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# Multi-objective optimisation of high-speed electrical discharge machining process using a Taguchi fuzzy-based approach

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(BQ) The paper describes the application of the fuzzy logic analysis coupled with Taguchi methods to optimise the precision and accuracy of the high-speed electrical discharge machining (EDM) process. A fuzzy logic system is used to investigate relationships between the machining precision and accuracy for determining the efficiency of each parameter design of the Taguchi dynamic experiments.

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Nội dung Text: Multi-objective optimisation of high-speed electrical discharge machining process using a Taguchi fuzzy-based approach

Materials<br />
& Design<br />
Materials and Design 28 (2007) 1159–1168<br />
www.elsevier.com/locate/matdes<br />
<br />
Multi-objective optimisation of high-speed electrical<br />
discharge machining process using a Taguchi fuzzy-based approach<br />
Yih-fong Tzeng<br />
a<br />
<br />
a,*<br />
<br />
, Fu-chen Chen<br />
<br />
b<br />
<br />
Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, No. 1 University Road,<br />
Yen-Chao, Kao-Hsiung 824, Taiwan<br />
b<br />
Department of Mechanical Engineering, Kun Shan University, No. 949 Da Wan Rd., Yung-Kang, Tainan Hsien 710, Taiwan<br />
Received 9 August 2005; accepted 19 January 2006<br />
Available online 3 April 2006<br />
<br />
tool steel SKD11<br />
<br />
Abstract<br />
The paper describes the application of the fuzzy logic analysis coupled with Taguchi methods to optimise the precision and accuracy<br />
of the high-speed electrical discharge machining (EDM) process. A fuzzy logic system is used to investigate relationships between the<br />
machining precision and accuracy for determining the eﬃciency of each parameter design of the Taguchi dynamic experiments. From<br />
the fuzzy inference process, the optimal process conditions for the high-speed EDM process can be easily determined as<br />
A1B1C3D1E3F3G1H3. In addition, the analysis of variance (ANOVA) is also employed to identify factor B (pulse time), C (duty cycle),<br />
and D (peak value of discharge current) as the most important parameters, which account for about 81.5% of the variance. The factors E<br />
(powder concentration) and H (powder size) are found to have relatively weaker impacts on the process design of the high-speed EDM.<br />
Furthermore, a conﬁrmation experiment of the optimal process shows that the targeted multiple performance characteristics are significantly improved to achieve more desirable levels.<br />
Ó 2006 Elsevier Ltd. All rights reserved.<br />
Keywords: Electrical discharge machining (EDM); Fuzzy logic analysis; Analysis of variance (ANOVA); Machining precision and accuracy<br />
<br />
1. Introduction<br />
Electrical discharge machining (EDM) is a thermal process with a complex metal-removal mechanism, involving<br />
the formation of a plasma channel between the tool and<br />
workpiece. It has proved especially valuable in the machining of super-tough, electrically conductive materials such as<br />
the new space-age alloys that are diﬃcult to machine by<br />
conventional methods [1]. For several decades, EDM has<br />
been an important manufacturing process for the mould<br />
and die industry. Although the EDM process is not aﬀected<br />
by material hardness and strength, it is much slower compared to the milling and turning processes. To speed up the<br />
process, large electrical current discharge is usually<br />
required, but concurrently the dimensional quality of the<br />
*<br />
<br />
Corresponding author. Tel.: +886 7 6011006; fax: +886 7 6011066.<br />
E-mail address: franktzeng@ccms.nkfuse.edu.tw (Y.-f. Tzeng).<br />
<br />
0261-3069/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.<br />
doi:10.1016/j.matdes.2006.01.028<br />
<br />
machined product inevitably became worse. On the other<br />
hand, it is well known that EDM process is very unstable<br />
owing to arcing when too much debris exists inside the<br />
gap. Therefore, how to develop an EDM process with the<br />
capability of high machining rate, and high precision and<br />
accuracy without major alterations to the EDM system<br />
remains a big challenge.<br />
To improve the EDM technology, many eﬀorts have<br />
been directed to enhance the process stability. Introducing<br />
foreign particles into the working ﬂuid was one of the useful approaches to improve the EDM performance. Example applications include the surface modiﬁcation method<br />
by EDM with a green compact electrode and powder suspended in working ﬂuid by Furutani et al. [2]; near-mirror-ﬁnish EDM technology using powder-mixed dielectric<br />
by Wong et al. [3]; the eﬀects of powder characteristics<br />
on precision and rough electrical discharge machining eﬃciency by Tzeng et al. [4–6]. The other approaches include<br />
<br />
1160<br />
<br />
Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168<br />
<br />
the use of ultrasonic vibration to assist EDM process for<br />
improving the material removal rate by Zhang et al. [7,8];<br />
the eﬀects of various process parameters on EDM by<br />
Hocheng et al. [9].<br />
Traditionally, the operating parameters of the EDM<br />
process are mainly set based on the trial and error experience of the operator or the information provided by the<br />
tool suppliers. This method is neither cost-eﬃcient nor useful for quality control. Taguchi proposes a procedure that<br />
applies orthogonal arrays from statistical design of experiments to eﬃciently obtain the best model with the least<br />
number of experiments [10]. However, most previous applications of the Taguchi methods emphasize only on single<br />
quality characteristic and, in comparison, paid little attention on multiple performance characteristics (MPCs) [11–<br />
15]. Nevertheless, the MPCs of a product are still generally<br />
required by the consumers. When optimising a process with<br />
MPCs, the objective is to determine the best process<br />
parameters that will simultaneously optimise all the quality<br />
characteristics of interest to the designer. The more frequently used approach is to assign a weighting for each<br />
response. However, to determine a deﬁnite weighting for<br />
each response in an actual case remains a diﬃcult task.<br />
In practice, the weighting method using engineering judgment together with the past experiences is still the primary<br />
approach to optimise MPCs [16]. The consequent results<br />
often include some uncertainties in the decision-making<br />
process. Some of the applications include the simultaneous<br />
optimisation of MPCs using the Taguchi’s quality loss<br />
function by Antony [17]; the optimisation technique for<br />
face milling stainless steel with MPCs by Lin [18]; and<br />
the investigation of the multiple surface quality characteristics of weld pool geometry in the tungsten inert gas welding process by Juang et al. [19]. However, the common<br />
outcomes from these approaches are increased human<br />
uncertainties due to the complex computational process,<br />
and unknown correlations amongst the MPCs. It is important to note that diﬀerent performance characteristics have<br />
diﬀerent relative weightings for tuning MPCs. Tong and Su<br />
present a procedure to optimise MPCs problems using the<br />
fuzzy multiple attribute decision-making process [20]. This<br />
procedure can reduce human uncertainties but requires<br />
rather complicated mathematical computations and is relatively diﬃcult to implement by individuals who have no<br />
adequate mathematical training. Using the fuzzy logic<br />
analysis, the MPCs can be easily dealt with by setting up<br />
a reasoning procedure for each performance characteristic<br />
and transform them into a single value of the multiple performance characteristic indices (MPCIs).<br />
Nowadays, the international market in the mould and<br />
die manufacturing industry has become highly competitive.<br />
To meet customer requirements for short delivery, high<br />
quality, and low cost, the EDM process must have the<br />
capability of high speed, versatility, ﬂexibility, and robustness. This paper thus seeks to use the application of the<br />
fuzzy logic analysis coupled with the Taguchi dynamic<br />
approach to develop a robust high-speed machining tech-<br />
<br />
nique that is optimised in terms of both the machining precision and accuracy, and is suitable for a range of product<br />
dimensions. It is anticipated that this developed technique<br />
would increase the competitiveness of mould and die manufacturers by providing them with ﬂexibility, rapid and<br />
eﬀective response to the ever-changing demands of<br />
customers.<br />
2. Experimental methods<br />
2.1. Process design for high-speed electrical discharge machining<br />
eﬀects<br />
BEST 230 die-sinking EDM is used with SHOMOS kerosene in the<br />
experiments. As one of the goals in the study seeks for high-speed machining performance, the tool electrode is connected to the positive polarity<br />
and large peak discharge current is applied. However, this setup leads to<br />
a worse dimensional precision, accuracy and surface roughness on the<br />
machined parts unless some complementary polishing eﬀect is introduced.<br />
Aluminum (Al) powder is therefore selected to add into the working ﬂuid<br />
for its appreciable eﬀects on improving process stability and machining<br />
accuracy [21,22]. For constant and better circulation of the Al powder during machining, a cylindrical tank and a new ﬁlter system is designed for<br />
use throughout the experiment. Since the Al powder is non-magnetic,<br />
the new ﬁlter system shown in Fig. 1 uses magnetic force to separate the<br />
work debris from the dielectric ﬂuid, while the powder passing through<br />
is sent back by the pump.<br />
<br />
2.2. Material and measurement<br />
The material machined in the study is tool steel SKD11. The electrolytic copper of 99.95% purity is selected as the tool electrode. Both of them<br />
have been extensively used in the mould and die manufacturing industry.<br />
Measurements of machined products are made by a Mitutoyo toolmaker’s<br />
microscope (MF Series). The main measurements are the entrance dimensions which are speciﬁed in the later section.<br />
<br />
2.3. Taguchi methods<br />
Any man-made system is viewed by Taguchi methods as an engineered<br />
system that comprises four main components as illustrated in Fig. 2. It is<br />
designed to employ energy transformation in converting input signal into<br />
speciﬁc, intended function requested by customers by applying the laws of<br />
physics.<br />
<br />
Fig. 1. Diagram of a self-designed ﬁlter system for the EDM.<br />
<br />
Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168<br />
<br />
1161<br />
<br />
response). In order for the EDM machine to perform well for all component parts that it is to process, the input dimensions are recommended to<br />
cover a range of expected values. After the process optimisation, a family<br />
of future products could be successfully machined.<br />
<br />
2.5. Dynamic signal-to-noise (S/N) ratio<br />
<br />
Fig. 2. Schematic of an engineering system.<br />
<br />
Taguchi methods advocate that appropriate design of the control factors makes the system transform energy very eﬃciently. Unintended eﬀects<br />
due to noise factors that are the hardly controllable variables can be minimized. In theory, when all the applied energy is transformed into creating<br />
its intended function without any noise eﬀects, a system reaches its ideal<br />
function. As shown in Fig. 3a, the most common way of expressing the<br />
system’s ideal function is [23]:<br />
<br />
Y ¼ bM;<br />
<br />
Energy transformed to perform the intended function ðwork done by signalÞ<br />
Energy transformed to other than the intended function ðwork done by noisesÞ<br />
À Á<br />
b2 À Vre<br />
The level of performance of the desired function<br />
b2<br />
¼ 10log<br />
¼<br />
ﬃ 10 log 2 ;<br />
The variability of the desired function<br />
d<br />
d2<br />
<br />
S=N ¼<br />
<br />
ð1Þ<br />
<br />
where a linear relationship exists between Y (= ideal output response) and<br />
M (= input signal). However, in reality, energy transformation of any systems does not happen as designed or intended due to noise factors disturbing the system. The reality of the system function therefore consists of<br />
nonlinear eﬀects between the input/output demonstrated by Fig. 3b. The<br />
real function Yr can thus be described as<br />
Y r ¼ f ðM; C 1 ; C 2 ; . . . ; C k ; N 1 ; N 2 ; . . . ; N p Þ<br />
¼ bM þ ferror ðM; C 1 ; C 2 ; . . . ; C k ; N 1 ; N 2 ; . . . ; N p Þ;<br />
<br />
To evaluate the process design, signal-to-noise (S/N) ratio is used in<br />
Taguchi methods as an index of robustness because it measures the quality<br />
of energy transformation. As the input signal, control factors, and noise<br />
factors come together into a system, their combined impacts on the output<br />
response through energy transformation create the system’s S/N ratio. The<br />
quality of energy transformation is expressed as the ratio of the energy<br />
transformed to perform the intended function to the energy transformed<br />
to other than the intended function. The higher the S/N ratio, the higher<br />
the quality. The dynamic S/N ratio formula is shown as follows [23]:<br />
<br />
ð2Þ<br />
<br />
where C1, C2,. . ., Ck are control factors and N1, N2,. . ., Np are noise factors, and ferror is the error function between the ideal and the reality.<br />
Orthogonal array is one of the important tools used in the experimental design of Taguchi methods. An L18 (21 · 37) was chosen for the experimental tests because it has a good even distribution of factorial<br />
interactions over the control factors. Taguchi parameter design strategy<br />
separates the control factors from the noises by using inner and outer<br />
arrays, respectively. Control factors are assigned in the inner array, while<br />
noise factors coupled with signal factors are arranged in the outer array<br />
for exposing the process to varying noise conditions. The purpose is to<br />
reach a level where the control factor does not vary much despite the inevitable presence of noise.<br />
<br />
2.4. Proposed ideal function of the EDM process<br />
The basic functionality of the EDM machine is to create a precise<br />
shape as the output requested by customers after receiving the input signal, i.e. the tool electrode. Therefore, from the standpoint of the ‘transformability’, the ideal function for this case is designed as electrode<br />
dimension (input signal) being proportional to product dimension (output<br />
<br />
ð3Þ<br />
where b is the slope of best-ﬁt line between the measured values and the<br />
inputs, and r2 the mean square around the best-ﬁt line.<br />
<br />
2.6. Control factors and levels<br />
Eight major control factors have been identiﬁed for the study. They are<br />
open circuit voltage (A), pulsed duration (B), duty cycle (C), pulsed peak<br />
current (D), powder concentration (E), regular distance for electrode lift<br />
(F), time interval for electrode lift (G), and powder size (H), respectively.<br />
The details of their levels are listed in Table 1. Factors B, C, and D are<br />
arranged based on the principle of energy-beam material processing. It<br />
is worth noting that factor D varied to keep the output power constant<br />
for a systematic comparison of the experimental results.<br />
<br />
2.7. Design of tool electrode and signal arrangement<br />
To develop a process with versatility, how to vary the signal experimentally is one of the most important steps in the Taguchi robust design.<br />
To achieve this objective, a special tool electrode with a range of geometrical characteristics is designed for use throughout the experiments.<br />
Fig. 4 illustrates the tool electrode designed by us. As shown in<br />
Fig. 4a, the tool electrode has two typical geometrical shapes to be<br />
machined, including rectangular and circle for which each has three<br />
kinds of dimensional sizes. Fig. 4b displays its 3D representation. The<br />
geometrical characteristics with six diﬀerent intended dimensions are<br />
arranged as the input signal given in Table 2.<br />
Table 1<br />
Control factors and their levels<br />
Control factors<br />
<br />
Level-2<br />
<br />
Level-3<br />
<br />
Open circuit voltage (V)<br />
Pulsed duration (Ton: ls)<br />
Duty cycle (CD: %)<br />
Pulsed peak current (Ip: A)<br />
<br />
E<br />
F<br />
<br />
Fig. 3. (a) The system’s ideal function, and (b) the reality.<br />
<br />
Level-1<br />
<br />
A<br />
B<br />
C<br />
D<br />
<br />
Powder concentration (Al: cm3/l)<br />
Regular distance for<br />
electrode lift (mm)<br />
Time interval for electrode lift (s)<br />
Powder size (lm)<br />
<br />
120<br />
12<br />
33<br />
12<br />
8<br />
6<br />
0.1<br />
1<br />
<br />
230<br />
75<br />
50<br />
18<br />
12<br />
9<br />
0.3<br />
6<br />
<br />
400<br />
66<br />
24 for C1<br />
16 for C2<br />
12 for C3<br />
0.5<br />
12<br />
<br />
2.5<br />
10–20<br />
<br />
4.0<br />
40<br />
<br />
G<br />
H<br />
<br />
0.6<br />
1<br />
<br />
1162<br />
<br />
Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168<br />
Table 3<br />
Signal and noise factors arrangement in the outer array<br />
Mi, i = 1–6<br />
Noise factors<br />
<br />
Fig. 4. (a) The top view, (b) and 3D representation of the tool electrode.<br />
<br />
Table 2<br />
Input signals in the outer array<br />
Input signal<br />
<br />
M1<br />
<br />
M2<br />
<br />
M3<br />
<br />
M4<br />
<br />
M5<br />
<br />
M6<br />
<br />
Intended<br />
dimension (mm)<br />
<br />
6.000<br />
<br />
8.458<br />
<br />
12.000<br />
<br />
16.971<br />
<br />
20.000<br />
<br />
25.456<br />
<br />
2.8. Noise factors and strategy<br />
Noise factors cause variability and deterioration of performance from<br />
the ideal function and lead to variability in the quality characteristic. Generally, there are a number of noise factors with the EDM process, such as<br />
machining time, electrode consumption, electrode shape and size, and<br />
aging working oil. It is clear that most of the above noise factors closely<br />
aﬀect the gap conditions. For the simpliﬁcation of experimentation, every<br />
experimental trial uses the totally new electrode with the same dimensions<br />
machined by CNC milling machine. Additionally, due to being hard control, Taguchi methods suggest the use of the compounding strategy to<br />
arrange them to be two extreme conditions [23]. To simulate the extreme<br />
noise conditions, N1 (with both ﬁltration and circulation system) and N2<br />
(without both ﬁltration and circulation system) are arranged under<br />
machining time. Their couple with signal factors assigned in the outer<br />
array of L18 is displayed in Table 3.<br />
<br />
3. Fuzzy logic analysis and analysis of variance<br />
3.1. Fuzzy logic methods<br />
Fuzzy logic is a mathematical theory of inexact reasoning that allows modeling of the reasoning process of<br />
human in linguistic terms [24]. It is very suitable in deﬁn-<br />
<br />
T1<br />
N1<br />
<br />
N2<br />
<br />
T2<br />
N1<br />
<br />
N2<br />
<br />
T3<br />
N1<br />
<br />
N2<br />
<br />
ing the relationship between system inputs and desired<br />
outputs. Fuzzy controllers and fuzzy reasoning have<br />
found particular applications in very complex industrial<br />
systems that cannot be modeled precisely even under various assumptions and approximations. A fuzzy system is<br />
composed of a fuzziﬁer, an inference engine, a data base,<br />
a rule base, and defuzziﬁer. In the study, the fuzziﬁer<br />
ﬁrstly uses membership functions to convert the crisp<br />
inputs into fuzzy sets, and then the inference engine performs a fuzzy reasoning on fuzzy rules to generate fuzzy<br />
values, then the defuzziﬁer converts these values into the<br />
crisp outputs. The ﬂow structure chart of the fuzzy logic<br />
controller coupled with Taguchi methods used in the<br />
study is shown in Fig. 5.<br />
Fuzzy values are determined by the membership functions that deﬁne the degree of membership of an object<br />
in a fuzzy set [25]. However, so far there has been no standard method of choosing the proper shape of the membership functions for the fuzzy sets of the control variables.<br />
Trial and error methods are usually exercised. Based on<br />
the fuzzy rules, the Mamdani implication method is<br />
employed for the fuzzy inference reasoning in this study.<br />
For a rule<br />
Ri : If x1 is Ai1 ; x2 is Ai2 ; . . . ; and xs is Ais ; then y i is C i ;<br />
i ¼ 1; 2; . . . ; M;<br />
<br />
ð4Þ<br />
<br />
where M is the total number of fuzzy rules, xj (j = 1, 2,. . .,<br />
s) are the input variables, yi are the output variables, and<br />
Aij and Ci are fuzzy sets modeled by membership functions<br />
lAij ðxj Þ and lCi ðy i Þ, respectively. Based on the Mamdani<br />
implication method of inference reasoning for a set of disjunctive rules, the aggregated output for the M rules is<br />
lCi ðy i Þ ¼ maxfmin½lAi1 ðx1 Þ; lAi2 ðx2 Þ; . . . ; lAis ðxs Þg;<br />
i<br />
<br />
i ¼ 1; 2; . . . ; M.<br />
<br />
ð5Þ<br />
<br />
The above equation is illustrated in Fig. 6. The graph represents the fuzzy reasoning process for two rules, R1 and<br />
R2, with two input variables that use triangular-shape<br />
membership functions. Using a defuzziﬁcation method,<br />
fuzzy values can be combined into one single crisp output<br />
value. The center of gravity, one of the most popular<br />
methods for defuzzifying fuzzy output functions, is employed in the study. The formula to ﬁnd the centroid of<br />
the combined outputs, ^i , is given by:<br />
y<br />
R<br />
y l ðy Þ dy<br />
^i ¼ R i Ci i<br />
y<br />
.<br />
ð6Þ<br />
lCi ðy i Þ dy<br />
The yielded value is the ﬁnal crisp output value obtained<br />
from the input variables.<br />
<br />
Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168<br />
<br />
1163<br />
<br />
Rule base<br />
<br />
Data base<br />
<br />
Fuzzy knowledge base<br />
<br />
Input<br />
<br />
Fuzzy inference<br />
engine<br />
<br />
Fuzzification<br />
<br />
Output<br />
<br />
Defuzzification<br />
<br />
Fuzzy logic controller<br />
<br />
MPCIs<br />
Dimensional precision<br />
(DA) and accuracy (DA)<br />
Control<br />
factors:<br />
A, B,,,,,,,,H<br />
<br />
Input signal:<br />
<br />
Machining output:<br />
Product dimension<br />
<br />
Intended dimension<br />
using tool electrode<br />
<br />
High-speed EDM process<br />
<br />
Noise<br />
factors:<br />
N1, N2<br />
<br />
Intent<br />
<br />
Voice of customer:<br />
Short delivery, high quality, low cost<br />
Fig. 5. Flow structure chart of the fuzzy logic controller coupled with Taguchi methods used in the study.<br />
<br />
If<br />
<br />
and<br />
µA12(x)<br />
<br />
µA11(x)<br />
<br />
then<br />
µC11(x)<br />
<br />
Combined & Defuzzified<br />
<br />
1<br />
min[µA11(x1*), µA12(x2*)]<br />
max[µC11(x1*), µC12(x2*)]<br />
µC(x)<br />
<br />
R1<br />
<br />
0<br />
<br />
0<br />
x1*<br />
<br />
x1<br />
<br />
0<br />
x2*<br />
<br />
x2<br />
<br />
y<br />
µC22(x)<br />
<br />
µA22(x)<br />
<br />
µA21(x)<br />
<br />
1<br />
R2<br />
<br />
0<br />
<br />
0<br />
x1*<br />
<br />
x1<br />
<br />
0<br />
x2*<br />
<br />
x2<br />
<br />
Mamdani Fuzzy Logic Reasoning Process<br />
<br />
y<br />
min[µA21(x1*), µA22(x2*)]<br />
<br />
Fig. 6. Mamdani implication methods with fuzzy controller operations.<br />
<br />

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