Steels are alloys of iron and carbon containing up to 1.5% of carbon. There are many forms of steel each of which is designed to serve a particular application in the field of engineering. An active research area is the surface engineering of components to improve the life and performance of parts used in automobiles and aerospace [1] .

Mild steel, by reasons of its dominance and workability among the classes of steel [2] , has found a broad relevance in the production of engineering components like cams, gears, shafts, pinions, keys, hand tools, agricultural equipment, etc. These components require the mechanical properties of impact strength, hardness and tensile strength for their safe and durable purposes.

The addition of carbon to the surface of low-carbon steels at temperatures within the austenitic region of the steel concern is called carburizing, which usually is between 850˚C and 950˚C for mild steels. Within this austenite temperature range, there is high solubility for carbon which is the stable crystal structure. When the subsequent high-carbon surface layer is quenched to form martensite hardening is accomplished, so that a high-carbon martensitic case with good fatigue and wear resistance is superimposed on a tough, low carbon steel core [3] -[5] .

The inward diffusion of carbon takes place at a rate which depends on the chemical composition of the steel, the carburizing temperature and the chemical composition of the carburizing mixture [6] [8] [10] [12] . For a successful carburization, a control of all these parameters; the carburizing temperature, carburizing time, and chemical composition of the carburizing compound must be achieved [7] [9] [11] . The study of process parameters in metals during heat treatment has been of considerable interest for some years [7] -[9] [13] ; but there has been relatively little work on optimization of process variables during the surface hardening process [14] since controlling parameters in carburization is a complex problem. Thus, the optimization of particle sizes, volume fractions of energizer, carburizing temperature and soaking time becomes imperative.

Response Surface Model (RSM) is a statistical tool and powerful mathematical method with a collection of statistical techniques by which interaction between multiple process variables can be identified with fewer experimental trials. It is widely used to examine and optimize the operational variables for experimental design, model development, test variables and condition optimization. While two major tools used in Taguchi method are the orthogonal array (OA) and the signal to noise ratio (SNR or S/N ratio). OA is a matrix of numbers arranged in rows and columns. Taguchi’s methods in general provide a significant reduction in the size of experiments, thereby speeding up the experimental process [15] . Efficiency of this method depends on the selection of suitable orthogonal array. The S/N ratio is expressed in decibels (dB). Theoretically, the S/N ratio is the ratio of signal to noise in terms of power.

Noorul and Jeyapaul [16] adopted orthogonal array, Grey relational analysis in the ANOVA using Taguchi method to find suitable level of indentified parameters, and significant association of parameters in order to increase response efficiency of the parameters. [15] -[19] proposed the efficient use of Taguchi’s parameter design to obtain optimum condition because it leads to minimum number of experimental and lower cost. Palanikumar et al. [20] adopted Response Surface Methodology in analyzing the variance for verification model in order to increase efficiency of cutting parameters for surface roughness. Statistical methodologies give rapid and reliable short-listing of process conditions, understanding interaction among them, and a tremendous reduction in total number of experiments, resulting in saving time, materials, chemicals and manpower. In spite of various advantages, statistical designs have been applied only to limited number of manufacturing processes.

This research work mainly focuses on the carburizing process parameters optimization of Graphite/Seashell media using UNS-G10170 steel specimen by Taguchi’s L₉ orthogonal array concept and Response Surface Model (RSM), and thereby determining the optimum values which will maximize the hardness value.

The Taguchi optimization method consists of the following steps: Each S/N ratio can be obtained from observations according to the formula of higher the better. For each significant factor, the level corresponding to the highest S/N ratio is chosen as its optimum level. A search for the factors that have a significant effect on the S/N ration is then performed through analysis of variance (ANOVA) of the S/N ratios [22] [23] .

Table 4 shows the average value of the hardness for each experimental point, as well as S/N ratios calculated by Equation (1). Average effect of each factor on the multiple quality characteristic at different levels was calculated. This is equal to the sum of all S/N ratios corresponding to a factor at a particular level divided by the number of repetitions of the factor level [23] . For example, the average S/N ratio of factor C at level 3 is calculated as being

Response graphs shown in Figures 1(a)-(e) are drawn using the values in Table 5 through Design Expert 6.0.6 statistical software (α = 0.05) and Minitab 16 statistical software. The factor levels corresponding to the maximum average effect are selected as the optimum level. The average factor effect is shown in Table 5, and the main effect plotted for SNR is shown in Figure 1(a). The delta values from Table 5 were calculated by subtracting the largest value from the lowest among the values in each column. Optimum condition for surface hardness is found by adopting the higher the S/N ratio is better as strategy. The largest S/N ratio for each factor would be preferred. Hence, the optimum (Maximum Hardness) setting of the parameters is A₂B₃C₁. Corresponding parameter values are listed in Table 6.

Main effects plots of factors can be used to depict a prelude conclusion about effects of processing parameters. These plots are shown in Figures 1(a)-(e). The furnace temperature peaked at 910˚C at soaking time of 9 hrs with energizer (seashell) particle size of 45 micron at hardness and S/N ratio values of 92 HRB and 39.28 dB for both plots in Figure 1(a) & Figure 1(b).

Figures 1(c)-(e) showed the interactions between processing parameters. Out of the three furnace temperatures (870˚C, 910˚C, 940˚C), 910˚C performed better at different particle sizes and gave increased hardness values at increasing soaking time as shown in Figure 1(c). Temperature 910˚C increased with an increased soaking

time while other temperatures (870˚C, 940˚C) showed increase and decrease as the soaking time increases. This is indicated in Figure 1(d).

Soaking time of 9 hrs and particle size of 45 micron interaction gave highest hardness value as shown in Figure 1(e). Particle size of 60 micron gave reasonable hardness value at soaking time of 3 hrs but later dropped with particle size of 90 micron showing good sign of hardness value. Particle size of 90 micron gave an increased hardness value with increasing soaking time but later decreased after soaking time of 6 hrs. The response graphs (Figures 1(a)-(e)) show the change in the hardness values when a given factor goes from lower level to higher level. The slope of the line determines the power of the control factors (temperature, soaking time and particle size) influence on surface hardness. Figure 1(a) clearly suggests a dominant influence, in a quantitative sense, of furnace temperature on the surface hardness.

The effect of furnace temperature can be explained by the fact that as the temperature increases the interaction between particle size and hardness value decreases i.e. decrease in particle size increases the hardness values. From Figures 1(a)-(e), it can be observed that the optimal combination of carburizing process parameters is A₂B₃C₁. In other words, using furnace temperature of 910˚C at soaking time of 9 hrs with energizer particle size of 45 micron is beneficial for surface hardness maximization. However, to find the relative contribution of each process parameters on the surface hardness and confirm initial assumption of the optimal condition, the statistical analysis through ANOVA was performed. The ANOVA results of S/N ratios are shown in Table 7. Figures 2-4 represent surface plots of hardness against process parameters.

This paper presents the Taguchi approach and Response Surface Model for optimization of hardness in carburized UNS-G10170 steel. The influence of carburizing parameters on hardness has been investigated. Taguchi technique, Response Surface Model and ANOVA were used for the numerical modeling and analysis. From the experimental results and derived models, the following conclusions can be drawn:

v It was observed that the furnace temperature should be kept at 910˚C, soaking time at 9 hrs, while energizer particle size of 45micron should be used in order to obtain optimal hardness value.

v The correlation between process parameters and hardness was derived using a regression analysis and an optimum parameter combination (A₂B₃C₁) for the maximum hardness was obtained by using the analysis of S/N ratios.

v The developed mathematical models through Taguchi approach and Response Surface Model correlate with experimental results of hardness which proved that the mathematical models derived are effective.