Tối ưu hóa đa mục tiêu quy trình gia công phóng điện tốc độ cao sử dụng phương pháp dựa trên Taguchi fuzzy

Materials & Design

Materials and Design 28 (2007) 1159–1168 www.elsevier.com/locate/matdes

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

Yih-fong Tzeng a,*, Fu-chen Chen b

a Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, No. 1 University Road, Yen-Chao, Kao-Hsiung 824, Taiwan b Department of Mechanical Engineering, Kun Shan University, No. 949 Da Wan Rd., Yung-Kang, Tainan Hsien 710, Taiwan

Abstract

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. From the fuzzy inference process, the optimal process conditions for the high-speed EDM process can be easily determined as A1B1C3D1E3F3G1H3. In addition, the analysis of variance (ANOVA) is also employed to identify factor B (pulse time), C (duty cycle), and D (peak value of discharge current) as the most important parameters, which account for about 81.5% of the variance. The factors E (powder concentration) and H (powder size) are found to have relatively weaker impacts on the process design of the high-speed EDM. Furthermore, a conﬁrmation experiment of the optimal process shows that the targeted multiple performance characteristics are signif- icantly improved to achieve more desirable levels. (cid:2) 2006 Elsevier Ltd. All rights reserved.

Received 9 August 2005; accepted 19 January 2006 Available online 3 April 2006

1. Introduction

machined product inevitably became worse. On the other hand, it is well known that EDM process is very unstable owing to arcing when too much debris exists inside the gap. Therefore, how to develop an EDM process with the capability of high machining rate, and high precision and accuracy without major alterations to the EDM system remains a big challenge.

Electrical discharge machining (EDM) is a thermal pro- cess with a complex metal-removal mechanism, involving the formation of a plasma channel between the tool and workpiece. It has proved especially valuable in the machin- ing of super-tough, electrically conductive materials such as the new space-age alloys that are diﬃcult to machine by conventional methods [1]. For several decades, EDM has been an important manufacturing process for the mould and die industry. Although the EDM process is not aﬀected by material hardness and strength, it is much slower com- pared to the milling and turning processes. To speed up the process, large electrical current discharge is usually required, but concurrently the dimensional quality of the

* Corresponding author. Tel.: +886 7 6011006; fax: +886 7 6011066.

To improve the EDM technology, many eﬀorts have been directed to enhance the process stability. Introducing foreign particles into the working ﬂuid was one of the use- ful approaches to improve the EDM performance. Exam- ple applications include the surface modiﬁcation method by EDM with a green compact electrode and powder sus- pended in working ﬂuid by Furutani et al. [2]; near-mir- ror-ﬁnish EDM technology using powder-mixed dielectric by Wong et al. [3]; the eﬀects of powder characteristics on precision and rough electrical discharge machining eﬃ- ciency by Tzeng et al. [4–6]. The other approaches include

Keywords: Electrical discharge machining (EDM); Fuzzy logic analysis; Analysis of variance (ANOVA); Machining precision and accuracy

E-mail address: franktzeng@ccms.nkfuse.edu.tw (Y.-f. Tzeng).

the use of ultrasonic vibration to assist EDM process for improving the material removal rate by Zhang et al. [7,8]; the eﬀects of various process parameters on EDM by Hocheng et al. [9].

response

nique that is optimised in terms of both the machining pre- cision and accuracy, and is suitable for a range of product dimensions. It is anticipated that this developed technique would increase the competitiveness of mould and die man- ufacturers by providing them with ﬂexibility, rapid and to the ever-changing demands of eﬀective customers.

2. Experimental methods

2.1. Process design for high-speed electrical discharge machining eﬀects

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1160

2.2. Material and measurement

BEST 230 die-sinking EDM is used with SHOMOS kerosene in the experiments. As one of the goals in the study seeks for high-speed machin- ing performance, the tool electrode is connected to the positive polarity and large peak discharge current is applied. However, this setup leads to a worse dimensional precision, accuracy and surface roughness on the machined parts unless some complementary polishing eﬀect is introduced. Aluminum (Al) powder is therefore selected to add into the working ﬂuid for its appreciable eﬀects on improving process stability and machining accuracy [21,22]. For constant and better circulation of the Al powder dur- ing machining, a cylindrical tank and a new ﬁlter system is designed for use throughout the experiment. Since the Al powder is non-magnetic, the new ﬁlter system shown in Fig. 1 uses magnetic force to separate the work debris from the dielectric ﬂuid, while the powder passing through is sent back by the pump.

2.3. Taguchi methods

The material machined in the study is tool steel SKD11. The electro- lytic copper of 99.95% purity is selected as the tool electrode. Both of them have been extensively used in the mould and die manufacturing industry. Measurements of machined products are made by a Mitutoyo toolmaker’s microscope (MF Series). The main measurements are the entrance dimen- sions which are speciﬁed in the later section.

Traditionally, the operating parameters of the EDM process are mainly set based on the trial and error experi- ence of the operator or the information provided by the tool suppliers. This method is neither cost-eﬃcient nor use- ful for quality control. Taguchi proposes a procedure that applies orthogonal arrays from statistical design of experi- ments to eﬃciently obtain the best model with the least number of experiments [10]. However, most previous appli- cations of the Taguchi methods emphasize only on single quality characteristic and, in comparison, paid little atten- tion on multiple performance characteristics (MPCs) [11– 15]. Nevertheless, the MPCs of a product are still generally required by the consumers. When optimising a process with MPCs, the objective is to determine the best process parameters that will simultaneously optimise all the quality characteristics of interest to the designer. The more fre- quently used approach is to assign a weighting for each response. However, to determine a deﬁnite weighting for each response in an actual case remains a diﬃcult task. In practice, the weighting method using engineering judg- ment together with the past experiences is still the primary approach to optimise MPCs [16]. The consequent results often include some uncertainties in the decision-making process. Some of the applications include the simultaneous optimisation of MPCs using the Taguchi’s quality loss function by Antony [17]; the optimisation technique for face milling stainless steel with MPCs by Lin [18]; and the investigation of the multiple surface quality character- istics of weld pool geometry in the tungsten inert gas weld- ing process by Juang et al. [19]. However, the common outcomes from these approaches are increased human uncertainties due to the complex computational process, and unknown correlations amongst the MPCs. It is impor- tant to note that diﬀerent performance characteristics have diﬀerent relative weightings for tuning MPCs. Tong and Su present a procedure to optimise MPCs problems using the fuzzy multiple attribute decision-making process [20]. This procedure can reduce human uncertainties but requires rather complicated mathematical computations and is rela- tively diﬃcult to implement by individuals who have no adequate mathematical training. Using the fuzzy logic analysis, the MPCs can be easily dealt with by setting up a reasoning procedure for each performance characteristic and transform them into a single value of the multiple per- formance characteristic indices (MPCIs).

Any man-made system is viewed by Taguchi methods as an engineered system that comprises four main components as illustrated in Fig. 2. It is designed to employ energy transformation in converting input signal into speciﬁc, intended function requested by customers by applying the laws of physics.

Nowadays, the international market in the mould and die manufacturing industry has become highly competitive. To meet customer requirements for short delivery, high quality, and low cost, the EDM process must have the capability of high speed, versatility, ﬂexibility, and robust- ness. This paper thus seeks to use the application of the fuzzy logic analysis coupled with the Taguchi dynamic approach to develop a robust high-speed machining tech-

Fig. 1. Diagram of a self-designed ﬁlter system for the EDM.

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1161

2.5. Dynamic signal-to-noise (S/N) ratio

response). In order for the EDM machine to perform well for all compo- nent parts that it is to process, the input dimensions are recommended to cover a range of expected values. After the process optimisation, a family of future products could be successfully machined.

Fig. 2. Schematic of an engineering system.

S=N ¼

Energy transformed to perform the intended function ðwork done by signalÞ Energy transformed to other than the intended function ðwork done by noisesÞ

To evaluate the process design, signal-to-noise (S/N) ratio is used in Taguchi methods as an index of robustness because it measures the quality of energy transformation. As the input signal, control factors, and noise factors come together into a system, their combined impacts on the output response through energy transformation create the system’s S/N ratio. The quality of energy transformation is expressed as the ratio of the energy transformed to perform the intended function to the energy transformed to other than the intended function. The higher the S/N ratio, the higher the quality. The dynamic S/N ratio formula is shown as follows [23]:

¼ 10log

ﬃ 10 log

ð1Þ

Y ¼ bM;

The level of performance of the desired function The variability of the desired function

(cid:2) (cid:3) b2 (cid:2) V e r d2

b2 d2 ; ð3Þ

Taguchi methods advocate that appropriate design of the control fac- tors makes the system transform energy very eﬃciently. Unintended eﬀects due to noise factors that are the hardly controllable variables can be min- imized. In theory, when all the applied energy is transformed into creating its intended function without any noise eﬀects, a system reaches its ideal function. As shown in Fig. 3a, the most common way of expressing the system’s ideal function is [23]:

where b is the slope of best-ﬁt line between the measured values and the inputs, and r2 the mean square around the best-ﬁt line.

2.6. Control factors and levels

where a linear relationship exists between Y (= ideal output response) and M (= input signal). However, in reality, energy transformation of any sys- tems does not happen as designed or intended due to noise factors disturb- ing the system. The reality of the system function therefore consists of nonlinear eﬀects between the input/output demonstrated by Fig. 3b. The real function Yr can thus be described as

Y r ¼ f ðM; C1; C2; . . . ; Ck; N 1; N 2; . . . ; N pÞ ð2Þ ¼ bM þ ferrorðM; C1; C2; . . . ; Ck; N 1; N 2; . . . ; N pÞ;

where C1, C2,. . ., Ck are control factors and N1, N2,. . ., Np are noise fac- tors, and ferror is the error function between the ideal and the reality.

2.7. Design of tool electrode and signal arrangement

Eight major control factors have been identiﬁed for the study. They are open circuit voltage (A), pulsed duration (B), duty cycle (C), pulsed peak current (D), powder concentration (E), regular distance for electrode lift (F), time interval for electrode lift (G), and powder size (H), respectively. The details of their levels are listed in Table 1. Factors B, C, and D are arranged based on the principle of energy-beam material processing. It is worth noting that factor D varied to keep the output power constant for a systematic comparison of the experimental results.

2.4. Proposed ideal function of the EDM process

Orthogonal array is one of the important tools used in the experimen- tal design of Taguchi methods. An L18 (21 · 37) was chosen for the exper- factorial tests because it has a good even distribution of imental interactions over the control factors. Taguchi parameter design strategy separates the control factors from the noises by using inner and outer arrays, respectively. Control factors are assigned in the inner array, while noise factors coupled with signal factors are arranged in the outer array for exposing the process to varying noise conditions. The purpose is to reach a level where the control factor does not vary much despite the inev- itable presence of noise.

To develop a process with versatility, how to vary the signal experi- mentally is one of the most important steps in the Taguchi robust design. To achieve this objective, a special tool electrode with a range of geomet- rical characteristics is designed for use throughout the experiments. Fig. 4 illustrates the tool electrode designed by us. As shown in Fig. 4a, the tool electrode has two typical geometrical shapes to be machined, including rectangular and circle for which each has three kinds of dimensional sizes. Fig. 4b displays its 3D representation. The geometrical characteristics with six diﬀerent intended dimensions are arranged as the input signal given in Table 2. The basic functionality of the EDM machine is to create a precise shape as the output requested by customers after receiving the input sig- nal, i.e. the tool electrode. Therefore, from the standpoint of the ‘trans- formability’, the ideal function for this case is designed as electrode dimension (input signal) being proportional to product dimension (output

Table 1 Control factors and their levels Control factors Level-1 Level-2 Level-3

A Open circuit voltage (V) Pulsed duration (Ton: ls) B C Duty cycle (CD: %) D Pulsed peak current (Ip: A)

120 12 33 12 8 6 0.1 1 230 75 50 18 12 9 0.3 6 400 66 24 for C1 16 for C2 12 for C3 0.5 12 E F Powder concentration (Al: cm3/l) Regular distance for electrode lift (mm)

G Time interval for electrode lift (s) H Powder size (lm) 0.6 1 2.5 10–20 4.0 40 Fig. 3. (a) The system’s ideal function, and (b) the reality.

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1162

ing the relationship between system inputs and desired outputs. Fuzzy controllers and fuzzy reasoning have found particular applications in very complex industrial systems that cannot be modeled precisely even under var- ious assumptions and approximations. A fuzzy system is composed of a fuzziﬁer, an inference engine, a data base, a rule base, and defuzziﬁer. In the study, the fuzziﬁer ﬁrstly uses membership functions to convert the crisp inputs into fuzzy sets, and then the inference engine per- forms a fuzzy reasoning on fuzzy rules to generate fuzzy values, then the defuzziﬁer converts these values into the crisp outputs. The ﬂow structure chart of the fuzzy logic controller coupled with Taguchi methods used in the study is shown in Fig. 5.

Table 3 Signal and noise factors arrangement in the outer array Mi, i = 1–6 Noise factors T1 N1 T2 N1 N2 N2 N2 T3 N1

the Mamdani

Fuzzy values are determined by the membership func- tions that deﬁne the degree of membership of an object in a fuzzy set [25]. However, so far there has been no stan- dard method of choosing the proper shape of the member- ship functions for the fuzzy sets of the control variables. Trial and error methods are usually exercised. Based on the fuzzy rules, implication method is employed for the fuzzy inference reasoning in this study. For a rule

Fig. 4. (a) The top view, (b) and 3D representation of the tool electrode.

Ri : If x1 is Ai1; x2 is Ai2; . . . ; and xs is Ais; then yi is Ci;

ð4Þ

i ¼ 1; 2; . . . ; M;

2.8. Noise factors and strategy

where M is the total number of fuzzy rules, xj (j = 1, 2,. . ., s) are the input variables, yi are the output variables, and Aij and Ci are fuzzy sets modeled by membership functions lAijðxjÞ and lCiðyiÞ, respectively. Based on the Mamdani implication method of inference reasoning for a set of dis- junctive rules, the aggregated output for the M rules is

lCiðyiÞ ¼ maxfmin

½lAi1 ðx1Þ; lAi2 ðx2Þ; . . . ; lAisðxsÞ(cid:4)g;

i ¼ 1; 2; . . . ; M.

ð5Þ

Table 2 Input signals in the outer array Input signal M1 M2 M3 M4 M5 M6 6.000 8.458 12.000 16.971 20.000 25.456 Intended dimension (mm)

3. Fuzzy logic analysis and analysis of variance

The above equation is illustrated in Fig. 6. The graph rep- resents the fuzzy reasoning process for two rules, R1 and R2, with two input variables that use triangular-shape membership functions. Using a defuzziﬁcation method, fuzzy values can be combined into one single crisp output value. The center of gravity, one of the most popular methods for defuzzifying fuzzy output functions, is em- ployed in the study. The formula to ﬁnd the centroid of the combined outputs, ^yi, is given by:

3.1. Fuzzy logic methods

ð6Þ

^yi ¼

R yilCiðyiÞ dy R lCi ðyiÞ dy

Fuzzy logic is a mathematical theory of inexact reason- ing that allows modeling of the reasoning process of human in linguistic terms [24]. It is very suitable in deﬁn-

The yielded value is the ﬁnal crisp output value obtained from the input variables.

Noise factors cause variability and deterioration of performance from the ideal function and lead to variability in the quality characteristic. Gen- erally, there are a number of noise factors with the EDM process, such as machining time, electrode consumption, electrode shape and size, and aging working oil. It is clear that most of the above noise factors closely aﬀect the gap conditions. For the simpliﬁcation of experimentation, every experimental trial uses the totally new electrode with the same dimensions machined by CNC milling machine. Additionally, due to being hard con- trol, Taguchi methods suggest the use of the compounding strategy to arrange them to be two extreme conditions [23]. To simulate the extreme noise conditions, N1 (with both ﬁltration and circulation system) and N2 (without both ﬁltration and circulation system) are arranged under machining time. Their couple with signal factors assigned in the outer array of L18 is displayed in Table 3.

Rule base

Data base

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1163

Fuzzy knowledge base

Output

Fuzzification

Defuzzification

Fuzzy inference engine

Input

Fuzzy logic controller

MPCIs

Dimensional precision

(DA) and accuracy (DA)

Control

factors:

A, B,,,,,,,,H

Input signal:

Machining output:

Product dimension

High-speed EDM process

Intended dimension using tool electrode

Noise

Intent

factors: N1, N2

Voice of customer: Short delivery, high quality, low cost

Fig. 5. Flow structure chart of the fuzzy logic controller coupled with Taguchi methods used in the study.

If

and

then

Combined & Defuzzified

µA11(x)

µA12(x)

µC11(x)

min[µA11(x1), µA12(x2)]

R1

max[µC11(x1), µC12(x2)] µC(x)

0 0 0

x1* x1

x2*

µC22(x)

µA22(x)

µA21(x) 1

R2

0 0 0

x1* x1

x2* x2

min[µA21(x1), µA22(x2)]

Mamdani Fuzzy Logic Reasoning Process

Fig. 6. Mamdani implication methods with fuzzy controller operations.

3.2. Normalisation of quality characteristics

squares of error) to its degrees of freedom. Then, the F-ra- tio is simply the ratio of MSK to MSE. Therefore, the con- tribution proportion of factor k, in percentage, is:

(cid:4)

(cid:5)

k ¼

(cid:5) 100%.

ð11Þ

Contribution percentage of factor SSK (cid:2) ðDOF (cid:5) SSEÞ SST

4. Experimental results and discussion

4.1. Process performance evaluation and MPCIs

To avoid the inﬂuences of the units of quality character- istics used for dimensional precision and accuracy on the process optimisation, normalisation of them may be required in order to provide fair information for selecting the optimal setting of parameters. In this case, ‘the-larger- the-better’, and ‘the-nominal-the-best’ criteria are adopted to convert their values into a range between 0 and 1, while 0 means the worst performance and 1 the best. The former is used for the dimensional precision of the machined prod- uct that is normalised by the following formula:

x1ðkÞ (cid:2) min

x1ðkÞ

ð7Þ

^x1ðkÞ ¼

k x1ðkÞ þ 5(cid:4) (cid:2) min

x1ðkÞ

½max k

and the latter is used for the accuracy normalisation by the following formula:

jx2ðkÞ (cid:2) xdej

;

ð8Þ

^x2ðkÞ ¼ 1 (cid:2)

x2ðkÞ (cid:2) xde

max k

Table 4 shows the entire experimental results about the calculated product’s dimensional precision and accuracy through Taguchi dynamic S/N ratio. The dimensional pre- cision values of the machined products are found to be between 11.435 and 20.573 db. Note that Trials 8 and 16 have the lowest dimensional precision values under 12.0 db and the highest dimensional accuracy over 1.038. This is attributed to the fact that higher heat inputs result in larger materials removed. Additionally, all of the dimen- sional accuracy values are larger than 1 due to the inevita- ble overcutting eﬀects by the EDM process. The experimental results suggest that the closer the dimensional accuracy to the target value (= 1), the larger the dimen- sional precision, and vice versa.

where ^xiðkÞ denotes the value after normalisation for the k th test (i = 1 for dimensional precision, and i = 2 for dimensional accuracy), xde the desired value of the dimen- sional accuracy (i.e. slope = 1), xi(k) the original experi- mental response, and maxkxi(k) the largest among all the tests, respectively.

3.3. The analysis of variance (ANOVA)

The quality characteristics evaluation strategy for the high-speed EDM process that has been designed as mem- bership function using the fuzzy model is illustrated in Fig. 7. As shown in Fig. 5, the calculated values of the dimensional precision and accuracy are normalised as the two input variables of the fuzzy logic controller. The out- put variable is the MPCI whose membership function is illustrated in Fig. 8.

ANOVA is performed to identify the process parameters of high-speed EDM that signiﬁcantly aﬀect the MPCs. An ANOVA table consists of sums of squares, corresponding degrees of freedom, the F-ratios corresponding to the ratios of two mean squares, and the contribution propor- tions from each of the control factors. These contribution proportions can be used to assess the importance of each factor for the interested MPC. The total sum of squares, SST, in the ANOVA is:

n X

ð9Þ

ðMPCIi (cid:2) MPCIÞ2;

SST ¼

i¼1

where MPCIi is the interested MPCIs response of the ith trial, MPCI is the overall average of the interested MPCIs responses, and n is the number of trials. SSK, the sum of squares of the tested control factor k, where k = A, B,. . ., H, can be calculated as:

mk X

# ;

ð10Þ

SSK ¼ mk

ðMPCIKj (cid:2) MPCIÞ2

j¼1

As shown in Figs. 7 and 8, there are ﬁve fuzzy sets for variables of dimensional precision and accuracy: very small (VS), small (S), medium (M), large (L), and very large (VL), and nine for the MPCIS: tiny (T), very small (VS), small (S), small-medium (SM), medium (M), medium-large (ML), large (L), very large (VL), and huge (H). The fuzzy rules in a matrix form used for the fuzzy logic controller are shown in Table 5. The total possible number of fuzzy rules used for this experimental controller is 25. After the two input variables are fuzziﬁed into the appropriate linguistic values, applying the logic rules in Table 5 along with Mam- dani inference, the fuzzy linguistic values and their mem- bership values for the output MPCI can be obtained. Then, the defuzziﬁcation method by the center of gravity in Eq. (6) is used to calculate the crisp value as the ﬁnal MPCIs outputs.

where MPCIKj is the average response for the jth level of factor k, and mk is the number of repetitions of each level of factor k. The estimated variance of factor k, MSK, is the ratio of SSK to its degrees of freedom (DOF), and the esti- mated variance of random error is the so-called mean squared error, or MSE, which is the ratio of SSE (sum of

Graphical presentation of the fuzzy logic reasoning pro- cedure for Test 1 results of L18 orthogonal array using the Matlab software is shown in Fig. 9, in which rows represent the 25 rules, and columns are the two-inputs/one-output variables. The locations of triangles indicate the deter- mined fuzzy sets for each input/output value. The height

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1164

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1165

Table 4 Experimental results of Taguchi orthogonal arrays and their performance evaluation No. Control factors Process performance evaluation Fuzzy logic analysis Quality normalised characteristics for DP and DA A B C D E F G H Precision S/N (db) Accuracy slope: b Precision S/N Accuracy slope: b MPCIs

µ (x)

1.0203 1.0197 1.0134 1.0244 1.0216 1.0288 1.0327 1.0382 1.0178 1.0242 1.0175 1.0193 1.0327 1.0275 1.0212 1.0402 1.0258 1.0303 0.3821 0.4214 0.6463 0.2633 0.3300 0.2222 0.1014 0.0170 0.4585 0.2348 0.4950 0.4280 0.1065 0.2157 0.3321 0.0000 0.2186 0.1442 0.4950 0.5100 0.6667 0.3930 0.4627 0.2836 0.1866 0.0498 0.5572 0.3980 0.5647 0.5199 0.1866 0.3159 0.4726 0.0000 0.3582 0.2463 0.4364 0.4637 0.6458 0.3296 0.3948 0.2533 0.1724 0.0981 0.5076 0.3099 0.5336 0.4735 0.1745 0.2654 0.4012 0.0385 0.2843 0.1952 1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2 1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3 1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 16.837 17.393 20.573 15.157 16.101 14.577 12.868 11.676 17.917 14.755 18.433 17.486 12.940 14.485 16.130 11.435 14.525 13.473 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 VS S M L VL

0 0.5 1.0

µ(x)

of the darkened area in each triangle corresponds to the fuzzy membership value for that fuzzy set. For Test 1, the input normalised value of dimensional precision is 0.382 which belongs to the fuzzy sets S and M, and corre- sponds to fuzzy rules 6–14, and 25. As for the accuracy, its input normalised value is 0.495 which belongs to M and corresponds to rules 3, 7, 12, 17, and 22. Applying the fuzzy rules listed in Table 5 and the membership values for the fuzzy sets, it is clear in Fig. 9 that the output MPCIs belong to SM and M. The defuzziﬁed output that gives the ﬁnal MPCIs value is calculated as 0.436 from the combined darkened areas shown in the bottom of MPCIs column in Fig. 9. The entire results of the calculated MPCIs for each of the 18 tests are shown in Table 4. It is noted that the lar- ger the dimensional precision and accuracy are, the larger the resulting MPCIs would be. That means that the param-

1 T VS

SM M ML

Fig. 7. The membership functions for the dimensional precision and accuracy.

Fig. 8. The membership functions for MPCI.

Table 5 The fuzzy rules in a matrix form

High-speed EDM process: MPCI Normalised dimensional accuracy (DA) VS S M L VL

Normalised dimensional precision (DP) VS S SM T VS S SM M VS S M L VL M ML S SM M ML L SM M ML L VL M ML L VL H Fig. 9. Fuzzy logic reasoning procedure for the Test 1 results.

eter design with higher MPCIs leads to better dimensional precision and accuracy of machined products.

4.2. High-speed EDM process optimisation through MPCIs

D (pulsed peak current). They are regarded as the most important process factors due to their combination directly aﬀecting the thermal input rate. It is also noticed that fac- tors E (powder concentration) and H (powder size) have relatively weaker impacts on the process.

shown in Table 6,

the combination level of A1B1C3D1E3F3G1H3 for control factors is predicted to give the largest fuzzy logic MPCIs using the following formula:

r0 X

ð12Þ

^gMPCI ¼ (cid:2)gm þ

ðgMPCIi (cid:2) (cid:2)gmÞ;

i¼1

where ^gMPCI is the predicted MPCIs for the optimal factor- levels, (cid:2)gm is the overall average of the MPCIs, gMPCIi is the largest MPCIs for the ith factor, and r0 is the number of the control factors that signiﬁcantly aﬀect the MPCs.

To determine the optimal conditions, it is required to ﬁnd the greatest MPCIs value among all possible combina- tions of the process parameters. The averages of MPCIs for each level of the control factors are then calculated as sum- marised in Table 6. The italised number in each column of factors is the highest MPCI for each factor, which also indicates the best level for each factor. The ranges, indicat- ing the diﬀerences between maximums and minimums, of MPCIs are ranked while 1 represents the largest range. Control factors with large range of MPCIs values among their levels have more signiﬁcant inﬂuences in the high- speed EDM process. It is clear that factor B (pulsed dura- tion) has the strongest eﬀect on the dimensional quality of machined products, followed by factors C (duty cycle) and

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1166

Table 6 Response eﬀect of MPCIs Factor A B C D E F G H

The relative eﬀect among the control factors for the MPCs can be veriﬁed by using the ANOVA so that the optimal combinations of the control factors can be accu- rately determined. From Table 7, it is also evident that the control factors B–D have the most signiﬁcant eﬀects, which coincides with the results of Table 6. They altogether account for about 81.5% of total variations of MPCIs. Moreover, the variance due to the noise factors is only 0.305%, indicating that the selection and arrangement of the control factors is adequate and logical and the results are highly reliable.

4.3. Conﬁrmation run

0.367 0.297

Level 1 Level 2 Level 3 Max–min Rank 0.070 6 0.477 0.303 0.216 0.261 1 0.244 0.340 0.413 0.169 2 0.415 0.312 0.269 0.147 3 0.309 0.301 0.386 0.085 4 0.287 0.345 0.364 0.078 5 0.353 0.314 0.329 0.039 8 0.306 0.329 0.362 0.056 7

Table 8 shows the results of the conﬁrmation run of the predicted optimal conditions, A1B1C3D1E3F3G1H3, as well as the comparisons with the initial trial and the best trial of the L18. According to Table 4, Test 3 oﬀers the largest MPCIs value of 0.6458 among all the 18 trials. Therefore, it is selected to be the best trial with 20.573 db for the dimensional precision and 1.0134 for the accuracy. The normalised values for the dimensional precision and for the accuracy are 0.6463 and 0.6667, respectively, so they both reach a highest satisfactory level in L18.

Table 7 Analysis of variance (ANOVA) Factor Variance F-ratio Sum of squares Degree of freedom Contribution percentage (%)

A B C D E F G H Error 0.022 0.212 0.086 0.068 0.027 0.020 0.005 0.009 0.001 1 2 2 2 2 2 2 2 2 0.022 0.106 0.043 0.034 0.013 0.010 0.002 0.005 0.001 31.633 154.303 62.894 49.678 19.288 14.304 3.291 6.902 1.000 4.830 47.119 19.206 15.170 5.890 4.368 1.005 2.108 0.305

The fuzzy analysis procedure for the optimal conditions is graphically presented in Fig. 10, displaying the calculated MPCIs of 0.673. So the optimal parameter design produces the best quality characteristics among all the trials. Com- paring to the initial trial, the MPCIs of the optimal condi- tions are improved by 54.21%, whilst the dimensional

Total 0.450 17 0.026 100.000

Table 8 Comparisons of the predictions and the actual machining results Level combinations Initial trial Optimal trial Best trial of L18 orthogonal array Test 1 Test 3 Conﬁrmation run A1B1C1D1E1F1G1H1 A1B1C3D3E3F3G3H3 A1B1C3D1E3F3G1H3

16.837/0.3821 1.02034/0.4950 0.4364/0.4280 S/N (db)/ normalised Slope: b/normalised Fuzzy logic MPCIs/predicted Improvement in MPCIs/predicted (%) 20.573/0.6463 1.0134/ 0.6667 0.6458/0.6424 47.98/50.09 21.187/0.6898 1.0123/0.6940 0.6730/0.7081 54.21/65.44

model that uses the observed MPCIs to predict MPCIs ensures reasonable predictions.

5. Conclusions

precision and accuracy are improved by 25.8% and 0.8%, respectively. It can be clearly seen that MPCIs are signiﬁ- cantly improved through Fuzzy logic operation, and in the mean time, both the dimensional precision and accu- racy of high-speed EDM process achieve the more desir- able values. Hence, the experimental results conﬁrm that the optimal the high-speed EDM process is achieved and the integrated MPCIs improve signiﬁcantly.

This paper illustrates that the application of a fuzzy logic analysis coupled with Taguchi dynamic experiment is sim- ple, eﬀective, and eﬃcient in developing a robust, versatile, and high speed EDM process. Optimisation of MPCIs in the process has been achieved through the proper system model simulation that it can meet more requirements requested by the customers. Based on the experimental results, the following conclusions can be drawn:

Fig. 11 shows the scatter plot using simple linear regres- sions for the observed MPCIs and the predicted values. It indicates that the optimal design obtained from the fuzzy logic analysis has the largest observed and predicted MPCIs. The R2 = 0.9959 of the simple linear regression

for about 81.5% of

I. The most important factors aﬀecting the precision and accuracy of the high-speed EDM process have been identiﬁed as factor B (pulse time), factor C (duty cycle), and factor D (peak value of discharge current), which account the process variance.

II. Due to having relatively weaker impacts on the high- speed EDM process by factors E (powder concentra- tion) and H (powder size), powder addition into the working ﬂuid in this case has a slight improvement in the targeted quality characteristics.

III. The following factor-level settings have been identi-

ﬁed to yield the best combination: factor A – level 1, factor B – level 1, factor C – level 3, factor D – level 1, factor E – level 3, factor F – level 3, factor G – level 1, factor H – level 3.

IV. Actual gain 0.6730 in MPCIs is very close to the pre- dicted 0.7081. It shows very good reproducibility and conﬁrms the success of the experiment.

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1167

V. Comparing to the initial trial, the MPCIs of the opti- mal parameter design are increased by 54.21%. The dimensional precision and accuracy are improved by 25.8% and 0.8%, respectively.

optimal conditions

0.9

References

0.8

R2 = 0.9959

0.7

Fig. 10. Fuzzy logic reasoning procedure for the results by the optimal conditions.

0.6

0.5

[1] Fallbohmer P, Altan T, Tonshoﬀ HK, Nakagawa T. Survey of die and mold manufacturing industry. J Mater Process Technol 1996;59:158–68.

0.4

C P M d e t c d e r

0.3

[2] Furutani K, Saneto A, Takezawa H, Mohri N, Miyake H. Accretion of titanium carbide by electrical discharge machining with powder suspended in working ﬂuid. Precis Eng 2001;25: 138–44.

0.2

0.1

[3] Wong YS, Lim LC, Rahuman I, Tee WM. Near-mirror-ﬁnish phenomenon in EDM using powder-mixed dielectric. J Mater Process Technol 1998;79:30–40.

0.1

0.2

0.3

0.4

0.6 0.7

0.8 0.9

[4] Tzeng YF, Lee CY. Eﬀects of powder characteristics on electrodis- charge machining eﬃciency. Int J Adv Manuf Technol 2001;17: 586–92.

0.5 Observed MPCIs

[5] Zhao WS, Meng QG, Wang ZL. The application of research on powder mixed EDM in rough machining. J Mater Process Technol 2002;129:30–3.

[6] Rebelo JC, Morao Dias A, Kremer D, Lebrun JL. The application of research on powder mixed EDM in rough machining. J Mater Process Technol 1998;84:90–6. Fig. 11. The scatter plot for the observed MPCIs and their predicted values.

Y.-f. Tzeng, F.-c. Chen / Materials and Design 28 (2007) 1159–1168 1168

[16] Elsayed EA, Chen A. Optimal

levels of process parameters for products with multiple characteristics. Int J Prod Res 1993;31: 1117–32. [7] Zhang QH, Zhang JH, Deng JX, Qin Y, Niu ZW. Ultrasonic vibration electrical discharge machining in gas. J Mater Process Technol 2002;129:135–8. [8] Zhixin J, Xing A, Jianhua Z. Study on mechanical pulse electric discharge machining. Precis Eng 1995;17(2):89–93. [17] Antony J. Simultaneously optimisation of multiple quality charac- teristics in manufacturing process using Taguchi’s quality loss function. Int J Adv Manuf Technol 2001;17:134–8.

[9] Hocheng H, Lei WT, Hsu HS. Preliminary study of material removal in electrical discharge machining of SiC/Al. J Mater Process Technol 1997;63:813–8. [18] Lin TR. Optimisation technique for face milling stainless steel with multiple performance characteristics. Int J Adv Manuf Technol 2002;9:330–5. [10] Ross PJ. Taguchi techniques for quality engineering. USA: McGraw- Hill; 1996.

[19] Juang SC, Tarng YS. Process parameter selection for optimizing the weld pool geometry in the tungsten inert gas welding of stainless steel. J Mater Process Technol 2002;l22:33–7. [11] Yu JP, Chang CC. Characteristic analysis of the EDMed surface of tungsten carbide using Taguchi method. In: International conference on precision engineering, Taipei; 1997. p. 657–63.

[20] Tong LI, Su CT, Wang CH. The optimisation of multi-response problems in Taguchi method. Int J Qual Reliability Manage 1997;14:367–80. [21] Yan H, Chen SL. Eﬀects of dielectric with suspended aluminum [12] Marafona J, Wykes C. A new method of optimizing material removal rate using EDM with copper-tungsten electrodes. Int J Machine Tools Manuf 2000;40:153–64. powder on EDM’’. J Chin Soc Mech Eng 1999;14(3):307–12.

[13] Vijaya M, Krishna R, Prabhakar O, Shankar NG. Simultaneous optimisation of ﬂame spraying process parameters for high quality molybdenum coatings using Taguchi methods. Surf Coat Technol 1996;79:276–88. [22] Tzeng YF, Lee CY. Eﬀects of powder additions on the electro- discharge machining process. In: Proceeding of the 16th national conference of chinese society of mechanical engineers, Taiwan, ROC; 1999. p. 195–202.

[23] Wu A. Taguchi methods. Michigan: ASI press; 1998. [24] Ross TJ. Fuzzy logic with engineering applications. McGraw-Hill [14] Alsaran, Celik A, Celik C. Determination of the optimum conditions for ion nitriding of AISI 5140 steel. Surf Coat Technol 2002;160: 219–26. Inc.; 1995. [25] Cherkassky V, Mulier F. Learning from data: concepts, theory, and methods. USA: Wiley; 1998. [15] Yang LJ. Plasma surface hardening of ASSAB 760 steel specimens with Taguchi optimisation of the processing parameters. J Mater Process Technol 2001;113:521–6.