CHAPTER 5 EXPERIMENTAL AND STATISTICAL METHODS FOR DRILLING
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1 CHAPTER 5 EXPERIMENTAL AND STATISTICAL METHODS FOR DRILLING 5.1 Introduction This chapter presents the method of selection of samples, experimental setup details drilling and statistical methods adopted for carrying out the experiments. A CNC vertical machining center was used for carrying out the drilling operations. A dynamometer was used to note the thrust force and torque during each operation. The chapter also addresses the output measurement procedures after the drilling operations are finished and the numerical data of input and output responses during drilling. A response surface based D-optimal design method was used for developing the design and optimizing it by using Design Expert software. 5.2 Selection of work samples Based on the detailed analysis on mechanical properties of developed composite samples as presented in chapter 4, three samples are selected as best ones. Samples with highest tensile, flexural and compressive strengths namely TV17J17, TV13J13G8 and TV10J10G14 are selected for the present drilling studies. The mechanical properties of selected samples are presented in Table 5.1 respectively. In order to easily identify the samples, sample numbers are given as I, II and III for samples V17J17, V13J13G8 and V10J10G14 respectively. Table 5.1 Mechanical properties of selected samples Sample number Sample Identity Tensile strength (MPa) Flexural strength (MPa) Compressive strength (MPa) Impact energy (J) I V17J II V13J13G III V10J10G
2 5.3 Machining setup Figure 5.1. Machining setup Figure 5.2. Schematic of drill tools 46
3 Drilling operations are carried out in a computer numerical control vertical machining center of Bharat Fritz Werner make with model BMV 40T20. The machine is controlled by Siemens 802D and has a speed range between 60 rpm to 6000 rpm with a motor capacity of 3.7 KW. The maximum tool traverse is 510 mm x 410 mm x 460 mm. The work sample is mounted on the machine table as presented in Figure 5.1. Four HSS drill tools are purchased from a local supplier and their point angles are ground to 60 0, 90 0, and respectively by using a high precision tool and cutter grinder as presented in Figure 5.2. The work samples used for the present study were cut in to a 100 mm square plate and 12 mm thick. 5.4 Response measurement Five responses namely Thrust force (Th), Torque (T), Surface roughness (Sr), Damage factor at entry (Di) and Damage factor at exit (Do) are measured for each drilling operation. The responses namely thrust force and torque are measured during drilling by using a multicomponent Kistler make piezoelectric dynamometer of model 9257B as presented in Figure 5.3. The dynamometer has a measuring range of -5 KN to +5 KN along x, y and z axis. The dynamometer is placed below the work as presented in Figure 5.1 in order to measure the thrust force and torque. Figure 5.3. Schematic of Kistler make dynamometer The drilled inner surface roughness of holes are measured by using a Mitutoyo make roughness tester of model SJ210. The roughness tester is mounted horizontally on a vernier height gauge and work sample was held vertically by using a machine vice. The entire setup is placed over a surface plate as presented in Figure 5.4. During this test, the test probe is 47
4 allowed to traverse through the inner surface of hole and three readings are taken near the entry, exit and at mid-way of hole. The average of three readings is calculated and noted as surface roughness of the corresponding hole. Figure 5.4. Surface roughness measurement Damage factor is at entry or exit is defined as the ratio of maximum diameter of damaged hole to the nominal diameter (Paneerselvam et al. 2014) as presented in Eqn 5.1. The maximum diameter of the hole as presented in Figure 5.5 is measured by using a Mitutoyo make tool makers microscope. Damage factor = (5.1) Figure 5.5. Damage factor measurement 48
5 5.5 Factors and levels Machining factors always affect the machinability of all machining operations. Machining factors may be spindle speed, spindle feed rate, depth of cut, tool profile, tool material or work material, tool angles etc. Although several researches have been done earlier by a combination of two or more factors as mentioned earlier, speed, feed, tool point angle are majorly addressed in recent works. The present study includes four input factors namely speed (S), feed (F), tool point angle (A) and work sample (D) for drilling. In these input factors, speed, feed and tool angle are selected as numerical factors with four levels and work sample is selected as a categorical factor with three levels. The assignment of numeric levels to each factors is based on survey of previous research (Velumani et al. 2013; Jayabal & Natarajan 2010; Birhan Işık & Ergün Ekici 2010) and the data are presented in Table 5.2. Table 5.2 Machining factors and levels Factors Type Level 1 Level 2 Level 3 Level 4 Speed (S) rpm Numerical Feed (F) mm/rev Numerical Tool angle (A) degree Numerical Work Sample (D) Categorical I II III Statistical design Response surface methodology (RSM) serves as an interaction of mathematical and statistical techniques for modelling and optimizing the response variable models involving quantitative independent variables. It is an important concurrent engineering tool in process development as the objectives of process performance improvement can be accomplished directly using RSM. The extensive applications of RSM are in a situation where several input variables potentially influence some performance measure or quality characteristic of the process. The performance measure or quality characteristic is called the response. The input variables are called independent variables and are subject to control of an engineer. Through the use of the design of experiments and applying regression analysis, the modelling of desired response to several independent input variables can be gained. 49
6 In order to study the main effect and interactions on the output response, a second order polynomial response surface equation (Cockran & Cox 1977) is used as presented in Eqn 5.2. k 2 y 0 i xi ii xi ijxix j (5.2) i1 k i1 Where, y represents the response, xi represents the coded independent variable, βo represents the mean of each observed response, the coefficient βi is linear terms, the coefficient βii is the quadratic term, the coefficient βij is the interaction term, k represents the number of pattern and Ɛ represents the random experimental error component. The coefficients, in the second order model, are determined by using Design Expert 8 Software. i j D-optimal design is one of the optimality technique in which the variance of regression coefficients in model equation is minimized (Montgomery 2008). In multiple regression setting, the matrix X is used to represent the data matrix of independent variables. D-optimal design minimizes the overall variance of the estimated regression coefficients by maximizing the determinant X T X. The first step of D-optimal is to define the functional form of relationship between the response (Y) and the independent variables. In the next step, a set of possible candidate points are generated for the model. Finally, from the developed candidates the subset that maximizes the determinant X T X is selected. This is the D-optimal design. There are two main advantages of using this technique. Firstly, it effectively optimizes the responses under the influence of factors with unequal levels. Secondly, it can optimize multiple responses which are influenced by both numerical and categorical factors (Rajmohan & Palanikumar 2013). In the present machinability study, speed, feed and tool angles are varied within four numerical levels whereas work sample is varied within three categorical levels. Hence, the selected design was called as a 4-factor mixed level factorial design and the design, analysis and optimization were done by using Design Expert software. A set of 28 experimental runs has been listed for the present design and the levels of each factors during these runs are presented in Table 5.3. The exact run conditions with measured responses are presented in Table
7 Table 5.3. Design Table Run No. Input factor-1 (Numeric) Input factor-2 (Numeric) Input factor-3 (Numeric) Input factor-4 (Categorical)
8 Table 5.4. Experimental runs and responses Run Speed (S) rpm Feed (F) mm/ rev Tool angle (A) degree Work (D) Th N T Nm Experimental Sr µm III II I II III I III I II I III II II I III III II I II III I II III I II I III III Di Do Drilling experiments have been conducted as per the run listed in Table 5.4 and output responses have been measured. 52
9 Summary Three samples have been selected on the basis of their mechanical properties for drilling studies. The specifications of computer numerical control machining center used for drilling in the present study has been addressed. The selection of input and output factors and their levels in the present study has been addressed. Four factors namely speed, feed, tool point angle and work sample are selected for drilling studies. The measurement techniques of output responses namely thrust force, torque, surface roughness, damage factor at entry and damage factor at exit are detailed with apparatus specifications. A RSM based D-optimal design criterion is used for modelling and optimization by using Design Expert software. The design table showing the runs and observed responses are listed. 53
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