78 CHAPTER 3 EXPERIMENTAL DESIGN 3.1 INTRODUCTION The objective of this study is to investigate the effect of process parameters such as radial rake angle, nose radius, cutting speed, cutting feed, and axial depth of cut on machining performance such as surface roughness, cutting force, tool wear acceleration amplitude of vibration and temperature rise in end milling operation. It is important to generate data by conducting experiments by varying various levels of process parameters and recording the response of machining performance at each set of levels. It is necessary in the experiment to have a clear layout of what exactly is to be studied, how the data to be collected and qualitative understanding of how these data are to be analyzed. This chapter describes the experimental setup used to conduct the experiments. Brief description of the tool material, workpiece material, instruments used to measure the response is also included. Experimental design methods used to select factors levels, range and also to select the suitable run order of the experimental trials are briefly described. Central composite rotatable design matrix which has been employed for conducting experiments are described and presented in this chapter. 79 3.2 EXPERIMENTAL SETUP The experiments were conducted on a HAAS vertical machining center (Figure 3.1): model tool room mill TM-1 with high speed steel end mill cutter under dry condition. The HAAS Vertical Computer Numerical Control machining center provides a room for a lager work piece with xyz travels 30” X 12” X 16”(762 mm X 305 mm X 406 mm). The specifications of HAAS vertical machining center used for conducting experiments are: (i) Power of spindle motor 7.5/5.5 kW (ii) Speed rage of the spindle motor 60–10000 RPM (iii) Guide ways type LM (iv) Max load on table 300 kgf (v) Feed (X & Y dir) 1–10000 mm/min (vi) Power supply (Basic machine) 14 kVA Figure 3.1 HAAS CNC vertical machining centre 80 The workpiece material Aluminum alloy 7075-T6 is acknowledged in Aircraft fittings, gears and shafts, fuse parts, meter shafts and gears, missile parts, regulating valve parts, worm gears, keys, and various other Commercial aircraft, aerospace and defense equipment owing to its high strength to weight ratio. The use of materials with low specific weight is an effective way of reducing the weight of structures. The favorable characteristic features such as moderate hardness, better transmission, heat treatable, high tensile strength and high corrosion resistance leads to the choice of Aluminum alloy 7075-T6. For conducting experiments to determine surface roughness, cutting force, vibration amplitude, tool wear and temperature rise test specimens of following sizes (50 mm x30 mm x 30 mm), and (100 mm x 50 mm x 30 mm)were cut from Aluminum alloy 7075-T6 bar. As per experimental design 32 identical specimens were cut to the above dimension as shown in the Figure 3.2. The workpiece is placed in the machining center using a machine vice. Figure 3.2 Work piece material (AluminiumAlloy, Al 7075-T6) The tool material was high Speed Tool Steels (HSS). HSS is inexpensive compared to other tool materials, is easily shaped, and has excellent fracture toughness, fatigue and shock resistance. The end mill cutter made is solid HSS used for our experiments. Nine end mill cutters with 81 different radial angle, nose radius are utilized for conducting experiments as shown in the Figure 3.3. The specifications of the geometry of the end mill used for conducting experiments are: (i) Number of flutes 4 (ii) Diameter of cutter 12 mm (iii) Shank length 70 mm (iv) Helix angle of flute 45° (v) Radial Rake angle 4°,8°,12°,16°,18°,20° (vi) Noseradius 0.4mm,0.6mm,0.8mm,1.0mm, 1.2mm Figure 3.3 End mill cutter with different radial rake angle and nose radius 3.2.1 Experimental Set-up for Surface Roughness Measurement Various methods are used to assess surface roughness. They can be divided into three categories: (1) subjective comparison with standard test surfaces, (2) stylus electronic instruments, and (3) optical techniques. Standard Test Surfaces Sets of standard surface finish blocks are available, produced to specified roughness values. To estimate the roughness of a given test specimen, the surface is compared with the standard both visually and by the ‘‘fingernail test.’’ In this test, the user gently scratches the surfaces of the specimen and the standards, judging which standard is closest to the specimen. Standard test surfaces are a convenient way for a machine operator 82 to obtain an estimate of surface roughness. They are also useful for design engineers in judging what value of surface roughness to specify on a part drawing. Stylus Instruments: The disadvantage of the fingernail test is its subjectivity.Several stylus-type instruments are commercially available to measure surface roughness—similar to the fingernail test, but more scientific. An example is the Profilometer, shown in Figure 3.4. In these electronic devices, a cone-shaped diamond stylus with point radius of about 0.005 mm (0.0002 in) and 90º tip angle is traversed across the test surface at a constant slow speed. The operation is depicted in Figure 3.4. As the stylus head is traversed horizontally, it also moves vertically to follow the surface deviations. The vertical movement is converted into an electronic signal that represents the topography of the surface. This can be displayed as either a profile of the actual surface or an average roughness value. Profiling devices use a separate flat plane as the nominal reference against which deviations are measured. The output is a plot of the surface contour along the line traversed by the stylus. This type of system can identify both roughness and waviness in the test surface.Averaging devices reduce the roughness deviations to a single value Ra. They use skids riding on the actual surface to establish the nominal reference plane. The skids act as a mechanical filter to reduce the effect of waviness in the surface; in effect, these averaging devices electronically perform the computations. Figure 3.4 Sketch illustrating the operation of stylus-type instrument 83 Stylus head traverses horizontally across the surface, while the stylus moves vertically to follow a surface profile. Vertical movement is converted into either (1) a profile of the surface or (2) the average roughness value. Optical Techniques most other surface-measuring instruments employ optical techniques to assess roughness. These techniques are based on light reflectance from the surface, light scatter or diffused, and laser technology. They are useful in applications where stylus contact with the surface is undesirable. Some of the techniques permit very-high-speed operation, thus making 100% inspection feasible. However, the optical techniques yield values that do not always correlate well with roughness measurements made by stylus-type instruments. The average roughness value was measured using MitutoyoSurftest SJ201 on the surface of the machined specimen as shown in the figure 3.5. The Surftest SJ201is a shop floor type surface roughness measuring instrument, which traces the surface of various machine parts, calculates their roughness standards, and displays the result. The measuring instruments consist of the detector unit with stylus for tracing. A pickup or stylus of the detector unit will trace the minute irregularities of the workpiece surface. The vertical stylus displacement produced during tracing the work surface is converted into electrical signals. The electrical signals are subjected to various calculation processes and the calculation results (measurement result) are displayed on the instrument liquid crystal display. RS 232 port is available on the instruments to acquire measured surface roughness value using Mituotyover 3.0 software in the personal computer. The cut off length used during the measurement was 0.8 mm and the measurement were taken at three places on the machined surface and the average of those values is noted. 84 Figure 3.5 3.2.2 A schematic diagram of experimental setup for surface roughness measurement Experimental Set-up for Cutting force Measurement The cutting forces:infeed force, crossfeed force and thrust force are measured by using syscon instruments; three axis milling tool dynamometer. The instruments works based on the strain gauge wheat-stone bridge principle. RS232 port is available in the instruments to acquire data while machining. The data is acquired in the data acquisition software and observations are tabulated to obtain the mathematical model. The workpiece is mounted on the specially designed machine vice with strain gauges measure the cutting force in all three directions. The experimental setup used for conducting the experiments is shown in Figure 3.6. 85 Figure 3.6 A schematic diagram of experimental setup for cutting force measurement Exclusively designed Dynamometers are used to measure the cutting forces of the tool point. An array of hydraulic, pneumatic and strain gauge instruments were used by the researchers earlier. But piezoelectric Dynamometers using quartz load measuring elements are generally employed for cutting force measurement. The Dynamometer is fixed between the tool or workpiece and non-rotating part of the machine tool structure. In order to determine the cutting forces into directional components, coordinate system is employed. Force components are connected to the axes of motion of the 86 machine tool in the milling process. Infeed force, crossfeed force and thrust force are the three resolved components of the force. The infeed force, acts in the x direction of the machine tool, tangent to the rotating tool. Crossfeed force acts in the y direction of the machine tool, which is normal to the rotating tool. The thrust force acts in the z direction of the machine tool which is parallel to the axis of the tool. 3.2.3 Experimental Set-up for Vibration Amplitude Measurement The experimental set-up for this research is bifurcated into: (1) hardware, and (2) software. In order to deduce the mathematical model and analyze the relationships among vibration amplitude, geometrical parameters (radial rake angle, nose radius of cutting tool) and machining parameters (cutting speed, cutting feed rate and axial depth of cut), the experimental setup should collect data for analysis. 184.108.40.206 Hardware set-up The hardware set-up requires the following equipment: (1) A HAAS vertical machining center with 10 tools with the capacity of multiple tool-change capability operates at a high spindle speed ranging to 10000 r. p. m. This machine is capable of 3-axis movement (along the x, y, and z planes). (2) A ER32- GPL 70mm tool holder, ER40 collect diameter 12mm with high-speed steel end mill cutting tool. (3) The piezoelectric accelerometer (Model Number ABRO AB102-A, S/No AB1234) is used to measure the response of the acceleration. The accelerometer is used to collect vibration data generated by the cutting action of the work tool. 87 (4) An ICP (internal integrated circuit preamplifier) battery power unit is fixed, not only to supply power for the accelerometer, but also to amplify the voltage of the signal coming from the accelerometer. In order to initiate a stronger signal, the battery power supply is set to the sensor kit. (5) A Handheld data recorder (COCO-80 Real Time FFT Analyzer & Data Collector) is used for recording data, analysis and feedback. Figure 3.7 A schematic diagram of experimental setup for vibration amplitude measurement 88 (6) An analog high-pass filter at 0.3 Hz @ (-3 dB) and 0.7 Hz @ (-0.1 dB) is constructed to filter unwanted high-frequency signals and allow only low- frequency information to pass through unattended (without a reduction in amplitude). (7) An accelerometer picks up with magnetic base one is attached to the spindle head (axial direction) to sense the vibration and another one is attached to the work piece holder (feed direction) to sense the vibration. The signal absorbed by the accelerometer pick up is transferred to the FFT analyzer. The FFT analyzer is interfaced with a computer for vibration analysis in Engineering Data Management software (EDM). 220.127.116.11 Software set-up The software set-up requires the following programs: (1) In this experiment the NC program has been written to operate the HAAS vertical machining center to perform the end milling cutting process. The geometrical parameters (radial rake angle, nose radius of cutting tool) and machining parameters (cutting speed, cutting feed rate and axial depth of cut) were reset in the CNC manually for each run according to different cutting conditions. (2) A statistical software QA Six Sigma DOE-PC IV and Minitap16 were applied to perform the basic statistical analysis and analyze the relationship among the vibration, geometrical parameters (radial rake angle, nose radius of cutting tool) and machining parameters (cutting speed, cutting feed rate and axial depth of cut). 89 The vibration amplitude is measured with twin-channel FFT analyzer (COCO 80), shown in Figure3.7 he acceleration amplitude is determined in the axial cutting direction in the spindle (channel I) and in the feed direction of the workpiece holder (channel II). The data are acquired in the FFT analyzers and are tabulated to obtain the mathematical model. Engineering Data Management (EDM) software received the digital vibration data form COCO-80 FFT Analyzer through the accelerometer. The data are acquired in the FFT analyzers and are tabulated to obtain the mathematical model. 3.2.4 Experimental Set-up for Temperature rise Measurement The temperature was measured by using K-type thermocouple. A hole of 1 mm was drilled in the work piece specimen at 2.5 mm below the machining surface. A K-type thermocouple was inserted into the hole and the initial temperature was noted using the digital thermometer. During machining maximum temperature was measured, the difference between the maximum and initial temperature gave the temperature rise as shown in Figure 3.8. Figure 3.8 A schematic diagram of experimental setup for temperature measurement 90 3.2.5 Experimental Set-up for Tool Wear Measurement After milling operation, end mills being utilized are changed with the new end mill. The milling process is interrupted for each experiment after completion and then the value of the wear is measured. The tool wear was measured using Metzer tool makers microscope on the flank surface of the end mill cutter specimen as shown in the figure 3.9. The tool makers microscope consists of 150mm X 150mm measuring stage, travel of 25mm and extendable up to 50mm with slip gauges, Gonimeter eyepieces 10X with scale, base illumination (diascopic) 12V/20W (variable intensity) incident illumination 12V/20W (variable intensity), Magnification 30X with a field of view 12mm and working distance 80 mm. The tool after milling is kept on the measuring stage and with the help of vernier scale and cross wire the tool wear is measured on the flank surface. The tool wear is measured off line with a tool maker’s microscope for each combination of cutting conditions in accordance with the ISO standards 8688. Figure 3.8. Shows experimental setup for the measurement of tool wear. An average of three measurements was used as a response value and is tabulated to obtain the mathematical model. Figure3.9 A schematic diagram of experimental setup for tool wear measurement 91 3.3 STRATEGY OF EXPERIMENTATION An experiment is a test or series of tests in which purposeful changes are made to the input variables of a process or system, so that the reason for changes can be observed and identified in the output response variables. Experiments are used to study the performance of processes and systems. The process or system can be visualized as a combination of machines, men, methods and other resources that transforms some input into an output that has one or more observable response. Some of the process variables are controllable, whereas other variables are uncontrollable. The objectives of conducting experiments are as follows 1. Determining which variables are more influential on the response 2. Determining the limits of input variables which will give the desired value of the response. 3. Determining the limits of input variables where the effects of uncontrollable variables are minimized. The general approach to planning and conducting the experiment is called the strategy of experimentation. It is essential to design the experiments on a sound basis rather than on the commonly employed trial and error method in conjunction with a small number of repeat experiments for confirmation of the results. However, for quality work and future predictions, trial and error methods are often little better than the guess work. Apart from the trial and error method of investigations, the commonly employed techniques by the researchers to analyze the effect of End milling process parameters on machining responses are: 1) Best-guess approach, 2) One-factor at-a-time approach, 3) Factorial design and 4) Response Surface Methodology. 92 Out of all these approaches RSM has been widely used by researchers to investigate the effect of process parameters on responses. Hence it is explained in detail. 3.3.1 Response Surface Methodology Response surface methodology is a general approach for obtaining the maximum value of a dependent (response) variable which depends upon several independent (explanatory) variables. This technique combines the Design of Experiments (DoE) and multiple regression. DoE is a general approach for designing any information-gathering exercises where variation is present. In machining-process modelling, DoE deals mainly with controlled experiments, where variations in the independent variables are under the control of the researcher. Response Surface Methodology (RSM) is a collection of statistical and mathematical methods that are useful for the modeling and optimization of the engineering science problems. In this technique, the main objective is to optimize the responses that are influenced by various input process parameters. RSM also quantifies the relationship between the controllable input parameters and the obtained responses. In modeling and optimization of manufacturing processes using RSM, the sufficient data are collected through design experimentation (Myers & Montgomery 1995). RSMhas several advantages compared to the classical experimental or optimization methods in which one variable at a time technique is used. First, RSM offers a large amount of information from a small number of experiments. Indeed, classical methods are time consuming and a large number of experiments are needed to explain the behavior of a system. Second, in RSM it is possible to observe the interaction effect of the independent parameters on the response. The model equation easily clarifies 93 these effects for binary combination of the independent parameters. In addition, the empirical model that relates the response to the independent variables is used to obtain information about the process. With respect to these, it may be said that RSM is a useful tool for the optimization of manufacturing processes. It is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response. Response surface designs are employed to investigate and predict the following important conditions of a process 1. The effect of a particular response by a given set of input variables over some specified region of interest. 2. The required values of variables are obtained to desirable or acceptable level of a response. 3. The required values of variables to achieve a minimum or maximum response and the nature of response surface near this minimal or maximal value (Sudhakaran 2012). If an experiment is conducted to determine the two levels of ‘x 1’ and ‘x2’ that will maximize the yield ‘y’ of a process, then ‘y’ is a function of the levels ‘x1’ and ‘x2’. This is shown in Equation (3.1) Y f ( X 1 , X 2 ) e (3.1) Where‘e’ represents the noise or error observed in the response ‘Y’. If the expected response is denoted by E(Y) = Y f ( X 1 , X 2 ) = , then the surface is represented as shown in Equation (3.2) f ( X1, X 2 ) (3.2) 94 In response surface methodology problem, the form of relationship between the response and the independent variables are unknown. Thus the first step in response surface methodology is to find a suitable approximation for the true functional relationship between ‘y’ and a set of independent variables. The function will be a first order model, if the response is a linear function of the independent variables. This is given by Equation (3.3) y b0 b1 X1 b2 X 2 .................... bi X i (3.3) The response will be a second order model if there is a curvature in the system. The second order model is given by Equation (3.4) k y b0 k bii X i 2 bi X i i 1 i 1 bij X i e (3.4) i j The eventual objective of RSM is a very efficient design for fitting the second order model. Therefore it was decided to use RSM designs which are well suited for engineering investigations. 3.4 CHOICE OF EXPERIMENTAL DESIGN Experimental design is a critically important tool in designing and analyzing an experiment. It is an approach which gives a clear idea in advance of exactly what is to be studied, how the data are to be collected and a qualitative understanding of how these data are to be analyzed. The various steps involved in the design of experiments are as follows 1. Identifying the important process control variables. 2. Finding the upper limits and lower limits of the selected control variables. 3. Developing the design matrix 95 3.4.1 Identification of the Process Variables The machining variables selected for our investigation are radial rake angle, nose radius of cutting tool, cutting speed, cutting feed rate and axial depth of cut. These variables are identified to be the controllable potential design factors that influence the machining performance such as surface roughness, cutting force, acceleration amplitude, tool wear and temperature rise during milling. It is important to choose the ranges over which these machining variables will be varied, and the specific levels at which the runs will be made. 3.4.2 Finding the Limits of the Process Variables The working ranges of all the selected variables are to be found to fix their levels and to develop the design matrix. The following methodology was adopted to identify the ranges of process parameters. The upper and lower limit of each process variable was estimated initially through trial runs. For instance, trial runs for varying values of cutting speed between 50 and 160m/min were conducted in order to identify the lower limit and upper limit of cutting speed. During the trial runs, the other variables were fixed at a constant value, i.e. at 12 º, R at 0.8 mm, fzat 0.04 mm/tooth, and ap at 2.5 mm. Later the specimen was scrutinized on the basis of surface roughness and the same factors form the basis for fixing the levels. The lower and upper limits for surface roughness were fixed at 75 and 155m/min based on the trial runs and they were coded as (-2) and (+2). Equation (3.5) (Montgomery2005, Montgomery & Peck 2005) is applied to measure the other levels of the process variable. All other variables are identified by applying the same procedure. After conducting trial runs the range of these machining variables influencing the machining performance 96 are found to be for radial rake angle angle 4 0 – 200, Nose radius 0.4mm to 1.2mm for cutting speed 75m/min – 115m/in, for feed rate 0.02 mm/rev – 0.06 mm/tooth and for axial depth of cut 1.5 mm – 3.5 mm. X i= 2(2X-(X max +X min )) (3.5) (X max -X min ) where Xi is the required coded value of a variable X. X is any value of the variable from Xmin to Xmax. The selected process parameters with their limits and notations are given in Table 3.1. All machining variables at the intermediate (0) level constitute the center points while the combination of each variable at either its lower value ( 2) or its higher value (+2) with the other two parameters at the intermediate level constitute the star points (Montgomery2005). The decided levels of the selected process parameters for the experiments with their units and notations are given in Table 3.1 and Table 3.2. Table 3.1Factors and selected levels for end milling experiments (5 factors and 5 levels) Parameter Units Levels Notation 0 -2 4 -1 8 0 12 1 16 2 20 Radial rake angle Degree ( ) Nose radius mm R 0.4 0.6 0.8 1 1.2 Cutting speed m/min Vc 75 95 115 135 155 Cutting feed mm/tooth fz 0.02 0.03 0.04 0.05 0.06 ap 1.5 Axial depth of cut mm 2 2.5 3 3.5 97 Table3.2 Factors and selected levels for finite element method (3 factors and 5 levels) Levels Parameters Notation Units Cutting speed Vc m/min Cutting Feed fz mm/tooth 0.06 Depth of cut ap mm 0.5 3.4.3 -1.682 -1 0 1 1.682 100 130 160 190 220 0.07 0.08 0.09 1 1.5 2 0.10 2.5 Developing the Design Matrix The general form of a quadratic polynomial which gives the relation between response surface ‘y’ and the process variable ‘x’ under investigation is given by Equation (3.6) k Y=bo + k bii xi 2 + bi xi + i=1 i=1 bij xi xi + i (3.6) i<j where b0 is the free term of a regression equation. The coefficient b1, b2, b3, b4, and b5 are linear terms. The coefficients b11, b22, b33, b44, and b55 are quadratic terms and the coefficient b12, b13, b14, b15, b23, b24, b25, b34, b35, and b45 are interaction terms. The term “ ” represents the error term (Cochran & Cox 1987). DaviesBox & Hunter (1978) have developed new designs specifically for fitting second order response surfaces called central composite rotatable designs which are constructed by adding further treatment combinations to those obtained from a 2k factorial. The total number of observations was reduced significantly by employing these designs. Each design consists of a two-level factorial matrix (2k) augmented by replicated 98 experiments at the center points and symmetrically located star points. For 2 to 4 factors, the central box was a full factorial design; for 5 or more factors it becomes a half fractional design. The center point was replicated to provide a measure of experimental error and hence in using second order rotatable designs no replication was needed in order to find the mean square error. Rotatable designs means that the standard error of the estimated response surface at any point on the fitted surface was the same for all points that are at the same distance from the center of the region. There were many experimental designs available for conducting the experiments. These include i) face centredCentral Composite Design (CCF) ii) central composite rotatable design with circumscribed/inscribed subsets (CCC/CCI) iii) Box and Hunter design (Montgomery & Peck 2005). In the present work the experiments were designed based on a central composite rotatable design with circumscribed subset having 32 and 20 experimental runs. This design was chosen as it had the following advantages 1. It is easy to locate the optimum point within the region of interest as the location of optimum point is not known before the experiment is conducted. 2. The ‘ ’ value in rotatable design is higher than that of face centered design. For example in the case of k = 3 designs, the experiment ranges will be extended by 1.68 times the original ranges defined by the experimenter. So it has extended design region beyond the defined variable bounds. Thus predicted responses at or near the axial points, which would have been extrapolations in a face centered design, will be within the design region in rotatable design. This is a very important 99 factor because the magnitude of prediction error increases geometrically with distance outside the design region. 3. Compared to face-centered CCDs, rotatable CCDs offer reduced prediction error for, and improved estimation of, quadratic curvature effects. 4. In rotatable design, second order polynomial function is used to estimate the response in terms of the machining process parameter under investigation. The polynomial function is used to estimate the response at a point on the fitted surface. These polynomial surfaces have a great advantage as they are easy to fit and the computation of response is easier. 5. The circumscribed subset is chosen as inscribing restricts the actual design region to the defined variable ranges by locating the axial points at the lower and upper bounds of the variable ranges. The inscribed design shrinks the design points such that the axial points are at ±1 values whereas the circumscribed design puts the design points equidistant from the centre. Hence the estimated precision of model coefficients is high in circumscribed design. The CCD design for five factors with five levels consists of 32 experiments. The design is subdivided into three parts. 1. One half replicates of a 25 factorial is represented by the first 16 design points which lie at the vertices of the regular polyhedral. These points are commonly identified as factorial design points. 100 2. The next 10 points (17-26) are the extra points which form a central composite design with as the radius of the sphere where the point are equi-spaced from the center. These points are termed as star points. For one half replicate, the extra point is taken to devise a central composite design. 3. The final six points (27-32) are included at the center in order to provide roughly equal precision of standard error yu with the sphere of radius . These points are termed replicated center points or axial points and have two functions. They provide (n-1) degrees of freedom for determining the experimental error, and they help to determine the precision of standard error at and near the center. More degree of freedom is offered by the replicated points at the center for calculating the experimental error and they estimate the precision of response at and near the center. The experimental errors include noise factor, environmental factor and manual factor during the measurements of values. The presence of curvature in the system is reported by the center runs. The selected design matrix for conducting experiments for surface roughness, cutting force, vibration amplitude temperature rise, and tool wear is shown in Table 3.3. 101 Table 3.3 Design matrix for conducting experiments for CNC end milling Specimen No 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Control Factors (Machining Parameters) Radial Nose Axial Cutting Cutting rake angle, radius , depth of speed, Vc feed, fz R cut,ap -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 1 1 1 -1 -1 -1 -1 -1 1 -1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 -1 1 -1 -1 -1 1 1 1 1 -1 1 1 -1 -1 1 1 1 -1 1 1 1 1 1 -2 0 0 0 0 2 0 0 0 0 0 -2 0 0 0 0 2 0 0 0 0 0 -2 0 0 0 0 2 0 0 0 0 0 -2 0 0 0 0 2 0 0 0 0 0 -2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Central composite rotatable second order response surface methodology was employed for determining the experimental run. The central composite design consists of a 2k factorial run, 2k axial or star runs and center 102 runs. These experimental designs consist of 32 experiments consisting of five machining variable with five specific levels. In this design matrix, thirty two experimental runs provide 15 estimates for studying the effect of five parameters on the responses. Out of the 15 estimates, 1 estimate is for the main effect of all the five parameters, 5 estimates for the main effects of the parameters, 6 quadratic estimates due to the main effects of the parameters and 6 estimates for the two factor interactions. The 32 experimental runs allowed the estimation of linear, quadratic and two way interactive effects of the process variables on the surface roughness, cutting force, vibration amplitude temperature rise, and tool wear for HSS end milling. Experiments were conducted at random to avoid schematic errors creeping into the experimental procedure.The selected design matrix for conducting experiments for finite element method is shown in Table 3.4. Table 3.4 Design matrix for conducting experiments for FEA Test No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Control factors Vc fz ap -1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 -1.682 0 0 1.682 0 0 0 -1.682 0 0 1.682 0 0 0 -1.682 0 0 1.682 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 103 The 20 experimental runs allowed the estimation of linear, quadratic and two way interactive effects of the process variables on response. Experiments were conducted at random to avoid schematic errors creeping into the experimental procedure. 3.5 SUMMARY The responses studied in this research are divided into seven sets of experiments, namely: experiments 1 to 5 for HSS end milling surface roughness, cutting force, vibration anmplitude,temperature rise and tool wear and experiments 6 and 7 for finite element analysis study. The CCD with circumscribed subset was chosen as it has many advantages compared to other designs. For experiments 1 to 5, five factor, five level CCD was employed where as for experiments 6 and 7 three factors, five level CCD was employed. The experimental setup consists of a HAAS vertical machining center: model tool room mill TM-1 for conducting experiments, MitutoyoSurftest SJ201 for measuring average surface roughness, Syscon instruments milling tool dynamometer for measuring cutting forces, COCO 80 FFT analyzer for measuring acceleration amplitude, Metzer tool makers microscope to measure flank tool wear and K-type thermocouple to measure the temperature rise during milling. A 2D and 3D thermo-mechanically coupled finite element model of dry 2D and 3D machining operations has been developed by using the commercial FEA software Deform-3D™.
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