A

pvppec©

K

1

omnmrpacpapvdta[

0d

Wear 261 (2006) 856–866

Modeling and simulation of surface roughness in magnetorheologicalabrasive flow finishing (MRAFF) process

Sunil Jha, V.K. Jain ∗Department of Mechanical Engineering, IIT Kanpur 208016, India

Received 1 September 2005; received in revised form 5 January 2006; accepted 24 January 2006Available online 20 March 2006

bstract

Magnetorheological abrasive flow finishing (MRAFF) process was developed for super finishing of internal geometries of hard materials. Thisrocess relies for its performance on magnetorheological effect exhibited by carbonyl iron particles along with abrasive particles in non-magneticiscoplastic base medium. The extent of finishing action depends on radial and tangential forces coming on abrasive particles due to carbonyl ironarticles (CIPs) arranged in columnar structure in the presence of external magnetic field. Experiments were conducted on stainless steel work

ieces with different combinations of CIP and SiC particles in MRP-fluid for same volume concentration. CIP chain structure and surface roughnessvaluation model have been proposed. Magnitudes of the forces on abrasive particles were then calculated and change in surface roughness wasomputed using the model developed to simulate final surface roughness.

2006 Elsevier B.V. All rights reserved.

hing

ptTsibaa[(

dssw

eywords: MRF; Magnetorheological polishing fluid; MRAFF; Precision finis

. Introduction

The ultra precision finishing technologies have grown rapidlyver recent years, and have tremendous impact on the develop-ent of new products and materials. With the advent of these

ew materials, manufacturing engineers are facing challenge ofachining and finishing these materials to meet their functional

equirements. The available traditional and advanced finishingrocesses alone are incapable of producing desired surface char-cteristics on complex geometries, and in exercising in-processontrol on finishing action. Abrasive flow machining (AFM) [1]rocess was developed to finish internal complex geometries byllowing abrasive laden polymeric medium to flow over it underressure. The abrading forces in AFM process are function ofiscosity of viscoelastic polymeric base medium, which is very

ifficult to control during operation. This lacks determinism inhe control of finishing action. In another process developed forutomated lens finishing, magnetorheological finishing (MRF)2], external magnetic field is used to control the rheological

∗ Corresponding author. Tel.: +91 512 2597916; fax: +91 512 2597408.E-mail address: vkjain@iitk.ac.in (V.K. Jain).

oApsaoihs

043-1648/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2006.01.043

roperties of polishing medium, hence adds determinism in con-rolling surface topography being generated during finishing.he present applications of MRF process are limited to flat,pherical and aspherical surfaces due to dwelling of work piecen the moving magnetorheological polishing (MRP)-fluid rib-on. To meet the finishing requirements of different geometriesnd incorporating better in-process control of finishing forces,hybrid process by combining AFM and MRF was developed

3], and named as magnetorheological abrasive flow finishingMRAFF).

A hydraulically powered MRAFF experimental setup wasesigned and fabricated to conduct finishing experiments. Atudy was made to understand the effect of magnetic fieldtrength on reduction in surface roughness (�Ra), and the resultsere reported elsewhere [3]. The role of magnetic field strengthn decrease in surface roughness value was clearly observed.fter preliminary study, the finishing performance of MRAFFrocess is found to be mainly dependent on MRP-fluid compo-ition for the same magnetic field strength, extrusion pressurend number of finishing cycles. MRP-fluid composition is one

f the key process parameters affecting final surface roughnessn MRAFF process due to its role in fluid structure formation;ence it is taken up as a main factor for the present study. In thistudy the effect of size of silicon carbide (SiC) abrasives and

S. Jha, V.K. Jain / Wear 261 (2006) 856–866 857

Nomenclature

a spacing between two abrasive particles passingover work piece (m)

A total projected area of spherical abrasive grain(m2)

A′ projected area of embedded portion of abrasive inthe work piece (m2)

B magnetic flux density (T)Df fixture inner diameter in finishing zone (m)Dp MRPF cylinder inner diameter (m)DCIP carbonyl iron particle diameter (m)Fm magnetic force on CIP in external magnetic field

(N)Fnormal normal force on abrasive particle (N)Fshear shear force on abrasive particle (N)H magnetic field strength (A/m)HBHN Brinell hardness (kgf/mm2)I magnetizing current (A)L length of electromagnet coil (m)Le MRP-fluid extruded (slug) length (m)Ls MRPF cylinder stroke length (m)Lspan CIP chain’s spanning length from one end to

another (m)m mass of CIP (kg)n number of turns per unit length (m−1)N number of abrasive grains in a line in a strokeNv number of particles in volume V of MRP-fluidNCIP number of CIP particles in a given MRP-fluidr1 core radius of electromagnet coil (m)r2 outer radius of electromagnet coil (m)Rnormal reaction force on abrasive particle due to FnormalRshear reaction force on abrasive particle due to Fsheart depth of indentation (m)V volume of MRP-fluid (m3)Vu volume of a unit cell (m3)VCIP volume of a CIP particle (m3)x distance from pole face (m)Yi Ordinate of roughness profile data (mm)

Greek lettersχm magnetic susceptibility of carbonyl iron particles

(CIPs) (m3/kg)φCIP volume fraction of CIPs in MRP-fluidµ0 magnetic permeability of free space (H m−1)σy yield point stress of stainless steel work piece in

shear (Pa)

cvsBsp

it

2

oiteomfltfiplmtptpta

ltcbiaici

3

τy Fluid shear stress (Pa)

arbonyl iron particles (CIPs) on decrease in surface roughnessalue was investigated on stainless steel work pieces. A micro-

copic study of CIP chain structure formation was conducted.ased on this observation and suitable assumptions related to

tructure formation, surface roughness was simulated using theroposed models (chain structures and surface roughness), and

d[

Fig. 1. Mechanism of MRAFF action.

t was compared with the experimental results as discussed inhe following sections.

. Magnetorheological abrasive flow finishing (MRAFF)

Finishing forces in MRAFF process are controlled by rhe-logical properties of MRP-fluid which comprises of carbonylron particles and very fine abrasives dispersed in viscoplas-ic base medium of mineral oil and grease. This compositionxhibits unique reversible change in its rheological propertiesn the application and removal of external magnetic field. Theagnetic field dependent yield stress and viscosity of MRP-uid can be controlled by controlling magnetizing current in

he electromagnet coils producing magnetic field across thenishing zone. The CIPs acquire magnetic dipole moment pro-ortional to magnetic field strength, and aggregate into chainike structure aligned in the field direction [4], embedding non-

agnetic abrasive particles in between (Fig. 1). Depending onhe size and volume concentration of abrasives and carbonyl ironarticles (CIPs), the bonding strength gained by the abrasiveshrough surrounding CIPs chains varies. To finish internal workiece surfaces in MRAFF process, the MRP-fluid was extrudedhrough the work piece passage in the presence of magnetic field,s shown in Fig. 1.

Abrasion occurs selectively only where the change in rheo-ogical properties of MRP-fluid takes place from near Newtoniano Bingham plastic due to CIPs chain formation. Due to CIPshain formation, non-magnetic abrasive particles get embeddedetween the chains, as shown in Fig. 1, and gain bonding strengthn proportion to the magnetic field strength to perform finishingction. In this way, the extent of abrasion of peaks by abrasivess controlled by magnetic field strength and the desired finishingharacteristics are controlled by changing magnetizing currentn the electromagnet.

. Experimentation

Finishing experiments were conducted on a speciallyesigned and developed hydraulically powered MRAFF setup3]. All experiments were conducted for 200 finishing cycles

858 S. Jha, V.K. Jain / Wear 2

FC

aflb6ptwrbMaumsdrs∼gbar

4

iRi8cw

edOitfiptpoottfswiiss

4

msflfspiobc[lFiones

TS

E

123456

ig. 2. Flow curves of MRP-fluids with 20 vol.% CS (Fluid 1) and HS (Fluid 2)IPs with 800 mesh SiC at 2000 G.

t 3.75 MPa hydraulic extrusion pressure and 0.531 T magneticux density. The MRP-fluid was prepared with 20 vol.% car-onyl iron powder and 20 vol.% silicon carbide abrasives in0 vol.% base medium of paraffin liquid and AP3 grease. Theolishing fluid was prepared by mixing abrasive and iron par-icles into nearly continuous phase (grease + oil) and stirringith the help of specially designed multi-blade mixer. This

esults in uniform dispersion of iron and abrasive particles in thease medium. The flow characteristics of two such preparationsRPF-20CS-20SiC800 and MRPF-20HS-20SiC800 at 2000 G

re shown in Fig. 2. The rheological behaviour of MRP-fluidsnder magnetic field was evaluated separately using capillaryagnetorheometer and is not discussed here due to different

cope of work. Magnetic field across the work piece was pro-uced with the help of C-shaped electromagnet, made of coldolled annealed steel. Experiments were conducted on stainlessteel ground work pieces (flat surfaces) with initial Ra value of0.30 �m. The experiments were conducted using two different

rades of carbonyl iron powders, CS and HS (BASF) along withlack silicon carbide of mesh size 800, 1200, and 2000. Beforend after every experiment, the surface roughness profiles wereecorded by Mahr Federal Surfanalyzer 5000.

. Modeling and simulation

The surface roughness measurement results are summarizedn Table 1. The change in Ra value was calculated as, �Ra = finala − initial Ra. The highest improvement from 0.32 to 0.09 �m

s observed in case of MRP-fluid containing CIP-CS and SiC-00 and the least improvement is found in CIP-HS and SiC-2000ombination for experiment nos. 1 and 6, respectively. Thereas not much improvement in surface roughness (Ra-value) for

it(i

able 1urface roughness results

xperiment no. CIP dia. (DCIP) (�m) SiC dia. (DSiC) (�m) DCIP/D

18.0 (CS) 19.00 0.9518.0 (CS) 12.67 1.4218.0 (CS) 7.50 2.40

3.5 (HS) 19.00 0.183.5 (HS) 12.67 0.283.5 (HS) 7.50 0.47

a �Ra = final Ra − initial Ra.

61 (2006) 856–866

xperiment nos. 4–6 (Table 1) corresponding to CIPs of 3.5 �miameter which is much smaller than SiC diameter (7.5–19 �m).ur hypothesis is that the chains formed from small carbonyl

ron particles of HS grade (3.5 �m) are not strong enough to holdhe bigger abrasive particles, and are unable to provide requirednishing force. The ability and extent of an abrasive particle toarticipate in finishing action in MRAFF process depends onhe normal indentation force and ability of CIPs to hold abrasivearticle. The overall force acting on abrasive particle dependsn volume fraction of CIP and on arrangement of CIPs. In casef smaller CIPs though more number of particles are present inhe fluid for same volume fraction but all are not contributingowards normal force on abrasive particle. Also the magneticorce on CIPs depends on their mass, which is less in case ofmaller particles. The interparticle magnetic force between CIPshich governs the holding force during shear and restrain break-

ng of chains is less in case of smaller particles. This reasonings supported in the following sections by the theoretical analy-is of chain structure formation and surface roughness profileimulation.

.1. Chain structure and unit cell modeling

The study of chain structure formation on the application ofagnetic field helped in understanding the role of particle size on

urface finish improvement. The structures of six different MRP-uid compositions were investigated. To study the magneticorces acting on abrasive particles during finishing operation,tructural arrangement of carbonyl iron particles around abrasivearticles should be well understood. It is known that the carbonylron particles acquire magnetic dipole moment in the presencef external magnetic field. Whenever dipolar interaction forcesetween the particles exceed their thermal interactions, the parti-les aggregate into chains of dipoles aligned in the field direction4]. These chains form columnar structure along the magneticines of force at higher concentration of carbonyl iron particles.or simplifying simulation of chain structure, it is assumed that

ron particles rearrange around SiC particles in the directionf magnetic field and repeat itself in a complete volume span-ing from one end to the other end of the fixture between thelectromagnet poles. Due to the presence of non-magnetic abra-ive particles in the MRP-fluid, the chains are rarely continuous;

nstead terminate at the abrasive particles if it comes in betweenhe chain path, the same is observed under optical microscopeFig. 3). Under the magnetic field, the SiC particles are dispersedn a dense network or structure of interconnected or cross-linked

SiC Initial Ra (�m) Final Ra (�m) �Raa (�m) %�Ra

0.32 0.09 −0.23 −71.870.28 0.17 −0.11 −39.280.31 0.23 −0.08 −25.800.26 0.23 −0.03 −11.540.28 0.24 −0.04 −14.280.25 0.24 −0.01 −4.00

S. Jha, V.K. Jain / Wear 2

Fig. 3. Optical micrograph showing carbonyl iron chain terminating on SiCabrasive particle (clearly visible in colored image). (For interpretation of thereferences to color in this figure caption, the reader is referred to the web versionof the article.)

Fo

paa

niatppfibaitMp

V

wMVitgmcsTp

pw(

N

wu1t1bTOacomdacaaCTa

TN

F

123456

ig. 4. Repetition of unit cubic cell with CIP and SiC arranged in the MRP-fluidn application of magnetic field.

articulate columns, rather than an isolated columnar structure,s is visible in Fig. 3. Interconnected structure was also observednd reported by Fermigier and Gast [5].

Iron particles are assumed to be uniform in size and homoge-ously distributed spheres that can be magnetically modeled asdentical induced dipole moments. The chain is formed by thelignment of spherical CIPs in the magnetic field, touching endo end diametrically. For non-magnetic silicon carbide abrasivearticles, it is assumed that there is a little movement of thearticles in MRP-fluid on the application of external magneticeld. They get trapped within the iron chains wherever they wereefore the application of magnetic field with slight adjustment,s shown in Fig. 4. So, the number of silicon carbide particlesn unit volume is calculated by considering their uniform dis-ribution inside the MRP-fluid. A unit cubic cell occupies the

RP-fluid volume Vu available around integer number of SiCarticles and calculated as

u = nV

NSiC(1)

afin

able 2umber of SiC and CIP particles calculated theoretically for six different combinatio

luid DCIP (�m) DSiC (�m) NCIP/mm3

18 19.00 6549618 12.67 6549618 7.50 65496

3.5 19.00 89089653.5 12.67 89089653.5 7.50 8908965

a NSiC/NCIP = 3.b NSiC/NCIP = 14.

61 (2006) 856–866 859

here n is integer number of SiC in the unit cell, V volume ofRP-fluid, and NSiC is the number of SiC particles in volume

. The number of CIPs is calculated that can be accommodatedn this unit cell volume based on the possible equilibrium posi-ions and space available. Thus, the unit cell volume will beoverned by the number of abrasive particles available in theedium. Calculations were done to estimate number of parti-

les per unit cell (volume depends on particle sizes) for particleizes specified in Table 1 and the results are summarized inable 2. The calculations for Fluid 1 are illustrated in followingaragraph.

Fluid 1 comprises of 20 vol.% CIP (CS grade) of averagearticle diameter 18 �m and 20 vol.% SiC of mesh size 800ith average particle diameter 19 �m. Number of iron particles

NCIP) in a given volume V of MRP-fluid is given by

CIP = φCIPV

VCIP(2)

here φCIP is volume fraction of CIP in MRP-fluid, V the vol-me of MRP-fluid, and VCIP is the volume of a single particle. Amm3 MRP-fluid contains 0.2 mm3 CIP and 0.2 mm3 SiC par-

icles. Considering volume of one CIP, the number of CIPs inmm3 is calculated from Eq. (2) and is 65,496. Similarly num-er of SiC particles in 1 mm3 MRP-fluid is found to be 55,710.he available volume per SiC particle is 1.795 × 10−5 mm3.nly one carbonyl iron particle in this volume will be able to get

ccommodated around SiC particle to apply force. Considering aube around SiC particle of volume 1.795 × 10−5 mm3, the edgef cube comes out to be = 26.18 �m. The only possible arrange-ent of CIP of average diameter 18 �m in this cube is along

iagonal of cube as shown in Fig. 5(a). Similarly, following thebove assumptions and procedure, arrangement of CIPs in unitubic cell around SiC for all other fluid compositions were madend the same are shown in Fig. 5. For experiment 4, though therere 160 CIPs per SiC, the structure shown in Fig. 5(d) shows onlyIPs exerting force on SiC particle to facilitate understanding.his is based on the assumption that only CIP particles presentround SiC in the cell will exert force on it. Other CIPs are

rranged in remaining space in cube along magnetic lines oforce, and it is assumed that their contribution to the force act-ng on an abrasive particle in contact with the work piece isegligible.

ns and size of basic repeating cubic cell

NSiC/mm3 NCIP/NSiC Cube edge assoc. withintegral number of SiC (�m)

55710 1.18 26.18187803 0.35a 25.20 (3 SiC)905415 0.07b 25.00 (14 SiC)55710 160.00 26.20

187803 14.00 18.00905415 10.00 10.30

860 S. Jha, V.K. Jain / Wear 261 (2006) 856–866

Fig. 5. Configuration of carbonyl iron particles and silicon carbide abrasives for six different MRAF-finishing experiments. (a) CIP-CS (18 �m), SiC-800 (19 �m);(b) CIP-CS (18 �m), SiC-1200 (12.67 �m); (c) CIP-CS (18 �m), SiC-2000 (7.5 �m); (d) CIP-HS (3.5 �m), SiC-800 (19 �m); (e) CIP-HS (3.5 �m), SiC-1200(

4

ssapmp

(

(

12.67 �m); (f) CIP-HS (3.5 �m), SiC-2000 (7.5 �m).

.2. Analysis of forces

To get an insight into the reasons for variation in reduction inurface roughness (�Ra) with different combinations of particleizes of carbonyl iron and silicon carbide, it is required to developmathematical model to predict the forces acting on abrasive

articles during MRAFF process. Following assumptions wereade to simplify the analysis and to understand the process

hysics:

(i) The SiC particles embedded in the carbonyl iron chainsare assumed to repeat and span from one end to anotherend of the fixture. This assumption is made to simplifythe physical model, though in actual case the chain likestructures formed between the magnetic poles are morecomplex as can be seen in Fig. 3. Iron chains many timesterminate at the abrasive particles that come in their wayand form clusters by aggregating into cylindrical columns.

(ii) All abrasive particles are assumed spherical of averagediameter, calculated from their mesh size number. In prac-tice, no two abrasive particles resemble each other in shape

and size.

iii) The abrasive particles are assumed uniformly distributedin MRP-fluid. It is observed microscopically also that thisassumption is not very much true in case of carbonyl iron

io

particles which are smaller as compared to abrasive parti-cles. The number of abrasive particles in contact with thework piece surface reduces significantly when mixed withsmaller CIPs (experiments 4–6).

(iv) It is assumed that a spherical abrasive particle penetratesinto the work piece surface under the action of the normalcomponent of magnetic force on carbonyl iron particles inthe presence of magnetic field.

(v) The MRP-fluid structure assumed at rest is field elongatedchains of particles agglomerates. The effect of fringingfield at the corners of the magnetic pole piece is neglectedbecause of the bigger size of pole piece than the work piecelength.

vi) The normal magnetic force on iron particles in a stationarysystem (no shearing applied), on the application of mag-netic field, shows steady rise with time after an initial jump.This normal force decreases with strain and reaches plateauvalue at large strains [6]. In calculating normal indentationforce this decrease is not considered and the normal forceis assumed constant, which results in comparatively higherindentation.

The MRP-fluid structure is deformed under shear stress andts flow is accompanied either by the rupture of chains, their slipver a wall as a unit or by a combination of these two processes

S. Jha, V.K. Jain / Wear 261 (2006) 856–866 861

n MR

[sft(tsmtstaicpatbtHmna

F

R

wasfl

σ

S

T�

d

wd

1

F

Ot

wfioexternal magnetic field, variation of magnetic flux density (B) iscalculated between the two pole pieces. Using Eqs. (6)–(8) formagnetic flux density due to a finite solenoid [9], the value of Bat a distance x from the coil 1 (Fig. 7), is the vector sum of B1

Fig. 6. (a) Forces on abrasive particle i

7]. The abrasive grain produces a groove on the work pieceurface under the action of magnetic force acting on CIPs. Thisorce acting on CIPs is transferred to the abrasive particle(s)rapped in the vicinity of CIPs. The cross-section of indentationor groove) corresponds to the profile of the penetrated portion ofhe grain. Under hydraulic pressure, when the penetrated abra-ive grain is translated horizontally, the removal of work pieceaterial takes place. This occurs only when tangential force by

he fluid (Fshear) on the projected area of the penetrating abra-ive (above the portion indented into the surface) is greater thanhe reaction force (Rshear) on the indented projected area of thebrasive due to the strength of the work piece material as shownn Fig. 6. The removal of material in front of the abrasive grainan takes place either by shearing action (chip formation) or byloughing action, which depends on the depth of indentationnd average cutting edge radius [8]. No evidences (experimen-al or theoretical) are available to prove either of the mechanismy which material is being removed during MRAFF. However,he forces acting per grain during MRAFF are substantially low.ence, to be on safer side, ploughing can be assumed as theechanism of material removal. Fnormal is the sum of compo-

ents of forces (normal to the work piece surface) acting on thebrasive particle due to all CIPs in the unit cell:

shear = (A − A′)τy (3)

shear = A′σy (4)

here A is the total projected area of abrasive grain, A′ projectedrea of indented part of abrasive in work piece surface, σy yieldtress of stainless steel (SS) work piece in shear, and τy is theuid shear stress.

Let us take following data to substitute in Eqs. (3) and (4):

y = 339.5 MPa for SS;

iC particle diameter = 19 �m(experiment1)

he indentation depth calculated from Eq. (5) derived from the

OAB in Fig. 6(b):

= Dg

2− 1

2

√D2

g − D2i (5) F

p

AFF process and (b) calculation of Di.

here Dg is the abrasive grain diameter in m, Di is the indentationiameter in m, is d = 9.98764 × 10−14 m.

Indented abrasive cross-sectional area (Fig. 6), A′ = 5.26 ×0−18 m2. From Eqs. (3) and (4):

shear = 1.4885 × 10−5 N; Rshear = 1.78577 × 10−9 N

n comparison, the Fshear is found to be much greater than Rshearo perform finishing action.

For finishing experiments two multilayered copper coils eachith 2000 turns of 17 SWG were used to produce magneticeld in the gap of 30 mm (Fig. 7). To calculate normal forcen any ferromagnetic particle (acts as a magnetic dipole) in the

ig. 7. (a) Electromagnet configuration for force calculation and (b) fixtureosition in the gap between electromagnet poles.

862 S. Jha, V.K. Jain / Wear 2

(f

B

w

B

B

we(nvasarvswiicw

B

wpdp

F

wsaau

F

OpBs

F

Tfsei

χ

(mMtwagtitpC

l∼vpowtpp

Fig. 8. Variation of magnetic flux density in the gap.

flux density due to coil 1) and B2 (flux density due to coil 2) asollows.

Hence:

� (x) = �B1(x) + �B2(30 − x) (6)

here

�1(x) = µ0In

2(r2 − r1)

⎡⎣(L + x)ln

√r2

2 + (L + x)2 + r2√r2

1 + (L + x)2 + r1

−x ln

√r2

2 + x2 + r2√r2

1 + x2 + r1

⎤⎦ (7)

�2(30 − x) = µ0In

2(r2 − r1)

×⎡⎣(L + 30 − x)ln

√r2

2 + (L + 30 − x)2 + r2√r2

1 + (L + 30 − x)2 + r1

−(30 − x)ln

√r2

2 + (30 − x)2 + r2√r2

1 + (30 − x)2 + r1

⎤⎦ (8)

here r1, r2 and L are core radius, outer radius and length oflectromagnet coil, respectively. x is the distance from pole faceFig. 7(a)), µ0 is magnetic permeability of free space, I is mag-etizing current, and n is number of turns per unit length. Theariation of flux density in the air gap due to electromagnet waslso experimentally measured using a Gauss meter. The mea-urements were done from coil 1 to coil 2 in forward directionnd then from coil 2 to coil 1 in backward direction. Both theseeadings were almost overlapping so average is taken and thealue of B is plotted a ‘*’ along with theoretical variation asolid line in Fig. 8. The relative permeability (µr) of iron coreas found out by measuring B in the presence and absence of

ron core and it was 7.26. The theoretical variation of B in the gaps quadratic, therefore after fitting the quadratic equation (dashed

urve in Fig. 8) to the experimentally obtained variation of B,e get

(x) = 203.22x2 − 5.0778x + 0.5711 (9)

f(

B

61 (2006) 856–866

here x is distance in meters with reference to coordinate axeslaced at work piece fixture (Fig. 7), and B is magnetic fluxensity at a distance x in Tesla. Force on a small ferromagneticarticle of mass m [10] is given by Eq. (10):

m = mµ0χmH∇H (10)

here µ0 is magnetic permeability of free space, χm magneticusceptibility of carbonyl iron particles (CIPs), m mass of CIP,nd H is magnetic field strength. For practical purposes, it isdvantageous to replace field strength with magnetic inductionsing relation B = �0H, so that Eq. (10) becomes

m = mχm

µ0B∇B (11)

wing to the bigger size of flat magnetic pole piece in com-arison to the diameter of work piece fixture, the variation ofin y direction is negligible, hence after neglecting it Eq. (11)

implifies to

m(x) = mχm

µ0B(x)

dB(x)

dx(12)

o calculate the force on an abrasive particle due to magneticorce on carbonyl iron particles near work piece surface, theirtructural arrangement and alignment are drawn as per possiblequilibrium structure in unit cell and are shown schematicallyn Fig. 5.

To evaluate the forces acting on CIPs, mass susceptibilitym of CS and HS grades is calculated using the M–B curves

Fig. 9). Parallel field vibrating sample magnetometer (VSM)odel 150A was used to find magnetic properties in terms of–B curve for CIPs. A magnetic field was generated by an elec-

romagnet driven by power supply, and a Hall-effect Gauss meteras used. A cylindrical disc shaped sample of 3 mm diameter

nd 2 mm thickness was prepared and placed in a cylindricallass tube between strong magnet coils of magnetometer. Whenhe mechanical vibrations were applied to the magnetic materialn a constant magnetic field, the induced voltage proportionalo the magnetic moment of the material was generated in theick-up coils. These are plotted to obtain curves for CS and HSIP grades as shown in Fig. 9.

To understand the arrangement of SiC and CIPs in a unit cell,et us consider Fluid 1. From Table 2, it is found that there are

1.18 carbonyl iron particles per abrasive particle in unit cellolume. With the abrasive particles in contact with the workiece top surface the possible arrangement of one CIP aroundne SiC particle in a cube of 26.18 �m edges is shown in Fig. 5(a)hich fits along diagonal direction only. Magnetic force Fm on

he CIP (φ = 18 �m) at a distance of 20.18 �m from the workiece surface, and at x = 3.02018 mm (3 mm is fixture and workiece thickness +0.02018 mm is perpendicular distance of CIP

rom the work piece surface) is calculated as follows from Eq.9):

= 0.557618 T

S. Jha, V.K. Jain / Wear 261 (2006) 856–866 863

Dv

Tu

χ

S1a

fiv

F

t

L

wlbpascrti

4

fotaiYiY

t(kgf/mm ) [11] using Eq. (15) given below:

TC

E

123456

Fig. 9. M–B curve for CIP of CS and HS samples.

ifferentiating Eq. (9) with respect to x and substituting thealue of x = 0.003028, we get

dB

dx= −3.85028

he value of χm at B = 0.557618 T obtained from B–M curvesing Eq. (13) is χm = 3.985 × 10−4 m3/kg:

m = M

H= µ0M

B(13)

ubstituting these values in Eq. (12), we get Fm = 16.216 ×0−9 N. Following the above procedure, forces for other cases

lso have been computed, and the same are given in Table 3.

The number of abrasive particles taking part in work piecenishing action during a single stroke can be calculated based onolume constancy of the MRP-fluid. The extrusion length (Le)

H

able 3alculated force and depth of indentation

xperiment no. CIP dia.(DCIP) (�m)

SiC dia.(DSiC) (�m)

For(×1

18.0 19.00 16.218.0 12.67 5.418.0 7.50 2.3

3.5 19.00 7.03.5 12.67 1.63.5 7.50 0.2

a Only those abrasives which are passing over the peaks in a line.

ig. 10. Cutting mechanism by abrasive particles surrounded by CIP clusters.

hrough the fixture cross-section can be evaluated as follows:

πD2pLs

4= πD2

f Le

4

e = D2pLs

D2f

(14)

here Dp and Ls are MRPF-cylinder piston diameter and strokeength, respectively. Df is the fixture’s inside diameter. The num-er of abrasive particles in an extrusion length of 459.201 mmassing over the peaks in a line are calculated from Le/a, whereis the edge of cube around each abrasive particle or linear

pacing between the center of two adjacent abrasive particles orlusters (Fig. 10). Number of abrasive particles passing over aoughness peak per stroke is equal to the number of abrasive par-icles or multiple thereof (if more than one abrasive in unit cell)n the extruded length, and is shown in last column of Table 3.

.3. Surface roughness simulation

Initial surface roughness data input to the model was takenrom the Surfanalyser 5000 instrument in the form of ordinatesf all sampled points in the profile at equal interval. To updatehe surface profile after each stroke, depth of indentation (d) byspherical abrasive on each peak is calculated from Eq. (5). The

nitial heights or depths on the surface are shown in Fig. 11 (Ya,b, Yc, Yd, and Ye,). The new peak heights updated after one

ndentation depth (or cutting by one grain) are calculated as Ya,′b = Yb − d, Y ′

c = Yc − d, Yd and Y ′e = Ye − d. The indenta-

ion diameter Di can be calculated from Brinell hardness number2

BHN = 2F

πDg

(Dg −

√D2

g − D2i

) (15)

ce/SiC particle0−9 N)

Depth of indentation(×10−14 m)

No. of abrasives inone strokea

79 9.987 1754006 4.997 2733318 3.620 3673632 4.335 1754014 1.492 2551132 0.372 44583

864 S. Jha, V.K. Jain / Wear 261 (2006) 856–866

t/dep

R

D

Fig. 11. (a) Abrasive grain approaching initial peaks/valleys of heigh

earranging Eq. (15) gives

i =

√√√√D2

g −(

Dg − 2 × 10−6Fi

9.81HBHNπDg

)2

(16)

wiae

Fig. 12. Flow chart for surface roughne

th and (b) new peak heights updated after one indentation depth (d).

here Fi is normal indenting force on abrasive in N, and HBHNs the work piece Brinell hardness number in kgf/mm2. Let usssume that each abrasive grain passing over the peaks penetratesqual to d and each abrasive grain is active. The new peak height

ss profile simulation in MRAFF.

ear 261 (2006) 856–866 865

Y

Y

IaTapcp

R

wfiolt

Table 4Comparison of experimental and theoretically simulated surface roughness val-ues after 200 finishing cycles

Experimentno.

CIP dia.(DCIP)(�m)

SiC dia.(DSiC)(�m)

InitialRa (�m)

Final Ra (�m) %Error

Expt. Theor.

1 18 19 0.32 0.09 0.21 +133.332 18 12.67 0.28 0.17 0.19 +11.763 18 7.5 0.31 0.23 0.24 +4.35456

mi

F

F

S. Jha, V.K. Jain / W

i after one stroke with Ng active grains/stroke is given by

′i = Yi − Ngd (17)

f the point is not a peak point in the data file (for example Ya

nd Yd in Fig. 11), then it is transferred to next profile as it is.o update the peak heights, new peak points were calculatedfter each stroke and updated profile data were passed on forrocessing in the next stroke. Before and after each stroke, theenter-line-average (CLA) surface roughness value (Ra) fromrofile data points was calculated using Eq. (18):

a =∑

i=1,...,N |Yi|N

(18)

here N is number of data points and Yi is roughness pro-

le height at the data points. To calculate final Ra value basedn theoretical indentation values, software in ‘C’ programminganguage was written as per flow chart shown in Fig. 12. Theheoretically obtained final Ra values after simulation are sum-

eioo

ig. 13. (a) Initial input profile, (b) final simulated profile and (c) measured final pro

ig. 14. (a) Initial input profile, (b) final simulated profile and (c) measured final profi

3.5 19 0.26 0.23 0.21 −8.693.5 12.67 0.28 0.24 0.25 +4.173.5 7.5 0.25 0.24 0.23 −4.17

arized in Table 4. These theoretically calculated Ra values aren close agreement with the experimental results with maximum

rror of 12% except for experiment 1. In experiment 1, the errors high due to assumption that MRP-fluid is in sheared state andnly one CIP is contributing force on abrasive particle. The-retically, force contribution on one SiC particle by only one

file after 200 cycles for experiment 2 with DCIP = 18 �m and DSiC = 12.67 �m.

le after 200 cycles for experiment 5 with DCIP = 3.5 �m and DSiC = 12.67 �m.

8 ear 2

CmtmolcwalpatcccpM

5

cappcca

(

A

ia(nFpDp

R

66 S. Jha, V.K. Jain / W

IP was considered (CIP/SiC = 1.18) though in actual experi-ental conditions neighboring CIPs will also exert force. Due

o contribution from more than one CIPs towards the total nor-al indenting force on abrasive particle, the total indentations

btained experimentally were higher than theoretically calcu-ated one and hence the error was more. This is prominent inase where size of CIP and SiC is almost equal and the structureas more closely packed. For experiments 2 and 5, the simulated

nd actual profiles are shown in Figs. 13 and 14. Comparativelyarge indentations are obtained theoretically when the abrasivearticles and CIPs are of approximately same size (experiment 1)s compared to the case when CIPs are smaller in size comparedo abrasive particles, say, in experiments 4–6. This conclusionlosely resembles with the experimental observations. Thus itan be concluded that the theoretical modeling and simulationlearly captures the fact that CIP and abrasive particle size ratiolays an important role in final roughness value obtained afterRAFF process.

. Conclusions

A model for the CIP chain structures around abrasive parti-le has been proposed based on microscopic study and possiblerrangement of particles with different size in MRP-fluid com-osition. Final surface roughness from initial profile data androposed surface roughness model has been simulated for allombinations of SiC and CIP sizes. Following are the main con-lusions made after experimental study, theoretical modeling,nd simulation:

(i) For the same magnetic flux density, the finishing forces onabrasive particles are mainly dependent on number of CIPsin their vicinity, their microstructural arrangement and size.The magnetic force on a carbonyl iron particle is a func-tion of particle volume, so size of CIP in comparison withabrasive size is an important factor affecting final surfaceroughness obtained in MRAFF process.

(ii) Compared to the same size of CIP and abrasive particle, thesurface finish improvement rate decreases with decrease inabrasive particles size (keeping CIP size constant) due to

decrease in indenting force and sharing of the same force bymore number of abrasive particles. This is also because ofdecrease in the interparticle magnetic force between CIPswhich governs the holding force during shear and restrain

[

[

61 (2006) 856–866

breaking of chains in case of smaller particles. The abrasiveparticles in these cases are too large to be effectively cap-tured by the CIP since it is easier to shear or slide throughthem due to lack of sufficient bonding force.

iii) The theoretically obtained profile for all experimentsexcept experiment 1, matches to a large extent with themeasured final profiles. This shows a close resemblance ofsimulated model with the process physics and mechanismof finishing action.

cknowledgements

We sincerely thank BASF Germany for arranging carbonylron powders of different grades for our research work. Wecknowledge the Council of Scientific and Industrial ResearchCSIR), New Delhi, India for their financial support for projecto. 5411/NS/02/EMRII entitled “Magnetorheological Abrasivelow Finishing (MRAFF)”. We also acknowledge financial sup-ort of Department of Science and Technology (DST), Newelhi, under DST-NSF Indo-US S&T cooperation program videroject no. DST-INT-US (NSF-PRO-101)/2002.

eferences

[1] L.J. Rhodes, Abrasive flow machining: a case study, J. Mater. Process.Technol. 28 (1991) 107–116.

[2] W.I. Kordonski, S.D. Jacobs, Magnetorheological finishing, Int. J. Mod.Phys. B 10 (23–24) (1996) 2837–2848.

[3] S. Jha, V.K. Jain, Design and development of magnetorheological abrasiveflow finishing (MRAFF) process, Int. J. Mach. Tool Manuf. 44/10 (2004)1019–1029.

[4] E.M. Furst, A.P. Gast, Micromechanics of magnetorheological suspen-sions, Phys. Rev. E61/6 (2000) 6732–6739.

[5] M. Fermigier, A.P. Gast, Structure evaluation in a paramagnetic latex sus-pension, J. Colloid Interf. Sci. 154 (1992) 522–539.

[6] S. Howard, R. Tanner, Shear rate dependence of the normal force of amagnetorheological suspension, Rheol. Acta 42 (1–2) (2003) 166–170.

[7] S. Gorodkin, N. Zhuravski, Surface shear stress enhancement under MRfluid deformation, Int. J. Mod. Phys. 16 (17–18) (2002) 2745–2750.

[8] J.N. Brecker, R. Brown, T. Matsuo, K. Saito, J.A. Sweeney, J.B. Vansaun,M.C. Shaw, Fourth Annual Report of Abrasive Grain Association on Inves-tigation of Abrasive Grain Characteristics, Carnegie Institute of Technol-ogy, USA, November 1969.

[9] www.netdenizen.com/emagnet/solenoids/solenoidonaxis.htm.10] A.W. Stradling, The physics of open-gradient dry magnetic separation, Int.

J. Miner. Process. 39 (1993) 19–29.11] H.W. Hayden, W.G. Moffatt, J. Wulff, The Structure and Properties of

Materials, vol. III, John Wiley and Sons, 1965.