 Open Access
 Total Downloads : 1531
 Authors : Asit Shukla, Dr.D. K.Singh
 Paper ID : IJERTV2IS90383
 Volume & Issue : Volume 02, Issue 09 (September 2013)
 Published (First Online): 21092013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Modelling and Optimization of Magnetic Abrasive Finishing Process
Modelling and Optimization of Magnetic Abrasive Finishing Process
Asit Shukla 1, Dr.D. K.Singh 2
1.M.Tech scholar at Madan Mohan Malviya Engineering College,Gorakhpur,India 2.Professor And Head of Department,Madan Mohan Malviya Engineering College,Gorakhpur,India
ABSTRACT
Increasing demand of high accuracy and high efficiency machining of difficulttomachine materials is making the application of abrasive finishing technologies increasingly important. One of such process is magnetic abrasive finishing (MAF) process. It can produce surfaces with surface finish in range of 0.041.00 Âµm and dimensional accuracy up to 0.5 Âµm. 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).
Keywords: Alloy steel, Magnetic Abrasive Finishing, Response Surface Methodology, Surface Roughness, Analysis of Variance(ANOVA), Genetic Algorithm, GA Toolbox, MATLAB,DESIGN EXPERT.

INTRODUCTION

Magnetic Abrasive Finishing
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). 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 selfsharpening, 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). Finishing pressure can be controlled via a magnetic field applications (Shinmura et al., 1993; Chang et al., 2002). Workpiece materials can be both magnetic (e.g., steel) as well as non magnetic (e.g., ceramics) and the material removal can be adjusted based on the size of the magnetic abrasives. Thus, MAF is a multifunctional precise finishing method one can use to obtain quality surface finishes efficiently (LiehDai et al., 2007). Jayswal et al. (2005) also proposed a mathematical
model for mechanics of material removal and a model for surface roughness during the MAF process. They developed a finite element code to evaluate the distribution of magnetic forces, considering magnetic flux density, type and size of magnetic abrasive particles and the working gap as the main parameters. By considering the Gaussian distribution of the ordinates of the surface profile, (Jain et al., 2007) modelled and simulated the surface profile obtained after MAF. This model predicts centreline average surface roughness value Ra obtained after MAF. Literature survey reveals that there are little contributions toward the simulation and modelling of the magnetic abrasive finishing process.
Figure1.1:Cylindrical work piece machining on magnetic abrasive finishing machine[1]
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


Formation of magnetic abrasive brush
Fig. 1.2 shows the configuration of magnetic abrasive brushes in which the magnetized abrasives spread in a row from the pole to the material. In considering only the magnetic field, a continuous function, it is estimated that the magnetized particles aggregate into bundles. However, the contact of the magnetized particles must be taken into account. Energy requirements in the production of magnetic abrasive brush using magnetic abrasives that are added little by little into the magnetic field are discussed as follows:

Magnetization energy, Wm, required to magnetize the abrasives to form bundles.

Repulsion energy, Wf , due to Faraday effect causes the bundles to repel from each other.

Tension energy, Wt, needed to counter act the curved bundles due to repelling particles.
Therefore, in order to form the magnetic abrasive brush sum of these energies, W, is necessary:
W = Wm + Wf + Wt (1)
The brush is formed in a stable state when W Is minimum, that is, dW = 0.
Figure 1.2: Configuration of magnetic abrasive brushes[2]


Applications
The process can be applied in many other fields,

Polishing of fine components such as printed circuit boards (PCB).

The removal of oxide layers and protective coatings.

Chamfering and deburring of gears and cams.

Automatic polishing of complicated shapes.

Polishing of flat surfaces.



EXPERIMENTATION

Experimental setup
A schematic diagram of the plane MAF apparatus is shown in Figure 2.1. The flatfaced electromagnet has been designed such that the centre part of the magnet acts as a north pole and
ferromagnetic abrasive particles (ratio of iron particles and SiC abrasive particles in the gap).

Work piece composition
Alloy steel is considered as work piece for the experimental work.
Table 2.1: Workpiece Material composition (Alloy Steel)
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 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 re 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
Alloying elements percentage
C 0.350.45
Mn 0.450.60
Si 1.311.81
Cr 0.200.30
Ni 0.100.30
Iron Rest
electromagnet is given by a device consisting of brass slip rings and electric carbon brushes.

Experimental design
The various levels of machining parameters 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
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
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.


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)

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 (Â¼2.35) at 95% confidence interval (a Â¼ 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.

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 (Âµm)
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.


OPTIMISATION WITH GA

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.

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


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 survivalofthefittest 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)


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

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

Result for Ra
S.N
CURRENT
(amp)
MACH
.GAP
(mm)
GRAIN SIZE
(Mesh no.)
No. Of Cycle
Ra (Âµm)
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 (Âµm)
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 Âµm.
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 Âµm 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 gap are the most influencing parameters .These largely affect surface roughness value and material removal.


CONCLUSIONS
By completing the above work it can be said that response of magnetic abrasive finishing process can be controlled by controlling process parameter variables, which are current(magnetic flux density),machining gap, abrasive grain size (mesh no.) and no. of cycle. Table 5.1 and 5.2 shows the various optimized solutions of the problem for MR and Ra respectively. For optimising responses genetic algorithm is used.The result obtained by GA are very accurate.
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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 (LEM21), Nov 36, Niigata, Japan, pp. 403408.

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