Experimental investigation into Ball end Magnetorheological Finishing of silicon

Accepted Manuscript Title: Experimental investigation into Ball End Magnetorheological Finishing of Silicon Author: K. Saraswathamma Sunil Jha P.V. Rao PII: DOI: Reference:

S0141-6359(15)00096-3 http://dx.doi.org/doi:10.1016/j.precisioneng.2015.05.003 PRE 6239

To appear in:

Precision Engineering

Received date: Revised date: Accepted date:

21-8-2014 26-3-2015 12-5-2015

Please cite this article as: Saraswathamma K, Rao SJ, P V, Experimental investigation into Ball End Magnetorheological Finishing of Silicon, Precision Engineering (2015), http://dx.doi.org/10.1016/j.precisioneng.2015.05.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights An experimental study through statistical design of experiments are employed to predict the effect of process parameters such as core rotational speed, working gap, and magnetizing current on surface roughness of Silicon wafer in BEMRF process.

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We examined the role of each process parameter on the effect of improving the surface finish.

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ANOVA study was carried out to know the individual effect on improvement of surface finish.

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Experimental investigation into Ball End Magnetorheological Finishing of Silicon K Saraswathamma1, Sunil Jha2, P V Rao3

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Department of Mechanical Engineering, University College of Engineering, Osmania University, Hyderabad500 007, India. Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India. 1

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Corresponding author: [email protected]

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K.Saraswathamma Assistant Professor

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Department of Mechanical Engineering University College of Engineering India.

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Osmania University, Hyderabad 500 007

TEL: +91 40-27097346 FAX: +91 40-27097250

Abstract

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E-mail: [email protected]

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Ball End Magnetorheological Finishing (BEMRF) is a novel finishing process employed in the finishing of 2D and 3D surfaces. The magnetorheological effect

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imparted by the magnetic particles introduced through water or other carrier medium governs the finishing action of BEMRF. Abrasive and carrier medium play a vital role in the surface quality of the silicon material exposed to BEMRF process. In the present study, deionized water was used as a carrier medium while cerium oxide acted as an abrasive to finish the silicon wafer. An experimental study through statistical design of experiments were employed to predict the effect of process parameters such as core rotational speed, working gap, and magnetizing current on a percentage reduction in surface roughness of silicon wafer in BEMRF process. Individual effect on surface roughness values in terms of arithmetical mean roughness (Ra) was studied by applying ANOVA. The maximum contribution is made by the working gap on the surface finish was found to be the most critical aspect. Coming next was the magnetizing current while the last contribution was provided by the core rotational speed.

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Keywords: Ball end Magnetorheological finishing, silicon wafer, working gap, core rotational speed, magnetic flux density.

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1. Introduction Electronic, mechanical, and optical industries prefer, highly finished surfaces

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owing to their excellent properties [1]. Reduction of surface and subsurface damages on

component surfaces, calls for a good to finishing of component under the moderate load

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conditions (with light forces). Also fine finishing of a component with close tolerances, demands precise control over the finishing forces, a situation that applies for all fine

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finishing methods. Consequently, many advanced finishing technologies such as magnetic field assisted finishing processes includes Magnetic abrasive finishing (MAF)

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[2], Magnetic float polishing (MFP), Magnetorheological finishing (MRF) [3],

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Magnetorheological abrasive flow finishing (MRAFF) [4], Magnetorheological Jet

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finishing (MRJF) [5], Magnetorheological abrasive honing (MRAH) [6], and Ball end Magnetorheological finishing (BEMRF) were developed [7]. These finishing processes,

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enable external control of the finishing forces that act on the component surface. This is achieved by controlling the magnetic field strength through variations in the applied current.

Chemo-mechanical polishing (CMP) process has long been a chosen method in

Si wafer manufacturing. CMP has the ability to finish silicon surfaces using polishing pad with abrasive slurry. The alkaline slurry used in CMP reacts with the surface and form silicates which enhances the surface finish quality [8]. However, the finishing forces in the CMP process are less controllable as they mainly depend on the polishing pad pressure. Hence, this process requires determinism in controlling the finishing action. MRF process uses the magnetically stiffened magnetorheological polishing

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(MRP) fluid to deterministically finish optically flat, spherical, and aspherical surfaces down to nanometres level [9, 10]. The finishing forces in the MRF process mainly depend on the behaviour of MRP fluid as well as machining parameters such as

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rotational speed of the tool, working gap between workpiece surface and the tip of the tool, and applied magnetic field strength. The recently developed BEMRF has been

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capable of finishing 2D and 3D surfaces of magnetic and non-magnetic materials [11].

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The MRF process was successfully applied for finishing a variety of materials including hard materials like WC–Ni composites, Al2O3-TiC, reaction bonded- silicon

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carbide and poly-silicon blanks [12, 13]. Kyung-In Jang et al. [14] were studied the mechanism of material removal of

electrochemomechanical Magnetorheological

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polishing process for finishing glassy carbon products. Kung-in Jang et al. [15] were proposed new deburring process in conjunction with magnetorheological fluid and this

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process applied successfully to remove metal burrs with a height of 200 μm and

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thickness of 1 μm in micro-moulds. Sidpara and Jain [16-18] developed and analysed

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the finishing forces in MRF process. They observed that normal forces are the predominant compared to the other forces. A study of the effect of input parameters (fluid composition parameters and

machine process parameters) of BEMRF process on the responses is essential to understand the surface finishing mechanism and for modelling the process. In this paper, an attempt has been made to comprehend the effect of machine process parameters such as core rotational speed, working gap and magnetic flux density on surface roughness of silicon wafer through statistical designing of experiments. Planning and analysis of the effect of process parameters on the percentage reduction in

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surface roughness (% reduction in Ra) have been undertaken by applying response surface methodology. 2. Magnetorheological polishing fluid

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Magnetorheological polishing (MRP) fluid is a mixture of micron sized noncolloidal iron particles and abrasives that are dispersed in aqueous or non-aqueous

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carrier medium. These fluids are smart controllable fluids exhibiting unique, reversible

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rheological properties on application and removal of the magnetic field.

Considering its higher magnetic saturation and least cost, Carbonyl Iron

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Particles (CIP) was chosen for preparation of MRP fluid. High purity Carbonyl Iron particles are prepared from decomposition of pentacarbonyl iron which are also

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magnetically softer.

Sidpara and Jain [18] conducted an experimental investigation to study the effect

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of chemical interactions of abrasive and carrier fluid. Their study revealed that carrier

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medium play crucial role in polishing of silicon.

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Type of abrasive plays a key role in finishing of brittle materials like glass and silicon. Cerium oxide is extensively used in glass polishing industry from several decades. Recent studies shows that CMP also utilising ceria slurries for polishing silicon due to its chemical properties. Cook illustrated chemical tooth of cerium oxide and its strong interaction with silicate ions which promotes the removal mechanism in silicon based material removal process [19]. Ceria abrasive is also utilized for finishing silicon and other related silicate glasses in the MRF process [16, 20-23]. Glycerol is used as stabilisers in water based MR fluids. Alkaline (viz NaOH, KOH) helps to improve the stability and resistance to rust of the iron particles and also maintains the pH (strong influence on CMP of Silicon) of the MRP fluid [24].

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3. BEMRF setup and experimentation Schematic sketch of Ball end MRF tool is displayed in Figure 1. In this process rotational speed was given to the tool while the feed rate (XY-movement) is given to the

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workpiece. The magnetic field at finishing spot was altered by varying the magnetizing current with variable regulated DC power supply. MRP fluid was injected through a

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fluid flow passage up to the tool tip surface. The slight magnetic field was applied (0.2

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A current) for avoiding free flow from the tip of the tool. The tool was lowered towards the workpiece to set a gap between the tool and the workpiece. A spot size of 20

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mm×10 mm size was finished on 1” diameter of 0.8 mm thick single crystal silicon wafer by giving Y-linear movement (velocity of 2.5 mm/sec). Si wafer was fixed in a

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groove of 26 mm diameter and 0.5 mm deep of die steel circular blank (50 mm diameter and 5 mm thick) using paraffin wax and resin mix and then the circular blank was fixed

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on the precision vice. Each spot was polished for 60 minutes and after every 20 minutes

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MRP fluid is removed and fresh fluid was injected for exposing new abrasives in the finishing zone. The temperature was controlled throughout the experiment by a cooling

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electromagnet coil with constant lower temperature bath unit. In this experimentation, fluid composition parameters such as CIP and abrasive

size and their concentration, base medium concentration were kept constant while machine process parameters such as core rotational speed, working gap, and magnetizing current were altered. The experiments conducted revealed the best fluid composition for finishing the Si wafer is 25% vol CIP, 6% vol ceria, 2.5% vol Glycerol, 0.75% vol NaOH, and 66.75% vol DI water. The present study employed the above fluid composition. Being water-based, small quantities of MRP fluid were prepared with the help of stirrer to ensure uniform distribution of CIP and abrasive particles in the base fluid. 6 Page 6 of 29

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Figure 1. Schematic Ball end MRF

4. Response surface regression analysis A two level, full factorial design with six central runs leading to the central

composite rotatable design was applied in the conduct of experiments. Analysis of variance (ANOVA) was conducted to ascertain the significance of the process parameters on the surface finish improvement. Table 1 lists the coded and actual values of altered process parameters used in BEMRF for finishing Si wafer. Experiments were conducted on Si wafer in random order following the experimental plan as shown in Table 2. Initial and final surface roughness values were measured using Taylor Hobson

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Talysurf. Percentage changes in mean line average value of surface roughness (Ra) was calculated using the following computation and the results are shown in Table 3.

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-------------- (1) A quadratic model was selected based on lack of fit test. A reduced model of

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ANOVA after dropping insignificant terms was shown in Table 3. The model F-value of 35.0 indicates the significance of the model. There is only a 0.01% chance that this

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large ‘model F-value’ could occur due to noise. Values of ‘Prob> F’ are less than 0.1

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and this further confirmed that the model is significant. In this case A, B, C, B2, &C2 are significant model terms. Other ANOVA parameters are shown in Table 4. Based on

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the coefficients calculated, the final equation for the reduction in Ra in terms of coded and actual factors respectively are as follows.

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The final equation for the reduction in Ra in terms of coded factors is

The final equation for the reduction in Ra in terms of actual factors is

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Table 1. Coded levels and actual values of machine process parameters S.NO

Process Parameter

Unit

Levels

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A-Core rotational speed (RS) B- Magnetizing current ( MC) C-Working gap (WG)

2

0

1

1.682

RPS

1.32

2

3

4

4.7

A

1.32

2

3

4

4.7

mm

0.6

0.8

1.1

1.4

1.6

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3

-1

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1

-1.682

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Magnetizing current (MC) A 2 2 4 4 2 2 4 4 3 3 1.31 4.68 3 3 3 3 3 3 3 3

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4 20 3 19 18 10 13 11 14 8 2 15 6 16 12 7 1 17 9 5

Core rotational speed (RS) RPS 2 4 2 4 2 4 2 4 1.31 4.68 3 3 3 3 3 3 3 3 3 3

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Run Order

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Std Order

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Table 2. Summary of responses

Working Gap (WG) mm 0.8 0.8 0.8 0.8 1.4 1.4 1.4 1.4 1.1 1.1 1.1 1.1 0.6 1.6 1.1 1.1 1.1 1.1 1.1 1.1

%Reduction in Ra 63.40 59.17 77.14 65.12 43.53 24.86 48.57 31.99 43.53 36.36 35.22 65.12 80.35 32.28 42.28 43.57 43.88 41.22 48.37 46.35

Table 3. Analysis of Variance (ANOVA) for percentage reduction in mean line average surface roughness

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Mean Square 810.3154 295.7985 494.1036 2833.76 108.9906 350.7542 20.05532

F Value 40.40401 14.74913 24.63703 141.2972 5.4345 17.48934

27.30376 3.896008

35.04068 5 4332.351 19

7.008137

0.0742

not significant

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245.7338 9

p-value Prob> F < 0.0001 significant 0.0018 0.0002 < 0.0001 0.0352 0.0009

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DOF 5 1 1 1 1 1 14

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Sum of Squares 4051.577 295.7985 494.1036 2833.76 108.9906 350.7542 280.7745

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Source Model A-RS B-MC C-WG B^2 C^2 Residual Lack of Fit Pure Error Cor Total

Table 4. Other ANOVA Parameters

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R-Squared Adj R-Squared Pred R-Squared Adeq Precision

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0.310028 6.895217 4.496273 3.815021

0.941707786 0.914803687 0.822023373 22.29834841

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Std. Dev. Mean C.V. % PRESS

5. Results and Discussions

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Based on the response surface model obtained from ANOVA analysis, the results

in terms of machine process parameters such as core rotational speed, magnetizing current and working gap on the effect of percentage reduction in Ra are computed and elaborated in the following sections. 5.1 Effect of working Gap

Working gap is the gap between the tip of the tool core and the workpiece

surface. From ANOVA Table 3, working gap is found as the most influencing process parameter on the percentage reduction in surface roughness. It is perceived from the Figure 2 that the percentage reduction in Ra decreases with an increase in the working gap. The average normal magnetic force acting in the working zone of the CIP is [1]

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where V is the volume of CIP, strength, and

is the susceptibility of CIP, H is the magnetic field

is the gradient of magnetic field strength. It is evident from equation

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(2) that magnetic force is proportional to the magnetic field strength and its derivative. And also magnetic field strength is a function of working gap [25]. The magnetic force

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acting on the CIP increases with decrease in the gap between the tool tip and silicon

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surface. Hence, the finishing force is transmitted to the abrasive particles. This would lead to an increased material removal and hence higher percentage reduction in surface

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roughness is achieved.

Figure 2. Influence of working gap on percentage reduction in Ra at 3 RPS core rotational speed

5.2 Effect of magnetizing current From Figure 3 it is observed that, percentage reduction in surface roughness is greater with an increase in the magnetizing current. Magnetic flux density of MRP fluid at

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finishing spot can be increased by increasing the supply of magnetizing current. The finishing pressure generated by a group of CIP in the working zone is given as [2]

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---------------- (3)

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It is evident from the equation (3) that the magnetic force acting on the abrasives rises

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with an increase in magnetic flux density and this result more material removal. The continued finishing at higher magnetic flux densities (magnetizing currents) steadily

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reduces the surface roughness owing to higher magnetic force.

Figure 3. The influence of magnetizing current on a percentage reduction in Ra at 1.1 mm working gap 5.3 Effect of core rotational speed Figure 4 depicts the effect of core rotational speed of percentage reduction in

surface roughness at different working gaps and at constant magnetizing current of 3 A.

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Figure 4 also reveals that, at all

working gaps percentage reductions in surface

roughness decreasing with increase in core rotational speeds. This may be due to the greater centrifugal action on CIP caused by higher working gaps, beyond the exerted

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interaction force. The centrifugal force acting on an abrasive particle is calculated by

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----------------------- (3)

Since centrifugal force is directly proportional to the square of the core rotational speed,

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magnetic normal force decreases with an increase in rotational speed. Due to this, CIPs are not able to hold the abrasive particles strongly during finishing. Response surface

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and contour plot (obtained from Stat-Ease Design Expert software) for the effect of rotational speed and working gap on a percentage reduction in surface roughness is

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shown in Figure 5. These plots also clearly demonstrating that better surface finish will

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be obtained at a lower level of core rotational speed and working gap.

Figure 4. Influence of core rotational speed of percentage reduction in Ra at 3 A current

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Figure 5. Effect of (a) 3D surface plot and (b) contour of variation of the percentage reduction in Ra value with magnetizing current and rotational speed of the tool core.

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The initial and final profiles of the surface roughness for the best finishing conditions are obtained at 0.6 mm gap, 3 A magnetizing current and 3 RPS core

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rotational speed and these are displayed in Figure 6 (a) and (b) respectively. The

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morphology of the silicon wafer surface was spotted at these finishing conditions using

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SEM at 2000X for initial and final surface as exhibited in Figure 7 (a) and 7 (b) respectively. A great improvement in the characteristics of the finished surface greatly improved as compared with the initial surface of a workpiece.

(a)

(b)

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Figure 6. Profile of surface roughness (a) before, and (b) after BEMRF for core

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rotational speed 3 RPS, 3 A current, and working gap 0.6 mm (Exp. No.13 in Table 2).

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(a)

(b)

Figure.7 SEM photograph at 2000X (a) before polishing and (b) after BEMRF at core

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rotational speed 3 RPS, 3 A current, and 0.6 mm working gap (Exp. No. 13 in Table 2) 6. Conclusions

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A detailed study via statistical design of experiments was carried out to study the

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machine process parameters of the BEMRF process on a percentage reduction in

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surface roughness on the silicon wafer surface. The final observations are indicated below:

 Working gap was found to be the critical process parameter for finishing silicon workpiece by Ball end Magnetorheological finishing. The increase in working gap decreases the percent reduction in surface roughness of the silicon workpiece.

 Increase in magnetizing current was found to increase in the percentage reduction in Ra values.  Less significant improvement in percentage reduction in Ra values for different core rotational speeds was observed at lower working gaps. However, at higher

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working gaps, percentage reduction in Ra decreases with increase in core rotational speed.

5. 6. 7. 8.

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9. 10.

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4.

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3.

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2.

Jain, V., et al., Chemo-mechanical magneto-rheological finishing (CMMRF) of silicon for microelectronics applications. CIRP Annals-Manufacturing Technology, 2010. 59(1): p. 323-328. Shinmura T., T.K., Hatano E.,Aizawa T, Study on Magnetic Abrasive Finishing. Annals of the ClRP Vol. 3, 1990. 3(1): p. 325-329. Kordonski, W. and D. Golini, Magnetorheological suspension-based high precision finishing technology (MRF). Journal of Intelligent Material Systems and Structures, 1998. 9(8): p. 650-654. Jha, S. and V. Jain, Design and development of the magnetorheological abrasive flow finishing (MRAFF) process. International Journal of Machine Tools and Manufacture, 2004. 44(10): p. 1019-1029. Tricard, M., et al., Magnetorheological Jet Finishing of Conformal, Freeform and Steep Concave Optics. CIRP Annals - Manufacturing Technology, 2006. 55(1): p. 309-312. Sadiq, A. and M. Shunmugam, Investigation into magnetorheological abrasive honing (MRAH). International Journal of Machine Tools and Manufacture, 2009. 49(7): p. 554560. Kumar Singh, A., S. Jha, and P.M. Pandey, Design and development of nanofinishing process for 3D surfaces using ball end MR finishing tool. International Journal of Machine Tools and Manufacture, 2011. 51(2): p. 142-151. Abiade, J.T., W. Choi, and R.K. Singh, Effect of pH on ceria-silica interactions during chemical mechanical polishing. Journal of materials research, 2005. 20(5): p. 11391145. Jacobs, S.D., et al. Magnetorheological finishing of IR materials. in Proc. SPIE. 1997. Kordonski, W. and D. Golini, Fundamentals of magnetorheological fluid utilization in high precision finishing. Journal of Intelligent Material Systems and Structures, 1999. 10(9): p. 683-689. Kumar Singh, A., S. Jha, and P.M. Pandey, Nanofinishing of a typical 3D ferromagnetic workpiece using ball end magnetorheological finishing process. International Journal of Machine Tools and Manufacture, 2012. 63(0): p. 21-31. Jung, B., et al., Magnetorheological finishing process for hard materials using sintered iron-CNT compound abrasives. International Journal of Machine Tools and Manufacture, 2009. 49(5): p. 407-418. Shafrir, S.N., J.C. Lambropoulos, and S.D. Jacobs, A magnetorheological polishingbased approach for studying precision microground surfaces of tungsten carbides. Precision Engineering, 2007. 31(2): p. 83-93. Jang, K.-I., et al., Mechanism of synergetic material removal by electrochemomechanical magnetorheological polishing. International Journal of Machine Tools and Manufacture, 2013. 70(0): p. 88-92. Jang, K.-I., et al., Deburring microparts using a magnetorheological fluid. International Journal of Machine Tools and Manufacture, 2012. 53(1): p. 170-175.

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References

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12. 13.

14. 15.

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21. 22. 23. 24. 25.

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List of Figures

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20.

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19.

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18.

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17.

Sidpara, A. and V. Jain, Experimental investigations into surface roughness and yield stress in magnetorheological fluid based nano-finishing process. International Journal of Precision Engineering and Manufacturing, 2012. 13(6): p. 855-860. Sidpara, A. and V. Jain, Theoretical analysis of forces in magnetorheological fluid based finishing process. International Journal of Mechanical Sciences, 2012. 56(1): p. 50-59. Sidpara, A. and V.K. Jain, Analysis of forces on the freeform surface in magnetorheological fluid based finishing process. International Journal of Machine Tools and Manufacture, 2013. 69(0): p. 1-10. Cook, L.M., Chemical processes in glass polishing. Journal of Non-Crystalline Solids, 1990. 120(1): p. 152-171. Kordonski, W.I. and S. Jacobs, Magnetorheological finishing. International Journal of Modern Physics B, 1996. 10(23n24): p. 2837-2848. Singh, A.K., S. Jha, and P.M. Pandey, Nanofinishing of Fused Silica Glass Using Ball-End Magnetorheological Finishing Tool. Materials and Manufacturing Processes, 2012. 27(10): p. 1139-1144. Kim, W.-B., S.-H. Lee, and B.-K. Min, Surface finishing and evaluation of threedimensional silicon microchannel using magnetorheological fluid. Journal of manufacturing science and engineering, 2004. 126(4): p. 772-778. Shorey, A.B., et al., Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing. Applied Optics, 2001. 40(1): p. 20-33. Jacobs, S.D., et al., DETERMINISTIC MAGNETORHEOLOGICAL FINISHING. 2002, EP Patent 0,858,381. Singh, A.K., S. Jha, and P.M. Pandey, Mechanism of material removal in ball end magnetorheological finishing process. Wear, 2013. 302(1–2): p. 1180-1191.

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Figure 1. Schematic Ball end MRF

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Figure 2. Influence of working gap on percentage reduction in Ra at 3 RPS core rotational speed

Figure 3. The influence of magnetizing current on a percentage reduction in Ra at 1.1mm working gap

Figure 4. Influence of core rotational speed of percentage reduction in Ra at 3 A current Figure 5. Effect of (a) 3D surface plot and (b) contour of variation of the percentage reduction in Ra value with magnetizing current and rotational speed of the tool core. Figure 6. Profile of surface roughness (a) before, and (b) after BEMRF for core rotational speed 3 RPS, 3 A current, and working gap 0.6 mm (Exp. No.13 in Table 2).

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Figure.7 SEM photograph at 2000X (a) before polishing and (b) after BEMRF at core rotational speed 3 RPS, 3 A current, and 0.6 mm working gap (Exp. No. 13 in Table 2) List of Tables

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Table 1: Coded levels and actual values of machine process parameters

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Table 2. Summary of responses

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Table 3. Analysis of variance (ANOVA) for percentage reduction in mean line average surface roughness

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Table 4. Other ANOVA Parameters

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Table 1: Coded levels and actual values of machine process parameters

2

A-Core rotational speed (RS) B- Magnetizing current ( MC) C-Working gap (WG)

Levels 0 1

-1.682

-1

RPS

1.32

2

3

A

1.32

2

3

mm

0.6

0.8

1.1

1.682

4

4.7

4

4.7

1.4

1.6

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3

Unit

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1

Process Parameter

cr

S.NO

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Table 2. Summary of responses %Reduction in Ra

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63.40 59.17 77.14 65.12 43.53 24.86 48.57 31.99 43.53 36.36 35.22 65.12 80.35 32.28 42.28 43.57 43.88 41.22 48.37 46.35

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cr

Working Gap (WG) mm 0.8 0.8 0.8 0.8 1.4 1.4 1.4 1.4 1.1 1.1 1.1 1.1 0.6 1.6 1.1 1.1 1.1 1.1 1.1 1.1

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Magnetizing current (MC) A 2 2 4 4 2 2 4 4 3 3 1.31 4.68 3 3 3 3 3 3 3 3

M

4 20 3 19 18 10 13 11 14 8 2 15 6 16 12 7 1 17 9 5

Core rotational speed (RS) RPS 2 4 2 4 2 4 2 4 1.31 4.68 3 3 3 3 3 3 3 3 3 3

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te

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Run Order

d

Std Order

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Table 3. Analysis of Variance (ANOVA) for percentage reduction in mean line average surface roughness F Value 40.40401 14.74913 24.63703 141.2972 5.4345 17.48934

p-value Prob> F < 0.0001 significant 0.0018 0.0002 < 0.0001 0.0352 0.0009

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Mean Square 810.3154 295.7985 494.1036 2833.76 108.9906 350.7542 20.05532

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DOF 5 1 1 1 1 1 14

not significant

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Sum of Squares 4051.577 295.7985 494.1036 2833.76 108.9906 350.7542 280.7745

27.30376 3.896008

35.04068 5 4332.351 19

7.008137

0.0742

an

245.7338 9

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te

d

M

Source Model A-RS B-MC C-WG B^2 C^2 Residual Lack of Fit Pure Error Cor Total

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Table 4. Other ANOVA Parameters R-Squared Adj R-Squared Pred R-Squared Adeq Precision

0.941707786 0.914803687 0.822023373 22.29834841

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0.310028 6.895217 4.496273 3.815021

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te

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M

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cr

Std. Dev. Mean C.V. % PRESS

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Figure 1. Schematic Ball End MRF

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Figure 2. Influence of working gap on percentage reduction in Ra at 3 RPS core

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rotational speed

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Figure 3. The influence of magnetizing current on a percentage reduction in Ra at 1.1

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mm working gap

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Figure 4. Influence of core rotational speed of percentage reduction in Ra at 3 A current

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Figure 5. Effect of (a) 3D surface plot and (b) contour of variation of the percentage

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reduction in Ra value with magnetizing current and rotational speed of the tool core.

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(b)

(b)

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Figure 6. Profile of surface roughness (a) before, and (b) after BEMRF for core

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rotational speed 3 RPS, 3 A current, and working gap 0.6 mm (Exp. No.13 in Table 2).

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(a)

(b)

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Figure.7 SEM photograph at 2000X (a) before polishing and (b) after BEMRF at core

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d

M

rotational speed 3 RPS, 3 A current, and 0.6 mm working gap (Exp. No. 13 in Table 2)

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