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NANO-FINISHING OF STAINLESS-STEEL TUBES USING

ROTATIONAL MAGNETORHEOLOGICAL ABRASIVE FLOW
FINISHING PROCESS
a a a
Manas Das , V. K. Jain & P. S. Ghoshdastidar
a
Department of Mechanical Engineering , Indian Institute of Technology Kanpur , Kanpur,
India
Published online: 05 Nov 2010.

To cite this article: Manas Das , V. K. Jain & P. S. Ghoshdastidar (2010) NANO-FINISHING OF STAINLESS-STEEL TUBES USING
ROTATIONAL MAGNETORHEOLOGICAL ABRASIVE FLOW FINISHING PROCESS, Machining Science and Technology: An International
Journal, 14:3, 365-389, DOI: 10.1080/10910344.2010.511865

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 Machining Science and Technology, 14:365–389
Copyright © 2010 Taylor & Francis Group, LLC
ISSN: 1091-0344 print/1532-2483 online
DOI: 10.1080/10910344.2010.511865

NANO-FINISHING OF STAINLESS-STEEL TUBES USING

ROTATIONAL MAGNETORHEOLOGICAL ABRASIVE FLOW
FINISHING PROCESS

Manas Das, V. K. Jain, and P. S. Ghoshdastidar

Department of Mechanical Engineering, Indian Institute of Technology Kanpur,
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Kanpur, India

A new polishing method called Rotational (R)-Magnetorheological Abrasive Flow

Finishing (MRAFF) process has been proposed by rotating a magnetic field applied to the
Magnetorheological polishing (MRP) medium in addition to the reciprocating motion provided
by the hydraulic unit to finish internal surface of cylindrical stainless steel (non-magnetic)
workpiece. By intelligently controlling these two motions uniform smooth mirror-like finished
surface in the range of nm has been achieved. For parametric analysis of the process, the
experiments have been planned using design of experiments technique and response surface
regression analysis is performed to analyze the effects of process parameters on finishing
performance. Analysis of Variance (ANOVA) is conducted and contribution of each model
term affecting percent improvement in surface finish is calculated. The experimental results are
discussed and optimum finishing conditions are identified from optimization study. The present
study shows that rotational speed of the magnet has most significant effect on output response
(percentage improvement in surface roughness, %
Ra ). The best surface finish obtained on
stainless steel workpiece with R-MRAFF process is 16 nm.

Keywords magnetorheological fluid, mirror finished surface, MR finishing, rotating

magnetic field, surface roughness

INTRODUCTION

High purity gas and liquid piping systems are required for critical
applications, such as aerospace components and semiconductor plants.
Highly finished inner surface of the pipes are essential to prevent
contamination of gas and liquid (Wang and Hu, 2005). A new finishing
method named as Rotational-Magnetorheological Abrasive Flow Finishing
(R-MRAFF) process has been developed to finish internal surface of
stainless steel pipe. The usual grinding method (entailing solid-solid

Address correspondence to V. K. Jain, Department of Mechanical Engineering, Indian Institute

of Technology, Kanpur, Kanpur 208016, India. E-mail: vkjain@iitk.ac.in
 366 M. Das et al.

contact) used for internal finishing of cylindrical steel workpieces could

not achieve surface finish in the nanometer range (Saglam et al.,
2005). Yamaguchi and Shinmura (1999) and Wang and Hu (2005) used
Magnetic Abrasive Finishing (MAF) process for internal finishing of tubes.
Shinmura et al. (1990) introduced axial vibration to the workpiece via
an eccentric cam mechanism along with the rotation to increase the
finishing performance in their MAF setup. However, their process cannot
be used to finish any complex shaped geometry because of non-fluidity
of the polishing medium, and hence the medium cannot be delivered to
inaccessible areas as the polishing medium uses loose magnetic abrasive
particles.
Abrasive Flow Machining (AFM) process has the capability of finishing
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internal geometry of any complex shaped workpiece (Jain et al., 1999). Yan
et al. (2007) introduced a spiral polishing method utilizing a fixed rotating
screw to take up the abrasive flow medium along with the screw’s spiral
groove. However, the efficiency of the AFM process depends mainly on the
rheological behaviour of polishing medium, which is least controllable and
hence affects final surface finish. Kordonski and Jacobs (1996) developed
magnetorheological finishing (MRF) process to polish optical lenses where
MRP (magnetorheological polishing) fluid is delivered over a rotating
wheel under magnetic field and the polishing occurs at a converging
gap formed by the surface to be finished and the rotating wheel. Seok
et al. (2007) fabricated a finishing setup to finish curved surfaces on
silicon-based micro-structures using MRP fluid. Recently, Jung et al. (2009)
reported a wheel type MR finishing process where MR polishing fluid is
supplied to a rotating permanent magnet by holding the workpieces on
a swinging mounting plate. The application of MRF process is restricted
to flat, convex, and concave surfaces, and it is not capable to finish any
complex geometrical surface.
Magnetorheological abrasive flow finishing (MRAFF) process is useful
for selectively finishing internal and external surfaces of complex-
shaped workpieces, and it can work within areas that are inaccessible to
conventional finishing methods (Jha and Jain, 2004). With the application
of a magnetic field, the polishing medium becomes stiff (the stiffness
of the medium can be controlled by changing magnetic field) (Shafrir
and Jacobs, 2007) and the medium conforms to the shape of the
workpiece surface to be finished (Tricard et al., 2006). Thus MRAFF
process eliminates the shape limitation of the workpiece surface. However,
MRAFF process gives low finishing rate in general and particularly on
hard materials. The finishing rate for stainless steel workpiece (hardness
358 BHN) is 0.65 nm/cycle (Jha and Jain, 2004) and it is 0.09 nm/cycle
(Jha and Jain, 2006) in case of silicon-nitride as harder workpiece material
(hardness 2718 BHN) at 37.5 bar pressure, and 0.6 T magnetic field
 Nano-Finishing Using R-MRAFF Process 367

for both the cases. Also, in MRAFF process with two core materials of
the H-shaped electromagnets, the existing magnetic field is not able
to generate uniformly distributed magnetic field gradient along the
inner periphery of the cylindrical workpiece. This results in non-uniform
finishing of cylindrical workpiece.
To resolve the above-stated problems, the R-MRAFF process is
developed for producing highly finished inner surface of non-magnetic
stainless-steel tube. In the R-MRAFF process, a rotational motion is
provided to the medium by a rotating magnetic field through permanent
magnets in addition to the existing reciprocating motion of MR polishing
medium through the hydraulic unit. By superimposing these two motions,
relatively high velocity in helical path can be obtained, and it is found that
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it plays a significant role in increasing material removal rate (MRR) and

decreasing surface roughness value (SRV).
The aim of this research work is to characterize the finishing
performance of R-MRAFF process at different process parameters, and
to understand the finishing mechanism. To explore the optimum
combination of finishing conditions, the experiments are designed on
the basis of response surface methodology (RSM) with central composite
rotatable design (CCRD). Also, the effect of finishing parameters on
surface finish is studied.

EXPERIMENTAL SETUP

Figures 1(a) and 1(b) show the schematic diagram and photograph
of R-MRAFF experimental setup, respectively. In R-MRAFF process, MRP
medium is extruded through the workpiece surface/fixture and it is given
up-down motion in the direction of the tube axis by driving two opposing
pistons in medium cylinders with the help of a hydraulic unit. At the
same time the polishing medium is rotated by imparting a rotational
motion to the permanent magnets (Nd–Fe–B, 45 mm × 25 mm × 20 mm)
surrounding the workpiece fixture and forcing the medium to rotate. The
relative motion between the inner surface of the pipe and MRP medium
provides an excellent smooth mirror finished surface. The stainless steel
tube (OD = 24 mm, ID = 18 mm, and height = 435 mm) is fixed to the
workpiece fixture which is connected to the entry and exit profile of
the medium cylinder, and the permanent magnets are installed outside
the tube with the help of a magnet fixture.
The magnet fixture has four slots to place magnets, which are 90◦
apart with each other, at its periphery. The distance between the pole
tips is set at 26 mm with 1 mm clearance between the pole tip and the
workpiece, to avoid collision between them. A variable frequency drive is
used to control the rotational speed of the motor, which in turn controls
 368 M. Das et al.
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FIGURE 1 (a) Schematic diagram of R-MRAFF experimental setup. (b) R-MRAFF experimental
setup.

the rotational speed (RPM) of the magnets. The MRP fluid is prepared by
homogeneously mixing 26.6 vol.% of electrolytic Fe powder (purity 99.5%,
250–300 mesh size) and 13.4 vol.% SiC abrasive with the base medium
(paraffin oil (48 vol.%) and AP3 grease (12 vol.%)) (Das et al., 2008).

Force Analysis
Figure 2(a) shows a two-dimensional schematic diagram of the rotation
of the magnet and, in turn, the medium for internal finishing by R-MRAFF
process. Figure 2(b) shows the distribution of magnetic flux density
around the cylindrical fixture simulated by Ansoft Maxwell® software.
When MRP fluid is supplied inside the cylinder, the magnetic particles
accumulate at the finishing area (Figure 2(a)) along the magnetic lines of
 Nano-Finishing Using R-MRAFF Process 369
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FIGURE 2 (a) Schematic diagram of R-MRAFF process for internal finishing of stainless-steel tube,
(b) Magnetic field vector (B) plot around workpiece fixture for MRP fluid (26.6 vol.% Fe, 13.4
vol.% SiC with 150 mesh size). Specifications of Nd–Fe–B permanent magnet: Maximum Energy
Product, (BH)max = 47.58 MGOe, residual induction, Br = 13.82 kG, coercive force, Hc = 10.78 kOe.

force (Figure 2(b)). SiC abrasives are pressed against the inner surface of
the cylinder by magnetic force (Figure 2(a)), Fm , given by Equation (1)
(Stradling, 1993),

Fm = V H H (1)

where, V is the volume of a magnetic (Fe) particle,  is the susceptibility

of the magnetic particle inside polishing medium, H is the magnetic
field intensity, and H is the gradient of the magnetic field intensity. As
seen in Figure 2(b), the magnetic lines of force follow a curved path in
between two adjacent magnets. The magnetic force has two components:
the tangential component (Fmt ) acts in the circumferential direction on
the workpiece surface and normal component (Fmn ) acts normal to the
workpiece surface. The force components acting on each abrasive particle
are shown in Figure 3.
The radial force, Fr (=kP , where, k is the constant of proportionality
k can be evaluated experimentally) acting on the abrasive grain is mainly
a function of extrusion pressure (P ) and medium viscosity. The axial force
(Fa ) is due to the reciprocation of the medium through pressure applied
to the polishing medium by the hydraulic unit and it is also proportional
to pressure (P ). Fa and Fr can also be calculated by simulating MRP
fluid inside workpiece. Due to the rotational motion of the magnetic
field, a centrifugal force (Fcen = mr 2 ) on the abrasive particle is also
generated, which helps in indenting the abrasive particles in the workpiece
surface. Therefore, the normal indentation force on the abrasive particle
 370 M. Das et al.
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FIGURE 3 (a) Schematic diagram of carbonyl iron particles’s chain structure, (b) Force
components acting on the abrasive particle in the finishing region.

is given as:

Findentation = (Fmn + Fcen + Fr ) (2)

Due to the rotation of the magnet, a tangential cutting force (Ft ) along the
direction tangent to the fluid rotation is generated by the abrasive particle
on the workpiece surface. Hence, the total cutting force (Fc ) on the
abrasive particle is the resultant of axial force (Fa ), tangential component
of magnetic force (Fmt ), and tangential cutting force (Ft ), and it is given as:

Fc = (Fmt + Ft + Fa ) (3)

Calculation of Helix Angle (
) and Arc Length of Helical Path (S)
Due to the resultant of the forces discussed in Equation (3), the path
followed by the active abrasive grain at the workpiece surface is helical in
nature (Figure 4). It generates cross hatch pattern (like honing operation)
of the finishing loci of the abrasive cutting edges on the finished surface,
which improves the oil retention capability of the finished surface. To
understand the effect of rotational speed of the magnet on finishing
performance in R-MRAFF and to compare R-MRAFF with MRAFF, it is
important to evaluate the arc length of the helical path traversed by an
active abrasive grain at the workpiece surface. Since the polishing medium
is semisolid, the path followed by an active abrasive particle in MRP fluid
will not be exactly equal to helix angle . However, for the calculation of
 Nano-Finishing Using R-MRAFF Process 371
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FIGURE 4 Helical path of the active abrasive particle followed in contact with the workpiece
surface.

helical arc length, the polishing medium along with abrasive particles is
assumed to be rigid body.
The helical curve can be represented by a parameterized vector
function (r (t )) as (Kreyszig, 2006):

r(t ) = rw cos t î + rw sin t ĵ + ct k̂ (4)

Here, the parameter ‘t ’ measures the angle between the OX axis

(Figure 4) and the line joining the origin to the projection of the point
r(t ) over the XOY plane, rw = inner radius of the workpiece = 9 mm.
Time taken by an abrasive particle to travel hw (height of the cylindrical
workpiece, Figure 4) with axial velocity, Va is hw /Va second. Hence, the
total number of revolutions made by an active abrasive particle along
the workpiece surface in time hw /Va second is hw N /60Va revolutions or
2hw N /60Va rad (=hw /c rad, after simplification). Here, N is RPM of
the magnet. In this time, the abrasive covers hw distance along the axial
direction.
Thus, in one revolution the fraction of the total workpiece height (hw )
covered by an abrasive is 60Va /N which is equal to pitch 2c. Hence, c =
Va /V . Where, V is angular velocity of the abrasive and is given as, V =
2N /60. Helix angle is given by (Kreyszig, 2006):

 = tan−1 (2c/2rw ) = tan−1 (c/rw ) (5)

 372 M. Das et al.

The arc length (s) of helical path is given by (Kreyszig, 2006):

s = t rw2 + c 2 = (hw /c) rw2 + c 2 (6)

The average axial velocity (Va ) of the medium at 37.5 bar extrusion
pressure in the finishing zone (inside the workpiece) is calculated as
240.67 mm/s from stroke length of piston in media cylinder (Figure 1),
diameter of the piston and inner diameter of the workpiece, and cycle time
of piston.

PRELIMINARY EXPERIMENTS
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The workpieces are prepared by a boring operation using a lathe.

Preliminary experiments are conducted to study the effect of abrasive
mesh size (M ), rotational speed of the magnet (S ), and finishing cycles
(N ) on % improvement in Ra (%
Ra ) by R-MRAFF. Here, Ra is center
line average surface roughness. Extrusion pressure (P ) is kept constant
at 37.5 bar. %
Ra is calculated as (
Ra /initial Ra ) ∗ 100, where
Ra =
initial Ra − final Ra . The average hardness of workpiece (378 HV) is
measured by micro-hardness testing machine. A special fixture is designed
to get initial and final surface roughness values at four different points at
the same location before and after finishing. The roughness measurements
are taken along the axial direction at the same points of the cylinder inside
the internal surface of the fixture. The direction of surface roughness
measurement (for both initial and final surface) is taken perpendicular to
the circular generatrix formed during boring operation. Magnetic field is
constant during experimentation as permanent magnets are used.

Effect of RPM of the Magnet

The experimental results are shown in Figure 5 and also in Table 1.
As can be seen from Figure 5(a), %
Ra increases with the increase
in the rotational speed of the magnet and it reaches an optimum
value at 150 RPM. With the increase in the RPM of the magnet the
tangential cutting force increases, which helps in cutting the undulations
on the workpiece surface. Also the centrifugal force acting on the
abrasive particles increases with increase in RPM, which helps in deeper
indentation in the workpiece surface. Further increase in the RPM of the
magnet beyond the optimum value decreases %
Ra .
Beyond the optimum rotational speed, due to the shear thinning
nature of the MRP fluid, medium shear strength as well as viscosity start
decreasing (Das et al., 2008). Figure 6 shows that viscosity of MRP fluid
decreases with increased RPM. With an increase in the RPM, the fluid
 Nano-Finishing Using R-MRAFF Process 373

FIGURE 5 Effect of RPM of the magnet on (a) % change in Ra , %
Ra , and (b) material removal
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(P = 375 bar, N = 1000 cycles, M = 180).

is strained. Beyond critical RPM, as the fluid is strained beyond its yield
stress, the Fe paticles’ chains break and the medium strength is decreased.
Thus, the bonding within and between the Fe particles chains is not
sufficient enough to overcome the resistance offered by the workpiece
to remove material in the form of -chips. Under these circumstances,
whenever the abrasive’s cutting edge tries to cut the roughness peak,
it rotates/rolls over the peaks and the abrasive moves forward without
cutting because it is not able to exert sufficient cutting force on the
workpiece to remove material (Jayswal et al., 2005). Hence, %
Ra is
decreased (Figure 5(a)), beyond 150 RPM of the magnet. The material
removal, MR (=initial wt. − final wt.) shows increasing trend at higher
rotational speed of the magnet. As the centrifugal force is increased with
the increase in the RPM of the magnet, it creates a deeper indentation on
the workpiece surface and removes more material.

TABLE 1 Effect of RPM of the Magnet on Surface Finish and Material Removal∗

Surface finish Material removal

RPM of Initial Final Ra
Ra Initial Final MR

Process the magnet Ra ( m) ( m) ( m) %
Ra wt. (g) wt. (g) (mg)

MRAFF 0 0.43 0.15 0.28 65.12 5.2170 55.2155 1.5

50 0.44 0.06 0.38 86.36 64.7210 64.7191 1.9
100 0.47 0.04 0.43 91.49 56.7969 56.7910 5.9
R-MRAFF 150 0.51 0.03 0.48 94.12 55.4872 55.4724 14.8
200 0.47 0.06 0.41 87.23 43.5151 43.4968 18.3
250 0.49 0.09 0.4 81.63 52.3225 52.2972 25.3
∗
Machining conditions are given in Figure 5.
 374 M. Das et al.
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FIGURE 6 Viscosity (kPa-s) Vs. rotational speed of the upper disk, n (rpm), curve obtained
from Anton Paar MCR 301 parallel plate rheometer at 0.6 T magnetic field for MRP fluid with
composition as discussed in experimental set-up section for 150 mesh size abrasive.

The comparison of R-MRAFF with respect to MRAFF (at 0 RPM) in

terms of %
Ra and material removal are also shown in Figures 5(a) and
5(b), respectively. In MRAFF process, medium reciprocates to and fro
and the abrasives shear the surface peaks that come in their path of
flow (straight line path) which is equal to the length of the cylindrical
workpiece (hw = 435 mm). Hence, the number of surface peaks that come
in contact with an active abrasive grain in MRAFF is minimum. But in
R-MRAFF process, due to the medium rotation as well as reciprocation,
the path followed by the active abrasive grains on the work surface is non
linear (i.e., helical, Figure 4) as the finishing path is resultant of these
two motions (Figure 3(b)). Hence, both material removal and %
Ra are
higher in R-MRAFF process as compared to MRAFF process because the
path traversed by the active abrasive grains in case of R-MRAFF is longer
than in case of MRAFF process for the same cycle time. The values of
helix angle and helical arc length calculated using Equations (5) and (6),
respectively, are shown in Table 2 at different RPM of the magnet. In all
cases, the traversed length by an active abrasive grain in case of R-MRAFF
process is more than MRAFF process (i.e., 43.5 mm) for the same single
cycle time.
 Nano-Finishing Using R-MRAFF Process 375

TABLE 2 Calculated Helix Angle and Helical Arc Length

at 37.5 bar Pressure for R-MRAFF∗

Magnet Calculated helix Calculated helical

RPM (N ) angle (degree) arc length, S (mm)

50 78.92 44.33
100 68.62 46.72
150 59.56 50.45
200 51.92 55.26
250 45.60 60.89
∗
Length of travel in case of MRAFF is 43.5 mm.

Effect of Abrasive Mesh Size

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During the experiments, higher mesh size (1000 mesh, avg. particle
size = 152 m) was taken first and then the lower mesh size (120 mesh,
avg. particle size = 12667 m) was used. The experimental results are
plotted in Figures 7(a) and 7(b) for %
Ra and material removal,
respectively. The details of the experimental results are provided in
Table 3. It is observed from Figure 7 that both %
Ra and material
removal increase with the decrease in SiC mesh size, achieving highest
improvement in surface roughness at 180 mesh size. At higher abrasive
mesh size, due to lesser size of abrasive diameter (in m), the number
of abrasives present in the polishing medium is increased for a fixed
concentration of abrasive. As a result the indentation force (Equation
(2)) acting on each abrasive particle decreases with increase in mesh size,
hence it results in reduced
Ra (and %
Ra ) and reduced material removal
(Figures 7(a) and 7(b)).
With further decrease in abrasive mesh size beyond 180 mesh, %
Ra
starts decreasing. This is due to deeper indentation/cutting by bigger size
abrasive particles (120 mesh size) which deteriorates surface topography.

FIGURE 7 Effect of abrasive mesh size on (a) % change in Ra , (%
Ra ); (b) material removal;
(c) AFM image of workpiece surface finished by MRP fluid with 120 mesh size abrasive (P =
375 bar, N = 1000 cycles, S = 100 RPM).
 376 M. Das et al.

TABLE 3 Effect of Abrasive Mesh Size on Surface Finish and Material Removal∗

Surface finish Material removal

Abrasive Initial Final Ra
Ra Initial Final MR

mesh size Ra ( m) ( m) ( m) %
Ra wt. (g) wt. (g) (mg)

120 0.57 0.07 0.50 87.72 52.0322 52.0058 26.4

180 0.59 0.05 0.54 91.53 51.2502 51.2268 23.4
220 0.6 0.09 0.51 85.00 57.0708 57.052 18.8
400 0.57 0.38 0.19 33.33 58.4302 58.4181 12.1
1000 0.62 0.45 0.17 27.42 51.1937 51.1893 4.4
∗
Machining conditions are given in Figure 7.
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Deep indentation by bigger size abrasive (120 mesh) is observed under

Atomic Force Microscope (AFM) on the finished surface (Figure 7(c))
which damages the finished surface. Although the surface finish is
deteriorated after reducing the mesh size from 180 to 120 (Figure 7(a))
the material removal is increased due to the increased penetration on the
workpiece surface by the bigger sized abrasive particles (Figure 7(b)).

Effect of Finishing Cycles

It is observed (Figure 8) that the surface roughness value decreases
with the increase in finishing cycles, and also there is a continuous
improvement of surface texture. The initial sharp roughness peaks are
easily cut by the abrasive particles because of smaller shearing area.
As the number of times a particular peak is cut by abrasive particles

FIGURE 8 Effect of number of finishing cycles on surface roughness value (final Ra value) (P =
375 bar, S = 150 RPM, M = 180).
 Nano-Finishing Using R-MRAFF Process 377

increases with the increase in the number of finishing cycles. The highest
finishing performance is obtained at 1600 cyles and the workpiece shows
a mirror finished surface (Figure 9b(i)). The initial surface profile is
shown in Figure 9a(i). The initial and finial (after 1600 cycles) surface
roughness plots are shown in Figures 9a(ii) and 9b(ii), respectively, and
Figures 9a(iii) and 9b(iii) show the atomic force microscope (AFM) images
for the same. After 1600 cycles, workpiece surface strats getting blurred
(Figure 9c(i)) and also surface finish starts deteriorating (Figure 9c(ii)).
When finishing cycles are increased beyond the optimum value, the
abrasive particles start producing scratch marks (Figure 9c(iii)) on
the already finished surface. Hence, surface roughness value increases.
Figure 9c(i) shows the blurred workpiece surface after 2400 finishing
cycles and Figure 9c(ii) shows the surface undulations on the roughness
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profile for the same.

After having obtained the optimum values of some significant
parameters from preliminary experiments, it is felt to perform parametric
analysis of the R-MRAFF process. For this purpose, the experiments are
planned according to the design of experiments and the analysis is
performed as per design of experiments (DOE).

FIGURE 9 (i) Photographs of internal workpiece surfaces after parting off; (ii) Surface roughness
profile, and (iii) AFM image of (a) initial workpiece surface (Ra = 570 nm); finished workpiece
surface after (b) 1600 cycles (Ra = 20 nm), and (c) 2400 cycles (Ra = 90 nm) (P = 375 bar, S =
150 RPM, M = 180).
 378 M. Das et al.

TABLE 4 Coded Levels and Corresponding Absolute Values of Process Parameters

Levels

S. No. Parameter Unit −2 −1 0 1 2

1 Hydraulic extrusion pressure (P ) bar 325 35 375 40 425

2 Number of finishing cycles (N ) 600 800 1000 1200 1400
3 Rotational speed of the magnet (S ) RPM 50 100 150 200 250
4 Mesh size of abrasive (M ) 90 120 150 180 210

EXPERIMENTATION FOR PARAMETRIC ANALYSIS

The aim of the present work was to study the effect of various
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process parameters (extrusion pressure (P ), number of finishing cycles

(N ), rotational speed of the magnet (S ), and mesh size of abrasive (M )) on
%
Ra and material removal of cylindrical stainless steel workpieces using
R-MRAFF process. Central composite rotatable design (CCRD) of RSM
(Montgomery, 2001) is used to plan the experiments. Table 4 shows the
coded levels (−2 to +2) and the absolute values of the process parameters.
A total of 30 experiments were conducted with 16 factorial runs (2k ),
8 axial runs (2k), and 6 center runs. ‘k’ is number of factors (in the
present case, k = 4) considered for DOE. Table 5 gives the summary of
the responses (%
Ra and material removal) obtained under different
finishing conditions. All the CCD (central composite design) terms are
considered in the model used in ANOVA to improve the accuracy of the
regression equation.

RESULTS AND DISCUSSION

Modeling and Optimization
The analysis of variance (ANOVA) of the models (Eq. (7) and Eq.
(8)) for %
Ra is given in Table 6(a). The model p-value (‘Prob > F ’)
of 0.004 for %
Ra and 0.001 for material removal being less than 0.05
(significance level,
) for 95% confidence interval implies that the models
are significant. In case of %
Ra , P , N , S , and S 2 are significant model
terms. In case of material removal, the terms N , S , M , SM and P 2 are
significant terms.

%
Ra = −5261 + 1049P − 008N − 056S + 011M + 277 ∗ 10−3 PN

+ 002PS − 133 ∗ 10−3 PM + 160 ∗ 10−4 NS + 175 ∗ 10−4 NM
− 922 ∗ 10−5 SM − 019P 2 − 316 ∗ 10−5 N 2 − 861 ∗ 10−4 S 2
− 82 ∗ 10−4 M 2 (7)
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TABLE 5 Plan of Experiments and Summary of Responses of Surface Finish and Material Removal

Parameters Surface finish Material removal

Extrusion
Run pressure, Finishing RPM Mesh size of Initial Final Initial Final
No. P (bar) cycle, N magnet, S SiC, M Ra ( m) Ra ( m) %
Ra weight (g) weight (g) MR (mg)

1 35.00 1200 100 120 0.30 0.030 90.00 58.9183 58906 123
2 40.00 1200 200 180 0.42 0.040 90.48 53.4834 534697 137
3 35.00 1200 200 180 0.37 0.070 81.08 58.1285 581204 81
4 37.50 1000 150 150 0.46 0.040 91.30 57.5197 574988 209
5 40.00 1200 200 120 0.37 0.030 91.89 50.3071 502836 235
6 40.00 800 200 180 0.35 0.090 74.29 59.1671 591598 73
7 40.00 800 100 180 0.47 0.060 87.23 49.1402 491288 114
8 37.50 600 150 150 0.37 0.070 81.08 48.0958 48089 68
9 37.50 1000 150 210 0.39 0.070 82.05 52.0484 520434 5
10 37.50 1000 150 150 0.44 0.040 90.91 53.9758 539507 251
11 37.50 1400 150 150 0.35 0.050 85.71 54.2914 542651 263
12 37.50 1000 150 150 0.40 0.040 90.00 55.2365 552133 232
13 42.50 1000 150 150 0.43 0.040 90.70 51.4048 513895 153
14 40.00 800 100 120 0.29 0.040 86.21 65.3753 653712 41
15 35.00 1200 200 120 0.30 0.060 80.00 51.5988 515748 24
16 37.50 1000 250 150 0.43 0.100 76.74 62.1048 620766 282
17 35.00 800 200 120 0.35 0.100 71.43 64.9063 648858 205
18 32.50 1000 150 150 0.29 0.070 75.86 59.1588 591507 81
19 40.00 1200 100 180 0.33 0.016 95.15 54.0125 53992 205
20 40.00 800 200 120 0.32 0.060 81.25 54.3567 543364 203
21 37.50 1000 50 150 0.45 0.080 82.22 54.0939 540888 51
22 37.50 1000 150 150 0.39 0.040 89.74 54.2366 542121 245
23 35.00 800 100 120 0.33 0.020 93.94 54.3892 5438058 862
24 37.50 1000 150 150 0.40 0.060 85.00 55.6523 556318 205
25 37.50 1000 150 150 0.39 0.030 92.31 49.9876 499691 185
26 35.00 1200 100 180 0.23 0.018 92.17 43.7602 437403 199
27 40.00 1200 100 120 0.26 0.020 92.31 58.8255 588075 18
28 35.00 800 200 180 0.23 0.060 73.91 59.7181 597107 74
29 37.50 1000 150 90 0.34 0.040 88.24 57.8854 578576 278

379
30 35.00 800 100 180 0.34 0.050 85.29 62.3393 623278 115
 380 M. Das et al.

TABLE 6(a) ANOVA for %
Ra and Material Removal (MR) for Stainless Steel Workpiece

% Reduction in Ra (%
Ra ) Material removal (MR)

p-value Percent p-value Percent

Source F value Prob > F contribution F value Prob > F contribution

Model 432 0.0040∗ 560 0.0010∗

Pressure (P ) 914 0.0086∗ 1435 100 0.3343 118
Cycle (N ) 1128 0.0043∗ 1772 1763 0.0008∗ 2093
RPM (S ) 1966 0.0005∗ 3088 955 0.0075∗ 1134
Mesh size (M ) 097 0.3395 153 1357 0.0022∗ 1612
PN 183 0.1957 288 091 0.3548 108
PS 381 0.0698 599 003 0.8576 004
PM 001 0.9234 002 010 0.7512 012
NS 245 0.1386 384 155 0.2322 184
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NM 105 0.3216 165 3.51E-04 0.9853 000

SM 002 0.8944 003 1779 0.0007∗ 2112
P2 237 0.1443 373 1137 0.0042∗ 1350
N2 261 0.1270 410 356 0.0789 422
S2 758 0.0148∗ 1190 344 0.0834 409
M2 089 0.3601 140 373 0.0725 443
Lack of Fit 333 0.0983∗∗ 366 0.0825∗∗
∗ ∗∗
– Significant term, – not significant.

TABLE 6(b) ANOVA for Final Ra

p-value Percent
Source F Value Prob > F contribution

Model 242 0.0504

Pressure (P ) 164 0.2193 482
Cycle (N ) 730 0.0164∗ 2147
RPM (S ) 1148 0.0041∗ 3376
Mesh size (M ) 142 0.2524 418
PN 166 0.2166 488
PS 152 0.2363 447
PM 091 0.3555 268
NS 011 0.7412 032
NM 025 0.6211 074
SM 011 0.7412 032
P2 002 0.8947 006
N2 025 0.6231 074
S2 731 0.0163∗ 2150
M2 002 0.8947 006
Lack of Fit 443 0.0570∗∗
∗ ∗∗
– Significant term, – not significant term.
 Nano-Finishing Using R-MRAFF Process 381

Material removal = −68755 + 3039P + 004N + 076S + 069M

+ 204 ∗ 10−3 PN + 156 ∗ 10−3 PS + 460 ∗ 10−3 PM
− 133 ∗ 10−4 NS + 333 ∗ 10−6 NM − 300 ∗ 10−3 SM
− 044P 2 − 385 ∗ 10−5 N 2 − 605 ∗ 10−4 S 2
− 175 ∗ 10−3 M 2 (8)

From the ANOVA, it has been observed that rotational speed of the
magnet has the highest contribution (31%) among all the main factors
and their interaction terms for (%
Ra ). But for material removal, finishing
cycle has the highest contribution (21%). With the increase in finishing
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cycles, the number of times the abrasive particles come in contact with a
certain peak increases, hence material removal increases.
An optimization study is also carried out to select the optimum
combination of parameters keeping input parameters in the selected range
(Table 4). The optimization results (Table 7) in terms of desirability
value, have been obtained from Design-Expert® software using Derringer
and Suich (1980) algorithm. The optimization is performed in terms of
desirability function (di ). The desirability function involves transformation
of each estimated response variable to a desirability value di , where
0 ≤ di ≤ 1. The individual desirabilities are then combined using their
geometric mean to find the overall desirability function (D) as:

D = (d1 × d2 × · · · × dk )1/k (9)

where k is the number of response variables. Design expert software

uses a direct search method to maximize the desirability function D
(Montgomery and Myers, 2002). A value of ‘1’ of ‘D’ represents the ideal
case. The best solution obtained was as follows: P = 40 bar, N = 1200
cycles, S = 149 RPM, and M = 153 (Table 7). It was observed that the
optimization routine returns slightly different results each time it is run.
This is due to the approximation error of the optimization algorithm and

TABLE 7 Optimization Results of Process Parameters for Maximum %
Ra

RPM of Abrasive
Soln. Extrusion pr. Finishing the magnet, mesh
No. (P ) (bar) cycle (N ) S (RPM) size (M ) %
Ra Desirability

1 40 1200 149 153 94.14 0.957 Selected

2 40 1200 148 156 94.12 0.957
3 40 1200 152 148 94.11 0.956
 382 M. Das et al.

iterative way (direct search method) of finding the solution of overall

desirability function, D (Eq. (9)).
The effects of process parameters on %
Ra and material removal
have been compueted using Eqs. (7) and (8), respectively, and the results
obtained are plotted and explained in parametric analysis section.
To test the validity of the methods, a few confirmation experiments
are carried out (Table 8); one at optimum parametric conditions and
three others at different experimental conditions within the range of the
parameters (Table 4). For 95% confidence interval the confidence band
is: lower limit for %
Ra is 86.32 and upper limit is 93.44. The %
Ra for
exp. Nos. 1, and 2 of the Table 8 fall within this confidence band. Hence,
the effectiveness of the response surface model is confirmed. However,
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for exp. No. 4 there is a little bit deviation and it is slightly more for
exp. No. 3. There are other factors (for example, magnetic flux density,
fluid composition etc.) which impact the response (%
Ra ) but have not
been considered in the current DOE analysis. Hence, for some cases
confirmation test results fall just outside the statistical confidence band for
the 95% confidence interval.
The best surface finish achieved in all the experiments (Table 5) after
finishing by R-MRAFF process is 16 nm in experiment number 19. Hence,
workpiece of experiment number 19 is chosen to compare the surface
generated by R-MRAFF process with initial surface. Figures 10a(i) and
10b(i) are the photographs of the internal surface of workpiece before
and after finishing by R-MRAFF process (experiment number 19, Table 5).
From initial workpiece surface (Figure 10a(i)) the letters “IITK” are not
reflected at all and the letters are clearly reflected like mirror from the
finished workpiece surface (Figure 10b(i)).
Figures 10a(ii) and 10b(ii) show the surface roughness profile of
initial and finished surface respectively, obtained by R-MRAFF process
for the same workpiece discussed here. In Figure 10a(ii), the periodic
peaks and valleys are generated due to the formation of generatrix during
boring operation. AFM image of the same is shown in Figure 10a(iii).

TABLE 8 Confirmation Results of Response Surface Model

Experimental conditions Experimental results

Soln. Pr., P Finishing Magnet SiC mesh Initial Final

No. (bar) cycle (N ) RPM, S size (M ) Ra ( m) Ra ( m) %
Ra

1 40 1200 149 150 0.29 0.02 93.10

2 35 1300 125 120 0.33 0.04 87.88
3 37.5 700 75 180 0.31 0.06 80.65
4 42.5 1100 225 150 0.34 0.05 85.29
 Nano-Finishing Using R-MRAFF Process 383
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FIGURE 10 (i) Photograph of internal workpiece surface after parting off, (ii) Surface roughness
profile, and (iii) AFM image showing surface texture of (a) initial workpiece surface (Ra = 330 nm),
that does not reflect the letters IITK, (b) final workpiece surface (Ra = 16 nm) after finishing by
R-MRAFF process in experiment number 19 of Table 5, which reflects the letters IITK.

After finishing by R-MRAFF process, the roughness profile became almost

straight line (Figure 10b(ii)) indicating very smooth surface. AFM image
of the same is shown in Figure 10b(iii).
The initial surface shows very high peaks and deep valleys formed
due to boring operation. After finishing with R-MRAFF process, a smooth
surface is obtained. The polishing medium in R-MRAFF process moves in
a helical path (Figure 4) and the abrasive cutting force is a resultant of
axial force and tangential force (Figure 3(b)). Hence, the abrasive cutting
marks generate cross hatch pattern as shown in Figure 10b(iii) like in
honing operation which would improve the lubricant holding capabilities
of the finished surface.
The ANOVA based on the final surface roughness value achieved
during R-MRAFF process is also provided in Table 6(b). It is observed from
this table that finishing cycles (N ), RPM of the magnet (S ), and quadratic
term of RPM of the magnet (S 2 ) are significant model terms. However, the
model is just at the boundary of being significant and not significant. It is
attributed to the variation in the initial surface roughness value as shown
in Table 5.
 384 M. Das et al.
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FIGURE 11 Effect of extrusion pressure on (a) %
Ra , and (b) material removal for different mesh
sizes (N = 1000 cycles, S = 150 RPM).

Parametric Analysis
Effect of pressure. It is observed from Figure 11(a) that %
Ra increases
with an increase in the extrusion pressure. The radial force is responsible
for indentation on the workpiece surface where as the axial force helps
in removing the material in the form of micro chips. With the increase in
extrusion pressure, axial force and radial force both increase and lead to
higher material removal rate. As the extrusion pressure increases, the shear
rate increases. At higher shear rate, due to the shear thinning nature of the
MRP fluid, the medium shear strength as well as viscosity start decreasing

FIGURE 12 Viscosity Vs. shear rate curve obtained from Anton Paar MCR 301 rheometer at 0.6 T
magnetic field for MRP fluid with composition as discussed in section 2 with 150 mesh size abrasive.
 Nano-Finishing Using R-MRAFF Process 385

(Das et al., 2008) (Figure 12). This shear thinning phenomenon of MRP
fluid is explained as follows. With the application of magnetic filed,
carbonyl iron particles (CIPs) in MRP fluid form strong chain structure
as shown in Figure 13(a) from their initial random state at zero magnetic
field.
Because energy is required to deform and rupture the chains, this
micro-structural transition is responsible for the onset of a large yield
stress. The fluid is strained with the application of extrusion presure
through a hydralic unit. Figure 13(b) shows an increasing resistance to an
applied shear strain,  due to yield stress. As the fluid is more strained
(i.e. with higher applied pressure) beyond its yield stress, the chains break
(Figure 13(c)) and the strength of the fluid starts decreasing rapidly.
Under this condition, the bonding within and between the iron particles
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chains is not strong enough to overcome the resistance offered by the

workpiece to remove material in the form of chips, and hence %
Ra tends
to stabilize (Figure 11(a)) or even decrease.
Material removal is increased (Figure 11(b)) due to the deeper
penetration of the abrasive particles in the workpiece surface as radial
force increases at higher extrusion pressure and it becomes maximum
at some optimum value. Beyond the optimum value, material removal
again decreases because the depth of penetration reduces due to the shear
thinning nature of the MRP fluid.
Effect of number of cycles. It is observed from Figure 14(a) that the
number of cycles has profound effect on finishing performance (%
Ra )
and at high no. of finishing cycles it tends to stabilize (i.e., it attains the
critical surface finish). The initial high rate of improvement of surface
finish is due to removal of sharp peaks. As the number of finishing cycles
increases, the number of time shearing takes place for a particular peak

FIGURE 13 Schematic diagram to illustrate the ideal CIPs chain structure with embedded abrasive
particles at magnetic field strength (H ) (a) Without any shear strain, (b) At applied shear strain
1 , (c) At applied shear strain 2 (2 > 1 ) (Jha and Jain, 2004).
 386 M. Das et al.
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FIGURE 14 Effect of finishing cycle on (a) %
Ra , and (b) material removal for different extrusion
pressures (M = 150, S = 150 RPM).

also increases; hence greater is the improvement in %
Ra value. At higher

finishing cycles, the shearing area of the roughness peaks increases and it
requires more no. of abrasive particles and higher shear (or cutting) force
to keep the same rate of %
Ra improvement. Since the shear force and %
abrasive concentration are constant for a constant value of magnetic flux
density and wheel rotational speed, the %
Ra tries to stabilize at higher
finishing cycles as shown in Figure 14(a). At higher pressure, depth of
indentation increases hence %
Ra is also higher. For the same reason
material removal increases with an increase in the finishing cycles and its
rate stabilizes at higher finishing cycles (Figure 14(b)). However, in both
the cases (%
Ra and material removal), the number of cycles at which the
response tends to stabilize also increases with increase in pressure.
Effect of RPM of the magnet. From ANOVA (Table 6(a)), it is found
that rotational speed has the highest contribution on %
Ra , and
their relationship is shown in Figure 15(a) giving optimum value at
around 160 RPM. Due to the combined effect of rotational motion and
reciprocating motion in R-MRAFF process, the length of finishing path
experienced by an active abrasive particle in the polishing medium in
R-MRAFF is higher than that in MRAFF. The length of finishing path
increases with an increase in RPM of the magnet (Table 2). Further,
the number of surface peaks that are sheared by an active abrasive particle
increases as RPM increases hence %
Ra and material removal increase
(Figure 15). With the increase in the rotational speed of the magnet, the
tangential cutting force which helps in smoothing the surface undulations
from the workpiece surface increases, and the centrifugal force which
helps the abrasive particles in indenting into the workpiece surface also
increases. As the RPM of the magnet is increased further beyond the
 Nano-Finishing Using R-MRAFF Process 387
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FIGURE 15 Effect of rotational speed of the magnet on (a) %
Ra , and (b) material removal for
different finishing cycles (P = 375 bar, M = 150).

optimum value, %
Ra decreases. The reason of which is already given in

the preliminary experiments section.
Effect of abrasive mesh size. The %
Ra increases with an increase in
the abrasive mesh size reaching to an optimal value at around 140 mesh
size for the given finishing conditions. Figure 16(a) shows the relation
between %
Ra and abrasive mesh size for different pressures. At lower
mesh number (120 mesh), the diameter of the abrasive particles is
bigger hence, the magnetic force is distributed amongst lesser number
of abrasive particles and the indentation force (and also indentation
pressure) acting on each abrasive particle is more. Hence, the bigger size

FIGURE 16 Effect of abrasive mesh size on (a) %
Ra , and (b) material removal for different
extrusion pressure (S = 150 RPM, N = 1000 cycles).
 388 M. Das et al.

SiC abrasive particles remove material by deeper penetration (i.e., deeper

scratch marks are generated; it is explained with AFM image (Figure 7(c)
in preliminary experiments section), and generate deeper irregularities
on the finished surface (or higher Ra value). As a result of this, with
lower abrasive mesh size (i.e., larger diameter of abrasive particles) lesser
improvement in Ra value is observed (Figure 16(a)) but the material
removal is higher due to deeper penetration by abrasives (Figure 16(b)).
At optimal abrasive mesh size, %
Ra is improved. Further increase in
the abrasive mesh size beyond the optimal value, %
Ra decreases. MRP
fluid with smaller abrasive particles produces a lower finishing efficiency
as shown in Figure 16(a). The smaller size SiC abrasive particles make a
shallower depth of cut. As the size of the abrasives diminishes, the number
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of the abrasives increases because of fixed abrasive concentration in MRP

fluid. Hence, normal indentation force (i.e., magnetic force) acting on the
smaller abrasive particle through Fe particle chains is transferred to the
larger number of abrasive particles. This reduces the finishing force and
depth of cut of each cutting edge of the abrasive. Hence, both finishing
efficiency (Figure 16(a)) and material removal (Figure 16(b)) decrease
with the increase in the abrasive mesh size.

CONCLUSIONS

Based on the presented study, following conclusions are drawn:

• R-MRAFF process is capable of achieving mirror finished surface in

the nanometer range on internal surface of cylindrical stainless steel
workpiece. Surface roughness as low as 16 nm is achieved by this process.
• The role of rotational speed of the magnet on % improvement in Ra in
R-MRAFF process is clearly distinguished. Rotational speed has 30.88%
contribution from main effect (linear term, S ) and 11.90% contribution
from quadratic term (S 2 ). With an increase in the rotational speed of
the magnet, %
Ra increases initially and there is an optimum value of
rotational speed at which finishing action is the best and beyond that
the surface finish deteriorates. The second highest significant parameter
is finishing cycles followed by extrusion pressure. They have 17.72% and
14.35% contribution, respectively, on %
Ra .
• The optimized process parameters in terms of highest %
Ra are: magnet
rotational speed = 149 RPM, extrusion pressure = 40 bar, abrasive mesh
size = 153, finishing cycles = 1200.
• From atomic force microscope images it is observed that the abrasive
cutting marks generate cross-hatch pattern in R-MRAFF process like
honing operation.
 Nano-Finishing Using R-MRAFF Process 389

ACKNOWLEDGMENTS
We acknowledge the Department of Science and Technology,
New Delhi for their financial support for Project No. SR/S3/NERC/
0072/2008 entitled “Rotational – magnetorheological abrasive flow
finishing (R-MRAFF)” under which this work has been done.

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