CHAPTER 4 EXPERIMENTAL DESIGN

Transcription

1 64 CHAPTER 4 EXPERIMENTAL DESIGN 4.1 INTRODUCTION In order to study the effects of process parameters of QPQ process on the mechanical behaviour like corrosion resistance, hardness, wear and friction with the help of mathematical models, it is essential to generate the data by carrying out experiments corresponding to the actual conditions of the process. It is important that the experiment should provide the required information within minimum time and effort. Therefore, it is imperative that the experimental plan and program is well prepared and designed to conduct the experiment. The design of experiments deals with the procedure of selecting the number of trials and conditions, essential and sufficient for solving the problem that had been set with the required precision for running the same. Aoki (1971) have dealt with this at length. The general quantitative approach, which is more logical than any other approaches, was selected for designing the experiments. Cochran and Cox (1957) and Davies (1978) recommended the factorial technique as one of the important statistical techniques for the design of experiments in engineering investigations. In the present work, a five level factorial technique was employed for developing design matrix to conduct the necessary experiments.

2 65 The forthcoming paragraphs discuss all the necessary details related to the technique used and the experimental setup developed for the present study. 4.2 BASE MATERIAL PREPARATION The AISI 316L SS was used as the metal substrate and the elemental composition of the same is given in Table 3.1. The AISI 316L SS alloy in as-received mill annealed condition was cut into cylindrical samples of 10 mm diameter and 25 mm length. Prior to the study, the AISI 316L SS samples were polished using silicon carbide emery papers of 120, 220, 320, 400, 500, 600 and 800 grit. Final polishing was done using 5 m and 1 m diamond pastes respectively in order to produce scratch-free mirror-finish surface. The polished specimens were then examined using an optical microscope for the presence of pits or scratches on the surface. The polished specimens were washed with detergent solution, degreased with acetone and thoroughly washed with distilled water. They were further subject to ultrasonic cleaning in acetone for 10 min. Finally, the resultant sample was rinsed in deionized water, dried and used for further studies. 4.3 EXPERIMENTAL SETUP in steps below: The experimental setup developed for the present study is described Pre Heating The specimens were pre heated to the temperature of 400 C using muffle furnace shown in Figure 4.1.

3 66 Figure 4.1 Muffle furnace The bath was prepared using a mixture of Cyanate (CNO - ), Nitrogen (N) and Carbonate (CO32 - ). The CNO - % was varied from 25 % to 45 %, according to the required level, as demanded by the DOE matrix. Likewise the temperature of nitrcarburizing process (T) was also varied in the range of 540 C to 640 C to meet the level requirements of the DOE matrix. The other process variable namely the time (t1) was also controlled in the range of 120 min to 240 min as per the required level. The bath used for this nitrocarburizing is shown in Figure 4.2.

4 67 Figure 4.2 bath Oxidizing The oxidizing bath was prepared which contains oxygen. The temperature of this bath was maintained at 400 C and the quench time was varied from 10 to 50 min to meet the level requirements of DOE matrix. The oxidizing bath is shown in Figure 4.3. Figure 4.3 Oxidizing bath

5 Polishing Polishing was done in order to obtain the original surface finish back. It was done using 1000 &1200 grit emery sheet and with a diamond paste of 5 µm and 1 µm Post Oxidizing Post oxidizing was done in order to improve the corrosion resistance, the temperature of the bath was maintained at 400 C and the quench time was varied from 10 to 50 min to meet the level requirements of DOE matrix. 4.4 RESPONSE SURFACE METHODOLOGY Response surface designs are commonly employed to investigate and predict the following important conditions of a process: The effect of a given set of input variables on a particular response over some specified region of interest. The required values of variables are obtained to acquire a desirable or acceptable level of response. The values of variables required to achieve a minimum or maximum response and the nature of response surface near this minimal or maximal value. The relationship between response and control variables is almost polynomial of second order because second order designs are well devised. Besides, second order response surfaces lend themselves to detect optimum conditions with ease.

6 69 It is worth observing that the most informative method of analysis of the results of a factorial experiment depends largely on the nature of the factors. If all the factors represent quantitative variables like time, temperature, amount of CNO -, it can be naturally assumed that the yield or response y as a function of the levels of these variables. This can be represented as in the equation (4.1) given below: y u = (x 1u, x 2u,.., x iu )+e u (4.1) where u=1, 2, N represents the number of observations in the factorial experiment and x iu represents the level of the i th factor in the u th observation. The function is called the response surface. The residual e u measures the experimental error of the u th observation. Knowledge of the function not only summarises the results of the experiment, but also predicts the response for values of the x iu which were not tested in the experiment. When the mathematical form of is not known, this function can sometimes be approximated satisfactorily, within the experimental region, by a polynomial in the variables x iu. Box and Hunter (1978) described some experimental designs and methods of analysis that have been developed for fitting first and second degree polynomials The Quadratic Response Surface The general form of a quadratic polynomial which give the relation between response surface y and the process variable x under investigation is given in the equation (4.2). (4.2) k k 2 0 i 1 i i i 1 ii i i j ij i j y b b x b x b x x where b 0 = constant, b i = linear term coefficient, b ii = quadratic term coefficient and b ij = interaction term coefficient.

7 70 Box and Hunter (1961) proposed central composite rotatable design for fitting a second order response surface based on the criterion of rotatability. From the result of the experiment, the standard error y u can be calculated at any point on the surface. This standard error will be the function of the coordinates x i at any point. In a rotatable design, this standard error is the same for all points that are equidistant from the center of the region. With five variables, Box and Hunter (1961) proposed a rotatable design obtained by making test at points equally spaced around the circumference of the sphere, plus one or more test at the center itself. The points on the circumference lie at the vertices of a regular polyhedra inscribed in a sphere. The factor is the radius of the sphere on which the points lie. The central composite rotatable design for five parameters with five levels consists of 32 experiments. The design may be sub divided into three parts as given below: i) The first 16 points represents ½ replicate of a 2 5 factorial which lie at the vertices of the regular polyhedral. These points are generally called as the factorial design points. The factorial design points are coded as ±1. ii) The next 10 points (17-26) are the extra points included to form a central composite design with the radius of the sphere consisting of points equally spaced form the center which is given in the equation (4.3). The value of must be 2 k/4 in order to make the design rotatable, but for the 5 and 6 variables, the size of the experiment is reduced by using a half-replicate of the 2 k factorial. With a half replicate, becomes 2 (k-1)/4. These points are called as star points. For ½ replicate, the extra point is included to form a central composite design. = ± [2 (k-1)/4 ] = ±2 (4.3)

8 71 iii) The last 6 points (27-32) are added at the center to give a roughly equal precision of standard error y u with the sphere of radius. These points are called replicated center points or axial points. The replicated points at the center have two purposes. They provide (n-1) degrees of freedom for determining the experimental error, and also determine the precision of standard error y u and at near the center where n are the number of center points. The center point is coded as 0. If the different combinations of process conditions are to be planned, it is important to randomize the sequence of the experiment Identification of the Process Variables Process parameters, which influence the mechanical behaviours of AISI 316L SS subjected to the QPQ process, have to be selected. It is also important to identify the correct process conditions for obtaining sound material properties. Among the many independently controllable QPQ process parameters, which affecting the performance of AISI 316L SS the chief parameters chosen for the present study are % of CNO - in nitrocarburizing bath (C), nitrocarburizing temperature (T), nitrocarburizing time (t1), oxidizing time (t2), post oxidizing time (t3) Determining the Limits of the Process Variables The working ranges of all process variables were achieved through many trial runs carried out by varying one of the process variables, while keeping the others constant. The extreme values of the variables were selected by examining the visible defects and the feasible rang of process parameters.

9 72 For experimental design matrix, the upper limit of a factor was coded as +2 and the lower limit as 2, the coded values for intermediate values was calculated through the equation (4.4). X i 2(2X (Xmax X min )) (X X ) max min (4.4) where Xi - The required coded value of a variable X, X - Is any value of the variable from X min to X max X min - Is the lower limit of the variable. X max - Is the upper limit of the variable. The decided levels of the selected process parameters of the experiment for QPQ process, with their units and notations are given in Table 4.1. Table 4.1 Process variables and their levels-five factors-five levels Process Parameters Bath chemistry- CNO - % Process temp Process time Notations Units Factor Level C % T ºC t1 min Oxidizing time t2 min Post oxidizing time t3 min

10 Development of Design Matrix In factorial design, the experiments are conducted for all possible combinations of the parameter levels and these combinations are presented in the form of a table which is shown on Table 4.2. In Table 4.2, the rows correspond to the different trials and the columns to the levels of the parameters which form a design matrix. Table 4.2 Design matrix for experiment (five factors-five levels) Trial No Bath CNO - %-C (%) Process Temperature-T ( C) Process Time-t1 ( min) Oxidizing Time-t2 (min) Post Oxidizing Time-t3 (min) `

11 74 Table 4.2 (Continued) Trial No Bath CNO - %-C (%) Process Temperature-T ( C) Process Time-t1 ( min) Oxidizing Time-t2 (min) Post Oxidizing Time-t3 (min) In this matrix, thirty-two experimental runs provide twenty one estimates for the effect of five parameters. One estimate for the main effect of five parameters, five linear estimates for main effects, five quadratic estimates due to main effects and ten estimates for the two factor interactions have been included as shown in equation (4.2). Thus the design matrix has allowed the estimation of linear, quadratic and two-way interactive effects of the QPQ process variables on the mechanical properties.

12 CONCLUDING REMARKS The required base materials were prepared to conduct the QPQ process. The experimental set up was developed to conduct the QPQ process with the required process parameter level. Prior to explaining the experimental design which was used for this research work, response surface methodology was discussed in detail. Finally the design matrix was developed.