Application of MATLAB INMODELING and Optimization of Unconventional Finishing Process

DOI : 10.17577/IJERTV2IS90835

Download Full-Text PDF Cite this Publication

Text Only Version

Application of MATLAB INMODELING and Optimization of Unconventional Finishing Process

Application of MATLAB INMODELING and Optimization of Unconventional Finishing Process

Asit Shukla [1],Shah FatehAzam [2],Dr. D. K.Singh [3]

  1. M.Tech scholar at Madan Mohan Malviya Engineering College,Gorakhpur, Uttar Pradesh, India,

  2. M.Tech scholar at Madan Mohan Malviya Engineering College,Gorakhpur,Uttar Pradesh, India [3]Professor and Head of Department,Madan Mohan Malviya Engineering College,Gorakhpur,India

ABSTRACT

Increasing demand of high accuracy and high efficiency machining of difficult-to-machine materials is making the application of abrasive finishing technologies increasingly important. Among those unconventional processes the magnetic abrasive finishing (MAF) and electric discharge machining (EDM)process are most importantly used in manufacturing industries. These processes can produce surfaces with surface finish in nanometerrange and dimensional accuracy up to 0.5 µm. In order to predict the effect of various machining parameters on material removal rate, tool wear rate and surface roughness value, it is important to model and optimise these machining parameters. In the present research work the process parameters of a MAF process are optimized using a very effective evolutionary algorithm termed as genetic algorithm (GA). Response Surface Methodology is applied for developing the models using the techniques of Design of Experiments and Central composite rotatable design was used to plan the experiments. The software used for design of experiments is Design Expert and that for implementing GA is MATLAB. The four input parameters under consideration are current to the electromagnetic coil (magnetic flux density),machining gap, grain size(mess no.) and number of cycles and two response variables are material removal(MR) and surface roughness value(Ra),tool wear rate(TWR).

Keywords: Alloy steel, unconventional Finishing process, MAF,EDM Response Surface Methodology, Surface Roughness, Analysis of Variance(ANOVA), Genetic Algorithm, GA Toolbox, MATLAB,DESIGN EXPERT

.

  1. INTRODUCTION

    1. Unconventional machining process

      Finishing is final operation involved in the manufacturing of components and is most labour intensive, time consuming and least controllable area. The need of better finishing of complicated shapes made of advanced materials and high accuracy are the main factors responsible for using advanced abrasive fine finishing processes (Jain,2002).

    2. Electric Discharge Machining

      Electrical discharge machining (EDM) is one of the most extensively used nonconventional manufacturing processes used for hard materials which are very difficult to machine with conventional techniques. EDM is sometimes referred to as spark machining, spark eroding, burning, die sinking or wire erosion. This is a manufacturing process whereby a desired shape is obtained using electrical discharges (sparks). English chemist Joseph Priestly laid the foundation for EDM by discovering the erosive effect of electrical discharges or sparks in 1770. However EDM was discovered in 1943 by two Russian

      scientists B. R. Lazarenko and N. I. Lazarenkowhen they explored the destructive properties of electrical discharges for constructive purpose. They developed a controlled process for machining difficult-to-cut materials. They invented and applied resistance capacitance (RC) relaxation circuit in EDM that was widely used till 1950s and after that several developments and advancements were made by different researchers in the field of EDM. Electrical Discharge Machining (EDM) is a non-conventionalmachining process, where electrically conductive materials is machined by using precisely controlled sparks that occur between an electrode and a workpiece in the presence of a dielectric fluid.It uses thermoelectric energy sources for machining extremely low machinability materials; complicated intrinsic- extrinsicshaped jobs regardless of hardness have been its distinguishing characteristics.

      Figure 1.1: Layout of Electric Discharge Machining

    3. Magnetic Abrasive Finishing (MAF)

      Figure1.2:Cylindrical work piece machining on magnetic abrasive finishing machine[1]

      MAF is an unconventional finishing process in which the cutting force is primarily controlled by the magnetic field. It reduces the possibility of microcracks on the surface of the workpiece, specially in hard brittle material, due to low forces acting on abrasive particles (Jain, 2002). This process is capable of producing surface roughness in the nanometer range on flat surfaces as well as internal and external cylindrical surfaces (Jain et al., 2001). The MAF process offers many advantages, such as self-sharpening, self- adaptability, controllability and the finishing tools require neither compensation nor dressing (Chang et al., 2002). In MAF, the workpiece is kept between the two poles of a magnet. The working gap between the workpiece and the magnet is filled with magnetic abrasive particles, composed of ferromagnetic particles and abrasive powder. Bonded or unbounded Magnetic abrasive particles can be used. In this process, usually ferromagnetic particles are sintered with fine abrasive particles (Al2O3, SiC, CBN, or diamond) and such particles are called ferromagnetic abrasive particles (Shinmura et al., 1986, 1990; Chang et al., 2002;

      Jain, 2009).

      Common magnetic materials

      • Iron and its oxides

      • Cobalt

      • Nickel

      • Steel and Stainless Steel

        Common Abrasive Materials

      • Synthetic Diamond

      • Cubic Boron Nitride CBN

      • Aluminium Oxide Al2O3

      • Silicon Carbide SiC

        Common Magnetic Abrasive Materials

      • White Alumina + Iron

      • Diamond + Iron

      • Tungsten Carbide + Cobalt

  2. EXPERIMENTATION

    1. Experimental setup

      A schematic diagram of the plane MAF apparatus is shown in Figure 2.1. The flat-faced electromagnet has been designed such that the centre part of the magnet acts as a north pole and outer case as south pole. The reason of doing so that it concentrates magnetic force at the Centre of the magnet. The gap between the flat workpiece

      ferromagnetic abrasive particles (ratio of iron particles and SiC abrasive particles in the gap).

    2. Work piece composition

      Alloy steel is considered as work piece for the experimental work.

      Table 2.1: Workpiece Material composition (Alloy Steel)

      Alloying elements percentage

      and the magnetic poles is known as working gap or

      machining gap and is filled with unbound magnetic abrasive particles. The iron particles are magnetized by the induced magnetic flux (by passing a current to the coil) and are coupled magnetically. These particles are concentrated in the machining gap. The finishing setup is attached to the main spindle of the machine through a holder. The current supplied to the coil of electromagnet is given by a device consisting of brass slip rings and electric carbon brushes.

      Figure 2.1: Schematic diagram of plane magnetic abrasive finishing setup. (Source D.K.Singh et. al.)

      During the design of the setup, the parameters that have been considered are magnetic flux density (current), machining gap, and composition of

      C 0.35-0.45

      Mn 0.45-0.60

      Si 1.31-1.81

      Cr 0.20-0.30

      Ni 0.10-0.30

      Iron Rest

    3. Experimental design

      The various levels of machiningparameters are selected based on the previous studies. The considered machining parameters and their coded levels are represented in table 2.2 Experiments have been planned using statistical technique to get useful inferences by performing minimum number of experiments. Design Expert software was used for designing of experiments.

      Table 2.2: Machining Parameters and Their Corresponding Variation Levels.

      Parameters(unit) levels

      -2 -1 0 1 2

      current (amp)0.5 0.63 0.75 0.88 1.0

      Machining gap (mm) 1.25 1.50 1.75 2.00 2.25

      Grain size(mesh no) 220 300 400 500 600

      Number of cycles 5 7 9 11 13

      TABLE 2.3: Table for Design of Experiments and Responses

      Where X1 X2 X3 X4 are in actual levels values of current, machining gap, grain size and no of cycles.

      ,whose coded values are in table 2.2.

  3. MODELLING OF PROCESS PARAMETERS

    In the present work response surface methodology is used to model the process.A central composite design is adopted to develop model.

    The statistical software (design expert) has been employed to analyse the experimental findings (Table2.3), and the following regression models have been evolved:

    Equation for material removal is given by-

    = 79.47 + 22.80 1 15.352 + 12.183

    + 19.234 3.0012 2.4922 2.5232

    3.9942 + 1.8712 + 1.0513

    + 4.3114 + 3.3423 + 33.4924

    + 11.8634 (2)

    And equation for surface roughness is given by-

    = 0.21 + 0.0551 0.0402 + 0.0383

    +0.0324 0.02912 0.00896322

    +0.00966832 0.01442 0.03312

    +0.00610213 0.03114 + 0.01123

    +0.03424+0.01334 (3)

    1. Analysis of variance (ANOVA) of regression

      Analysis of variance (ANOVA) is a procedure for assigning sample variance to different sources and deciding whether the variation arises within or among different population groups. Samples are described in terms of variation around group means and variation of group means around an overall mean. If variations within groups are small relative to variations between groups, a difference in group means may be inferred. Hypothesis Tests are used to quantify decisions. ANOVA table for MR and Ra is shown in table 3.2 and table 3.3 respectively.

      Table3.2:Analysis of variance(ANOVA) of regression for Ra

      Sourcedofss

      f p percentage

      Regression

      14 0.0482 6.42 0.0003

      84.9

      Residual error

      16 0.0086 –15.1

      Total30 0.0568 – – 100

      Table3.3:Analysis of variance(ANOVA) of regression for MR

      Sourcedofss f p percentage

      Regression 14 8758.70 6.59 0.0002 82.6

      Residual error 16 1519.10- – 17.6

      Total30 10277.80 – -100

      *significance at 95% confidence interval.

      F value for Ra is found to be 6.59 which is greater than standard f value(2.35),means our data is highly correlated and p value is almost found to be zero.

      The analysis of variance (ANOVA, Table 4 and5) indicates that the variance ratio (F) is more than the standard value of F (¼2.35) at 95% confidence interval (a ¼ 0.05) for both the responses. Their P values come out to be zero .These statistical terms i.e., variance ratio (F) and P value are used tomeasure the significance of the regression under investigation. On the basis of these F and P values, it can be concluded that there is a good correlation between the predicted and the experimental values. Therefore, the regression Equation 2 for Ra and Equation 3 for material removal (MR) can be used to predict the responses of the MAF process.

      Fig 3.1 plot of actual vs predicted value for Ra

      Fig 3.2 plot of actual vs predicted value for mr

      Figure 3.1,3.2 shows the graphs between actual and predicted value.it clearly indicates a straight line which means our model responses mr and Ra are very close to the actual values.

    2. Percentage contribution of factors

      Table3.4for percentage contribution of factors in responses is also presented based on the result of anova. It clearly indicates the contribution of different factors in reduction in surface roughness value and amount of material removed.

      Table3.4:Percentage Contribution Of Factors

      Factors

      MR

      (mg)

      Ra (µm)

      Current (Magnetic flux density) X1

      30.63%

      33.33%

      Machining gap X2

      14.01%

      17.66%

      Grain mesh number X3

      9.69%

      17.38%

      Number of cycles X4

      21.99%

      11.40%

      Error

      23.68%

      20.23%

      Total

      100

      100

      Error obtained is due to the negligence of higher order terms in the analysis of variance of regression. From the above table it can be concluded that material removal and reduction in surface roughness is affected mostly by current to the electromagnet.

  4. OPTIMISATION WITH GA

    1. Genetic algorithm

      The EA holds a population of individuals (chromosomes), which evolve my means of selection and other operators like crossover and mutation. Every individual in the population gets an evaluation of its adaptation (fitness) to the environment. In the terms of optimization this means, that the function that is maximized or minimized is evaluated for every individual. The selection chooses the best gene combinations (individuals), which through crossover and

      mutation should drive to better solutions in the next population.

    2. Basic steps of GA

      • Generate initial population

      • Calculation of the values of the function that we want to minimize of maximize.

      • Check for termination of the algorithm

      • Selection

      • Crossover

      • Mutation

      • New generation

    3. Fitness function

      The fitness function is any function, which you want to optimize. For standard optimization algorithms, it is known as the objective function. GAs follows the survival-of-the-fittest principle of nature to make a search process.

      GAs are naturally suitable for solving maximization problems. All minimization problems are usually transformed into maximization problems by suitable transformations.

      Fitness function for MR

      function y = objective(x)

      (1) = ((307.80428) + (89.19921 (1)) (172.1285

      (2)) (0.097110 (3)) (29.64022 (4)

      48.02137 1 2 9.96576 2 2

      0.0000698313 3 2 0.24947 4 2

      + 14.96249 1 2 + 0.022038 1 3

      + 4.31306 1 4 + 0.035112 2 3

      +(16.74442 (2) (4)) + (0.015611 (3) (4)));

      Fitness function for Ra

      function ra =shukla(x)

      (1) = ((0.46892) + (1.60717 (1)) + (0.043693

      (2)) (0.00046892 (3)) + (0.010948 (4))

      0.46689 1 2

      0.035851 2 2

      + (0.00000026781 ((3)^2))

      (0.000872671 ((4)^2))

      (0.26191 (1) (2))

      + (0.000128469

      (1) (3)) (0.031227 (1) (4)) + (0.000114900

      (2) (3)) + (0.016755 (2) (4)) + (0.000016887

      (3) (4)));

      These functions acts as the fitness functions for our problem. variation of factors for both the functions are as follows-

      0.5<x1<1.0

      1.25<x2<2.25

      220<x3<600 and 5<x4<13

      The above two fitness functions are used in ga toolbox in matlab.this toolbox can be easily accessed by simply typing gatool in matlab command window.

      Fig 4.1:Snapshot of GA toolbox(matlab 2011a)

  5. RESULTS AND DISCUSSION

    S.N

    CURRENT

    (amp)

    MACH. GAP

    (mm)

    GRAIN SIZE

    (Mesh no.)

    No. Of Cycle

    MR

    (mg)

    1

    0.50

    1.25

    220

    5

    84.5233

    2

    0.911

    1.391

    324.731

    10.555

    93.1472

    3

    0.692

    1.25

    220

    5

    99.3082

    4

    .999

    1.787

    385.298

    10.807

    106.6533

    5

    .824

    2.055

    551.59

    11.04

    109.8263

    6

    .865

    1.25

    510.798

    7.808

    107.0072

    7

    .932

    1.25

    461.009

    7.602

    110.6545

    8

    .688

    1.507

    591.371

    10.132

    91.6999

    9

    .677

    2.232

    462.717

    12.983

    108.3185

    10

    .972

    1.25

    531.048

    5.364

    113.0458

    S.N

    CURRENT

    (amp)

    MACH. GAP

    (mm)

    GRAIN SIZE

    (Mesh no.)

    No. Of Cycle

    MR

    (mg)

    1

    0.50

    1.25

    220

    5

    84.5233

    2

    0.911

    1.391

    324.731

    10.555

    93.1472

    3

    0.692

    1.25

    220

    5

    99.3082

    4

    .999

    1.787

    385.298

    10.807

    106.6533

    5

    .824

    2.055

    551.59

    11.04

    109.8263

    6

    .865

    1.25

    510.798

    7.808

    107.0072

    7

    .932

    1.25

    461.009

    7.602

    110.6545

    8

    .688

    1.507

    591.371

    10.132

    91.6999

    9

    .677

    2.232

    462.717

    12.983

    108.3185

    10

    .972

    1.25

    531.048

    5.364

    113.0458

    1. Result for MR

      TABLE 5.1 Result From Genetic Algorithm for MR

      Based upon the result obtained from data the final optimized value of MR is found to be 109.8263 mg.

      Fig5.1: Fitness curve for MR

      120

      100

      80

      60

      40

      20

      0

      MR

      OPTIMAL

      MR

      120

      100

      80

      60

      40

      20

      0

      MR

      OPTIMAL

      MR

      Iteration 1

      Iteration 2

      Iteration 3

      Iteration 4

      Iteration 5

      Iteration 6

      Iteration 7

      Iteration 8

      Iteration 9

      Iteration 10

      Iteration 1

      Iteration 2

      Iteration 3

      Iteration 4

      Iteration 5

      Iteration 6

      Iteration 7

      Iteration 8

      Iteration 9

      Iteration 10

      Fig5.2: Iterations vs MR

    2. Result for Ra

      S.N

      CURRENT

      (amp)

      MACH

      .GAP

      (mm)

      GRAIN SIZE

      (Mesh no.)

      No. Of Cycle

      Ra (µm)

      1

      0.634

      1.291

      220

      5

      0.1655

      2

      0.880

      1.962

      330.791

      11.962

      0.2029

      3

      0.811

      1.832

      230.399

      12.307

      0.1932

      4

      0.511

      1.908

      327.37

      9.476

      0.1258

      5

      1.000

      1.804

      289.305

      12.957

      0.1905

      6

      0.569

      2.083

      417.661

      7.689

      0.1192

      7

      0.882

      1.872

      285.913

      8.388

      0.1939

      8

      0.574

      1.647

      471.117

      6.449

      0.1371

      9

      0.691

      1.808

      372.037

      5.293

      0.1389

      10

      0.566

      2.209

      558.993

      8.164

      0.1554

      S.N

      CURRENT

      (amp)

      MACH

      .GAP

      (mm)

      GRAIN SIZE

      (Mesh no.)

      No. Of Cycle

      Ra (µm)

      1

      0.634

      1.291

      220

      5

      0.1655

      2

      0.880

      1.962

      330.791

      11.962

      0.2029

      3

      0.811

      1.832

      230.399

      12.307

      0.1932

      4

      0.511

      1.908

      327.37

      9.476

      0.1258

      5

      1.000

      1.804

      289.305

      12.957

      0.1905

      6

      0.569

      2.083

      417.661

      7.689

      0.1192

      7

      0.882

      1.872

      285.913

      8.388

      0.1939

      8

      0.574

      1.647

      471.117

      6.449

      0.1371

      9

      0.691

      1.808

      372.037

      5.293

      0.1389

      10

      0.566

      2.209

      558.993

      8.164

      0.1554

      TABLE 5.2: Result From Genetic Algorithm for Ra

      Based upon the result obtained from data the final optimized value of Ra is found to be 0.2029 µm.

      0.25

      Optimal

      solution

      0.25

      Optimal

      solution

      0.2

      0.15

      0.1

      0.05

      Ra

      0.2

      0.15

      0.1

      0.05

      Ra

      0

      0

      Iteration 1

      Iteration 2

      Iteration 3

      Iteration 4

      Iteration 5

      Iteration 6

      Iteration 7

      Iteration 8

      Iteration 9

      Iteration 10

      Iteration 1

      Iteration 2

      Iteration 3

      Iteration 4

      Iteration 5

      Iteration 6

      Iteration 7

      Iteration 8

      Iteration 9

      Iteration 10

      Fig 5.3:Iteration vs Ra

      Based upon the result obtained from data the final optimized value of Ra is found to be 0.2058 µm and that for MR is 109.8263 mg. Corresponding values for parameters are shown in their respective rows. Some of the readings are found to be out of range so they are neglected. Current and machining ap are the most influencing parameters .These

      largely affect surface roughness value and material removal.

  6. CONCLUSIONS

By completing the above work it can be conclude that response of any unconventional finishing process can be controlled by controlling process parameter variables. Table 5.1 and 5.2 shows the various optimized solutions of the problem for MR and Ra respectively for mafprocess.For optimising responses genetic algorithm is used.The result obtained by GA are very accurate.

Also the same methodology can be applied on any of the unconventional processes such as electric discharge machining(EDM),ECM etc.

REFERENCES

[1]: Jain, V.K., 2002. Advanced MachiningProcesses. Allied Publishers Pvt. Ltd., New Delhi, pp: 57-76.

[2]: Jain, V.K., 2009. Magnetic field assisted abrasive based micro-/nano-finishing. J. Mater. Process. Technol., 209: 6022-6038.

[3]: D.K. Singh, V.K. Jain, V. Raghuram, Experimental investigations into magnetic abrasive finishing of alloy steel, Proceedings of JSME sponsored International Conference on Leading Edge Manufacturing in 21st Century (LEM-21), Nov 36, Niigata, Japan, pp. 403 408.

[4]: T. Shinmura, K. Takajava, E. Hatano, Study on magnetic abrasive processapplication to plane finishing, Bull. Jpn. Soc. Prec. Eng.19 (4) (1985) 289291.

[5]: Jain, V.K., P. Kumar, P.K. Behra and S.C. Jayswal, 2001. Effect of working gap and circumferential speed on the performance of magnetic abrasive finishing process. Wear, 250: 384-390.

[6]: Jayswal, S.C., V.K. Jain and P.M. Dixit, 2005. Modeling and simulation of magnetic abrasive finishing process. Int. J. Adv. Manuf. Technol.

[7]: Elman C. Jameson, Electrical Discharge Machining, Society of Manufacturing Engineers (2001), p.1.

[8]: Antoine Descoeudres, Characterization of electrical discharge machining plasmas, Ph.D. Thesis (2006), School PolytechniqueFederale de Lausanne, Thèse EPFL, no 3542.

Leave a Reply