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Phương trình liên quan tới độ nhám và mòn bề mặt dụng cụ cắt (phần 2)

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CUTSE International Conference 2008, 24-27 November 2008, Miri, Sarawak, Malaysia

Modeling and Optimization of Tool Life and Surface
Roughness for End Milling Titanium Alloy Ti–6Al–
4V Using Uncoated WC-Co Inserts
Turnad L. Ginta, A.K.M. Nurul Amin, A.N.M Karim,
Anayet U. Patwari
Department of Manufacturing and Materials Engineering
International Islamic University Malaysia
Kuala Lumpur, Malaysia
Email: turnad70@yahoo.co.id

Abstract— This paper presents an approach to establish models
and the efforts in optimization of tool life and surface roughness
in end milling of titanium alloy Ti–6Al– 4V using uncoated WCCo inserts under dry conditions. Response surface methodology
coupled with small central composite design (CCD) was
employed in developing the tool life and surface roughness
models in relation to primary cutting parameters such as cutting
speed, axial depth of cut and feed. Flank wear has been
considered as the criteria for tool failure and the wear was
measured under a Hisomet II Toolmaker’s microscope. Mitutoyo
surftest was utilized for surface roughness measurements.
Design-expert version 6.0.8 software was applied to establish the
first-order and the second-order models and develop the
contours. The adequacy of the predictive model was verified
using analysis of variance (ANOVA) at 95% confidence level.
Keywords-response surface; tool life;surface roughness;RSM

I.

INTRODUCTION

In order to establish an adequate functional relationship
between the responses (such as surface roughness, cutting
force, tool life/wear) and the cutting parameters (cutting speed,
feed, and depth of cut), a large number of tests are needed,
requiring a separate set of tests for each and every combination
of cutting tool and work piece material. This increases the total
number of tests and as a result the experimentation cost also
increases. As a group of mathematical and statistical
techniques, response surface methodology (RSM) is useful for
modeling the relationship between the input parameters
(cutting conditions) and the output variables. RSM saves cost
and time by reducing number of experiments required.
RSM is a dynamic and foremost important tool of design of
experiment (DOE), wherein the relationship between
response(s) of a process with its input decision variables is
mapped to achieve the objective of maximization or
minimization of the response properties[1][2]. Many
machining researchers have used response surface
methodology to design their experiments ...
CUTSE International Conference 2008, 24-27 November 2008, Miri, Sarawak, Malaysia
Modeling and Optimization of Tool Life and Surface
Roughness for End Milling Titanium Alloy Ti–6Al–
4V Using Uncoated WC-Co Inserts
Turnad L. Ginta, A.K.M. Nurul Amin, A.N.M Karim,
Anayet U. Patwari
Department of Manufacturing and Materials Engineering
International Islamic University Malaysia
Kuala Lumpur, Malaysia
Email: turnad70@yahoo.co.id
M.A. Lajis
Faculty of Mechanical and Manufacturing
UTHM, 86400 Batu Pahat
Johor, Malaysia
Abstract This paper presents an approach to establish models
and the efforts in optimization of tool life and surface roughness
in end milling of titanium alloy Ti–6Al– 4V using uncoated WC-
Co inserts under dry conditions. Response surface methodology
coupled with small central composite design (CCD) was
employed in developing the tool life and surface roughness
models in relation to primary cutting parameters such as cutting
speed, axial depth of cut and feed. Flank wear has been
considered as the criteria for tool failure and the wear was
measured under a Hisomet II Toolmaker’s microscope. Mitutoyo
surftest was utilized for surface roughness measurements.
Design-expert version 6.0.8 software was applied to establish the
first-order and the second-order models and develop the
contours. The adequacy of the predictive model was verified
using analysis of variance (ANOVA) at 95% confidence level.
Keywords-response surface; tool life;surface roughness;RSM
I. I
NTRODUCTION
In order to establish an adequate functional relationship
between the responses (such as surface roughness, cutting
force, tool life/wear) and the cutting parameters (cutting speed,
feed, and depth of cut), a large number of tests are needed,
requiring a separate set of tests for each and every combination
of cutting tool and work piece material. This increases the total
number of tests and as a result the experimentation cost also
increases. As a group of mathematical and statistical
techniques, response surface methodology (RSM) is useful for
modeling the relationship between the input parameters
(cutting conditions) and the output variables. RSM saves cost
and time by reducing number of experiments required.
RSM is a dynamic and foremost important tool of design of
experiment (DOE), wherein the relationship between
response(s) of a process with its input decision variables is
mapped to achieve the objective of maximization or
minimization of the response properties[1][2]. Many
machining researchers have used response surface
methodology to design their experiments and assess results.
Kaye et al [3] used response surface methodology in predicting
tool flank wear using spindle speed change. A unique model
has been developed which predicts tool flank wear, based on
the spindle speed change, provided the initial flank wear at the
beginning of the normal cutting stage is known. Alauddin et al.
[4] applied response surface methodology to optimize the
surface finish in end milling inconel 718. Mansour et al [5]
developed a surface roughness model for end milling of a semi
- free cutting carbon casehardened steel. They investigated a
first-order equation covering the speed range 30–35 m/min and
a second order generation equation covering the speed range
24–38 m/min. They suggested that an increase in either the
feed or the axial depth of cut increases the surface roughness,
whilst an increase in the cutting speed decreases the surface
roughness. Oktem et al used response surface methodology
with a developed genetic algorithm (GA) in the optimization of
cutting conditions for surface roughness [6]. S. Sharif et al used
factorial design coupled with response surface methodology in
developing the surface roughness model in relation to the
primary machining variables such as cutting speed, feed, and
radial rake angle [7]. Ginta et al [8] used response surface
methodology in assessing tool life in end milling titanium alloy
Ti-6Al-4V with uncoated WC-Co inserts. They found that an
increase of cutting speed, axial depth of cut and feed by 100%,
will lead to reduction of tool life by 70%, 27%, and 37%,
respectively.
II. M
ATHEMATICAL MODEL
Models for the machining responses for end milling in
terms of the cutting parameters can be expressed as:
ml
z
k
dfCVR =
(1)
Where R is the experimental (measured) responses (such as
surface roughness, cutting force, tool life, etc), V is the cutting
speed (m/min), f
z
is the feed (mm/tooth), and d is the axial
depth of cut (mm). C, k, l, and m are model parameters to be
estimated using the experimental results. To determine the
constants and exponents, this mathematical model can be
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