
(2) Handbook data only applies to a particular machining situation. This data may not be
suitable for slightly different machining situations.
*School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin, 9, Ireland.
1353
1354
M.A. El Baradie
(3) Handbooks are manually input--output oriented, and hence lack compatibility with the
objective of integrated automation of the manufacturing system.
In spite of these characteristics, handbooks are the major source of machinability data for
CNC machine tools [I].
This paper presents the development of a fuzzy logic model for machining data selection. The objective of the model is to facilitate the computerization of the vast information
available in machining data handbooks. The model is based on the relationship which
exists for any specific material between its hardness (input) and the corresponding recommended cutting speed and feed rate (output).
In general, if the material hardness is high then the corresponding cutting speed is low,
and vice versa-if the material hardness is low, then the cutting speed is high. Fuzzy logic
can be applied to any process in which a human being plays an important role which
depends on his subjective assessment. For example, the skilled lathe operator, using his
intuition and experience, decides which cutting tool type and which cutting speed and
feed rate he selects when machining an aluminum alloy (soft material) or when machining
a nickel-base super alloy (very hard material).
Also, if it is rough turning he selects a strategy of high feed and depth of cut and keeps
the speed low (within the recommended range). On the other hand, if it is finish turning
he selects a strategy of high speed together with fine feeds and shallow cuts. The material
hardness, for example, can be classified as very hard, hard, medium, etc. and the cutting
speed can be classified as very low, low, medium, etc.
The theory of fuzzy sets and algorithms developed by Zadeh [6, 7] can be used to
evaluate these imprecise linguistic statements directly. Sutton and Towill [10] applied the
fuzzy set theory for modelling the helmsman action in ship steering.
Mamdani [8] and King and Mamdani [9] applied the fuzzy set theory for the modelling
and control of a small boiler steam engine combination. The heat input to the boiler was
used to control the boiler pressure and the steam engine speed was controlled by adjusting
the throttle opening at the input of the engine cylinder.
Kouatli and Jones [11] developed a fuzzy controller for a robot welding system. The
objective is to control the speed of the robot arm to carry out the welding in the same
manner as the human welding operator. The fuzzy set shapes have been chosen as a
"fuzzimetric arcs". A scale for partioning the universe of discourse was determined by
using the welder's expertise and knowledge. The fuzzy reasoning is based on a compositional rule of inference. The speed of the robot arm, controlled by the fuzzy logic controller, varies with the cavity size of the workpiece being welded.
Different applications of the fuzzy control technique use a specific shape of the fuzzy
set which is dependent on the system behaviour identified by the knowledge engineer. So
far there is no standard method of choosing the proper shape of the fuzzy sets of the
control variables [ 11].
The most widely used shapes are triangular, trapezoidal and arcs. For example, for
modelling the helmsman action in ship steering [10] the trapezoidal shape was found to
be the best shape for that specific application. Also, for modelling the welding process
and imitating the skilled operator hand movements, fuzzimetric arcs were found to be the
best shape [11]. In this paper the triangular shape has been selected to describe the fuzzy
variables for machining parameters, i.e. the material hardness and the cutting speed.
Additionally, an example from the machining data handbook [4] has been used to illustrate
the application of the fuzzy logic model for metal cutting.
2.
VARIABLES AFFECTING TOOL LIFE
The variables affecting the tool life may be listed as:
(1) the cutting conditions--speed, feed and depth of cut;
(2) the tool material;
(3) the work material.
A fuzzy logic model for machining data selection
1355
In addition, the tool geometry, the cutting fluid and the type and condition of the machine
tools used are also important.
2.1. Effect of cutting condition-speed, feed and depth of cut
The variables of speed, feed and depth of cut are of considerable importance since they
control the rate of metal removal and the production rate. Tayior's experimental work showed
that the tool life varied with the cutting speed by the following well-known equation:
VT" = C,
c~,°
(l)
or T= .....
V TM
where T is the cutting time (min) that it takes to develop a flank wear land of certain
dimension, V is the cutting speed (m min-~), n is an exponent that depends on cutting
conditions and C, is a constant parameter, sometimes called the Taylor constant, which
can represent the cutting speed for 1 rain tool life.
Similar trends occur for the feed and depth of cut, and so the tool life may be
expressed as
K
T = ~:l,f~l,:dl%
(2)
where T is the tool life (min), V is the cutting speed (m min-~),fis the feed (mm rev-~), d
is the depth of cut (mm), k is a constant for a given tool work combination and tool geometry
and l/n, lln~ and lln2 are exponents of the speed, feed and depth of cut, respectively.
Equation (2) is an extension of the Taylor equation, and has been suggested by a number
of workers. The values of the exponents 1/n, lln~ and 1/n2 as well as k will depend on
the failure criteria. It is also found that the exponents will vary with different tool and
work materials. The exponents describe the effect of the variables on tool life. The larger
the value of lln the steeper the V-T slope and the greater the change in tool life for a
given change in cutting speed. It is usually found that l/n>lln~>llnz so that the cutting
speed has the greatest influence on the tool life, followed by the feed and the depth of
cut, respectively.
2.2. Effect of tool material
The exponent n (or l/n) in Equation (i) shows the effect of speed on tool life. The
smaller the value of n (or the larger l/n) the greater the effect of speed on tool wear and
tool life. From experimental data the exponent n for a range of tool materials is shown
in Table 1. It is seen that high-speed steel is the most sensitive to speed changes, although
it has been said that oxides and sintered carbides can be used at considerably higher cutting
speeds than high-speed steel.
2.3. Effect of work material
The work material, like the tool material, is a major variable affecting the tool life. The
common variables considered are the work material composition and microstructure (heat
treatment), its hardness and work-hardening properties. The work-material hardness is the
easiest variable to measure and relate to tool life. As might be expected, the harder the
Table I. Approximate variation of speed exponent n for different tool materials
Tool material
Speed exponent n
High-speed steel
Carbides
Oxides/ceramics
0.08--0.2
0.2-0.49
0.5-0.7
1356
M.A.
El Baradie
work material the lower the tool life. A number of investigations [12] have shown that
the cutting speed for a fixed tool life is related to the hardness by the following equation:
=
Constant
(BHNy
(3)
where Vr is the cutting speed for a fixed tool life T, and BHN is the Brinell hardness
number. The constants in Equation (3) will depend on the work material and tool material.
The exponent x will vary with tool material. Equation (3) is a useful approximate relation.
although considerable scatter in Vr occurs for any given hardness value, and furthermore.
free machining additives can greatly increase this scatter as seen in Fig. 1.
It is apparent that the Brinell hardness, which gives an average hardness measurement,
is not the only work-material variable to account for the effect of work-material properties
on tool life. The hardness of the work-material constituents and their properties will influence the average hardness and the tool life. However, while it is difficult to predict accurately the best machining conditions for a given workpiece material in a given machining
operation, data from the handbook usually represents a good starting point from which to
proceed to the optimum by progressive change. The machining data handbook [4] is a
very comprehensive source of such data.
Equation (3) is illustrated in Fig. 2, showing the approximate values of cutting speed
for 1 min tool life against the hardness for a range of tool and workpiece materials. Fig.
250
800
700
200
600
"6
£
E
500
o
150
8
"7
.5
E
E
0
0 0
400
C - 6 carbide
I00
300
0
>
200
o\
o
50
o
100
ooo
o8 o
o
o ~
o
200
300
400
500
560
Brinell hardness number
Fig. 1. Relation between cutting speed for a fixed tool life and Brinell hardness when turning wrought steel
[121.
A fuzzy logic model for machining data selection
1357
Brinnel hardness number
6O
100
80
70
80 90 100
150
200
300
400
I
I
I
I
l)
500
15o00
60
t0000
Heat-treated steels
°
,o
40
8000
20
6OOO
5O00
4OOO
10
200o
8
1500
.c
6
~o
"-
looo
4
soo
$
4
6OO
3O0
Iron
200
1.0
0.8
0.6
~
i
0.4
0.2
"~-
150
Aluminum
alloys
Brass
,[
100
8O
Cold-drawn
steel, cast
'1 iron, bronze
Cast
steel
't"
6O
5O
40
30
0.1 I
200
I
l
I
I
300
400
500
600
I
1
800
i
I
I
1000
1500
1"20
2000
Tensile strength, MN/m 2
Fig. 2. Approximate cutting speed for one-minute tool life, showing the effects of tool and workpiece materials
and cutting speed [13].
2 also shows the rapid decrease in tool life with increasing hardness of the workpiece
material.
3.
MACHINING D A T A H A N D B O O K S
The Machining Data Handbook [4] provides starting recommendations for important
machining situations in an effort to help personnel associated with material removal processes. This condensed and integrated source of machining information is useful to manufacturing, process, industrial and method engineers, NC programmers, etc.
Data were obtained from the recommendations of metal producers, machine tool manufacturers and cutting tool and cutting fluid manufacturers, as well as from handbooks,
machinability reports and miscellaneous literature on machining. Valuable data were also
derived from Metcut Research Associates, government machinability data centre files and
technical personnel. The machining data obtained from industry were generally those that
are currently being used in production operations [4].
A thorough review of the information obtained from the literature and from industry
has indicated that the recommended speeds and feeds for any machining operations may
vary considerably. The optimum performance or efficiency of any machining operation
includes factors in addition to the proper selection of speeds and feeds. Variables such as
part configuration, condition of the machine, type of fixturing, dimensional tolerance and
surface roughness all affect performance. Because the effects of these variables on tool
life axe not always precisely known, it becomes difficult to recommend optimum conditions
1358
M . A . El Baradie
for a machining operation. Therefore the recommendations for speeds, feeds and other
parameters presented in the handbook are nominal recommendations and should be considered only as good starting points [4].
The speeds and feeds for the various operations, based on the data obtained from the
many sources, represent a "tool life" of approximately 1-2 h of cutting time for most of
the common alloys when using high speed steel or brazed carbide tools. A tool life of
30--60 rain is applicable for indexable-insert carbide tools. In actual shop operations, the
time between tool changes might be three to four times these values because of the loading
and unloading times associated with most machining operations. Generally, a tool life in
excess of 2 h actual cutting time would indicate that the speed and feeds are too low and
hence could be increased to achieve nearly optimum production at minimum cost.
The machining data handbook provides starting machining recommendations (speeds,
feeds, tool materials, etc.) for conventional machining processes (turning, milling, drilling,
boring, tapping, planning, broaching, sawing and cut-off operations). The work materials
are classified in 61 groups covering a wide range of materials (ferrous, non-ferrous, etc.)
Appendix A shows a table (A1) from the machining data handbook [4], and gives the
recommended cutting speeds and feed-rates for turning the particular material group carbon
steels, wrought (low carbon 1005-1025). This data will be used in this paper to demonstrate the application of fuzzy logic to the selection of machining parameters. Table 2
summarizes this information, while Fig. 3 shows the plotting of the data for 1 mm depth
of cut.
4.
FUZZY ALGORITHMS
The knowledge extracted from the machining data handbook may be organised in a
logic control rules format which imitates/describes the behaviour of the process planning
engineer/skilled machine tool operator. The input is the material hardness and the output
is the cutting speed, which can be described by the following fuzzy expressions:
Material hardness
Cutting speed
Very hard
Hard
Medium
Soft
Very soft
Very low
Low
Medium
High
Very high
Table 2. Recommended cutting speed ranges and feed rates for different cutting tools (material: carbon steel,
hardness; 75-275 BHN).(Data extracted from machining data handbook, Appendix A.)
Tool material
Depth of cut (mm)
Speed range (m rain- ~)
Feed (mm rev ~)
High speed steel (ISO 54, 55)
I
4
8
16
38-56
29--44
23-35
18-27
0.18
0.40
0.50
0.75
Carbide tool, uncoated (brazed,
ISO P10-P40)
Carbide tool, uncoated
(indexible, ISO PI0-P40)
Carbide tool, coated (ISO
CP10-CP30)
I
125-165
0.18
4
8
16
110-135
87-105
67-81
0.50
0.75
1.00
1
155-215
4
8
16
120-165
95-130
73-100
0.50
0.75
1.00
0.18
I
230-320
0.18
4
8
16
150-215
120-170
-
0.40
0.50
-
A fuzzy logic model for machining data selection
1359
350
Depth of cut
--
I
m m
Machining Handbook Recommendation
300
Coated Carbide
,-,
.=_ 250
g2oo
Uncoated Carbide (Indexible)
~150
Uncoated Carbide (Brazed)
100
50
o
High Speed Steel
.
70
,
I
,
,
.
90
l
,
110
,
,
I
,
130
,
,
I
,
150
t,
I
.
,
170
•
I
,
,
190
.
i
,
210
.
,
I
,
230
,
,
I , .
250
,
I
270
Hardness (BHN)
Fig. 3. Machining data handbook recommended cutting speed ranges for different cutting tool materials at 1 mm
depth of cut.
Hence five rules can be constructed as follows:
•
•
•
•
•
rule
rule
rule
rule
rule
1:
2:
3:
4:
5:
if
if
if
if
if
material
material
material
material
material
is
is
is
is
is
very hard, then speed is very low;
hard, then speed is low;
medium, then speed is medium;
soft, then speed is high;
very soft, then speed is very high.
These rules are in the form of an expert system which imitates the skills of the machine
tool operator.
4.1.
Universe partitioning
After establishing the fuzzy rules and developing the control algorithm, the second step
is to partition the universe of the input and output using the triangular shape. Figure 4
shows the material hardness membership (input) and the cutting speed membership
(output). From Fig. 4 the discretized universes of the fuzzy variables (material hardness
and cutting speed) are derived as shown in Table 3 and Table 4.
The input universe "material hardness" should be partitioned according to the minimum
and maximum values allowed to control the system (Hardnessmin-Hardnessm~x). On this
basis the universe of the hardness should be in the range of (0-8), with any value above
this range assumed to be infinity and a zero value implying that the material hardness is
almost a minimum value. It has been assumed that the value of 0 is assigned to "HardnesSmin" and the value of 8 to "Hardnessmax".
In a similar manner the universe of the output, which is cutting speed, should be partioned according to the range of speed required. It can be seen from Table 2 that the
various output speed ranges depend on the selected cutting tool material and on the depth
of cut. There are 16 output speed ranges, and hence any output speed range should be
partioned in the range (0-8), where any value above the limit of the universe is infinity
and the zero level is assumed to be the minimum speed.
It has been assumed that the value of 0 is assigned to "speedmi," and the value of 8 is
assigned to "speedma~", for any output speed range,
1360
M.A. El Baradie
1 [Very Soft
0
1
0
Soft
Medium
2
3
4
Hard
5
6
Very Hard
7
8
Matcrial Hardness
(a) Material Hardness Membership
IVeryLow Low
0(~
I
2
Medium
3
4
5
High VeryHigh
6
7
8
Cutting Speed
(b) Cutting Speed Membership
Fig. 4. Membership functions.
Table 3. Universe of material hardness
Fuzzy terms
Very soft
Soft
Medium
Hard
Very hard
0
1
2
1
0
0
0
0
0.5
0.5
0
0
0
0
1
0
0
0
Discrete universe of material hardness
3
4
5
6
0
0.5
0.5
0
0
0
0
1
0
0
0
0
0.5
0.5
0
0
0
0
I
0
7
8
0
0
0
0.5
0.5
0
0
0
0
1
1361
A fuzzy logic model for machining data selection
Table 4. Universe of cuuing speed
Fuzzy terms
Very low
Low
Medium
High
Very high
Discrete universe of cutting speed
0
1
2
3
4
5
6
7
1
0
0
0
0
0.5
0.5
0
0
0
0
1
0
0
0
0
0.5
0.5
0
0
0
0
1
0
0
0
0
0.5
0.5
0
0
0
0
1
0
0
0
0
0.5
0.5
8
0
0
0
0
I
4.2. Fuzzy relation
The fuzzy relation is the relation between the input and the output of the control system,
such as that between the fuzzy sets "very hard" and "very low" in the first rule of section
4 for example. Then the relationship between the input (very hard) and the output (very
low) can be found using Cartesian product expressions of the two sets:
R = input*output
where * represents the Cartesian product. In the case of rule 1, the relation would be
R1 = (material hardness)very ~,a*(speed value)very tow
which has a membership function of
~R 1 = min I . t ~ h.~ m.t~i~l, l ~ , y tow .,p,~
From Table 3, the very hard fuzzy set is defined as:
Very hard = 0/0 + 0/1 + 0/2 + 0/3 + 0/4 + 0/5 + 0/6 + 0.5/7 + 1/8
and from Table 4, the fuzzy set very low is defined as
Very low = 1/0 + 0.5/1 + 0/2 + 0/3 + 0/4 + 0/5 + 0/6 + 0/7 + 0/8
The relationship between very hard and very soft will be as shown in Table 5.
The second rule can be developed as follows: if material is hard, then speed is low,
and the fuzzy sets "hard" and "low" are defined by
Hard = 0/0 + (3/1 + 0/2 + 0/3 + 0/4 + 0.5/5 + 1/6 + 0.5/7 + 0/8
and
Table 5. Rule 1
Universe of cutting speed
0
1
2
3
4
5
0
0
0
0
0
0
0
0
0
0
2
3
4
5
6
7
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
0
0
0
8
I
0.5
0
0
Universe Rl=of
0
material hardness
1
6
7
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1362
M . A . E1 Baradie
Low = 0/0 + 0.5/1 + 1/2 + 0.5/3 + 0/4 + 0/5 + 0/6 + 0/7 + 0/8
The relationship between hard and low will be as shown in Table 6. In a similar manner
rules 3-5 can be established.
4.3.
Rules combination
The second relation (R2) can be combined only when an input is such that it is within
the "hard" material classification and allows the "low" speed value to be inferred. Hence
the first and second relations may be combined together to produce one which allows an
input to be either "very hard" or "hard". The combination operator may be assumed to
be an "OR" function which is represented as the maximum of the membership values of
the two different relations. The fuzzy statement combined from the two fuzzy rules R1
and R2 will be as follows:
If material type is very hard, then speed is very low
OR
if material type is hard, then speed is low
which is equivalent to:
far I + R2 = m a x { ~tR,,laR2 }
and is represented as shown in Table 7.
Thus the total combination of the five relations using the "OR" operator is the maximum
of the memberships. Thus the fuzzy algorithm is as follows:
Table 6. Rule 2
Universe R2=of
0
material hardness
1
2
3
4
5
6
7
8
Universe of cutting speed
3
4
5
0
I
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0.5
0.5
0
0
0
0
0
0.5
I
0.5
0
0
0
0
0
0.5
0.5
0.5
0
0
0
0
0
0
0
0
0
0
6
7
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
7
8
0
Table 7. Rule l+rule 2
Universe of
material hardness 0
RI+R2=
I
2
3
4
5
6
7
8
0
1
2
0
0
0
0
0
0
0
0
0
0.5
l
0
0
0
0
0.5
1
0.5
0.5
0
0
0
0
0.5
I
0.5
0
Universe of cutting speed
3
4
5
0
0
0
0
0
0
0
0
0
0.5
0.5
0.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
A fuzzy logic model for machining data selection
If
If
If
If
If
material
material
material
material
material
type
type
type
type
type
very low OR
low OR
medium OR
high OR
very high
very hard THEN speed =
hard THEN speed =
medium THEN speed =
soft THEN speed =
very soft THEN speed =
=
=
=
=
=
1363
This algorithm can be represented in the relation R which has a membership function of
~. ~---i"~7.X{ [..I.RI,IJ.R2,~J.R3,~J.R4,~J.R5 }
which can be represented by the following relation shown in Table 8. This relation is in
fact the model of the action of the process planning engineer/machine tool operator. Combining this relation with any value of the material hardness that lies in its universe (0-8)
results in the required average speed output.
The defuzzified output which gives the average speed value can be obtained from the
following formula:
Average value =
X Speed value x ~t(s)
x~t(s)
For a hardness universe of "4", for example, the average speed result would be
Speed value =
0.5x3 + lx4 + 0.5x5
=4
0.5 + 1 + 0.5
Table 9 gives the relation between the hardness universe (0-8) and the averaged values
of output speed. Combining this relation with any value of the material input hardness that
lies in its universe (0-8) results in the required speed output range [Speed{mi,~-Speed~m,~,)].
Table 8. Membership function for the relation Ix.
Universe of
0
material hardness
1
2
3
4
5
6
7
8
2
Universe of cutting speed
3
4
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0.5
1
0
0
0
0
0.5
0.5
0.5
0.5
0
0
0
0
0.5
1
0.5
0
0
0
0.5
0.5
0.5
0.5
0.5
0
0
0
0.5
1
0.5
0
0
0
6
7
0
0
0.5
1
0.5
0.5
0.5
0.5
0.5
0
0
0
0.5
1
0.5
0
0
0
0
0
0.5
0.5
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0
0
Table 9. Averaged value of speed for a specific hardness universe
Hardness universe partitioning
Averaged speed
0
1
2
3
4
5
6
7
8
7.66
6.50
6.00
5.00
4.00
3.00
2.00
1.50
0.33
8
1364
M.A. El Baradie
5. APPLICATIONOF THE FUZZY LOGIC MODEL TO METALCUTTING
In the previous section the fuzzy algorithms have been defined and the fuzzy relationships between the material hardness as an input and the cutting speed as an output have
been established. As mentioned in section 2, the data presented in Appendix A from the
Machining Data Handbook [4] and summarized in Table 2 will be used to demonstrate
the application of the fuzzy logic model in the selection of machining parameters.
It can be seen from Appendix A and Table 2 that the material group "Carbon Steel,
Wrought" (Low Carbon 1005-1025) is divided into four groups depending on the hardness:
(1)
(2)
(3)
(4)
from
from
from
from
85 to 125 BHN;
125 to 175 BHN;
175 to 225 BHN;
225 to 275 BHN.
There are four types of cutting tools:
(1)
(2)
(3)
(4)
high speed steel (ISO $4, $5);
carbide tool, uncoated (bronzed, ISO PI0-P40);
carbide tool, uncoated (indexible, ISO PI0-P40);
carbide tool coated (ISO CPI0-CP30).
For each of the four hardness-tool group combinations there are four different depth of
cut selections, mainly 1, 4, 8 and 16 mm. Hence at each hardness-tool combination at a
selected depth of cut, the recommended cutting speed and feed rate are presented. It can
be seen from Fig. 5 that for the four different tool materials there is only one material
hardness range, i.e. 75-275 BHN, which should be partioned in the universe range (0-8),
while for each tool material there are four different output speed ranges depending on the
selected depth of cut. Thus in all there are sixteen output speed ranges as shown in Fig. 5.
For the case of high speed steel tool, for example, the input and the outputs are as
follows:
OUTPUT
(Speed Range, Feed)
INPUT
(Hardness Range: 75-275 BHN)
I
High Speed Steel Tool
(ISO 54,55)
~
1 mm -----¢ 38-56 (m/min), 0.18 (mm/rev)
4ram
~ 29.-44 (m/rain), 0.40 (mm/rev)
8ram
; 23-35 (m/rain), 0.50 (mm/rev)
16 mm p 18-27 (m/rain), 0.75 (mm/rev)
I Carbide Uncoated Brazed Tool I
(ISO PI0-P40)
[
I 1 mm
125-165(m/min), 0.18 (mm/rev)
4ram ~ 110-135 (m/rain), 0.50 (mm/rev)
Smm
~ 87-105 (m/rain), 0.75 (mm/rev)
16 mm , 67-81 (m/rain), 1.00 (mm/rev)
I Carbide Uncoated Indexiblel
( I S O PIO-P40)
I
1 mm
I 4mm
8mm
Carbide Coated Too1
(ISO CP10-CP30)
]
I
-----¢ 155-215 (m/rain), 0.18 (mm/rev)
~ 120-165 (m/rain), 0.50 (mm/rev)
"----¢ 95-130 (m/rain), 0.75 (mm/rev)
16 mm ---¢, 73-100 (m/rain), 1.00 (mm/rev)
lmm
4ram
l gram
16 mm
230-320 (m/rain), 0.18 (mm/rev)
P150-215 (m/rain), 0.40 (mm/rev)
P 120-170 (m/min), 0.50 (mm/rev)
*
P
Fig. 5. The one input (hardness range) and the 16 outputs (speed ranges and feeds) for differentcutting tool
materials at differentdepth of cuts.
A fuzzy logic model for machining data selection
1365
Output (speed range)
Input (hardness)
75-275 (BHN)
38-56
29--44
23-35
18-27
m
m
m
m
min-1
min-t
min-i
min -I
(at
(at
(at
(at
1 mm depth of cut)
4 mm depth of cut)
8 mm depth of cut)
16 mm depth of cut)
(Note: for convenience, to partition the hardness range into equal intervals, the range 75275 BHN was used instead of 85-275 BHN as listed in the table.) Hence the speed range
for each depth of cut should be partitioned in the range (0-8), according to the averaged
speed levels given in Table 9. For each speed range, any value above the limit of the
universe is infinity and the zero level is assumed to be the minimum speed, i.e. 38, 29,
23 or 18 m min- 1, which should be added to the final output. As an example for the case of
1 mm depth of cut, the minimum speed=38 m min- i and the maximum speed=56 m min- t.
Hence to partition any speed range in the range (0-8) a range factor was derived based
on the difference between maximum and minimum speed and divided by the arranged
speed at the level 0.
Speed range factor = Speedt~,)-Speed,,i.~
Averaged speed(0)
Hence for the case of 1 mm depth of cut:
Speed range factor (RF) -
56 - 38
- 2.35
7.66
This speed scale factor should be multiplied by all the averaged speed range values in
Table 9 and then added to the minimum speed, i.e. 38 m min -1. The procedure is shown
in Table 10. The same procedure was carried out for all the cutting tools speed range
outputs, and the results are shown in the tables in appendix B and are plotted in Fig. 6,
Fig. 7, Fig. 8, Fig. 9 for 1, 4, 8 and 16 mm depth of cuts, respectively.
6.
CONCLUSIONS
The results presented in Figs 6--9 show a very good correlation between the Machining
Data Handbook's recommended cutting speed ranges and that predicted using the fuzzy
logic model. The figures illustrate the relationship between the hardness for wrought low
carbon steels (75-275 BHN) and the cutting speeds, for four different cutting tool
materials. There are four depth of cuts-I, 4, 8 and 16 mm, giving the choice for finish or
rough cut.
The fuzzy logic model presented in this paper for metal cutting is based on the assumption that the relationship between a given workpiece material hardness and the recommended cutting speed of that material is an empirical-imprecise relationship. For
example, if the material is very hard the cutting speed is very low, and on the other hand
Table 10. Speed range factor
Input hardness
(BHN)
Universe
partioning
Averaged speed
(AS)
ASxrange factor AS x RF + speed (minimum)
(RF = 2.35)
75
100
125
150
175
200
225
250
275
0
1
2
3
4
5
6
7
8
7.66
6.50
6.00
5.00
4.00
3.00
2.00
1.50
0.33
i8
15
14
12
9
7
5
4
0.77
18+38
15+38
14+38
i 2+38
9+38
7+38
5+38
4+38
0.77+38
=56
=53
=52
=50
--47
--45
---43
--42
=38.77
1366
M.A. El Baradie
350
Depth of cut = I nun
Machining Handbook Recommendation
Fuzzy Logic Prediction
•
300
Coated Carbide
,--, 250
..=
g200
Uncoated Carbide (Indexible)
4,)
~0150
Uncoated Carbide (Brazed)
o 100
High Speed Steel
50
0
. , ,
70
1
.
,
90
,
I
.
I10
,
,
I
.
130
,
,
I
.
150
,
,
I
*
170
, .
I
,
,
,
190
I
.
210
,
,
1
,
230
,
,
I , . ,
250
I
270
Hardness (BHN)
Fig. 6. Fuzzy logic model predicted cutting speeds for wrought carbon steel at 1 mm depth of cut.
250 •
Depth of cut = 4 nun
Machining Handbook Recommendation
Fuzzy Logic Prediction
200
I
•
.
Coated Carbide
Uncoated Carbide (Indexible)
150
P
Uncoated Carbide (Brazed)
. ~ 100
O
50
•
High Speed Steel
a
70
90
110
130
150
170
190
210
230
250
270
Hardness (BHN)
Fig. 7. Fuzzy logic model predicted cutting speeds for wrought carbon steel at 4 mm depth of cut.
if the material is very soft, the cutting speed is very high. The theory of fuzzy sets can
be used to describe and evaluate these imprecise linguistic statements directly in order to
develop a computerized machinability data base systems.
This imprecise relationship has been emphasized in section 2 of this paper, as it has
usually been found that metal cutting data are susceptible to an appreciable amount of
scatter. This is due to the non-homogeneity of the material structure being cut and its
effect on the measurement of the machining response data.
Hence, while it is difficult to accurately predict the best machining conditions for a
given workpiece material in a given machining operation, handbook data usually represents
A fuzzy logic model for machining data selection
200
175
1367
Depth of cut .: 8 nun
Machining Handbook Recommendation
• Fuzzy Logic Prediction
-it
150
+ 125 -
•
it
Coaled Carbide
Uncoated Carbide (lndexible)
v
~100
=
Uncoated Carbide (BraTed)
•~- 75
50
•
High Speed Steel
25 ~
0
11
1
70
I
t
90
I
[
a
t
110
J
I
t
11
130
I
J
J
150
I
I
I
I
170
t
]
I
t
190
t
L
i
t
210
t
I
t
i
230
t
I
t
t
250
t
I
270
Hardness (BHN)
Fig. 8. Fuzzy logic model's predicted cutting speeds for wrought carbon steel at 8 mm depth of cut.
150
Depth of cut = 16 mm
Machining Handbook Recommendation
Fuzzy Logic Prediction
125 ~-
•-= 100
.
~
Uncoated Carbide (Indexible)
75 "
"
"
Coated Carbide (Barazed)
eu~
..=
==
50
High Speed Steel
25 "
0
•
70
,
•
I
90
,
,
,
I
,
110
,
,
I
•
130
,
,
l
,
,
,
1
,
t
,
1
,
,
,
l
,
150 170 190 210
Hardness (BHN)
,
,
1
,
230
,
,
1
,
250
,
,
1
270
Fig. 9. Fuzzy logic model's predicted cutting speed for wrought carbon steel at 16 mm depth of cut.
a good starting point from which to proceed to the optimum by progressive change. Handbooks are the major source of machinability data for many industrial companies. However,
handbooks are manually input--output oriented, and so lack compatibility with the objective
of integrated automation of the manufacturing system.
Sample data from the Ref, [4] has been used to demonstrate the application of the fuzzy
logic model for metal cutting to the development of a computerized machinability data
base system.
Thus the following conclusions can be drawn:
(1) The strategy and action of the skilled machine tool operator when selecting the cutting
1368
M.A. El Baradie
speed and feed rate for a given material can be described by the theory o f fuzzy sets,
as his strategy and action are based on intuition and experience.
(2) The relationship between a given material hardness and the r e c o m m e n d e d cutting
speed can be d e s c r i b e d and evaluated by the theory o f fuzzy sets.
(3) The c o m p u t e r i z a t i o n o f the M a c h i n i n g Data H a n d b o o k provides process planners and
C N C p r o g r a m m e r s with an easy access to a vast information source. It also provides
integrated automation o f the manufacturing system.
(4) The fuzzy logic m o d e l p r o p o s e d suggest the possibility o f d e v e l o p i n g an expert system
that can be used by the process planner as an aid o f establishing the strategy o f machining data selection for a specific m a c h i n i n g process.
REFERENCES
[1] Balakrishnan, P. and DeVries, M. F., A review of computerized machinability data base systems. In: Proc.
NAMRC-X 1982, pp.348-356.
[2] Balakrishnan, P. and DeVries, M. F., Analysis of mathematical model building techniques adaptable to
machinability data base systems. In: Proc. NAMRC-XI 1983.
[3] El Baradie, M. A., Surface roughness model for turning grey cast iron (154 BHN). Proc. Instn Mech. Engrs
1993, 207, 44-54.
[4] Metcut Re,arch Associates Inc. Machining Data Handbook, 3rd edn, Vols I and 2. Cincinnati, 1980.
[5l Singh, R. and Raman, S., Metex-an expert system for machining planning. Int. J. Prod. Res. 1992. 30,
1501-1516.
[61 Zadeh, L. A., Fuzzy sets. Inf. Control 8, 338-353 (1965).
[71 Zadeh, L. A., Fuzzy algorithms. Inf. Control 1968, 12, 94-102.
[81 Mamdani, E. H., Application of fuzzy algorithms for the control of dynamic plant. Proc. lEE 1974, 121.
1585-1588.
[9] King, P. J. and Mamdani, E. H., The application of fuzzy control systems to industrial processes. Automatica
1977, 13, 235-242.
[101 Sutton, R. and Towill, D. R., An introduction to the use of fuzzy sets in the implementation ot control
algorithms. J. Inst. Elect. Radio Engrs 1985, 55, 357-367.
[I 1] Kouatli, I. and Jones, B., An improved design procedure for fuzzy control systems. Int. J. Math. Tools
Manufact. 1991, 31, 107-122.
[12] Field, M., Relation of microstructure to the machinability of wrought steels and cast iron. In: International
Research in Production Engineering, p. 188. American Society of Mechanical Engineers, New York, 1963.
[13] Boothroyd, G., Fundamentals of Metal Machining and Machine Tools, p. 147. McGraw-Hill, New York.
1975.
A fuzzy logic model for machining data selection
O
O
1
~
1369
1
O
O
.r"
•
e~
~J
-~
o . . .o.
~
~
g
7
~7
~J
Z
m
e~
e-
'N
.~.
.r.,N
~7
¢-
-~'~_ ~
-6
.,.~
"O
~
I
-
1370
M . A . El Baradie
o
~
~_,.,
o
~
~.~
_
r.
~
0
~
~
~
~
~
~
0
~
~
<
N
o
~oo
~
~o
~:~. ~ ' ~ ° °
~
r~
c~
oo
.~, o
"5 :-3.
E~
~i~ ~
o~
A fuzzy logic model for machining data selection
1371
APPENDIX II
Table BI. Fuzzy logic model's predicted cutting speeds for carbon steel, wrought, at 1 mm depth of cut
Material hardness
(BHN)
75
100
125
150
175
200
225
250
275
Cutting speed (m rain-~)
H.S.S.
Carbide uncoated,
brazed
Carbide uncoated,
indexible
Carbide coated
56
53
52
50
47
45
43
42
38.77
165
159
156
151
146
141
135
133
126.72
215
206
202
194
186
178
171
167
157.58
320
306
301
289
277
265
254
248
233.87
Table B2. Fuzzy logic model's predicted cutting speeds for carbon steel, wrought, at 4 mm depth of cut
Material hardness
(BHN)
75
100
125
150
175
200
225
250
275
Cutting speed (m min ~)
H.S.S.
Carbide uncoated,
brazed
Carbide uncoated,
indexible
Carbide coated
44
42
41
39
37
35
33
32
29.64
135
131
130
126
123
120
117
115
111.07
165
158
155
149
143
138
132
129
121.94
215
205
201
192
184
175
167
163
152.79
Table B3. Fuzzy logic model's predicted cutting speeds for carbon steel, wrought, at 8 mm depth of cuts
Material hardness
(BHN)
75
100
125
150
175
200
225
250
275
Cutting speed (m min -~)
H.S.S.
Carbide uncoated,
brazed
Carbide uncoated,
indexible
Carbide coated
35
33
32
31
29
28
26
25
23.52
105
102
101
99
96
94
92
91
87.77
130
125
122
118
113
109
104
102
96.50
170
162
159
153
146
140
133
13 0
122.15
1372
M.A. El Baradie
Table B4. Fuzzy logic model's predicted cutting speeds for carbon steel, wrought, at 16 mm depth of cut
Material hardness
Cutting speed (m rain-t)
(BHN)
75
100
125
150
175
200
225
250
275
H.S.S.
Carbide uncoated,
brazed
Carbide uncoated,
indexible
27
26
25
24
23
22
21
20
18.38
81
79
78
76
74
72
71
70
67.6
100
96
94
91
87
84
80
78
74.16
Carbide coated