Fuzzy Logic Model For Predicting Of Cutting Force In Turning Of Hardened 17-4 PH Stainless Steel
Ali KALYON*, Mustafa AY*
*Karabuk University, Technology Faculty, Karabuk
*Marmara University, Technology Faculty, İstanbul
Abstract
Turning is the most important production technique among machining processes. The studies that are being
conducted for years point out the fact that there are a number of parameters and conditions that determine the life
of cutting tools and the quality of work piece in turning. The factors influential in the life of cutting tools and the
quality of the product produced as well as such parameters as the geometrical properties of cutting tools, feed
rate, cutting speed, cutting depth, coatings, work piece and the rigidity of cutting tools all increase the life of
cutting tools and the surface quality of the product produced. They, at the same time, reduce the manufacturing
costs and energy.
This paper presents a comparison of experimental results and fuzzy logic based model for estimating the cutting
forces in turning. Cutting forces has been experimentally observed during the turning of hardened 17-4 PH
stainless steel ( EN 1.4542) through PVD coated inserts. The effect of feed rate, tool nose radius and cutting
depth on cutting forces has been examined experimentally. As a result the optimal machining, production
machining parameters for turning operations can easily be detected.
Keywords: Turning, Cutting Force, Fuzzy Logic
INTRODUCTION
A considerable amount of investigations has been directed toward the prediction and measurement of cutting
forces. That is because the cutting forces generated during metal cutting have a direct influence on the generation
of heat, and thus tool wear, quality of machined surface and accuracy of the work piece [1]. In machining; the
significance of optimizing the performance and conditions of cutting has become salient for keeping the
longevity of cutting tools and cutting down on raw materials costs through manufacturing work pieces in the
required quality. In order to achieve this, the factors that are influential in determining the life of cutting tools
and the quality of work piece are being examined by the scientists.
Stainless steels are widely used in industry since application of such materials leads to increase in service life
and reduction of energy consumption. In this regard, precipitation hardened, stainless steels with good corrosion
resistance, high strength, low distortion, excellent weldability and high hardness (up to 49 HRC), are of
considerable interest. Alloy 17-4 PH is the most well know material among the precipitation hardened stainless
steels with unique properties which is used in oil, gas and aerospace industries [2].
Cutting forces have a direct influence on specific cutting pressure and power consumption, tool wear and heat
generation. In order to achieve good machinability and to improve the product quality, it is desirable to have
minimum values of cutting force and surface roughness. However, the requirement of optimal combination of
cutting parameters is different for each of these aspects and depends on the type of material being machined [3]
.
Fuzzy logic is a mathematical theory of inexact reasoning that allows modeling of the reasoning process of
humans in linguistic terms. It is very suitable in defining the relationship between system inputs and desired
outputs. Fuzzy logic is one of the most successful of today's technologies for developing sophisticated control
systems. It is also popular for its ability to develop rule-base expert systems. Fuzzy controllers and fuzzy
reasoning have found particular applications in very complex industrial systems that can not be modeled
precisely even under various assumptions and approximations [4].
There have been many successful applications of fuzzy set theory in metal machining. In the study they have
conducted, Khidhir et al have described a modification approach applied to a fuzzy logic based model for
predicting cutting force where the machining parameters for cutting speed ranges, feed rate, cutting depth and
approach angle are not overlapping. As a result of their study, the modification approach fuzzy logic based
model produced the cutting force data providing good correlation with response surface data [5]. In the study
they have conducted, Hashmi et al have described an adjustment approach applied to a fuzzy logic based model
for selecting cutting speed where the machining data for speed ranges between the different cutting depth are not
overlapped. As a result of their study, application of a fuzzy logic based model for selecting cutting speed in a
turning operation for non overlapping cutting speed ranges is possible by using superimposition scheme [4].
Yaldız et al have developed fuzzy model for the prediction of the cutting forces in turning over a wide range of
turning conditions. They used AISI 1040 steel as the work piece material. Feed force, thrust force and main
cutting force were measured for three combinations of cutting speed, feed rate and cutting depth. Study results
demonstrated the potential of approach for monitoring cutting forces in the workshop environment [1]. Kayacan
et al have established using fuzzy logic programming methods for economical tool usage, based on tool wear in
turning operations. Due to work piece material hardness and type of cutting tool, a fuzzy logic solution model
established to determine the best suitable cutting speed, feed rate and cutting depth parameters. As a result of this
study, the economic turning machining parameters for the appropriate tool wear can be detected [6] . In the study
Roy has conducted, a genetic algorithm trained fuzzy expert system is developed to predict the surface finish in
ultra precision diamond turning operation of Al6061/SiCp metal matrix composite. As a result of study,
proposed system can produce efficient knowledge base of fuzzy expert system for predicting the surface finish in
diamond turning [7]. In the study they have conducted, Hashmi et al developed a model based on fuzzy logic
for selecting cutting speed in single point turning operations. Model applied to three types of steel materials and
four different types of cutting tool materials. Fuzzy logic principles have applied for selecting cutting conditions
in the turning process in machining operation. System developed with using programming language. Between
inputs and the predicted using fuzzy logic model outputs have good correlation [8].
The objective of this work is to develop a fuzzy logic based model to predict cutting force for turning operation
of hardened 17-4 PH stainless steel with using PVD coated inserts. And also analysis the effect of feed rate, tool
nose radius, cutting depth on cutting forces. Fuzzy model output illustrates can help to understand the process
parameters effect on cutting force.
MATERIAL AND METHOD
17-4 PH steel belongs to precipitation-hardening (PH) stainless steels group and it is more common than any
other type of materials from this group due to balanced combination of good mechanical properties and excellent
corrosion resistance. This alloy is a martensite stainless steel containing approximately 17 wt. % Cr, 4 wt. %Ni,
3 wt.% Cu and it is strengthened by the precipitation of submicroscopic copper rich particles in the martensite
matrix. Mechanical properties of the steel depend on the heat treatment parameters. Heat treatment enables
obtaining the following mechanical properties: tensile strength 900-1400 N/mm2 , yield point 590-1280 N/mm2 ,
impact resistance 20-135 J, hardness 27-44 HRC [9].
A commercial 17-4 PH stainless steel bar of 18 mm diameter was used
composition of the steel is listed in Table 1.
as
a material. The chemical
Table 1. Chemical compositions of 17-4 PH stainless steel (wt.%) [10]
C
Mn
P
Cr
Mo
Ni
Al
Co
Cu
Nb
Ti
Fe
0.041
0.78
0,02
15.91
0.40
4.69
0.001
0.063
3.42
0.22
0.002
73.9
Physical vapor deposition (PVD) TiA1N coated inserts which have been manufactured by Kennametal firm and
that has been developed on unalloyed carbide infrastructure that is highly resistant against KC5010 deformation
and after treatment inserts with different nose radius have been used as cutting inserts during the metal removing
process. A Johnford TC 35 CNC Fanuc OT x-z axis turning lathe, a Kistler 9121 power sensor for power
measurement, a Kistler 5019b type load amplifier and DynoWare analysis program have been used in the tests.
In this experimental study, feed rate (f), tool nose radius (rd), cutting depth (d) have been selected as cutting
parameters. The results of test have been obtained by cutting in the work bar with 36 HRC hardness on CNC
turning lathe. The parameters for feed rate, cutting depth, tool nose radius are shown in Figure 1, 2, 3
respectively.
DESIGN OF MAMDANI FUZZY LOGIC MODEL
In the proposed fuzzy model, three inputs of feed rate, cutting depth and tool nose radius were used to predict,
cutting force as shown in Fig 1,2,3 and a single output, cutting force were used as shown in Fig 4. The crisp
inputs of these machining parameters are expressed using three fuzzy linguistic variables of {LOW, MEDIUM,
HIGH}, {SHALLOW, MEDIUM, DEEP}, {SMALL, MEDIUM, LARGE} as depicted in Fig 1,2,3. Even
though the shape of the membership function (MF) can take different forms such as triangular, trapezoidal,
gaussian, sigmoid, generalized bell shape, etc., the triangular functions were used here in since they are simple
and commonly used MF in the literature [10]. The triangular shaped curves for the input MFs are specified by
three parameters {a, b, c} to uniformly distribute the curves along the input variable ranges as defined in Fig
1,2,3. The parameters, i.e. feed rate, are specified using the following expression.
0
Triangle (X; a, b, c, ) =
x−a
{b−a
c−x
c−b
0
x≤0.1
0.1≤x≤0.2
0.2≤x≤0.3
0.3≤x
On the other hand, outputs of these machining parameters are expressed using seven fuzzy linguistic variables
of {LOWEST, LOWER, LOW, MEDIUM, HIGH, HIGHER, HIGHEST} as depicted in Fig 4 .
The max-min inference method was selected as the aggregation procedure for unification of all output derived
from the output to get the crisp number. The defuzzification method employed in this study is the centroid of
gravity in which the expression for calculating centroid of gravity is given as:
𝑥∗ =
∫ 𝜇𝑖 (𝑥)𝑥𝑑𝑥
∫ 𝜇𝑖 (𝑥)𝑑𝑥
where 𝑥 ∗ is the defuzzified output, 𝜇𝑖 (𝑥) is the aggregated MF and 𝑥 is the output variable [11].
Fuzzy model for turning operation
The fuzzy model that has been designed for predicting cutting force for the turning operation uses three inputs
and one output. Feed rate, cutting depth, tool nose radius are the inputs and the cutting force is the output of the
system. The fuzzy expressions for feed rate, cutting depth, tool nose radius and cutting force are shown in Figure
1, 2, 3, 4 respectively. The first step in establishing the algorithm for selecting the cutting condition is to choose
the shape of fuzzy membership functions or fuzzy sets for the process variables based upon experimental data.
Triangular shape are used for the membership function for the input and the output variables.
Fuzzy rules are a set of linguistic statements which establishes the relationship between the input and the output
in a fuzzy system. They are defined based on experimental work, expert and engineering knowledge. The
number of fuzzy rules in a fuzzy system is related to the number of fuzzy sets for each input variable. In this
study, there are three input variables each of which is classified into three fuzzy sets and there are seven cutting
force states to be determined.
Figure 1. Feed rate membership function
Feed rate
(mm/rev)
Membership
Function
0.1-0.2
Low
0.1-0.3
Medium
0.2-0.3
High
Figure 2. Cutting depth membership function
Cutting Depth
(mm)
Membership
function
0.4-0.8
Shallow
0.4-1
Medium
0.8-1
Deep
Figure 3. Tool nose radius membership function
Tool nose
radius (mm)
0.4-0.8
Membership
function
Small
0.4-1.2
Medium
0.8-1.2
Large
Figure 4. Cutting force membership function
Cutting Force (N)
Membership function
250,555
Lowest
275,136
Lower
309,048
Low
353,667
Medium
369,586
High
403,133
Higher
463,136
Highest
RESULTS
Using the experimental results a fuzzy logic model has been used to achieve the best parameters for the turning
operations. Turning operation has been carried out in accordance with the parameters feed rate, cutting depth,
tool nose radius which are given Figure 1, 2, 3. Experimental results are given in Table 2.
Table 2. Experimental and fuzzy
logic model results
Figure 5. Comparison of experimental and fuzzy logic model results
Predicted
cutting
force (N)
500
1
250,555
258
450
2
275,136
278
3
309,048
313
4
353,667
344
5
369,586
375
Cutting Force (N)
Experimental
cutting force
(N)
Sq.
400
Experimental
result
Fuzzy logic
model result
350
300
250
200
1
6
403,133
412
7
463,136
453
2
3
4
5
6
7
Experiment sequence
Fuzzy logic model can be used to analyze the effects of the selected process parameters on cutting force. It can
be observed from Fig. 6.a, for a given cutting depth and feed rate, the cutting force sharply increases with the
increase in feed rate and cutting depth. The minimal cutting force results with combination of low feed rate and
low depth of cut. When the feed rate is high, the cutting force is sensitive to tool nose radius, as depicted in Fig
6.b. An decrease in cutting depth sharply reduces the cutting force. It is also observed that, cutting force
variation is minimal with variations of tool nose radius at higher values of feed rate. When the cutting depth is
constant, the cutting force is sensitive to tool nose radius as depicted in Fig 6.c. When the cutting depth is
constant cutting force decrease with the increase tool nose radius. Maximum cutting force results with
combination high cutting depth and feed rate.
Figure 6. a)Effect of feed rate, cutting depth on cutting force b)Effect of tool nose radius and feed rate on cutting
force c) Effect of tool nose radius and cutting depth on cutting force
a)
b)
c)
From the above discussions it can be concluded that the cutting force is highly sensitive to cutting depth and feed
rate. On the other hand, tool nose radius has less effect on cutting force. The cutting force has a tendency to
reduce with decrease in cutting depth and feed rate. On the other hand, when feed rate increases, cutting force is
increases, cutting force decreases due to increased tool nose radius.
Finally it can be concluded that fuzzy logic model can predict the response for any new input process
parameters with high accuracy. The performance of fuzzy logic model can be further improved by defining more
number of levels for the input process parameters. However, this calls for large number of experiments to be
performed and hence, is costly and time consuming
CONCLUSION
A fuzzy based model developed in this work, to predict cutting force turning operation of hardened 17-4 PH
stainless steel with using PVD coated inserts. This analysis was carried out by developing cutting force model
using fuzzy logic with feed rate, cutting depth and tool nose radius as process parameters.
The cutting force are highly sensitive to both feed rate and cutting depth. On the other hand, tool nose has the
least effect. The cutting force has a tendency to reduce with decrease in cutting depth and feed rate. On the other
hand, when feed rate increases, cutting force is increases, cutting force decreases due to increased tool nose
radius.
The results obtained from the fuzzy logic are highly consistent with the experimental results. For selecting
cutting condition for hardened 17-4 PH stainless steel using different parameters can be described by the fuzzy
logic model. The ability of predicting outputs of a machining process without carrying out actual experiment will
help us to develop automatic manufacturing system. Quality loss by designing the products and processes to be
insensitive to variation in variables is a novel concept to manufacturers and quality engineers.
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