A Fuzzy Logic Approach for Optimization of Hardness in Induction Hardening Process AMIT KOHLI a, HARI SINGH b a Department of Mechanical Engineering, D.A.V Institute of Engineering & Technology, Jalandhar 144008, India b Department of Mechanical Engineering, National Institute of Technology, Kurukshetra 136119, India Abstract The study finds the effect of different input parameters that are feed rate, dwell time, current and gap between the induction coil & work-piece on the output parameters that are Hardness at rolled {H(R)}, Normalized {H(N)} and Hardened Tempered {H(T)} conditions of the material (AISI 1040 steel). The degree of membership function of an object in a fuzzy set is defined by membership functions (MF). It has been found that after the formulation of rules, the optimum value of hardness at any points (may be in decimal place) in between the low and high limits of the process parameters selected, can be found out. The predicted results are compared with a reliable set of experimental data for the validation of fuzzy model and mathematical model (developed by response surface methodology). It was found that proposed fuzzy model gives the better results than mathematical results and it was well in agreement with experimental results. By Intelligent, model based design and control of induction hardening process parameters in this study will surely help to enables dramatically decreased product and process development cycle times, improved product quality, decreased product cost and maintains the competitive position of steel in applications requiring high strength to-weight ratio at an affordable cost. Keywords: Medium Carbon Steel (EN8D), Induction Hardening, Fuzzy Logic 1.Introduction Surface hardening is the most important mechanical property for the metals which are worked under friction and treatment condition. Most important characteristic for the material hardening is hardness value [1]. By increasing the surface hardness value through induction hardening, wear resistivity, fatigue life, impact strength, compression strength and resistant of twist force are increased [2]. According to Stickels and Malender [3, 4] induction hardening is one most widely employed to improve component durability. Timothy et. al. [5] took four different input variables feed rate, gap between coil and workpiece, quench distance and part temperature with hardness as output variable and applied design of experiment and neural network approach in case of the induction hardening process. According to Timothy for complex processes with interactions among variables, traditional SPC methods are insufficient. Fuzzy logic is one of the artificial intelligence techniques that have ability to tackle the problem of complex relationships among variables that cannot be accomplished by more traditional methods. This method was discovered by Zadeh in 1965 [6]. It is a mathematical theory of inexact reasoning that allows modeling in linguistic terms of the reasoning process of human [7]. It is widely used for engineering, medical, economical problems and particular applications in very complex industrial systems [8].Fuzzy controllers and fuzzy reasoning are suitable in defining the relationship between system inputs and desired outputs. The Mamdani implication method is employed for fuzzy inference reasoning in this paper. The degree of membership function of an object in a fuzzy set is defined by membership functions which help in determining fuzzy [9]. 2. Induction Hardening Process Parameters In order to identify the process parameters affecting the output parameter of induction hardened part, an Ishikawa cause and effect diagram was constructed as shown in Figure 1. Kanyan [11] took distance between coil and material, cooling time, applied power and frequency as effecting parameters. Here experimental results and fuzzy results were compared. Y.Tolik.et.al[12] took heating time ( feed rate) and temperature as process parameters and concluded that depending upon the process parameters selected the induction hardening treatment helps in improvement of wear characteristics. Material selected by him was AISI 4140 steel. By using the methodology developed in his research, a significant improvement in the process was achieved. The selection of process parameters of interest was based upon the studies of Timothy et al. [5],Kanyan [11] and Tolik.et al[12]. The following parameters were thus selected for the present work that is dwell time, feed rate, gap between coil & work-piece and current at three different conditions of the material that is rolled, normalized and hardened tempered.
Figure 1: Ishikawa Cause and Effect Diagram of Induction Hardened Part 3. Experimental Details For performing the experiments, the medium frequency induction hardening machine (10 KHz), Power 120 kw, spindle speed 400 r.p.m, make Unitherm is used. Maximum job holding length of the machine is 609.6 mm (distance between two spindles). A source of high frequency electricity is used to drive a large alternating current through a copper coil. The passage of current through this coil generates a very intense and rapidly changing magnetic field in the space within the work coil. The core of the component remains unaffected by this treatment [13]. The material used for induction hardening is AISI 1040 steel bars. Its composition is 0.45%C, 0.65%Mn, 0.21%Si, 0.03%S and 0.025%P. This material is suitable for a wide variety of automotive components like axle and spline shafts [14]. In this investigation four factors are being studied and their low and high levels are shown in the Table 1. The conditions were selected after performing the pilot runs and literature survey. The response variable investigated is hardness at three different conditions of the material as mentioned earlier. The hardness was measured by Rockwell hardness testing machine for C scale at 150 Kg load, having diamond indentor at 120 degree. Table 1: Factors and Levels for Response Surface Study Factors Low level(-1) High level(+1) Feed rate (mm/s) 2 4 Dwell time (sec) 5 7 Current (Ampere) 125 135 Gap between work-piece and inductor coil (mm) 5 7 4. Fuzzy Logic Model For Induction Hardening Process (Hardness as Response) The modeling of induction hardening system has been done using fuzzy inference system (FIS). In this study, three angular membership functions are selected for fuzzy model as shown in the Figure 2. Feed Rate(mm/s) Dwell Time(sec) Hardness (HRC) Current (A) Gap (mm) Figure 2: Fuzzy Logic Model of Induction Hardening (Response: Hardness)
4.1 Membership Function for the Input and Output Parameters (Hardness as Response) This step is to define linguistic assigned to the variables and that was done via fuzzy subsets and their associated membership functions. A membership function assigns numbers between zero and one, called the grades of membership, to the range of the possible of the variable. Zero membership value indicates that it is not a member of the fuzzy-set; one represents a complete member. A membership function can have any shape but preferably symmetric. The standard shapes of membership functions include trapezoidal, triangular and bell shaped. Six membership functions were generated for each input variable (feed rate, dwell time, current, and gap between the induction coil and work-piece) as shown in Figure 3 (a, b, c and d). Input variable Feed Rate (a) Input variable Dwell Time (b) (c) (d) Figure 3: Membership Function Plots for Hardness (a) Current (b) Dwell Time (c) Feed Rate (d) Gap between the Work-Piece and Induction Coil Membership function for hardness as output variable at three different conditions (as-rolled, normalized, and hardened tempered) of the material are given in Figure 4 (a, b and c). (a) (b)
(c) Figure 4: Membership Functions for Hardness at (a) Rolled (b) Normalized (c) Hardened tempered condition of the material The location of triangles indicates the determined fuzzy sets for each input /output. 4.2 FIS Rules Employed in Model (Hardness as Response) For obtaining optimized solution, the rules at the rule base have been defined correctly and thirty rules have been written based upon the experimental results. While preparing the rules, fuzzy method was used. Some selected rules are reported in Figure 5, using MATLAB 7.0.4 environment using Mamdani-type of fuzzy inference system in fuzzy logic toolbox. The Figure 5 shows the formulation of rules based upon experiment results of RSM for hardness at three different conditions of the material. Similarly, the formulation of rules was done for other responses. Figure 5: Formulation of Rules (Response: Hardness) Control surfaces as shown in Figure 6 give the interdependency of input and output parameters guided by the various rules in the given universe of discourse. Control surface given in Figure 6 (a, b and c) shows dependency of hardness at three different conditions (as-rolled, normalized and hardened tempered) on dwell time and feed rate. (a) (b)
(c) Figure 6: Control Surfaces of Fuzzy Model Showing Inter Dependency of Hardness on Dwell Time and Feed Rate a) As-Rolled b) Normalized c) Hardened Tempered Condition The set of rules along with membership function is shown in rule viewer of fuzzy model (Figure 7). Figure 7.7 reveals that after the formulation of rules, the optimum value of hardness at any setting between the low and high limits of the process parameters can be predicted. Figure 7: Rule Viewer of Fuzzy Model (Response: Hardness) The Figure 7 clearly shows that at feed rate 3.09 mm/s, dwell time 5.83 sec, current 128 ampere and gap between the work-piece and induction coil 5.79 mm the predicted optimum of hardness at rolled, normalized and hardened tempered conditions are HRC 52.1, 54.1 and HRC 56 respectively. Similarly for different sets of data points in the identified universe of discourse of undertaken parameters various other of hardness in induction hardening process can also be predicted from the fuzzy model. Results predicted from this fuzzy model and mathematical models have been compared with the experimental results for its validation in the following sections given below. H (R) = [-88.27+23.57 x Feed rate+9.43x Dwell time+0.77 x Current+6.8xGap-0.31 x Feed rate x Dwell time-0.09 x Feed rate x Current-0.31 x Feed ratexgap-0.06 x Dwell time x Current-1.3 x (Feed rate) 2-0.55 x (Gap) 2 ] H (N) = [-112.76+25.79x Feed rate+12.68xdwell time+1.01x Current +6.13xGap-0.31xFeed rate x Dwell time-0.11xfeed ratexcurrent-0.09 x Dwell timexcurrent-1.44x (Feed rate) 2-0.57 x (Gap) 2 ] H (HT) = [-91.44+30.69xFeed rate+14.71xdwell time+0.88xcurrent-2.19 x Gap -0.37 x Feed rate x Dwell time-0.15xfeed ratexcurrent-0.1xdwell timexcurrent+0.05xcurrentxgap-1.42x (Feed rate) 2-0.42x (Gap) 2 ]
5. Results and discussion Table 2 gives the comparison of the predicted responses using developed fuzzy model and reported experimental data. Table 2: Comparison of fuzzy model and experimental data for various responses Feed rate 3.23 3.22 2.7 2.52 3.39 3.57 3.83 2.9 2.17 2.4 2.6 2.6 Dwell time 6 5.96 5.7 5.52 5.96 5.96 6.13 6.48 6.57 6.3 6.65 6.65 Current 130 133 131 129 132 134 135 129 134 128 132 126 Gap 6 5.96 5.43 5.7 5.61 5.87 6.74 5.43 5.7 6.3 6.91 6.91 H (R) fuzzy 55.8 57 54.3 52 57.8 57.1 57 56.8 54.8 52 54.3 54.1 Experimental 55.4 56.4 54.2 53.5 56.63 56.23 55.54 55.67 54 52.3 54 53.4 % variation 0.72 1.06 0.18 2.8 2.06 1.54 2.62 2.02 1.48 0.57 0.55 1.31 H(N) fuzzy 56.7 58 55.4 54 57.9 58 58 57.6 55.7 53.9 54.3 54.2 Experimental 56 57.6 55 53.8 57.3 58 58.4 57.7 55 53.2 53.9 53.9 % variation 1.25 0.69 0.72 0.37 1.04 0 0.68 0.17 1.27 1.31 0.74 0.55 H(HT) fuzzy 57.6 59.2 56.7 56 59 59.2 58.2 58.7 56.4 55.9 56.1 56.1 Experimental 57 58.8 55.9 56 58.8 59 57.94 58.7 55.8 55.6 55.9 56 Table 3 gives the comparison of the predicted responses using developed mathematical model and reported experimental data. Table 3: Comparison of mathematical model and experimental data for various responses Feed rate 3.23 3.22 2.7 2.52 3.39 3.57 3.83 2.9 2.17 2.4 2.6 2.6 Dwell time 6 5.96 5.7 5.52 5.96 5.96 6.13 6.48 6.57 6.3 6.65 6.65 Current 130 133 131 129 132 134 135 129 134 128 132 126 Gap 6 5.96 5.43 5.7 5.61 5.87 6.74 5.43 5.7 6.3 6.91 6.91 55.37 55.74 55.26 54.3 55.7 55.58 54.07 55.7 55.53 54 54.8 53.9 9 H(R) mathematical Experimental % variation 0.05 1.17 1.9 1.49 1.64 1.15 2.65 0.05 2.83 3.2 1.4 1.1 55.4 56.4 54.2 53.5 56.63 56.2 55.5 55.6 54 52 54 53.4 H(N) 56.7 57.1 56 55 57.1 57.1 55.7 56.6 55.8 54 55 54.4 mathematical Experimental 56 57.6 55 53.8 57.3 58 58.4 57.7 55 53.2 53.9 53.9 % variation 1.35 0.79 1.81 2.23 0.35 1.51 4.5 1.83 1.45 1.5 2.04 0.92 H(HT) 58.1 58.4 58 57 58.4 58.4 57 58.5 58 56 57 56.4 mathematical Experimental 57 58.8 55.9 56 58.8 59 57.9 58.7 55.8 55.6 55.9 56 % variation 1.92 0.64 3.75 1.78 0.68 0.98 1.62 0.29 3.94 0.7 1.96 0.71 Table 4 gives the average percentage error of various responses from fuzzy and mathematical models. In the present study the total data points involved was 12.
Table 4: Average percentage error of various responses from fuzzy and mathematical model Process Parameters Fuzzy calculated (% variations) Mathematical model (% variations) Hardness(rolled) H(R) 1.41 1.56 Hardness(rolled) H(N) 0.73 1.69 Hardness (hardened tempered) H(HT) 0.53 1.58 Out of various outputs generated by fuzzy models, the total average error is 1.43 % and from mathematical model it is 1.69 % respectively. Thus the system gave overall 98.57% accuracy from fuzzy model and 98.31% from mathematical model. Thus it can be conducted that there is a close relation between the experimental and simulated results for various responses of induction hardening process from fuzzy model in comparison with mathematical model. Conclusion 1. This paper has set out to apply the fuzzy logic to predict hardness as response at different condition of the material (rolled, normalized and hardened tempered conditions) in induction hardening process. It has been found that results generated by fuzzy model and mathematical model (by response surface methodology) are close to the experimental results with98.57 % and 98.31% accuracy respectively. 2. Fuzzy logic system was found to be more flexible and easy to comprehend than mathematical model and hence can act as an alternative to the conventional modeling techniques. Present study supports that fuzzy logic technique can be introduced as a viable alternative to carry out analysis without conducting actual experiments. Fuzzy logic allowed the modeling and on-line control problem to be treated simultaneously. References [1] Bodart, O, Bourean, AV and Touzani, R. (2001). Numerical Investigation of Optimal Control of Induction Heating Process, Applied Mathematical Model; vol 25: pp 697-712. [2] Kayacan, MC (1991). Design and construction of a set up for induction hardening. M.Sc thesis, University of Gaziante. [3] Stickels, CA (1984). Steel and its Heat Treatment; Second Edition; 3. [4] Melander, M. (1984). Theoretical and experimental study of stationary and progressive induction hardening, Journal of Heat Treating,; 2: 145-65. [5] Timothy James Stich, Julie K Spoerre and Tomas Velasco (2000). The Application of Artificial Neural Networks to Monitoring and Control of an Induction Hardening Process Journal of Industrial Technology, vol16: pp. 1-11. [6] Zadeh, LA. (1978). Fuzzy Sets as a Basis for a Theory of Possibility, Elsevier, 3-10. [7] Ross, TJ. (1995). Fuzzy Logic with Engineering Application: McGraw Hill Inc. [8] Zadeh, LA. (1978). Fuzzy Sets as a Basis for a Theory of Possibility, Elsevier, 3-10. [9] Cherkassky and Mulier, F. (1998). Learning from data: Concepts, Theory, and Methods; Wiley, USA. [10] Hankins, Judy (2001). Infusion Therapy in Clinical Practice: 42. [11] Kayan, MC. (2004)). A Fuzzy Approach for Induction Hardening Parameter Selection, Journal of Materials and Design, 25: 155-161. [12] Totik, Y, Sadeler, R, Altun, H and Gavgali, M. (2003). The effects of Induction Hardening on Wear Properties of AISI 4140 Steel in dry sliding conditions, Journal of Materials & Design, 24: 25-30. [13] Jacobs, JA and Kilduff, TF. (1994). Engineering Materials Technology: Structure, Processing, Properties and Selection, Prentice Hall Career And Technology. 2 nd ed. New Jersey. [14] Oberg, E, Green, RE. (1996). Machinery s Handbook.25 th ed, Industrial Press, New York.