Taguchi fuzzy
- 1. TAGUCHI-FUZZY BASED MAPPING OF EDM-MACHINABILITY OF ALUMINIUM FOAM SHANKHA SHUBHRA GOSWAMI ROLL:- 17101203011 M.TECH (ME) QUALITY ASSESSMENT AND CONTROL
- 2. INTRODUCTION • Investigations are on for finding suitable methods of metal foam machining, one of which is by the use of EDM. Authors have also investigated the machining possibility of the developed closed cell aluminium foam using Wire-EDM. It is found that during machining aluminium foam in Wire-EDM, frequent wire breakages and interruptions in machining took place. This may be due to the presence of uneven pores or larger pores inside the matrix. It is therefore decided to carry out experimental investigations of machining of aluminium foam using EDM. Thus of all the other methods, EDM may prove to be an excellent and versatile means for machining of metallic foams. • In this paper, an attempt has been made to identify the possibility of utilising EDM to machine such materials. The Taguchi-fuzzy based mapping has been performed for identifying the effects of different process parameters of EDM on the productivity i.e. maximum MRR and m
- 3. Test material • The material under investigation is the closed cell aluminium foam, produced through liquid metallurgy route in the laboratory. Aluminium alloy used for the production of foam is 24345 IS 733 (4 % Cu; 0,5 % Mg; 1 % Si; 0,6 % Mn; 0,7 % Fe; 0,2 % Zn and Ti and rest Al). Tab. 1 summarises the comparison of mechanical properties of aluminium foam produced and those of the aluminium alloy used for foam production. • • Table 1 Mechanical properties of aluminium foam and aluminium alloy • • • Properties Aluminium foam Aluminium alloy • (density, 0,4 g/cm3) (density, 2,7 g/cm3) E * / Gpa 1,5 69 pl* / Mpa 2,5 120
- 4. Parameter’s Input Parameters Value symbols Min (1) Max (2) a Duty Cycle, ζ / % 1 32 b Pulse on time, TON / μs 0,25 3000 c Gap Voltage, S v / V 1 100 d Pulse Current, I p / A 1 50 Table 2 Values of parameters
- 5. All the experiments are carried out in CNC controlled EMT 43 Elektra with liquid paraffin as dielectric. The tool used for the experiments is of 10 × 5 cm size, made from thin strip of electrolytic copper sheet (99,96 % pure). The work piece is mounted on the EDM and the depth of cut 14 mm is provided for each experiment. The response variables selected in this study are Material Removal Rate (MRR) and Tool Wear Rate (TWR). The MRR and TWR are the machining efficiency of the process and the wear of copper electrode respectively, and are defined as follows: The work piece and electrode are weighed before and after each experiment using an electric balance with a resolution of 0,01 mg to determine the value of MRR and TWR. For each set of values, three experiments are performed in randomised sequence in order to eliminate the influence of systematic errors, as recommended by Taguchi. The S/N ratios are calculated based on "Higher the better" for MRR, and "Smaller the better" for TWR. The results are summarised in Tab. 3
- 6. Table. 3 Taguchi's L8 Orthogonal array for design of experiments and the experimental results S. No a b ab c ac bc d MRR (S/N) TWR (S/N) 1 1 1 1 1 1 1 1 55,81 164,74 2 1 1 1 2 2 2 2 69,12 142,99 3 1 2 2 1 1 2 2 110,97 101,47 4 1 2 2 2 2 1 1 81,52 151,61 5 2 1 2 1 2 1 2 85,45 137,91 6 2 1 2 2 1 2 1 65,59 158,99 7 2 2 1 1 2 2 1 10 140,51 8 2 2 1 2 1 1 2 53,99 129,53
- 9. Parametric mapping using fuzzy logic Fuzzy logic has great capability to capture human commonsense reasoning, decision-making and other aspects of human cognition, Kosko (1997). According to Klir and Yuan (1998), fuzzy logic involves a fuzzy inference engine and a fuzzification-defuzzification module. A fuzzy- rule based inference engine comprises three basic units: fuzzifier, inference engine and defuzzifier (Fig. 2). The prime function of the system is to establish mapping from inputs to outputs: from cause to effect. However, this mapping mechanism is not built on any precisely defined analytical equation, instead, it is constructed on human knowledge, experience and intuitions often represented in natural languages in the form of if-then rules.
- 10. The input variables (MRR and TWR) are represented by membership functions having three levels, namely low, medium and high as shown in Figs. 3 and 4. The output variable (Productivity) is represented by membership functions having five levels namely low, low-medium, medium, medium-high and high (Fig. 5).
- 11. The assigned fuzzy rules base consists of if-then control rules with two inputs and one output. The rules used are – If MRR is Low and TWR is Low then Productivity is Medium – If MRR is Low and TWR is Medium then Productivity is Low Medium – If MRR is Low and TWR is High then Productivity is Low – If MRR is Medium and TWR is Low then Productivity is Medium High – If MRR is Medium and TWR is Medium then Productivity is Medium
- 12. Variable Membership Levels Range Type of Membership function curve function no. 1 Low < 58 Asymmetrical polynomial curve open to the left Input variable MRR 2 Medium 25 - 100 Trapezoidal Curve (Range: 10-115) 3 High >68 Asymmetrical polynomial curve open to the right 1 Low < 125 Asymmetrical polynomial curve open to the left Input variable TWR 2 Medium 132-138 Trapezoidal Curve (Range: 100-175) 3 High >170 Asymmetrical polynomial curve open to the right 1 Low <0,2 Asymmetrical polynomial curve open to the left Output variable 2 Low Medium 0,1-0,4 Trapezoidal Curve Productivity 3 Medium 0,35-0,65 Trapezoidal Curve (Range: 0-1) 4 Medium High 0,6-0,9 Trapezoidal Curve 5 High >0,8 Asymmetrical polynomial curve open to the right Table 6 Membership function properties
- 13. – If MRR is Medium and TWR is High then Productivity is Low Medium – If MRR is High and TWR is Low then Productivity is High – If MRR is High and TWR is Medium then Productivity is Medium High – If MRR is High and TWR is High then Productivity is Medium. Figure 6 Surface plot of MRR, TWR and productivity
- 14. Conclusion • Taguchi-fuzzy based mapping of aluminium foam machining reveals some useful facts. From ANOVA analysis of MRR it is found that if interaction between duty cycle - pulse is on time, pulse current and duty cycle are the significant process parameters at 95 % confidence limit. However, for TWR, pulse current is the significant parameter at 95 % confidence limit. In order to maximize the productivity not only the MRR should be high but also the TWR should be low. This is because the low TWR will not only reduce the cost of production of a tool but also minimise the tool changing time. • Therefore, in order to achieve the higher productivity, fuzzy logic is used to optimise the two output parameters MRR and TWR. Productivity is the highest when MRR ranges between 95 and 110 and TWR ranges between 100 and 115. From the Taguchi-fuzzy based mapping it is observed that the parameters pulse current, duty cycle, pulse on time, and interaction between duty cycle - pulse on time are the most significant parameters for achieving the maximum productivity.