C. College of. Engineering, Guntur for proving support and stimulating environment in which the term paper has been worked out. We also thank all the faculty ...
MULTI RESPONSE OPTIMIZATION USING GREY RELATIONAL ANALYSIS, TOPSIS AND PCA-TOPSIS A PROJECT REPORT Submitted in partial fulfillment of the requirements for the award of the degree of BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING BY D.SUNEEL (Y12ME831) K.SATYAKIRAN (L13ME997)
J.GEETHA (Y12ME851)
J.AMARNATH (Y12ME849)
M.JUDSON PAUL (L13ME1004)
Under the esteemed guidance of Dr. G.SRINIVAS RAO, M.E.,Ph.D Professor, Dept. of Mechanical Engineering
DEPARTMENT OF MECHANICAL ENGINEERING
R.V.R. & J.C. COLLEGE OF ENGINEERING (Autonomous) (Affiliated to Acharya Nagarjuna University) (Accredited by NBA & NAAC with ‘A’ Grade) Chandramoulipuram :: Chowdavaram
GUNTUR – 522 019, A.P
2015-16
DEPARTMENT OF MECHANICAL ENGINEERING
R.V.R & J.C.COLLEGE OF ENGINEERING (Autonomous) Chandramoulipuram : : Chowdavaram, GUNTUR – 522 019
CERTIFICATE
This is to certify that the Project Report entitled MULTI RESPONSE OPTIMIZATION USING GREY RELATIONAL ANALYSIS, TOPSIS AND PCATOPSIS that is being submitted by Mr./Ms. D.SUNEEL (Y12ME831), K.SATYAKIRAN (L13ME997), J.GEETHA (Y12ME851), J.AMARNATH (Y12ME849), M.JUDSON PAUL (L13ME1004) in partial fulfillment for the award of the Degree of Bachelor of Technology in Mechanical Engineering is a bonafide work carried out by him/her under my guidance and supervision.
Signature of Guide Dr. G.SRINIVAS RAO, M.E.,Ph.D Professor, M.E.
Signature of HOD Dr.K.RAVINDRA, Ph.D Professor & Head, M.E.
EVALUATION SHEET
1.
Title of the Project
:
MULTI RESPONSE OPTIMIZATION USING GREY RELATIONAL ANALYSIS, TOPSIS AND PCA-TOPSIS
2.
Year of submission
:
3.
Date of examination
:
4.
Student’s Name
:
APRIL-2016
D.SUNEEL
(Y12ME831)
K.SATYAKIRAN
(L13ME997)
J.GEETHA
(Y12ME851)
J.AMARNATH
(Y12MW849)
M.JUDSON PAUL (L13ME1004) Name of the guide
:
Designation
6.
Result
Dr. G.SRINIVAS RAO, M.E.,Ph.D
Professor
: Approved
: Not Approved
INTERNAL EXAMINER Name:
EXTERNAL EXAMINER Name:
ACKNOWLEDGEMENT
We take this opportunity to convey our gratitude to all those who have been kind enough to offer their advice and provide assistance when needed which has led to the successful completion of the term paper. We extend our sincere thanks to our guide G.SRINIVAS RAO, Professor, Department of Mechanical Engineering for his consistent guidance and support. We are thankful to our project in charges RAMA KOTESWARA RAO V, Assistant professor, TARACHAND V, Assistant professor, Department of Mechanical Engineering for providing support and stimulating environment in which the project has been worked out. We also wish our graceful thanks to DR. K. RAVINDRA, Professor and Head of Department of Mechanical Engineering for his help and cooperation. We are thankful to our principal DR. A. SUDHAKAR, R.V.R. &J.C. College of Engineering, Guntur for proving support and stimulating environment in which the term paper has been worked out. We also thank all the faculty members of department of mechanical engineering with whose timely help the completion of our term paper possible.
D. SUNEEL
(Y12ME831)
K. SATYAKIRAN
(L13ME997)
J. GEETHA
(Y12ME851)
J. AMARNATH
(Y12ME849)
M. JUDSON PAUL (L13ME1004)
CONTENTS TITLE
PAGE NO.
ABSTRACT
1
1. INTRODUCTION
2
1.1 INTRODUCTION
3
1.2 MATERIAL SELECTION
5
1.2.1 MATERIAL
5
1.2.2 CHEMICAL COMPOSITION
6
1.2.3 PHYSICAL PROPERTIES
6
1.2.4 MECHANICAL PROPERTIES
6
1.2.5 THERMAL PROPERTIES
7
1.2.6 APPLICATIONS
7
1.3 TURNING OPERATION
8
1.4 CUTTING SPEED, FEED RATE, DEPTH OF CUT, NOSE RADIUS AND RAKE ANGLE
9
1.5 EFFECTS OF PARAMETERS ON SURFACE ROUGHNESS
10
1.6 MULTICRITERIA DECISON MAKING
13
2. LITERATURE REVIEW 2.1 LITERATURE REVIEW
14 15
2.1.1 PARAMETERS EFFECTING SURFACE TOUGHNESS
15
2.1.2 PARAMETRIC OPTIMIZATION
20
3. PROBLEM FORMULATION
25
3.1 SCOPE
26
3.2 GAPS IN RESEARCH
27
3.3 OBJECTIVES
27
3.4 METHODOLOGY OF RESEARCH
28
4. SELECTION OF PARAMETERS AND EXPERIMENTAL EQUIPMENT
30
4.1 SELECTION OF PROCESS AND TOOL PARAMETERS
31
4.2 EQUIPMENT USED
32
4.2.1 ENGINE LATHE
32
4.2.2 DIFFERENT TOOLS USED
32
4.2.3 CARBIDE INSERTS
33
4.2.4 TALYSURF
35
5. EXPERIMENTAL DESIGN AND OPTIMIZATION TECHNIQUES 5.1 TAGUCHI EXPERIMENTAL DESIGN
36 38
5.1.1 TAGUCHI PHILOSOPHY
39
5.1.2 EXPERIMENTAL DESIGN APPROACH
40
5.1.3 LOSS FUNCTION
42
5.1.4 S/N RATIO
43
5.1.4.1 APPLICATION OF S/N RATIO
44
5.1.4.2 ADVANTAGE OF S/N RATIO OVER AVERAGE
46
5.1.4.3 EFFECT OF S/N RATIO ON ANALYSIS
47
5.1.4.4 WHEN TO USE S/N RATIO ON ANALYSIS
48
5.1.5 PROCEDURE FOR EXPERIMENTAL DESIGN AND ANALYSIS
49
5.1.5.1 SELECTION AND APPLICATION OF ORTHOGONAL ARRAYS 49 5.1.5.2 SELECTION OF INNER AND OUTER ARRAYS
52
5.1.5.3 EXPERIMENTATION AND DATA COLLECTION
52
5.1.5.4 DATA ANALYSIS
52
5.1.5.5 PARAMETER DESIGN STRATEGY 5.2 ORGANIZATION OF EXPERIMENTS
55 58
5.2.1 SELECTION OF OA AND PARAMETER ASSIGNMENT
58
5.2.2 SELECTION OF RESPONSES
60
5.2.2.1 SURFACE ROUGHNESS
60
5.2.2.2 MATERIAL REMOVAL RATE
61
5.3 MODELLING
61
5.4 MULTI-RESPONSE OPTIMIZATION
62
5.4.1 GREY RELATIONAL ANALYSIS
62
5.4.2 TECHNIQUE FOR ORDER PREFERENCE BY SIMILARITY TO IDEAL SOLUTION
64
5.4.3 PRINCIPAL COMPONENT ANALYSIS BASED TOPSIS
67
6. ANALYSIS AND RESULTS
74
6.1 SINGLE RESPONSE OPTIMIZATION
76
6.1.1 RESPONSE GRAPH METHOD
76
6.1.1.1 SURFACE ROUGHNESS
76
6.1.1.2 MATERIAL REMOVAL RATE
77
6.2 MODELLING
79
6.3 ANALYSIS OF VARIANCE
79
6.3.1 SURFACE ROUGHNESS RAW DATA
80
6.3.2 SURFACE ROUGHNESS S/N DATA
80
6.3.3 MATERIAL REMOVAL RATE S/N DATA
82
6.4 MULTIRESPONSE OPTIMIZATION
82
6.4.2 TECHNIQUE FOR ORDER PREFERENCE BY SIMILARITY TO IDEAL SOLUTION
83
6.4.3 PRINCIPAL COMPONENT ANALYSIS BASED TOPSIS 6.5 PREDICTED S/N RATIOS AT DIFFERENT OPTIMAL CONDITIONS 7. CONCLUSIONS AND RECOOMENDATIONS FOR FUTURE WORK
84 87 88
7.1 CONCLUSIONS
89
7.2 RECOMMENDATIONS FOR FUTURE WORK
91
8. REFERENCES
92
LIST OF TABLES TABLE NO. TABLE PAGE NO. 1.1 CHEMICAL COMPOSITION 6 1.2 PHYSICAL PROPERTIES 6 1.3 MECHANICAL PROPERTIES 6 1.4 THERMAL PROPERTIES 7 2.1 SUMMARY OF LITERATURE REVIEW – SURFACE ROUGHNESS 15 2.2 SUMMARY OF LITERATURE REVIEW – OPTIMIZATION 20 5.1 STANDARD ORTHOGONAL ARRAYS 50 5.2 DESIGN PARAMETERS AND THEIR LEVELS 58 5.3 THE EXPERIMENTAL LAYOUT: L18 ORTHOGONAL ARRAY 58 6.1 THE EXPERIMENTAL RESULTS: L18 ORTHOGONAL ARRAY 75 6.2 AVERAGE RESPONSE OF RAW DATA AND RANKING OF FACTOR EFFECTS 76 6.3 AVERAGE RESPONSE OF S/N DATA AND RANKING OF FACTOR EFFECTS 76 6.4 AVERAGE RESPONSE OF RAW DATA AND RANKING OF FACTOR EFFECTS 77 6.5 AVERAGE RESPONSE OF S/N DATA AND RANKING OF FACTOR EFFECTS 78 6.7 ANOVA (POOLED) 80 6.8 ANOVA (INITIAL) 80 6.9 ANOVA (POOLED) 81 6.6 ANOVA 82 6.11 VALUES FOR GREY RELATIONAL ANALYSIS 82 6.12 LEVEL AVERAGES OF GREY RELATIONAL GRADE (S/N DATA) 83 6.13 VALUES FOR TOPSIS METHOD 83 6.14 LEVEL AVERAGES FOR RELATIVE CLOSENESS (S/N DATA) 83 6.15 CORRELATION MATRIX 84 6.16 EIGEN VALUES 84 6.17 EIGEN VECTORS 84 6.18 VALUES FOR PCA-TOPSIS METHOD 86 6.20 PREDICTED S/N RATIOS AT DIFFERENT OPTIMAL CONDITIONS 87
LIST OF FIGURES FIGURE NO. DESCRIPTION PAGE NO. 1.1 ISHIKAWA CAUSE AND EFFECT (FISH BONE) DIAGRAM 5 1.2 TURNING OPERATION 8 1.3 TURNING WITH DIFFERENT RAKE ANGLE TOOLS 12 4.1 ENGINE LATHE 32 4.2 NEGATIVE RAKE ANGLE TOOL HOLDERS 33 4.3 INSERTS WITH DIFFERENT NOSE RADII 35 4.4 SET-UP FOR MEASURING SURFACE ROUGHNESS 35 5.1 LOSS FUNCTIONS 43 5.2 DISTRIBUTION OF PERFORMANCE AROUND MEAN 45 5.3 DISTRIBUTIONS FOR DATA SETS 47 5.4 TAGUCHI EXPERIMENTAL DESIGN AND ANALYSIS FLOW DIAGRAM 51 5.5 FACTOR EFFECTS ON RESPONSE 56 5.6 REPRESENTATION OF CLOSENESS TO THE ALTERNATIVE 66 5.7 REPRESENTATION OF CLOSENESS TO THE ALTERNATIVE 73 6.1 RESPONSE PLOT FOR SURFACE ROUGHNESS 77 6.2 RESPONSE PLOT FOR MATERIAL REMOVAL RATE 78 6.3 SCREE PLOT 85 6.4 VARIATION MODE CHARTS 85
ABSTRACT In the recent past hard turning of material is gaining more and more importance owing to versatility of hard material to be used as cutting tools & for many applications where high life expectancy of components demand. Hard turned material has the peculiar property to withstand high stress, fatigue resistance, excellent wear & corrosion resistance. There are many factors which affect the hard turning, i.e. Tool variables include tool material, nose radius, cutting edge geometry etc; Work piece variables include material and other mechanical properties; Cutting conditions include cutting speed, feed and depth of cut. The response to be considered for observation is cutting force, surface roughness, tool wear and material removal rate etc. In this work the cutting parameters namely process parameters such as cutting speed, feed, depth of cut and tool parameters such as nose radius, rake angle are considered as input factors to study their effects on responses surface roughness and material removal rate. The work piece material considered for this study is AISI 52100 due to its wide range of industrial applications. In this study, the experiments were carried out as per L18 orthogonal array design. This study highlights the use of Grey relational analysis (GRA), Technique for order preference by similarity to ideal solution (TOPSIS) and principal component analysis based TOPSIS (PCA-TOPSIS). Analysis of variance (ANOVA) was also used to find out the most influenced cutting parameters on the responses. From the results, it can be observed that PCA-TOPSIS is the best optimization technique compared to the remaining techniques. 1
CHAPTER 1
INTRODUCTION
2
INTRODUCTION This chapter describes the introductory to importance of hard turning and surface roughness. Effect of surface roughness on functional material AISI 52100 steel and different parameters effecting surface roughness and optimization methods for parametric optimization.
1.1 INTRODUCTION Manufacturers around the world continuously try hard for better solutions in order to be in competition for machined components. The trend is towards higher quality, lower cost and smaller batch sizes. Achievement of high quality, in terms of dimensional accuracy and surface quality along with increased production rate and saving in cost is an increasing challenge in modern machining enterprises. There is an increasing use of technology in several industrial applications, especially in automotive and bearing industries because of its advantages of higher flexibility, higher production rate, lower cost per part, and significantly less costly machine tools. However, success of this technology in the precision machining is to be able to achieve the demands of the part quality and reasonable tool life which depends on fully understanding the specific machining process and correct selection process conditions such as cutting parameters, lubrication conditions, tool geometry etc. Hard turning is a process, in which materials in the hardened state (50–60 HRC) are machined. The traditional method of machining the ferrous materials includes rough turning, heat treatment, and then finished by grinding process. Hard turning eliminates the series of operations required to produce the component and 3
thereby reducing the cycle time and hence resulting in productivity improvement. Since adequate surface roughness can be achieved by hard turning. While hard turning can achieve impressive results, however, since parts can typically be finished in a single chucking, hard turned parts often show superior concentricity and perpendicularity characteristics to their ground counterparts. The performance of hard turning is measured in terms of surface roughness, tool wear, cutting forces, and power consumed. Surface roughness is one of the most important quality measures as it influences functional properties of machined components. Surface roughness, in hard turning, has been found to be influenced by a number of factors. There are two types, factors which can be controlled and factors which cannot be controlled easily called noise factors. Controllable process parameters include feed rate, cutting speed, depth of cut, tool geometry (i.e., nose radius, rake angle etc.) and noise factors such as vibrations of tool, work piece and machine tool, tool wear, variability of work material and tool material etc. Surface roughness refers to the relatively closely spaced or fine surface irregularities mainly in the form of feed marks left by the cutting tool on the machined surface. It plays a very important role in the performance as good quality turned surface significantly improves fatigue strength, corrosion resistance and creep life. Surface roughness also affects several functional attributes such as contact causing surface friction, wearing and light reflection, heat transmission of holding and distributing lubricant, load bearing capacity and resistance to fatigue. Increased understanding of surface generation mechanisms can be used to optimize machining processes and improve component functionality.
4
The factors that are influencing surface roughness are presented through Fish-bone diagram.
Figure 1.1 Ishikawa Cause and Effect (Fish Bone) diagram
1.2 MATERIAL SELECTION: 1.2.1 MATERIAL: AISI 52100 alloy steel is known as a high carbon, chromium containing low alloy steel. Alloy steels contain different varieties of steels that exceed the composition limits of Mn, C, Mo, Si, Ni, Va, and B set for carbon steels. They are designated by AISI four-digit numbers. They respond more quickly to mechanical and heat treatments than carbon steels. Has high hardness capability and excellent deformation to wear resistance. 5
AISI 52100 alloy steel can be machined using conventional techniques. The machinability of this steel can be improved by performing spherodizing annealing process at 649°C (1200°F) before machining. In order to reduce the machining stress AISI 52100 alloy steel is heated at 816°C (1500°F) followed by quenching in oil. Before performing this process, it is subjected to normalizing heat treatment at 872°C (1600°F) followed by slow cooling
1.2.2 CHEMICAL COMPOSITION: The following table shows the chemical composition of AISI 52100 bearing steel. Table 1.1 Chemical composition Element Iron, Fe Chromium, Cr Carbon, C Manganese, Mn Silicon, Si Sulfur, S Phosphorous, P
Content (%) 96.5 - 97.32 1.30 - 1.60 0.980 - 1.10 0.250 - 0.450 0.150 - 0.300 ≤ 0.0250 ≤ 0.0250
1.2.3 PHYSICAL PROPERTIES: The physical properties of AISI 52100 alloy steel are listed in the following table.
Properties Density Melting point
Table 1.2 Physical properties Metric
Imperial
7.81 g/cm3
0.282 lb/in³
1424°C
2595°F
1.2.4 MECHANICAL PROPERTIES: The mechanical properties of AISI 52100 alloy steel are outlined in the following table. Table 1.3 Mechanical properties Properties
Metric 6
Imperial
Bulk modulus (typical for steel) Shear modulus (typical for steel)
140 GPa 80 GPa 190-210 GPa
20300 ksi 11600 ksi 2755730458 ksi
0.27-0.30
0.27-0.30
Hardness, Brinell Hardness, Knoop (converted from Rockwell C hardness) Hardness, Rockwell C (quenched in oil from 150°C tempered) Hardness, Rockwell C (quenched in water from 150°C tempered)
875
875
62
62
64
64
Hardness, Rockwell C (quenched in oil)
64
64
Hardness, Rockwell C (quenched in water) Hardness, Vickers (converted from Rockwell C hardness) Machinability (spheroidized annealed and cold drawn. Based on 100 machinability for AISI 1212 steel)
66 848
66 848
40
40
Elastic modulus Poisson's ratio
1.2.5 THERMAL PROPERTIES: The thermal properties of AISI 52100 alloy steel are given in the following table. Table 1.4 Thermal properties Properties Metric Thermal expansion co-efficient (@ 23-280°C/73.411.9 36°F, annealed) µm/m°C Thermal conductivity (typical steel)
46.6 W/mK
Imperial 6.61 µin/in°F 323 BTU in/hr.ft².°F
1.2.6 APPLICATIONS: 1. Oil hardened steel balls typically used for bearing manufacture. 2. Taps, Gauges, swaging dies, Ejector pins. It is a good quality steel for wear resisting machine parts and for press tools which do not merit a more complex quality.
7
1.3 TURNING OPERATION: In a machining process, turning plays an important role in reducing a particular work piece form the original stock to desired shape and size. In order to obtain a finished machine part by machining a blank, definite motions must be imparted to the blank and cutting tool. These motions are divided into working and auxiliary motions. These are two working motions: primary cutting motion and the feed motion. In lathe, the primary cutting motion is rotatory and it is imparted to the blank which is secured in some manner to the lathe spindle. Feed, a forward (translational or progressive) motion, is imparted to the cutting tool (single- point cutting tool in our case) which is rigidly clamped in the tool holder. The primary cutting motion enables the cutting process (chip formation) to be accomplished, while feed motion extends the cutting process (machining) to the whole surface to be machined on the work.
Figure 1.2 Turning operation 8
1.4 Cutting speed, feed, depth of cut, nose radius and rake angle: The cutting speed is travel of a point on the cutting edge relative to the surface of the cut in unit time in the process of accomplishing the primary cutting motion. The maximum value of the cutting speed is equal to V
Dn 1000
m / mm
Where, D is the maximum diameter of the surface of the cut, mm. From this formula one can find the rotational speed. n
1000 V rpm D
In longitudinal turning the cutting speed is constant during the whole cut (if the diameter of the blank is same over its full length and if the rotational speed is constant). The feed is the travel of the cutting edge in the direction of the feed motion relative to machined surface in unit time. The rate of feed may be expressed either as the distance travelled by the tool in one minute or as the feed per revolution , the distance of relative travel of the tool during one revolution of the work piece. The feed per minute is denoted by Sm in mm per minute (mm/min) while the feed per revolution is S mm per revolution (mm/rev). They are related by the equation. S
Sm mm / rev n
Where, n is the rotational speed of the work, rpm. The depth of cut is the thickness of the layer of metal removed in one cut, or pass, measured in a direction perpendicular to the machined surface. The depth of cut 9
is always perpendicular to the machined surface. The depth of cut is always perpendicular to the direction of feed motion and in external longitudinal turning, it is half the difference between the work diameters of machined surface obtained after one pass. t
Dd 2
A larger nose radius produces a smoother surface at lower feed rates and a higher cutting speed. Large nose radius tools have, along the whole cutting period, slightly better surface finish than small nose radius tools. For single point cutting tool most important angle is back rake angle. The back rake angle affects the ability of the tool to shear the work material and form the chip. It can be positive or negative. Positive rake angles reduce the cutting forces resulting in smaller deflections of the workpiece, tool holder, and machine. If the back rake angle is too large, the strength of the tool is reduced as well as its capacity to conduct heat. In machining hard work materials, the back rake angle must be small, even negative for carbide, PCBN and diamond tools. The higher the hardness, the smaller the back rake angle shall be used. The turning process is affected by process parameters, tool parameters and work piece characteristics; tool material etc. The effect of process and tool parameters is described as follows:
1.5 EFFECTS OF PARAMETERS ON SURFACE ROUGHNESS: Cutting speed: At lower speeds, the surface roughness increases because of built up edge formation, after that the speed increases, the height of built up edge is reduced and at 10
certain speed, it disappears. This leads to a corresponding reduction in surface roughness. For further increase in cutting speed, the surface roughness continues to decrease the friction between the tool and flank and the machined surface and also to the reduction in plastic formation. Feed: It may be mentioned that, rate of feed in the range of 0.12 to 0.15 mm per revolution has a negligible effect on the surface which increases sharply upon a further increase in feed, If the nose radius value is not equal to zero. Surface roughness
f2 r 0 8r
1
The formula for the micro irregularities is Surface roughness
f cot 1 cot 2
2
Where, „f‟ is the feed, α1= plane approach angle, α2 = end cutting edge angle. According to the above formula, the surface roughness decreases with increase in the nose radius. There is a maximum limit of nose radius beyond which further increases do not necessarily improve the surface finish. The nose radius must be sufficiently large so that feed marks of the tool on the work piece can be avoided. Surface finish improves with increased nose radius due to the reduction in the sawtooth effect of the ridges. The equation (2) can be used if the nose radius is zero. If the nose radius is zero the plane approach angle α1 plays a major role in determining the surface roughness value. Depth of cut: 11
Variation of depth of cut has the minor effect on the micro geometry of machined surface. Nose radius: Surface roughness greatly depends on the nose radius. The effect of nose radius can be combined with feed (as it is also one of the major factor) and the surface roughness is given by SR
f2 8 r
Rake angle: Positive: chip formation occurs by mode I fracture (crack opening) ahead of the cutting tool. This causes the chips to bend upwards along the tool rake. Eventually, the bending force generates a fracture and the chip is separated from the work piece. Negative: chips form by buckling of the fibres under compressive load applied by the cutting edge, which can result in micro cracking and poor surface finish.
Figure 1.3 Turning with different rake angle tools
12
1.6 MULTI CRITERIA DECISION MAKING: Multiple criteria decision making (MCDM) refers to making decisions in the presence of multiple, usually conflicting, criteria. Although MCDM problems are widespread all the time, MCDM as a discipline only has a relatively short history of about 30 years. The Multi criterion Decision-Making (MCDM) are gaining importance as potential tools for analyzing complex real problems due to their inherent ability to judge different alternatives (Choice, strategy, policy, scenario can also be used synonymously) on various criteria for possible selection of the best/suitable alternative (s). These alternatives may be further explored in-depth for their final implementation. Engineering judgement has up until now being used primarily to optimize the multi-response problem. Unfortunately, an engineer‟s judgement increases the uncertainty during the decision making process. One approach to solve this problem entails assigning weight for each response. The weighted sum model (WSM) is the earliest and probably the most widely used method. The weighted product model (WPM) can be considered as a modification of the WSM, and has been proposed in order to overcome some of its weakness. The analytic hierarchy process (AHP), as proposed by Saaty is a later development and it has recently become popular. Recently modification to the AHP is considered to be more consistent than the original approach. Some other widely used methods are ELECTRE, Goal Programming, Grey Relational Analysis, PROMETHEE, VIKOR, TOPSIS, Fuzzy based MCDM methods etc.
13
CHAPTER 2
LITERATURE REVIEW
14
LITERATURE REVIEW Literature review relevant to the present study has been divided into two parts. First part contains a comprehensive review of the existing literature on AISI 52100 steel and parameters that effect the surface roughness. In the second part, literature review concerning the Multi-Objective optimization techniques for parametric optimization.
2.1 LITERATURE REVIEW Numerous investigations have been done by the researchers reflecting the effect of Cutting speed, feed rate, depth of cut and nose radius and rake angle on the surface roughness, material removal rate and their combinations in hard turning and parametric optimization using different MCDM techniques and summary of their work is illustrated below and tabulated in the following subsections categorize, their research conclusions in the same field.
2.1.1 PARAMETERS AFFECTING SURFACE ROUGHNESS Table 2.1 Summary of literature review-Surface Roughness
Author/Year
Design/Modell ing Technique
Work piece/Tool material
Parameters under investigation
Thiele J.D, Melkote S.N. (1999)
Full factorial design/ ANOVA
AISI 52100 steel /CBN
Noordin M.Y, Venkatesh V.C, Sharif S, Elting S, Abdullah A. (2004) Chou Y.K, Song H.
Response surface methodology, ANOVA
AISI 1045 steel bars / coated carbide
Edge Reparation: 22.86hone, 93.98hone, 121. 92 hone, 25.4 Chamfer (µm) Work piece hardness (HRC): 41, 47, 57 Feed rate (mm/rev): 0.05, 0.10, 0.15 Cutting speed(m/min): 240-375 Feed (mm/rev): 0.18- 0.28 Side cutting edge angle : -5º - 0º
Not defined
AISI 52100/ Alumina, titanium -
Nose radius (mm): 0.8, 1.6, 2.4. Cutting speed (m/sec): 2-3
15
(2004)
Yusuf Sahin A, Riza Motorcu. (2005)
Grzesik W, Wanat T, (2006)
Central composite design/ Response surface methodology, ANOVA Not defined
-carbide composite (70% Al2O3 and 30% TiC) AISI 1040 steel / coated carbide
AISI 5140 (DIN41Cr4)/ conventional and wiper ceramic insert
Feed rate (mm/rev) :0.05–0.6 Depth of cut (mm) :0.2 Flank Wear (mm): 0–0.2. Cutting speed (m/min): 181, 208, 240, 276, 317 Feed rate (mm/rev): 0.1, 0.13, 0.15, 0.18, 0.21 Depth of cut (mm): 0.36, 0.43, 0.5, 0.58, 0.66 Turning with conventional tools Feed (mm/rev): 0.04–0.4 Depth of cut (mm): 0.25 Cutting speed (m/min): 100 Nose radius (mm): 0.8 Turning with wiper tools Feed (mm/rev): 0.1–0.8 Depth of cut (mm): 0.25 Cutting speed (m/min): 100 Cutting speed (m/min): 135, 185, 240 Feed rate (mm/rev): 0.04, 0.05,0.063 Depth of cut (mm): 1.00, 1.50 Cutting speed (m/min): 100, 150, 200 Feed (mm/rev): 0.10,0.20, 0.32 Effective rake angle: 6°, 16°, 26° Nose radius (mm): 0.4, 0.8, 1.2 Cutting speed (m/min): 55, 74, 93 Feed rate (mm/rev): 0.04, 0.08,0.12 Depth of cut (mm): 0.1, 0.15, 0.2
Thamizhmanii S, Saparudin S, Hasan S. (2007)
L18 orthogonal array design/ Taguchi method, ANOVA
SCM 440 alloy steel / coated ceramic
Singh D, Rao P.V. (2007)
Full factorial design /Response Surface Methodology. ANOVA Response Surface Methodology (RSM) ANOVA
AISI 52100 / Mixed ceramic inserts
L27 orthogonal array design/ Second order model, ANOVA
Alpha-beta titanium alloy (Grade 5) / CVD–(TiNTiCNAl2O3- TiN) coated carbide Cold-work tool steel AISI P20/ carbides Inserts
Cutting speed (m/min): 40, 60, 80 Feed rate (mm/rev): 0.13, 0.179, 0.22 Depth of cut (mm): 0.50, 0.75, 1.00
4140 steel / HSS
Cutting speed (m/min): 16, 47, 92, 137, 167 Feed rate (mm/rev): 0.032, 0.1, 0.2, 0.3, 0.368 Depth of cut (mm): 0.160, 0.5, 1, 1.5, 1.84 Cutting speed (m/min): 5 , 10, 15 Feed rate (mm/rev): 0.1, 0.2, 0.3 Cutting environment: MQL (1), Comp. air (2), Dry (3)
Lalwani D.L, Mehta N.K, Jain P.K. (2008) Ramesh S, KarunamoorthL, Palanikumar K. (2008) Cakir M.C, Ensarioglu C, Demirayak I. (2009)
Kahraman F. (2009)
Erol Kilickap, Mesut, Huseyinoglu, Ahmet, Yardimeden. (2010) Chinnasamy
One factor at a time (OFAT)/ Linear Model, Second Order Model, Power Model Central composite design/Response Surface Methodology (RSM) Box-Behnken design / Response Surface Methodology (RSM), ANOVA Full factorial
MDN250 steel /Ceramics
AISI 1045/ TiN coated HSS drills
Brass C26000
16
Cutting speed (m/min): 120, 160, 200 Feed rate (mm/rev): 0.12, 0.18, 0.22. Cutting depth (mm): 1, 1.5, 2
Cutting speed (rpm): 2500, 3250,
Natarajan , Muthu. S, Karuppuswamy. P. (2011) Gaurav Bartarya, S.K.Choudhury. (2012)
design/Artificial Neural Networks (ANN)
metal/CNMG 120408 insert
3500 Feed rate (mm/rev): 0.05, 0.12, 0.15 Depth of cut (mm): 0.2, 0.3, 0.4
Full factorial design/ Second order models, ANOVA
EN31bearing steel (60±2 HRc)/ CBN insert
Srinivas Rao G, Suneel D, Manikanta K.G.S.V, Praveen D. (2016)
Central composite facecentred design/ Second order model
AISI52100 steel/ Carbide inserts
Cutting speed (m/min): 167, 204, 261 Feed rate (mm/rev): 0.075, 0.113, 0.15 Depth of cut (mm) 0.1, 0.15, 0.2 Cutting speed (m/min): 60, 75, 90 Feed rate (mm/rev): 0.052, 0.078, 0.104 Depth of cut (mm): 0.2, 0.4, 0.6 Nose radius (mm) : 0.4 ,0.8, 1.2 Rake angle: 0º,6º,12º
Thiele et al. (1999) revealed that increasing the edge hone radius tends to increase the surface roughness and the effect of edge hone on the surface roughness decreases with the increase of workpiece (AISI 52100 steel) hardness. Noordin et al. (2004) revealed that feed has most significant effect and side cutting edge angle and it‟s interaction provides secondary contribution to surface roughness and tangential force while turning AISI 1045 steel. Chou et al. (2004) presented that large tool nose radii have only the advantage of finer surface finish yet tool wear is comparable and specific cutting energy is slightly higher and also concluded that large and small nose radius tools generate shallower and deeper white layers respectively. Sahin et al. (2005) observed that, in turning AISI 1040 steel feed rate is main influencing factor on surface roughnes and surface roughness increases with the increase of feed rate but decreases with the increase of cutting speed and depth of cut respectively, also first order effect of depth of cut on surface roughness is insignificant.
17
Grzesik et al. (2006) concluded that finish hard turning with wiper inserts provides comparable surface roughness to the effects obtained at lower feed rate during conventional operations. And surfaces generated with lower feeds have better bearing properties. Thamizhmanii et al. (2007) revealed that depth of cut of 1 to 1.5 can be used for lower surface roughness. Singh et al. (2007) investigated and presented that parameters cutting speed, feed rate, effective rake angle and nose radius are the primary influencing factors affecting surface roughness. Developed models indicates that feed rate is the dominating factor affecting surface roughness followed by nose radius, cutting speed and effective rake angle. Lalwani et al. (2008) presented that cutting speed has no significant effect on surface roughness while feed rate provides primary contribution and interaction between feed arte and depth of cut, quadratic effect of feed rate and interaction effect of speed and depth of cut have secondary effect. Ramesh et al. (2008) concludes that feed rate is the most influencing factor and depth of cut is the least significant factor on surface roughness while machining titanium alloy. Cakir et al. (2009) concludes that higher feed rates leads to higher surface roughness whereas cutting speed has contrary effect and cutting depth has no significant effect on AISI P20 tool steel. Positive effect for higher cutting speed is noticed using CVD coated insert but surface roughness values obtained when employed PVD coated insert is lower.
18
Kahraman (2009) observed that feed rate and cutting speed have significant effect on surface roughness in machining AISI 4140 steel and the developed model did not have high predictive power as the predicted surface roughness values have average absolute error of 3.18%. Kilicka et al. (2010) concluded that from RSM model and optimization results, that predicted and measured values are quite close indicating model can be effectively used for prediction of surface roughness and to select level of drilling parameters for AISI 1045 steel. Natarajan et al. (2011) observed that feed rate is the most influencing factor on surface roughness followed by spindle speed and depth of cut while turning brass C26000 non-ferrous material. Increase in feed rate causes the surface roughness to increase and then decrease. For lower depth of cut, as feed rate increases, surface roughness decreases and then increases. Bartarya et al. (2012) concluded that depth was the most influential parameter affecting three cutting forces followed by feed and the most efficient cut can be achieved for relatively lower and moderate cutting speeds with moderate depth of cut in the range of 0.1-0.2 for nearly all feed values in the range of 0.075-0.15. Srinivas Rao et al. (2016) reflected that the factors depth of cut and rake angle have no significant effect on surface roughness, but its interaction with cutting speed, feed rate and nose radius has significant effect on surface roughness.
19
2.1.2 PARAMETRIC OPTIMIZATION Table 2.2 Summary of literature review-Optimization
Author/Year
Design/Optimi zation Technique
Responses
Parameters under investigation
Nihat Tosun. (2006)
L9 Orthogonal array design/ Grey relational analysis
Surface Roughness (µm), Burr height (mm)
Ramakrishnan.R Karunamoorthy. (2008)
L9 Orthogonal array design / Multi-Response Signal to Noise (MRSN) ratio L18 , L16 Orthogonal array designs/Weighted Principal Components (WPC) method
Mean Material removal rate (mm2/min), Mean Surface Roughness (µm) For L18 design Kerf, Material removal rate (mm3/min) For L16 design Surface Roughness, Material Removal Rate (mm3/min), Wire Wear Ratio
L9 Orthogonal array design/ Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) L9 Orthogonal array design/ Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)
Surface Roughness (µm), Tool wear (mm-2), Material Removal Rate (mm3/min)
Cutting speed(m/min): 150, 200, 250 Feed rate (mm/rev): 0.02, 0.06, 0.1 Cutting depth (mm): 0.5, 1,1.5 Tool nose run off (mm): 0.1, ±0.3, 0.1
Process time (s), Relative Tool Wear ratio, Process Energy (W), Concentration of aerosol (mg/m3), Dielectric consumption (cm3) For Full factorial design Surface Roughness (µm), Tool wear rate(mg/min), Material Removal Rate (mg/min) For Modified L18 design
Peak current (A): 2, 4.5, 7 Pulse duration (µs): 2, 261, 520 Dielectric level (mm): 40, 60, 80 Flushing pressure (kg/cm2): 0.3, 0.5, 0.7
Susanta Kumar Gauri, Shankar Chakraborty. (2009)
Tian- Syung Lan (2009)
Sivapirakasam S. P, Jose Mathew , Surianarayanan. M. (2011)
Susanta Kumar Gauri, Rina Chakravorty, Shankar Chakraborty. (2011)
Full factorial design, modified L18 Orthogonal array design/ Weighted principal components WPC, PCA based GRA method, PCA-TOPSIS.
20
Drill type: HSS, TiN, Carbide Cutting speed (rpm): 450, 1120, 1800 Feed rate(mm/rev):0.1, 0.2, 0.3 Point angle: 90º, 118º, 130º Pulse on time (µs): 0.6, 0.8, 1.2 Delay time (µs): 4, 6, 8 Wire feed speed (m/min): 8,12, 15 Ignition current (A) : 8, 12 ,16 For L18 design Open circuit voltage, Pulse duration, Wire speed, Flushing pressure For L16 design Pulse on time, Wire tension, Delay time, Wire feed speed, Ignition current intensity
For Full factorial design Tool material: TI, HCS Grit size: 220, 320, 500 Power rating (W): 100, 200, 300, 400 For Modified L18 design Tool material: HCS, HSS. Titanium, Ti alloy, Cemented carbide Abrasive type: Alumina, Sic, Boron
Tool wear rate(mg/min), Material Removal Rate (mg/min) Anish Nair, Govindan.P, Ganesan.H. (2014)
Sagar P. Bhise, Pantanwan.P.D, Rajiv B. (2014)
Ravi Pratap Singh, Jatinder Kumar, Ravinder Kataria, Sandeep Singhal (2015) KumarAbhishek, Saurav Datta , Siba Sankar Mahapatra. (2016)
Ramesh.S, Viswanathan.R, Ambika.S. (2016)
L25 Orthogonal array design / PCA, PCA utility Theory, PCA based GRA method, PCATOPSIS. L18 Orthogonal array design/Process Capability based Technique for Order Preference by Similarity to Ideal Solution (PCR-TOPSIS) Full factorial design/ Graph theory , Matrix method
Surface Roughness(µm) :Ra,Rz,Rq, Material Removal Rate (mm3/min)
carbide Grit size: 220, 320, 500 Power rating (W): 100, 200, 300, 400 Slurry concentration(%): 20, 25, 30 Cutting speed (rpm):3000, 3500, 4000, 4500, 5000 Feed (mm): 550, 600, 650, 700, 750 Depth of cut (mm) 0.1, 0.2, 0.3, 0.4, 0.5
Surface Roughness(µm), Cylindricity(µm), Machining time(min).
Cutting tool material: Coated carbide tool, CBN tool Cutting speed (m/min) 50, 55, 60 Feed rate (mm/min) 5, 10,15 Depth of cut (mm) 0.05, 0.1, 0.15
Surface Roughness (µm), Tool wear rate(mg/min), Material Removal Rate (mg/min)
Tool material: TI, HCS Grit size: 220, 320, 500 Power rating (W): 100, 200, 300, 400
L16 orthogonal array design/Fuzzy based Genetic Algorithm, Fuzzy based Harmonic search, Taguchi method L27 orthogonal array design/ Grey Relational Analysis, TOPSIS
Thrust (KN), Torque (KN-mm), Delamination factor- Fd(in), Fd(out)
Cutting speed (rpm) 1000, 1400, 1800, 2200 Feed rate (mm/min) 200, 250, 300, 350. Cutting depth (mm) 5, 6, 8, 10
Surface Roughness(µm), Tool flank wear(mm)
Cutting speed (m/min) 40, 80, 120 Feed rate (mm/rev) 0.1, 0.15, 0.2 Depth of cut (mm) 0.50, 0.75, 1.00
Tosun (2006) determined the optimal drilling parameters for the multi-performance characteristics (surface roughness and burr height) in drilling process using grey relational analysis. Ramakrishnan et al. (2008) concluded that MRSN ratio with Taguchi‟s parameter design is a simple, systematic, reliable and more efficient tool for optimizing multiple 21
performance characteristics of WEDM process parameters and concurrent optimal machining parameters for MRR and surface roughness were studied by assigning different weight factor and identified that the pulse on time, delay time and ignition current were influenced more than wire feed speed on the performance characteristics but wire feed speed played a very significant role for allocating equal importance to both responses. Gauri et al. (2009) effectively optimized multiple responses of a WEDM process using the weighted principal component (WPC) analysis method for this two sets of past experimental data on WEDM processes are analysed as two separate case studies and results showed that the optimal conditions derived based on the WPC method offered significant improvement in overall quality level and also there is no need for any input from the engineer(s) during analysis of the experimental data in the WPC method. Tian- Syung Lan (2009) proposed optimization approach using orthogonal array and TOPSIS for parametric optimization though it is a hard solving matter because of interactions between parameters. Sivapirakasam et al. (2011) proposed a combination of Taguchi method and TOPSIS to solve multi-response parameters in green electrical discharge machining and illustrated that the method was efficient and effective for multi-attribute decision making problems in green manufacturing. Gauri et al. (2011) compared three methods WPC, PCA-based GRA, PCA-TOPSIS for optimization of multiple correlated responses of USM process and found that WPC and PCA-based TOPSIS methods results in better optimization performance
22
than PCA-based GRA method and concluded that WPC is preferable because of its simpler computational procedure. Nair et al. (2014) optimized multi-responses (Ra, Rz, Rq, MRR) using PCA, PCA combined with utility theory, PCA combined with grey relational analysis, PCA combined with TOPSIS techniques and concluded that PCA combined with utility theory, PCA combined with grey relational analysis, PCA combined with TOPSIS gave best results. Sagar et al. (2014) optimized responses surface roughness, cylindricity, machining time using PCR-TOPSIS method and the optimal parameter set obtained was cross validated by grey relational analysis and found that values are in well agreement with each other. Pratap et al. (2015) proposed graph theory and matrix method based methodology and validated for machinability evaluation of titanium work material in ultrasonic machining and suggested that, graph theory and matrix method based approaches can be utilized for any machining problem related to optimization of multiple, correlated responses of interest. Abhishek et al. (2016) proposed fuzzy-embedded Harmonic Search algorithm for optimization of multiple performance characteristics, the Fuzzy Interference system (FIS) is adopted to convert multi-responses into single response and effectiveness fuzzy-embedded HS algorithm is compared with GA and Taguchi‟s optimization philosophy and concluded that fuzzy-embedded HS algorithm can fruitfully be applied to any production process for offline quality control for the process performance yields.
23
Ramesh et al. (2016) optimized multi-responses using grey relational analysis and TOPSIS methods and found that results of Fuzzy TOPSIS are in agreement with grey relational analysis.
24
CHAPTER 3
PROBLEM FORMULATION
25
PROBLEM FORMULATION After reviewing the literature critically, the scope of the problem and the objectives of the study have been formulated. The present investigation mainly focussed on parametric optimization.
3.1 SCOPE For the AISI 52100 bearing steel under investigation from the literature most of the works concentrated only on process parameters cutting speed, feed rate, depth of cut, less number works have been reported the effect of tool parameters independently. Investigation on the effect both process and tool parameters had not been studied. Cutting tool parameters also shows significant effect on desired responses. From orthogonal array designs we cannot model response surfaces as of in other designs. So, we have to continue with main effects model but the main effects models will not be able to predict the exact responses as coefficient of multiple determination (R-squared) will not be 100% all the time. As it is the case we can determine only the optimum levels of the parameters under investigation. In order to find optimum levels many techniques have been proposed but assigning weights to the responses is still engineer‟s choice where the results may vary and one cannot be able to obtain true optimum. In most of the studies correlation between the desired responses is not considered which ultimately leads to poor results. Even though some investigations were carried out to transform correlated data to uncorrelated they did not perform any hypothesis test to confirm that whether the correlation is significant or not, whether to 26
go through complex calculations to un-correlate the responses or to simply choose a method which is mathematically less sound and gives best results.
3.2 GAPS IN RESEARCH On the thorough scrutiny of the published work on the surface roughness and parametric optimization, the following observations have been made: There is very few information available in the direction of effect of both the process and tool parameters on surface roughness. There are conflicting opinions from various researchers regarding the effect of some of the variables on the response parameters. Literature lacks in furnishing the consistent and sufficient theory on correlation of the responses. Sufficient efforts have not been undertaken in the direction of optimization of correlated responses.
3.3 OBJECTIVES In light of above mentioned gaps, present investigation aims to develop following objectives. To identify the parameters that significantly effects the responses surface roughness and material removal rate. To study the correlation between the responses. To perform hypothesis test regarding transformation of correlated responses. ANOVA for experimental data and results. To find percentage of contribution of each parameter.
27
To find optimum levels for parameters after analyzing the results of optimization techniques used.
3.4 METHODOLOGY OF RESEARCH The proposed research work was aimed to investigate the effect of process and tool parameters on the surface roughness and material removal rate. The work comprises of following phases: Commercially available AISI 52100 bearing steel is selected for study. Carbide inserts (SNMG 1204A TN2000) with different nose radius are used and different rake angle tools that specially designed as per requirement are made by PLUTO tools Inc. are used. Taguchi orthogonal inner array design is employed for the current study. Engine lathe is used to perform experimentation as of design matrix. Work-pieces of 300mm length and 65mm diameter were considered for experimentation. These bars were centred and cleaned by removing a 2mm depth of cut from the outside surface prior to actual machining process Grooves of 5mm length and 5mm depth for every 15mm length are made on the material under investigation. Projected material of 15mm length is subjected to experimentation as per design matrix. Each trail is replicated thrice.
28
Surface roughness of every projected part is measured thrice at different locations on the circumference of each and the average of the three is taken into consideration. From regression analysis main effects model and power models for responses are developed. ANOVA-initial, pooled was calculated and % contribution of factors is calculated. Pooled ANOVA has been done using pooling up technique Parametric optimization is carried out using grey relational analysis, technique for order preference by similarity to ideal solution, principal component analysis based technique for order preference and similarity to ideal solution methods and optimal parameters are obtained. Comparison of these three optimization techniques has been done and the real optimal parameter setting was found.
29
CHAPTER 4
SELECTION OF PARAMETERS AND EXPERIMENTAL EQUIPMENT
30
SELECTION OF PARAMETERS AND EXPERIMENTAL EQUIPMENT This chapter contains description of selection of process and tool parameters, experimental equipment used.
4.1 SELECTION OF PROCESS AND TOOL PARAMETERS After going through literature and Ishikawa diagram, we came to conclusion that not only process parameters such as cutting speed, feed rate, depth of cut etc., effecting the surface roughness but also tool parameters are showing significant effect on surface roughness. But only a handful of research has taken place on tool parameters. Although some authors quoted tool parameters no work has been done in the combination of both process and tool parameters. In this regard to find which tool parameters are more influential, we have conducted a pilot study and measured the responses for different parameters and after thorough examination and having brainstorming session, keeping in mind the cost of material and experiments number we came to conclusion, that to limit our work to two tool parameters. Finally, for current study three process parameters cutting speed, feed rate, depth of cut and two tool parameters nose radius, rake angle are considered. The cutting speed is taken in the range of 60m/min-90m/min and feed rate 0.052mm0.104mm, depth of cut 0.2mm-0.6mm, nose radius 4mm-12mm, effective rake angle (back rake angle) 0º-12º.
31
4.2 EQUIPMENT USED 4.2.1 ENGINE LATHE TMX-230 Engine lathe which is electric power driven is used for hard turning process and is shown in fig.
Figure 4.1 Engine lathe
4.2.2 DIFFERENT TOOLS USED ISO Designation the tool holder was PSBNR 2525M12, Back rake angle -6, Side rake angle Relief angle
-6, 6.
We have considered three different rake angle tools which we had specially ordered for our requirement from PLUTO TOOLS Inc. These three different tools are with varying back rake angle 0°, 6° and 12°.
32
Figure 4.2 Negative rake angle tool holders
4.2.3 CARBIDE INSERTS In this investigation, carbide inserts with different geometry were used. ISO designation of the carbide inserts, which were used in the experiments, was as under: SNMG 120404 TN2000 SNMG 120408 TN2000 SNMG 120412 TN2000 Where, S - Insert shape N - Insert clearance angle M - Tolerance class G - Insert features In 120404, 12 - Size 33
04 - Thickness (3/16 inches) 04 - Corner radius (1/64 inches) 08 - Corner radius (1/32 inches) 12 - Corner radius (3/64 inches) In TN2000, T - Type of operation (turning) N - Type of material (non-ferrous) 20 - Application area (medium machining) 00 - Version GRADE TN2000:- Coated carbide MT-CVD/CVD–TiN–TiCN–Al2O3–TiN. CVD– coated cobalt–enriched substrate has required bulk toughness added with multi–layer MTCVD coating that provides the wear resistance and crater resistance required in steel machining TN2000 is an optimum grade and the first choice in medium machining of steel. TN2000 provides required chip impact resistance to give larger tool life.
34
Figure 4.3 inserts with different nose radii
4.2.4 TALYSURF The root mean square value of the surface roughness of the turned surface was measured by surftest 211 (MITUTOYO, JAPAN made) with a cutoff length 8mm.
Figure 4.4 Set-up for measuring surface roughness
35
CHAPTER 5
EXPERIMENTATION DESIGN AND OPTIMIZATION TECHNIQUES
36
EXPERIMENTATION DESIGN AND OPTIMIZATION TECHNIQUES This chapter gives a brief description of Taguchi experimental design procedure with an introduction to Taguchi OA experimentation and techniques used for optimization of process and tool parameters. A properly planned and executed experiment is of utmost importance for deriving clear and accurate conclusions from the experimental observations. Design of experiments is considered to be a very useful strategy for accomplishing these tasks. The technique of defining and investigating all possible conditions in an experiment involving multiple factors is known as the design of experiments (DOE). This technique is also referred to as factorial design. In general, it establishes the methods for drawing inferences from observations when these are not exact but subject to variation. Secondly, it specifies appropriate methods for collection of the experimental data. Furthermore, the techniques for proper interpretation of results are devised. The application of experimental design techniques early in process development can result in (Montgomery, 2015)
Improved process yields.
Reduced variability and closer conformance to nominal or target requirements
Reduced development times.
Reduced overall costs.
37
Since then, several innovations have been introduced to extract maximum possible usage from the concept such as full factorial, fractional factorial designs, Response Surface methodology, Taguchi method etc.
5.1 TAGUCHI EXPERIMENTAL DESIGN In the traditional one-factor-at-a-time approach, only one factor at a time is evaluated keeping remaining factors constant during a test run. This type of experimentation reveals the effect of the chosen factors on the response under certain set of conditions. The major disadvantage of this approach is that it does not show what would happen if the other factors are also changing simultaneously. This method does not allow studying the effect of the interaction between the factors on the response characteristic. The interaction is the failure of one factor to produce the same effect on the response at different levels of another factor (Montgomery, 2015). On the other hand, full-factorial designs require experimental data for all the possible combinations of the factors involved in the study; consequently a very large number of trials need to be performed. Therefore, in the case of experiments involving relatively more number of factors, only a small fraction of combinations of factors are selected that produces most of the information to reduce experimental effort. This approach is called fractional-factorial design of experiment. The analysis of results in this approach is complex due to non-availability of generally accepted guidelines for both design of experiments and analysis of results. The Taguchi method provides a solution to this problem and is used in present investigation.
38
5.1.1 TAGUCHI’S PHILOSOPHY Taguchi‟s comprehensive system of quality engineering is one of the great engineering achievements of the 20
th
century. His methods focus on the effective
application to engineering strategies rather than advanced statistical techniques. It includes both upstream and shop-floor quality engineering. Upstream methods efficiently use small-scale experiments to reduce variability and remain cost-effective, and robust designs for large-scale production and marketplace. Shop-floor techniques provide cost-based, real time methods for monitoring and maintaining quality in production. Taguchi‟s quality philosophy in a nutshell (Khosrow, 1989).
n important dimension of quality of a manufactured product is the total loss generated by that product to society.
In a competitive economy, continuous quality improvement and cost reduction are necessary for staying in business.
A continuous quality improvement program includes incessant reduction in the variation of product performance characteristic about their target values.
A customer‟s loss due to a product‟s performance variation is often approximately proportional
to
square
of
deviation
of
performance
characteristic from its target value.
The final quality and cost of a manufactured product are determined to a large extent by engineering designs of the product (or process) parameters on the performance characteristics.
Statistically planned experiments can be used to identify the settings of product (and process) parameters that reduce performance variation. 39
Taguchi‟s proposes an “off-line” strategy for quality improvement as an alternative to an attempt to inspect quality into a product on the production line. He observes that poor quality cannot be improved by the process of inspection, screening and salvaging. No amount of inspection can put quality back into the product. Taguchi recommends a three-stage process: system design, parameter design and tolerance design. In the present work Taguchi‟s parameter design approach is used to study the effect of process and tool parameters on the surface roughness and material removal rate of AISI 52100 steel.
5.1.2 EXPERIMENTAL DESIGN APPROACH Taguchi recommends orthogonal arrays (OA) for conducting experiments. These OA‟s are generalized Graeco-Latin squares. To design an experiment one should select the most suitable OA. When the problem is only to study the main factors, the factors can be assigned in any order to each column of the OA. When we have main factors and some interactions to be studied, we have facilitated to tools to assignment of factors and interactions to columns of Orthogonal arrays (Krishnaiah, 2012). 1. Interaction tables. 2. Linear graphs. Present investigation is limited to main factors. In the Taguchi method the results of the experiments are analyzed to achieve one or more of the following objectives (Ross, 1988): To estimate the best or the optimum condition for a product or process. 40
To estimate the contribution of individual parameters and interactions. To estimate the response under the optimum condition. The optimum condition is identified by studying the main effects of each of the parameters. The effects indicate the general trend of influence of each parameter. The knowledge of contribution of individual parameters is a key in deciding the nature of control to be established on a production process. The analysis of variance (ANOVA) is the statistical treatment most commonly applied to the results of the experiments in determining the present contribution of each parameter against a stated level of confidence. Study of ANOVA table for a given analysis helps to determine which of the parameters need control (Ross, 1988). Taguchi suggests two different rules to carry out the complete analysis of the experiments (Roy, 2010). First, the standard approaches, where the results of a single run are the average of the repetitive runs are processed through main effect and ANOVA (Raw data analysis). In the second approach which Taguchi strongly recommends for multiple runs is to use S/N ratio for the same steps in the analysis. The S/N ratio is a concurrent quality metric linked to the loss function. By maximizing the S/N ratio, the loss associated can be minimized. The S/N ratio determines the most robust set of operating conditions from variation within the results. The S/N ratio is treated as response parameter (transform of raw data) of the experiment. Taguchi recommends the use of outer OA to force the noise variation into the experiment i.e., the noise is intentionally introduced into the experiment (Ross, 1988). Generally, processes are subjected to many noise factors that in combination strongly influence the variation of the response. For extremely “noisy” systems. It is not 41
generally necessary to identify controllable parameters and analyze them using an appropriate S/N ratio (Roy, 2010). In the present investigation, both the analysis: the raw data analysis and S/N data analysis have been performed. The effects of the selected process and tool parameters on the quality characteristic surface roughness and material removal rate have been investigated through the plots of the main effects based on raw data. The optimum condition for each of the quality characteristics have been established through S/N data analysis. No outer array has been used.
5.1.3 LOSS FUNCTION The quality of a product is defined as the loss imparted by the product to society from the time the product is shipped to the customer. The loss may be due to failure, repair, variation in performance, noise etc. The loss is mainly due to functional variation/process variation. Taguchi quantified this loss through a quality loss function. The quality characteristic is the object of interest of a product or process. Generally, the quality characteristic will have target. There are three types of targets (Besterfield et al., 1999). Nominal-the best: When we have a characteristic with bi-lateral tolerance, the nominal value is the target. That is, if all parts are made to this value, the variation will be zero and it is the best. L y k y m
2
Where, y value of the quality characteristic L y loss in rupees per product
42
m target value of y k proportional constant
Smaller-the better: It is a non-negative measurable characteristic having an ideal target as zero. Larger-the better: It is also a non- negative measurable characteristic that has an ideal target as infinity. For each quality characteristic, there exist some function which uniquely defines the relation between economic loss and the deviation of the quality characteristic from its target. Taguchi defined this relation as a quadratic function termed Quality Loss Function (QLF).
Figure 5.1 Loss functions
5.1.4 S/N RATIO For more experiments, trial runs are easily and inexpensively repeated. For others, repetitions of tests are expensive as well as time consuming. Whenever possible, trials should be repeated, particularly if strong noise factors are present .Repetition offers several advantages. First, the additional trial data confirm the original data points. Second, if noise factors vary during the day, then repeating trials through the day may reveal their influence. Third, additional data can be analysed for variance around a target value. 43
When the cost of repetitive trials is low, repetition is highly desirable. When the cost is high or interference with the operation is high, then the number of repetitions should be determined by means of an expected payoff for the added cost. The payoff can be the development of a more robust production procedure or process, or by the introduction of production process that greatly reduces product variance. Repetition permits determination of variance index called signal-to-noise ratio (S/N) ratio. The greater this value, the smaller the product variance around the target value. The basic definition of S/N ratio is – to capture variability; all conditions of a planned experiment are repeated such that they have multiple results. A common approach to analyse such results is to use the average of the trial results for the optimum condition. Unfortunately, average alone does not capture complete information about the variability present (Roy, 2010).
5.1.4.1 APPLICATION OF S/N RATIO The change in quality characteristics of a product under investigation in response to a factor introduced in the experimental design is the “signal” of the desired effect. However, when an experiment is conducted, there are numerous external and internal factors assigned into the experiment that influence the outcome. These uncontrollable factors are called the noise factors, and their effect on the outcome of the quality characteristic under test is termed “noise”. The S/N ratio measures the sensitivity of the quality characteristic being investigated in a controlled manner to those influencing factors (noise factors) not under control. Taguchi effectively applied this concept to establish the optimum condition from the 44
experiments. The aim of any experiment is always to determine the highest possible S/N ratio for the result. A high value of S/N ratio implies that the signal is much higher than the random effects of the noise factors. Product design or process operation consistent with highest S/N always yields the optimum quality with minimum variance. From quality point of view, there are three typical categories of S/N ratios:
1 r 1. For smaller the better (STB), S / N ji 10 log yijk2 r k 1 1 r 1 2. For larger the better (LTB), S / N ji 10 log 2 r k 1 y ijk s 2ji 3. For nominal the best (NTB), S / N ji 10 log 2 y ji
Where, y 2ji
1 r 1 r 2 y S ( y jik y ji ) 2 , jik ji r 1 r k 1 k 1
r is the number of repeated experiments, yjik is the experimental value of the ith response variable in the jth trial at the kth replication.
Figure 5.2 Distribution of performance around mean The constant 10 has been purposely used to magnify S/N number for each analysis 45
and negative sign is used to set S/N ratio of “larger the better” type relative to the square deviation of “smaller the better” type.
5.1.4.2 ADVANTAGE OF S/N RATIO OVER AVERAGE To analyse the results of experiments involving multiple runs, use of the S/N ratio over average of results is preferred. Analysis using S/N ratio will offer the following advantages (Roy, 2010): 1. It provides guidance to selection of the optimum level based on the least variation around the target and also on the average value closest to the target. 2. It offers objective comparison of two sets of experimental data with respect to variation around the target and the deviation of the average from the target value. To know how S/N ratio is used in analysis, consider the following two sets of observations, which have a target value of 75: Observation A: 55, 58, 60, 63, 65 Deviation of mean from target Observation B: 50, 60, 75, 90, 100 Deviation of mean from target
Mean = 60.2 = (75 – 60.2) = 14.8 Average = 75.0 = (75-75) = 0.0
These two sets of observations may have come from the two distributions is shown below
46
Figure 5.3 Distributions for the data sets Observe that set B has an average value that equals the target value, but it has a wide spread around it. On the other hand, for set A, the spread around its average is smaller, but the average itself quite far from the target. Which one of the two is better? Based on average value, observation B appears to be better. Based on consistency, observation A is better. How can one credit A for less variation? How does one compare the distanced of the averages from the target? Surely, comparing the averages is one method. Use of the S/N ratio offers an objective to look at two characteristics together.
5.1.4.3 EFFECT OF S/N RATIO ON ANALYSIS Use of S/N ratio of the results, instead of the average values, introduces some minor changes in analysis (Roy, 2010). Degrees of freedom of the entire experiment is reduced. DOF with S/N ratio = number of trials–1 (i.e, no: of repetitions is reduced to 1) DOF in case of standard analysis = (number of trials × number of repetitions) - 1 The S/N ratio calculation is based on data from all observations of a trial condition. The set of S/N ratios then be considered as trials results without
47
repetitions. Hence the DOF, in the case of S/N, is the number of trials – 1. The rest of the analysis follows the standard procedure. S/N ratio must be converted back to meaningful terms. When the S/N ratio is used, the results of the analysis such as estimated performance from the main effects or confidence interval, are expressed in terms of S/N ratio. To express the analysis in terms of the experimental result, the ratio must be converted back to the original units of measurement. S/N = -10log (MSD) Mean square deviation (MSD) =
1 r 2 y jik r k 1
(for smaller the better type)
2 Yexpected
Therefore, MSD 10 S / N /10
& Yexpected MSD
1/ 2
Or
Yexpected 10 S / N / 2
5.1.4.4 WHEN TO USE S/N RATIO FOR ANALYSIS Whenever an experiment involves repeated (two or more) observations at each of the trial conditions, the S/N ratio has been found to provide a practical way to measure and control the combined influence of deviation of the population mean from the target and the variation around the mean. In standard analysis, the mean and the variation around the mean are treated separately by a main effect study and ANOVA respectively. In the present work we studied mean and variation around the mean using both the studies. 48
5.1.5
PROCEDURE
FOR
EXPERIMENTAL
DESIGN
AND
ANALYSIS Taguchi experimental design and analysis is described in the following paragraphs.
5.1.5.1 SELECTION AND APPLICATION OF ORTHOGONAL ARRAYS Nomenclature of arrays L = Latin square
Lq(bc)
q = number of trials b = number of levels c = number of columns (factors)
Degrees of freedom associated with the OA = q – 1 In selecting an appropriate OA, the following prerequisites are required:
Selection of process parameters and/or their interactions to be evaluated. Selection of number of levels for the selected parameters.
The following steps can be followed for designing an OA experiment (Matrix experiment) (krishnaiah, 2012): Determine the degrees of freedom required for the problem under study. Note the levels of each factor and decide the type of OA. (2-level or 3-level). Select the orthogonal array which satisfies the following conditions. (a) Degrees of freedom of OA > df required for experiment. (b) Possible number of interactions of OA > the number of interactions to be studied. Table of standard orthogonal arrays is shown below: 49
Table 5.1 Standard orthogonal arrays Two-level series Three-level Four-level series Mixed-level 4 5 Lseries (3 ) L (4 ) L18series (21, 37)$ 9 15 L8 (27) L27 (313) L64 (421) L36 (211, 312) 3 15 40 LL164 (2 )) L81 (3 ) 31 L32 (2 ) L12 (211)* * Interactions cannot be studied $ Can study one interaction between the 2-level factor and one 3-level factor 4. Draw the required linear graph for the problem. 5. Compare with the standard linear graph of the chosen OA. 6. Superimpose the required linear graph on the standard linear graph to find the location of factor columns and interaction columns. 7. Draw the layout indicating the assignment of factors and interactions. The rows indicate the number of experiments (trials) to be conducted.
50
Figure5.4 Taguchi Experimental Design and Analysis Flow diagram 51
5.1.5.2 SELECTION OF INNER AND OUTER ARRAY’S Taguchi separates factors (parameters) into two main groups: Controllable factors Noise factors Controllable factors are factors that can easily be controlled. Noise factors, on the other hand, are nuisance variables that are difficult, impossible, or expensive to control. The noise factors are responsible for the performance variation of a process. Taguchi recommends the use of outer array for noise factors and inner array for the controllable factors. If an outer array is used the noise variation is forced into the experiment. However, experiments against the trial condition of the inner array may be repeated and in this case the noise variation is unforced in the experiment. The outer array, if used will have the same assignment considerations. In our investigation no noise factors are used.
5.1.5.3 EXPERIMENTATION AND DATA COLLECTION The experiment is performed against each of the trial conditions of the inner array. Each experiment at a trial condition is repeated simply (if outer array is not used) or according to the outer array (if used). Randomization should be carried for to reduce bias in the experiment.
5.1.5.4 DATA ANALYSIS A number of methods have been suggested by Taguchi for analyzing the data: observation method, ranking method, column effect method, ANOVA, S/N ANOVA, plot of average responses, interaction graphs, etc. In the present investigation, following methods are used. 52
1. Plot of average response curves Develop average response table by averaging the response values corresponding to each level for each factor and then draw response curves. 2. ANOVA for raw data 3. ANOVA for S/N data Steps for conducting ANOVA: (a) Find correction factor CF CF
T2 q
Where, T grand total q total number of observations
(b) SSTotal computed using the individual observations (response) data q
SSTotal Y j2 CF j 1
(c) The factor (effect) sum of squares is computed using the level totals
A2 A2 A2 SS A 1 2 .......... m CF q Am q A1 q A2 Where, Am level ' m' total of factor A q Am number of observations(trials) used in Am
In the similar way SS (sum of squares) is found for other factors.
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(d) Error sum of squares is calculated by subtracting the sum of all factor sums of squares from the total sum of squares. SS e SSTotal SS A SS B ...... upto last factor
This error of sum of squares is due to replication of experiment, is called experimental error or pure error When experiment is not replicated, the sum of squares of unassigned columns is treated as error sum of squares. Even when all columns are assigned and experiment not replicated, we can obtain error variance by pooling the sum of squares of small factor/interaction variances. When all columns are not assigned and experiment is replicated, we will have both experimental error (due to replication) and error from unassigned columns. These two errors can be combined to get more degrees of freedom and F-tested the effects. Polling of sum of squares: 1. Polling down: In this approach, we get the largest factor variance with the pooled variance of all the remaining factors. If that factor is significant, the next largest factor is removed from the pool and the F-test is done on those two factors with the remaining pooled variance. This is repeated until some insignificant F-value is obtained. 2. Pooling up: The smallest factor variance is F-tested using the next larger factor variance. If no significant F-exists, these two are pooled together to test the next larger factor effect until some significant F is obtained. As a rule of thumb, pooling up to one-half of degrees of freedom has been suggested. In the case of saturated design this is equivalent to have one-half of the effects in 54
the ANOVA after pooling. It has been recommended to use pooling up strategy. Under pooling up strategy, we can start with lowest factor/interaction variance and the next lowest and so on until the effects are equal to one-half of degrees of freedom used in the experiment. The plot of average responses at each level of a parameter indicates the trend. It is a pictorial representation of the effect of a parameter on the response. Typically, ANOVA for OA‟s are conducted in the same manner as other structured experiments. The S/N ratio is treated as a response of the experiment, which is a measure of the variation within a trial when noise factors are present. A standard ANOVA is conducted on S/N ratio (Krishnaiah, 2012).
5.1.5.5 Parameter Design Strategy When the ANOVA on the raw data (identifies control factors which affect average) and the S/N data (identifies control factors which affect variation) are completed, the control factors may be put into four classes (Phadke, 1989): Class I:
Factors which affect both average and variation (significant in both ANOVAs)
Class II:
Factors which affect variation only (significant in S/N ANOVA only)
Class III:
Factors which affect average only (significant in raw data ANOVA only)
Class IV:
Factors which affect nothing (not significant in both ANOVAs)
The parameter design strategy is to select the proper levels of classes I and II to reduce variation and class III to adjust the average to the target value. Class IV may 55
be set at the most economical level since nothing is affected; Figure 5.5 shows example plots for the four classes of factors.
Figure 5.5 Factor effects on response
The fundamental parameter design approach is to move all but one design (control) parameter to a region of low response slope to make those parameters insensitive to 56
variation. The remaining factor(s) should be linear (adjustment) factors to obtain the appropriate average response (quality characteristic). When starting with two level experiments, insignificant factors are already parameter designed and significant factors may be investigated further to discover nonlinear properties, if possible. Percent contribution (C): The percentage contribution indicates the contribution of each factor/interaction to the total variation. By controlling the factors with high contribution, the total variation can be reduced leading to improvement of process/product performance. The percent contribution due to error before pooling indicates the accuracy of the experiment.
%C
SS factor SSTotal
Prediction of mean: After determination of the optimum condition, the mean of the response at the optimum condition is predicted. This mean is estimated only from
the significant parameters. The ANOVA identifies the significant parameters. Suppose, parameters C, D, F are significant out of A, B, C, D, E, F and C2 , D2 , F2 (second level of C, D and F) is the optimal treatment (Besterfield, 1999).
T T C2 T D2 T F2
Where,
estimate of response T overall average of response data
In the present work, the process and tool parameters which affect the surface roughness and material removal rate are selected in range and experiments were conducted. 57
5.2 ORGANISATION OF EXPERIMENTS The experiments which were conducted as explained below.
5.2.1 SELECTION OF OA AND PARAMETER ASSIGNMENT In experimentation, Taguchi‟s mixed level design was selected as it was decided to keep five parameters that are being studied at three levels. The selected process and tool parameters and their levels are given in Table 5.2 .Five three level parameters have 10 DOF, i.e., the total DOF required will be 10 [5×2]. The most appropriate orthogonal array in this case is L18 (21×37) OA with 17 [= 18-1] DOF.
Factor symbol v f d r α
Table 5.2 Design parameters and their levels Factor Level „-1‟ Level „0‟ Cutting speed (m/min) Feed (mm/rev) Depth of cut (mm) Nose radius(mm) Rake angle(º)
60 0.052 0.2 4 0
75 0.078 0.4 8 6
Level „+1‟ 90 0.104 0.6 12 12
L18 (21×37) orthogonal array design is a mixed level (2-level & 3-level) design in which 1st column is for 2-level factor and remaining 7 columns for 3-level factors. For this work parameters are assigned to first five 3-level factor columns. The design matrix is shown below.
Exp.No. 1 2 3 4 5 6
Table 5.3 The experimental layout: L18 Orthogonal Array SR MRR v f d r α (µm) (mm3/min) -1 -1 -1 -1 -1 -1 0 0 0 0 -1 +1 +1 +1 +1 0 -1 -1 0 0 0 0 0 +1 +1 0 +1 +1 -1 -1 58
7 +1 -1 8 +1 0 9 +1 +1 10 -1 -1 11 -1 0 12 -1 +1 13 0 -1 14 0 0 15 0 +1 16 +1 -1 17 +1 0 18 +1 +1 SR = Surface Roughness MRR = Material Removal Rate
0 +1 -1 +1 -1 0 0 +1 -1 +1 -1 0
-1 0 +1 +1 -1 0 +1 -1 0 0 +1 -1
+1 -1 0 0 +1 -1 -1 0 +1 +1 -1 0
Here are some of the properties and considerations of this design (Khosrow, 1989): 1. This is a main-effects-only design; i.e., response is approximated by a separable function. A function of many independent variables is called separable is it can be written as a sum of functions where each component function of only one independent variable. 2. For estimating the main effects there are two degrees of freedom associated with each three-level factor, one degree of freedom with the overall mean. We need at least one experiment for every degree of freedom. Thus, the minimum number of experiments needed is 2 × 6 + 1 × 3 + 1 = 16. Our design has 18 experiments. A single-factor-by-single-factor experiment would need only 16 experiments, two fewer than 18. But such an experiment would yield far less precise information compared with the orthogonal array experiment. 3. The columns of the array are pair-wise orthogonal. That is, in every pair of columns, all combinations of levels occur and they occurs an equal number of time.
59
4. Consequently, the estimates of the main effects of all factors and their associated sums of squares are independent under the assumption of normality and equality of error variance. So the significance tests for these factors are independent. In general, these estimates would be correlated with those for any of the other seven factors. 5. The estimates of the main effects can be used to predict the response for any combination of the parameter levels. A desirable feature of this design is that the variance of the prediction error is the same for all parameter-level combinations covered by the full factorial design. 6. It is known that the main-effect-only models are liable to give misleading conclusions in the presence of interactions. If we wished to study all twofactor interactions, with no more than 18 experiments we would have enough degrees of freedom.
5.2.2 SELECTION OF RESPONSES The effect of process and tool parameters was studied on the following responses for hard turning of AISI 52100 bearing steel material 1. Surface Roughness (SR) 2. Material Removal Rate (MRR)
5.2.2.1 Surface Roughness (SR) The surface roughness of the machined surface is measured using Surf-test SJ-210, MITUTOYO made with a cut-off length 8mm. As the cut-off length of the surf-test instrument is 8mm the 15mm length of work-piece material which we measured is enough to give accurate results. The surface roughness values are measured thrice 60
along the diameter of the work-piece and the average of those values is used as the response. This way was preferred because there will be unavoidable variability in measuring surface roughness.
5.2.2.1 Material Removal Rate (MRR) Effect of material removal rate is very important for designing process and cutting tool selection to ensure the quality of the product. The material removal rate in turning operation is the volume of material/metal that is removed per unit time (mm3/min). The response is calculated for each trial in design matrix using the formula MRR 1000 v f d mm 3 /min
5.3 MODELLING As stated earlier for our L18 design only main effects model can be formulated. Accordingly L18 design data has been used to fit the first order model. The input data to MINITAB software is provided in coded form of factors i.e. -1 to +1. To be precise, value of the factor in coded scale is = (actual value of factor – central value in the range)/ (difference between the maximum value and central value in the range). Applying backward linear regression, which eliminates the insignificant factors one at a time, option of MINITAB is used, and the surface roughness (SR) model is developed. And power model (non-linear equation) is also developed using LevenbergMarquardt‟s algorithm. Using the non-linear regression equation option in MINITAB, setting the initial values for the parameters at k (constant) = 1, v = 1, f = 1, d = 1, r = 1, α = 1 and allowing the algorithm for 200 iterations, desired non-linear equation is obtained. 61
5.4 MULTI-RESPONSE OPTIMIZATION 5.4.1 GREY-RELATIONAL ANALYSIS Steps in grey relational analysis The grey relational analysis is used in conjunction with orthogonal array to draw inferences about the effect of the factors and their interactions on multiple responses. The steps of grey relation analysis are as follows. STEP-1: Identify the responses and number of response variables be ' p ' , for the selected orthogonal array number of trails be ' q ' , number of replications with respect to each trial be 'r ' . STEP-2: Find the normalized values of the responses using the following equations: For the „higher is better‟ performance variable, the formula for the response variable ' i ' is given below for each replication k 1,2,....,r.
X ijk*
X ijk MIN j 1, 2,...,q ( X ijk ) MAX j 1, 2,...,q ( X ijk ) MIN j 1, 2,...,q ( X ijk )
Where,
X ijk* =The normalized value after grey relational generation of the „higher is the better‟ type of response variable for the k th replication of j th trial j 1,2,....,q and k 1,2,....,r. For „higher is better‟ type of response variables, the formula for the response variable 'i ' is given below for each replication k 1,2,....,r.
X ijk*
MAX j 1, 2,....,q ( X ijk ) X ijk MAX j 1, 2,...,q ( X ijk ) MIN j 1, 2,...,q ( X ijk ) 62
for j 1,2,....,q. Where,
X ijk* = The normalized values after grey relation generation of the „lower is better‟ type response variable for the k th replication of the j th trial, j 1,2,....,q and k 1,2,....,r.
STEP-3: Find the maximum of normalized values regardless of the response variables, trials and replications, let this maximum value be ' R' , which is known as reference value, its formula is given as:
R MAX( X ijk* ) for i 1,2,...., p ; j 1,2,....,q and k 1,2,....,r. STEP-4: Find the absolute difference between each normalized value and the reference value ' R' , regardless of the response variables, trials and replications. let it be ijk .
ijk X ijk* R STEP-5: Find the grey relational coefficient for each of the normalized values ( X ijk* ) using the following equation.
Gijk
MINijk ( Dijk ) [ MAXijk ( Dijk )] Dijk [ MAXijk ( Dijk )]
Where,
Gijk = Grey relational coefficient for the i th response variable, j th trail and k th replication,
= distinguishing coefficient in range of 0 to 1(0.5 is widely accepted). 63
STEP-6: Find the grey relational grade for each trial using the following formula. p
r
R j i 1 k 1
Gijk Pr
STEP-7: Rank is given for the grey relational grade, higher the first rank and followed. STEP-8: Find the average grey relational grade at each level for each factor by writing the grey relational grades against the trials of the orthogonal array. STEP-9: Find the optimum level for each factor based on „higher is better‟ characteristic
5.4.2 Technique for Order Preference based Similarity to Ideal Solution (TOPSIS) STEP-1: Obtain the evaluation matrix consisting of ' q ' alternatives and ' p' criteria (responses), with the intersection of each alternative and criteria given as given as x ji .
[ x ji ]q p
x11 x 21 . . . . x q1
x12
x13
x22 . .
x23 . .
. .
. . xq 3
xq 2
......... x1 p ......... x2 p . . . . . . . . ......... xqp
Here each criteria (variable) is a column matrix and observations fall in rows. x23 indicates 2nd observation of 3rd response.
STEP-2: Obtain normalized data matrix, R using the relationship.
64
R ji
x ji q x ji j 1
i 1,2,...., p ; j 1,2,....,q
STEP-3: Obtain the weighted decision matrix, V by multiplying each column of R by the corresponding weight. V ji W ji R ji
Here, equal weightage is given for both the responses, W j1 0.5 , W j 2 0.5 Such that, W j1 W j 2 1 . Step-4: Determine the ideal and the negative-ideal solutions. The ideal value set, V , and the negative-ideal value set, V are determined as follows:
V (maxV ji i L)or(minV ji i L' ), j 1,2,....,q V1 ,V2 ,....., VP
V (minV ji i L)or(maxV ji i L' ), j 1,2,....,q V1 , V2 ,....., VP
Where,
L i 1,2,.....,p V ji , a lar ger response is desired
L' i 1,2,.....,p V ji , a smaller response is desired
Step-5: Calculate the separation measures. The separation of each alternative from the ideal solution ( S j ) is given as follows: 65
p
(v
j
S
i 1
ji
vi )
The separation of each alternative from the negative ideal solution ( S j ) is denoted as below: p
(v
S j
i 1
ji
vi )
Step-6: Calculate the relative closeness of various alternatives to the ideal solution, which is considered as the C * . Ideal solution is a point which is best of everything & Negative ideal solution is point where all the worst exists.
Figure 5.6 Representation of closeness to the alternative The C * for the j th trial can be computed using the following equation:
C * j
S j S j S j
If j th alternative is at the Ideal solution, then S j = 0,
C *j = 1 =100% If j th alternative coincides with Negative Ideal solution, then S j = 0,
C *j = 0 66
The relative closeness of the alternative shows the closeness to the ideal solution, and value is between 0 and 1.If the value is closer to „1‟ then the alternative is closer to the ideal solution.
5.4.3 PRINCIPAL COMPONENT ANALYSIS BASED TOPSIS (PCA-TOPSIS) Step-1: Before performing PCA depending on the type of response desired calculate S / N ratio using formulae given below:
1 r For smaller the better (STB), S / N ji 10 log yijk2 r k 1 1 r 1 For larger the better (LTB), S / N ji 10 log 2 r k 1 y ijk s 2ji For nominal the best (NTB), S / N ji 10 log 2 y ji r r 1 1 ( y jik y ji ) 2 Where, y 2ji y jik , S 2ji r k 1 r 1 k 1
Step-2: Normalize the S / N ratio of each response variable using the following equation:
y ji
SN ji SN SN SNi
Where,
SN ji S / N ratio of i th response variable in j th trial SN mean of S / N ratio of i th response variable SN SNi S tandard deviation of S / N ratio for i th response variable
67
Step-3: Find correlation matrix for the normalized responses. Step-4: Perform Bartlett‟s sphericity test on raw response data. Bartlett‟s spericity test: H0 (null hypothesis): Correlation matrix of responses is equal to identity matrix. H1 (Alternate hypothesis): Correlation matrix of responses is not equal to identity matrix. Test statistic:
2 p 5 (q 1) ln R 6
2p ( p1) 2
Where, p( p 1) degrees of freedom 2 p number of responses
q number of trials
Under H0, it follows 2 distribution with
p ( p 1) degrees of freedom. 2
If the null hypothesis is rejected then we go to next step otherwise there is no need to perform principal component analysis. Step-5: Conduct PCA on normalized S/N ratios of response variables and obtain the eigen values, and eigen vectors and proportion of variance explained by different principal components. Procedure to conduct PCA:
Solve the characteristic equation, S I 0 . Where, 68
S Correlation matrix of order p p
eigen values (1 , 2 , 3 , 4 ,...., p ) I Identity matrix of order p p
Once the eigen values ‟s are determined proportion of variance explained by each PC (Principal Component) and cumulative variance can also be calculated.
From the eigen values, the eigen vector for each eigen value ( ) can be computed by solving,
S I ai
0 , subjected to aiT ai 1
Where, ai eigen vector of order p 1 for i
ai1 a i2 ai 3 ai . . . ai p
Step-6: Determine the number of principal components retained. The number of principal components retained should account for 100% variation in the original values. For extracting PC‟s there different methods they are listed below:
Cumulative percentage of total variance
Kaiser‟s rule (eigen-value criteria)
Average root method 69
Broken stick method
Scree plot
Bartlett‟s Hypothesis test
Scree plot is the efficient method and is used in the current work. Step-7: Develop the variation mode charts and determine the optimization direction of the selected principal components. The variation mode chart of the l th (l 1,2,..., q and q p) principal component ( Z l ) is the plot of the upper and lower variation extent limits, VEL1 Z l and VEL2 Z l , respectively, with respect to p response variables. The values of VEL1 Z l and VEL2 Z l are computed using the following equations:
VEL1 Zl 3a11 1 ,3a21 1 ,.....,3a p1 1 ,
VEL2 Zl 3a11 1 ,3a21 1 ,.....,3a p1 1 ,
Where 1 is the eigenvalue of the l th (l 1,2,..., q and q p) principal component. The optimization direction of each selected principal component with respect to the integrated response is determined according to the variation mode charts for the principal components. For example, positive values of VEL1 Z l for all the variables imply that the S/N ratios of each response can be enhanced simultaneously, and therefore, the principal component Z 1 will be considered as the LTB type with respect to the integrated response. A principal component can also be STB type. It may be noted that this knowledge is necessary for the determination of the ideal and negativeideal solutions as described in step 9. Here 'l ' should be equal to ' p ' as we should not consider eigenvalues that are greater than 1 only. 70
Step-8: Calculate principal component scores from eigenvectors using the formula given below. D jl al1 X j1 al 2 X j 2 ..... alp X jp .
i.e., for principal component score will be D j1 a11 X j1 a12 X j 2 ..... a1p X jp (for PC1) D j 2 a21 X j1 a22 X j 2 ..... a2 p X jp (for PC2)
.... .... D jl al1 X j1 al 2 X j 2 ..... alp X jp . (for PC l )
Step-9: Establish a normalized matrix, where ' q ' trials are the possible alternatives for all the principal components. The normalized matrix for j th trial and l th principal component score is evaluated using formula given below. R jl
D jl q 2 D jl j 1
Where, R jl represent the normalized value of the l th principal component score
corresponding to the j th trial. Step-10: Obtain the weighted matrix. The weighted performance measure for the l th attribute corresponding to the j th trial V jl can be derived as follows: V jl l R jl
Step 11: Determine the ideal and the negative-ideal solutions. 71
The ideal value set, V , and the negative-ideal value set, V are determined as follows:
V (maxVjl l L)or(minVjl l L' ), j 1,2,....,q V1 ,V2 ,.....,Vp V (minVjl l L)or(maxVjl l L' ), j 1,2,....,q V1 , V2 ,....., VP
Where,
L l 1,2,.....,p V jl , a lar ger response is desired
L' l 1,2,.....,p V jl , a smaller response is desired
Step-12: Calculate the separation measures. The separation of each alternative from the ideal solution ( S j ) is given as follows:
S j
p
(v l 1
jl
vl )
The separation of each alternative from the ideal solution ( S j ) is denoted as below:
S j
p
(v l 1
jl
vl )
Step-13: Calculate the relative closeness of various alternatives to the ideal solution, which is considered as the C . Ideal solution is a point which is best of everything & Negative ideal solution is point where all the worst exists.
72
Figure 5.7 Representation of closeness to the alternative The C for the j th trial can be computed using the following equation:
Cj
S j S j S j
If j th alternative is at the Ideal solution, then S j = 0,
C j = 1 =100% If j th alternative coincides with Negative Ideal solution, then S j = 0,
Cj = 0 The relative closeness of the alternative shows the closeness to the ideal solution, and value is between 0 and 1.If the value is closer to „1‟ then the alternative is closer to the ideal solution.
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CHAPTER 6
ANALYSIS AND REULTS
74
ANALYSIS AND RESULTS This chapter contains analysis and discussion of results for the methods stated in chapter 5. As concluded from the literature and pilot study, three process and two tool parameters are used as input parameters and the responses as surface roughness and material removal rate. Experiments were conducted according to L18 orthogonal array design. The trial and results are shown in Table 6.1 Table. 6.1 The experimental results: L18 Orthogonal Array SR MRR SNSR SNMRR Exp.no. v f d r α (µm) (mm3/min) (dB) (dB) 1 -1 -1 -1 -1 -1 4.07 624 -12.19 55.90 2 -1 0 0 0 0 3.79 1872 -11.57 65.44 3 -1 +1 +1 +1 +1 4.57 3744 -13.19 71.46 4 0 -1 -1 0 0 3.01 780 -9.57 57.84 5 0 0 0 +1 +1 3.47 2340 -10.80 67.38 6 0 +1 +1 -1 -1 4.75 4680 -13.53 73.40 7 +1 -1 0 -1 +1 2.65 1872 -8.46 65.44 8 +1 0 +1 0 -1 3.37 4212 -10.55 72.48 9 +1 +1 -1 +1 0 3.68 1872 -11.31 65.44 10 -1 -1 +1 +1 0 3.56 1872 -11.02 65.44 11 -1 0 -1 -1 +1 4.86 936 -13.73 59.42 12 -1 +1 0 0 -1 5.1 2496 -14.15 67.94 13 0 -1 0 +1 -1 3.26 1560 -10.26 63.86 14 0 0 +1 -1 0 3.94 3510 -11.90 70.90 15 0 +1 -1 0 +1 4.32 1560 -12.70 63.86 16 +1 -1 +1 0 +1 2.37 2808 -7.49 68.96 17 +1 0 -1 +1 -1 3.68 1404 -11.31 62.94 18 +1 +1 0 -1 0 4.26 3744 -12.58 71.46 SNSR = S/N ratio for Surface Roughness SNMRR = S/N ratio for Material Removal Rate
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6.1 SINGLE RESPONSE OPTIMIZATION From L18 orthogonal array design, factor affects at three levels can be obtained and interaction affects cannot be studied. Since the experimental design is orthogonal, it is then possible to separate out the effect of each parameter at different levels. The influence of each control factor on the response considered i.e. surface roughness has been performed with level mean analysis. A level mean of a factor (mean response) is the average of the response value of experiments in which the factor is at the particular level. The control factor with the strongest influence is determined by the difference between mean values of the factor at high and low levels (Δ).
6.1.1 RESPONSE GRAPH METHOD 6.1.1.1 SURFACE ROUGHNESS The average response of surface roughness for both raw data and S/N data is shown in Table 6.2 and Table 6.3. Table 6.2 Average response of raw data and ranking of factor effects v f d r α Level -1 4.325 3.153 3.937 4.088 4.038 Level 0 3.792 3.852 3.755 3.660 3.707 Level +1 3.335 4.447 3.760 3.703 3.707 Δ 0.99 1.294 0.182 0.428 0.331 Rank 2 1 5 3 4 Table 6.3 Average response of S/N data and ranking of factor effects v f d r α Level -1 -12.642 -9.832 -11.838 -12.065 -11.998 Level 0 -11.460 -11.643 -11.303 -11.005 -11.325 Level +1 -10.283 -12.943 -11.280 -11.315 -11.061 Δ 2.359 3.111 0.558 1.06 0.929 Rank 2 1 5 3 4
76
-5
4
-7
3
-9
2
-11
1
-13
0
-15
v1v2v3
f1 f2 f3
d1d2d3
r1 r2 r3
S/N ratio
Surface Roughness
5
SR SNSR
α1α2α3
Fig. 6.1 Response Plot for Surface Roughness From both raw data and S/N ratio of surface roughness same trend is observed in case of cutting speed, feed rate and nose radius, deviation has been observed in case of depth of cut and rake angle. The depth of cut in case of S/N data depicts that, surface roughness decreases with increasing depth of cut whereas in case of raw data first decreases and then increases. The rake angle in case of S/N data depicts that, surface roughness decreases with increasing rake angle whereas in case of raw data first decreases and then maintains constant. But through average ranking method both S/N ratio data and raw data showed that feed rate is more influential on surface roughness followed by cutting speed, nose radius, rake angle, depth of cut.
6.1.1.2 MATERIAL REMOVAL RATE The average response of material removal rate for both raw data and S/N data is shown in Table 6.4 and Table 6.5. Table 6.4 Average response of raw data and ranking of factor effects v f d r α Level -1 1924 1586 1196 2561 2496 Level 0 2405 2379 2314 2288 2275 Level +1 2652 3016 3471 2132 2210 Δ 728 1430 2275 429 286 Rank 3 2 1 4 5
77
100
3100
90
2100
80
1100
70
100
60
v1 v3 f1 f3 d1 d3 r1
S/N ratio
Material Removal Rate
Table 6.5 Average response of S/N data and ranking of factor effects v F D r Α Level -1 64.272 62.911 60.904 66.092 66.092 Level 0 66.210 66.433 66.925 66.092 66.092 Level +1 67.79 68.932 70.446 66.092 66.092 Δ 3.518 6.021 9.542 0 0 Rank 3 2 1 -
MRR SNM RR
r3 α1 α3
Fig. 6.2 Response Plot for Material Removal Rate
As we computed material removal rate using cutting velocity, feed rate and depth of cut, there should be not effect of tool parameters on material removal rate but in the raw data table Table 6.4 we observe that there is a change in influence of tool parameters on the response this is due to noise and this noise is eliminated in S/N ratio table Table 6.5, the tool parameter influence on the response is unchanged. From the Table 6.4 and Table 6.5 it is observed that the material removal rate is highly influenced by depth of cut followed by feed rate, cutting speed.
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6.2 MODELLING Applying backward linear regression for main effects model and non linear regression using Levenberg-Marquardt algorithm for power model, the developed surface roughness equations are given by: SR = 3.817-0.495v+0.647f – 0.192 r - 0.166 α (R-square value= 0.915) SR =221.048 v-0.616 f0.498 d-0.057 r-0.104 α-0.005 (S = 0.2184)
Explained variance value of 0.915 indicates that 91.5% of the The R-square Total variance variability in surface roughness was explained by the model. It can be observed that all input parameters except depth of cut are coming into model. Based on the mathematical model, it can be observed that feed and cutting speed are showing a prominent effect on the surface roughness followed by rake angle and nose radius. The surface roughness increases with increase in feed rate and decreases with increase in cutting speed, nose radius and rake angle. Perhaps it is consistent with the level means analysis of L18 data. Coefficient of determination value is not given for non-linear regression; Standard error of regression (S) value should be used for analyzing goodness of fit (Andrej N et al. 2010). Our model fitted well as S value is low.
6.3 ANALYSIS OF VARIANCE Analysis variance is performed to find the factors which are significant for the responses surface roughness and material removal rate. 79
6.3.1 SURFACE ROUGHNESS RAW DATA Table 6.6 ANOVA (initial) DOF MS F0
SOURCE OF SS C RANK VARIATION (%) v 2.946 2 1.473 31.159* 2 30.877 * f 5.028 2 2.514 53.185 1 52.704 d 0.128 2 0.064 1.359 5 1.346 * r 0.667 2 0.333 7.056 3 6.992 α 0.440 2 0.220 4.653 4 4.612 error (pure) 0.331 7 0.047 TOTAL 9.541 17 SS = Sum of Squares, DOF = Degrees of freedom, MS = Mean square, F 0 = Fisher‟s ratio, C = Contribution to response, * = Significant at 95% confidence level, F table value = 4.74 Table 6.7 ANOVA (pooled) SOURCE OF SS DOF MS F0 VARIATION v 2.946 2 1.473 18.015* f 5.029 2 2.514 30.749* r 0.667 2 0.333 4.079* error(pooled) 0.899 11 0.082 TOTAL 9.542 17 * = Significant at 95% confidence level, F table value = 3.98
C (%) 30.877 52.704 6.992
RANK
C (%) 30.588 52.792 1.907 6.551 5.107
RANK
2 1 3
6.3.2 SURFACE ROUGHNESS S/N DATA Table 6.8 ANOVA (initial) SOURCE OF SS DOF MS F0 VARIATION v 2 16.665 8.332 35.064* f 2 28.762 14.381 60.517* d 2 1.039 0.519 2.186 r 2 3.569 1.785 7.509* α 2 2.783 1.391 5.855* error (pure) 1.663 7 0.238 TOTAL 54.482 17 * = Significant at 95% confidence level, F table value = 4.74 80
2 1 5 3 4
Table 6.9 ANOVA (pooled) DOF MS F0
SOURCE OF SS VARIATION v 2 16.665 8.332 27.748* f 2 28.762 14.381 47.890* r 2 3.569 1.785 5.943* α 2 2.783 1.391 4.633* error(Pooled) 2.703 9 0.300 TOTAL 54.482 17 * = Significant at 95% confidence level, F table value = 4.26
C (%) 30.588 52.793 6.551 5.108
RANK 2 1 3 4
For pooling of insignificant factors into error Pooling Up technique is used. It observed that form the raw data and S/N data for surface roughness, depth of cut is the insignificant factor and it is not necessary to consider it for the effect of surface roughness. In case of raw data even rake angle is observed to be insignificant. The similar trend is observed in average response and ranking factors tables and main effects model. In average response and ranking factors table‟s last rank is given to depth of cut followed by rake angle. In the main effects model the factor depth is eliminated in backward regression analysis due to its insignificant effect. Cutting speed, feed rate and nose radius are the significant factors in both ANOVA‟s so, these are the factors which affect both average and variation, assigned to class I. Rake angle effects only variation as it is significant in S/N ANOVA only, assigned to class II. From ANOVA tables it is also observed that the main contribution to surface roughness is due to feed rate followed by cutting speed, nose radius and rake angle.
81
6.3.3 MATERIAL REMOVAL RATE S/N DATA Table 6.10 ANOVA DOF MS F0
SOURCE OF SS VARIATION v 2 37.335 18.668 4.69E+12* f 2 109.789 54.895 1.38E+13* d 2 279.417 139.708 3.51E+13* Error 4.37E-11 11 3.97E-12 TOTAL 426.543 17 * = Significant at 95% confidence level, F table value = 3.98
C (%) 8.753 25.739 65.507
RANK 3 2 1
This ANOVA is presented only find the percentage contribution of factors to material removal rate. It is observed that main contribution to material removal rate depth of cut and is followed by feed rate and cutting speed.
6.4 MULTI-RESPONSE OPTIMIZATION According to the steps stated in chapter.5 optimization has been performed.
6.4.1 GREY RELATIONAL ANALYSIS Table 6.11 Values for Grey relational analysis X1j X2j Δ1j Δ2j G1j G2j Rj 0.377 0 0.623 1 0.445 0.333 0.389 0.479 0.308 0.520 0.692 0.490 0.419 0.455 0.194 0.769 0.806 0.231 0.383 0.684 0.533 0.765 0.038 0.234 0.962 0.681 0.342 0.511 0.597 0.423 0.403 0.577 0.554 0.464 0.509 0.128 1 0.872 0 0.364 1 0.682 0.897 0.308 0.103 0.692 0.829 0.419 0.624 0.634 0.885 0.366 0.115 0.577 0.812 0.695 0.520 0.308 0.479 0.692 0.510 0.419 0.465 0.564 0.308 0.436 0.692 0.534 0.419 0.477 0.088 0.077 0.912 0.923 0.354 0.351 0.353 0 0.461 1 0.538 0.333 0.481 0.407 0.674 0.231 0.326 0.769 0.605 0.394 0.499 0.425 0.711 0.575 0.288 0.465 0.634 0.549 0.286 0.231 0.714 0.769 0.412 0.394 0.403 1 0.538 0 0.462 1 0.520 0.760 0.520 0.192 0.479 0.808 0.510 0.382 0.446 0.308 0.769 0.692 0.230 0.419 0.684 0.552 SNR = Signal to noise ratio of the grey relational grade (R) *
*
82
SNRj -8.193 -6.845 -5.456 -5.824 -5.865 -3.321 -4.088 -3.162 -6.654 -6.433 -9.051 -7.799 -6.027 -5.198 -7.897 -2.384 -7.007 -5.165
T 17 13 7 8 9 3 4 2 12 11 18 15 10 6 16 1 14 5
Table 6.12 Level Averages of Grey relational grade (S/N data) v f d r α Level-1 -7.29645 -5.49161 -7.43788 -5.83632 -5.91843 Level 0 -5.68891 -6.18832 -5.96492 -5.65188 -6.01996 Level+1 -4.74343 -6.04887 -4.326 -6.2406 -5.79041 Average grey relational grade = -5.909 Predicted grey rational grade (S/N data) for v3 f1 d3 r2 α3 = -2.365 Predicted SR from the main effects model = 2.421, Predicted MRR = 2808
6.4.2 TECHNIQUE FOR ORDER PREFERENCE BY SIMILARITY TO IDEAL SOLUTION Table 6.13 Values for TOPSIS method Rj1 Rj2 Vj1 Vj2 Sj+ S j0.247 0.056 0.123 0.028 0.190 0.031 0.229 0.169 0.115 0.085 0.134 0.069 0.277 0.339 0.138 0.169 0.079 0.142 0.183 0.071 0.091 0.035 0.177 0.064 0.210 0.212 0.105 0.106 0.110 0.092 0.288 0.423 0.144 0.212 0.072 0.183 0.161 0.169 0.080 0.085 0.127 0.093 0.204 0.381 0.102 0.191 0.037 0.170 0.223 0.169 0.111 0.085 0.133 0.071 0.216 0.169 0.108 0.085 0.132 0.073 0.295 0.085 0.147 0.042 0.185 0.016 0.309 0.226 0.155 0.113 0.129 0.085 0.198 0.141 0.099 0.071 0.144 0.070 0.239 0.318 0.119 0.159 0.071 0.135 0.262 0.141 0.131 0.071 0.153 0.048 0.144 0.254 0.072 0.127 0.085 0.129 0.223 0.127 0.111 0.063 0.153 0.055 0.258 0.338 0.129 0.169 0.071 0.143 SNC* = Signal to noise ratio of Relative closeness (C*)
C* 0.141 0.340 0.642 0.264 0.453 0.718 0.423 0.821 0.348 0.357 0.079 0.396 0.328 0.655 0.241 0.604 0.266 0.668
SNC* -17.022 -9.375 -3.843 -11.553 -6.871 -2.879 -7.472 -1.705 -9.170 -8.949 -22.060 -8.036 -9.688 -3.675 -12.372 -4.385 -11.492 -3.505
V 0.072 , 0.211 , V 0.155 , 0.028
Table 6.14 Level Average for Relative closeness (S/N data) v f D r Α Level-1 -11.5478 -9.84498 -13.9449 -9.43556 -8.47054 Level 0 -7.83954 -9.19644 -7.49129 -7.90439 -7.7044 Level+1 -6.28823 -6.63413 -4.23938 -8.33561 -9.50061 Average relative closeness = -8.558 Predicted relative closeness (S/N data) for v3 f3 d3 r2 α2 = 1.464 Predicted SR from the main effects model = 3.881, Predicted MRR = 5616 83
6.4.3 PRINCIPAL COMPONENT ANALYSIS BASED TOPSIS (PCA-TOPSIS) Table 6.15 Correlation matrix Variables NSR NMRR NSR -0.0998 1 NMRR -0.0998 1 Bartlett’s sphericity test: H0: Correlation matrix of responses is equal to identity matrix. H1: Correlation matrix of responses is not equal to identity –matrix. From Table 6.15 correlation matrix is not an identity matrix and null hypothesis can be rejected, therefore we perform PCA. Table 6.16 Eigenvalues PC1 PC2 Eigenvalue 1.0998 0.9002 Variability (%) 54.9882 45.0118 Cumulative % 54.9882 100.0000 PC1 = Principal Component 1, PC2 = Principal Component 2 Table 6.17 Eigenvectors PC1 PC2 NSR 0.7071 0.7071 NMRR -0.7071 0.7071
84
Figure 6.3 Scree plot VEL1 Z1 2.2246 , 2.0127 , VEL2 Z1 2.2246 , 2.0127
VEL1 Z 2 2.2246 , 2.0127 , VEL1 Z1 2.2246 , 2.0127
3 2 1 0 -1 -2 -3
3 2 1 0 -1 -2 -3 SR
MRR
SR
(a) VMC for PC1
MRR
(b) VMC for PC2
Figure 6.4 Variation mode charts From the figure on examination of variation mode charts (VMC) for the first principal component, the S/N ratio of each response can be increased simultaneously and hence, the first principal component is determined as the larger the better (LTB) type. The second principal component reveals that the directions of variation mode for the responses SR and MRR are completely opposite, and since SR is more important than MRR, the second principal component is also treated as LTB type. 85
Yj1 -0.405 -0.059 -0.967 1.059 0.369 -1.154 1.677 0.511 0.084 0.245 -1.265 -1.499 0.672 -0.247 -0.694 2.219 0.084 -0.626
Table 6.18(a) Values for PCA-TOPSIS method Yj2 Dj1 Dj2 Rj1 -2.034 1.152 -1.724 0.266 -0.129 0.049 -0.133 0.011 1.073 -1.442 0.075 -0.333 -1.648 1.913 -0.416 0.442 0.258 0.078 0.443 0.018 1.459 -1.849 0.216 -0.427 -0.129 1.277 1.094 0.295 1.277 -0.542 1.264 -0.125 -0.129 0.150 -0.032 0.035 -0.129 0.264 0.082 0.061 -1.331 0.0462 -1.84 0.010 0.369 -1.322 -0.799 -0.306 -0.445 0.789 0.160 0.183 0.961 -0.854 0.505 -0.198 -0.445 -0.176 -0.805 -0.041 0.574 1.163 1.975 0.269 -0.628 0.503 -0.385 0.116 1.073 -1.201 0.316 -0.278
Table 6.18(b) Values for PCA-TOPSIS method Vj1 Vj2 Sj+ SjCj 0.293 -0.397 0.873 0.764 0.466 0.013 -0.031 0.678 0.622 0.478 -0.367 0.017 0.959 0.452 0.320 0.487 -0.096 0.550 1.011 0.648 0.019 0.102 0.585 0.718 0.551 -0.470 0.049 1.039 0.472 0.312 0.325 0.252 0.259 1.042 0.800 -0.138 0.291 0.645 0.787 0.549 0.038 -0.007 0.644 0.656 0.505 0.067 0.019 0.605 0.695 0.535 0.012 -0.422 0.997 0.482 0.326 -0.336 -0.184 1.041 0.274 0.208 0.201 0.0368 0.506 0.813 0.616 -0.217 0.116 0.781 0.595 0.432 -0.045 -0.185 0.832 0.487 0.369 0.296 0.454 0.191 1.164 0.859 0.128 -0.089 0.651 0.686 0.5129 -0.306 0.073 0.879 0.522 0.372 SNC = Signal to noise ratio of relative closeness (C) V 0.487 , 0.454 , V 0.470 , 0.422
86
Rj2 -0.440 -0.034 0.019 -0.106 0.113 0.055 0.279 0.323 -0.008 0.021 -0.469 -0.204 0.041 0.129 -0.206 0.505 -0.098 0.081
SNCj -6.621 -6.406 -9.892 -3.773 -5.176 -10.104 -1.929 -5.203 -5.936 -5.435 -9.740 -13.633 -4.202 -7.282 -8.652 -1.318 -5.799 -8.580
Table 6.19 Level Average for Relative closeness (S/N) data v f D r α Level-1 -8.62139 -3.87995 -6.75382 -7.37638 -7.59382 Level 0 -6.5317 -6.60128 -6.65444 -6.49762 -6.23554 Level+1 -4.79441 -9.46626 -6.53924 -6.0735 -6.11814 Average relative closeness = -6.6497 Predicted grey rational grade for v3 f1 d3 r3 α3 = 0.828245 Predicted SR from the main effects model = 1.599, Predicted MRR = 2808
6.5 PREDICTED S/N RATIOS AT DIFFERENT OPTIMAL CONDITIONS Table 6.20 Predicted S/N ratios at different optimal conditions Optimization method
GRA TOPSIS PCA-TOPSIS Single response optimization
Optimization criteria SNR SNC* SNC S/N ratio of SR
Optimal condition V3 f1 d3 r2 V3 f3 d3 r2 V3 f1 d3 r3 V3 f1 d2 r2
α3 α2 α3 α3
Predicted S/N ratio (dB) SR MRR -7.679 68.968 -11.779 74.988 -4.076 68.968 -10.922 65.446
Total (dB) 61.289 63.209 64.892 54.524
From the table 6.20 it is found that the best optimal results are obtained through PCATOPSIS method. So, even when the correlation between the responses is small it should be taken care otherwise results will leads to non-optimal conditions, which eventually leads to quality loss.
87
CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
88
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK 7.1 CONCLUSIONS In this work, the effect of the process and the tool parameters on surface roughness and material removal rate has been studied and response parameters were optimized using MCDM techniques. The salient conclusions resulting from the present investigation are summarized as follows: 1. The depth of cut does not have significant effect on surface roughness. 2. Feed rate is the most influencing factor for the response surface roughness. 3. The parameters, cutting speed, feed rate and nose radius are responsible for the effect of both average (mean) and variation of surface roughness. 4. Rake angle effects only for the variations of surface roughness. 5. More than one half of the contribution is shown by depth of cut for the variation of material removal rate. 6. Surface roughness increases with increasing feed rate and decreases with increasing cutting speed, nose radius and rake angle. 7. Even a small amount of correlation effects the estimation of optimal setting. 8. Principal component analysis method takes care of correlation perfectly and leads to the best optimal solution when combined with TOPSIS. 9. The optimal setting of the parameters; cutting speed is 90m/min, feed rate is 0.052mm, depth of cut is 0.6mm, nose radius is 12mm, back rake angle is 12º. 10. The predicted optimal values of the responses surface roughness and material removal rate are 1.599µm and 2808 mm3/min respectively. 89
11. PCA-TOPSIS method is the best optimization technique compared to Grey Relational Analysis and TOPSIS with S/N ratio of SR and MRR as criteria.
90
7.2 RECOMMENDATIONS FOR FUTURE WORK There is scope for further research can be carried out in this area as given below.
1. By varying the tool geometry on the same material the effects of responses can be studied. 2. By varying the work piece material and considering the process and tool parameters responses can be optimized. 3. By using different nano cutting fluids one can study the effects different parameters on temperature. 4. Levenverg-Marquardt‟s algorithm can be performed incorporating different search algorithms. So, try to find the search technique when combined Marquardt‟s algorithm for non-linear regression which can converge at faster rate. 5.
In case of goodness of fit estimation for non-linear regression, simulation studies can be carried out to outrank that S gives better estimation than Rsquared.
6.
Artificial neural network trained Harmonic search algorithm can used to find optimal levels in case of orthogonal arrays.
7.
Comparison of Optimality of responses (D-optimality etc.,) with the experimental designs can be made.
8. Comparison between orthogonal arrays and response surface models can be developed. 9. Combine PCA with other techniques and find the which gives best optimum. 91
CHAPTER 8
REFRENCES
92
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