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Finite element prediction of material removal rate due to electro-chemical spark machining

International Journal of Machine Tools &Manufacture 46(2006)1699–1706

Finite element prediction of material removal rate due

to electro-chemical spark machining

K.L.Bhondwe,Vinod Yadava ?,G.Kathiresan

Mechanical Engineering Department,Motilal Nehru National Institute of Technology,Allahabad 211004,India

Received 11August 2005;received in revised form 31October 2005;accepted 14December 2005

Available online 17February 2006

Abstract

Electro-chemical spark machining (ECSM)is an innovative hybrid machining process,which combines the features of the electro-chemical machining (ECM)and electrodischarge machining (EDM).Unlike ECM and EDM,ECSM is capable of machining electrically non-conducting materials.This paper attempts to develop a thermal model for the calculation of material removal rate (MRR)during ECSM.First,temperature distribution within zone of in?uence of single spark is obtained with the application of ?nite element method (FEM).The nodal temperatures are further post processed for estimating MRR.The developed FEM based thermal model is found to be in the range of accuracy with the experimental results.Further the parametric studies are carried out for different parameters like electrolyte concentration,duty factor and energy partition.The increase in MRR is found to increase with increase in electrolyte concentration due to ECSM of soda lime glass workpiece material.Also,the change in the value of MRR for soda lime glass with concentration is found to be more than that of alumina.MRR is found to increase with increase in duty factor and energy partition for both soda lime glass and alumina workpiece material.r 2006Elsevier Ltd.All rights reserved.

Keywords:Electro-chemical spark machining;Material removal rate;Finite element method;Gaussian heat ?ux distribution;Soda lime glass;Alumina

1.Introduction

Technologically advanced industries like automobile,aeronautics,nuclear,etc.are demanding the advanced materials with high strength,temperature resistance and high strength to weight ratio.This need has given birth to the evolution of materials like ceramics,high strength alloys,?ber-reinforced composites and so many.But for realistic progress in the industries,advancements in materials should go hand in hand with the advancement in machining processes.

It has been found that the advanced materials are dif?cult to machine by the conventional machining processes.It is no longer possible to produce parts with better surface ?nish,close tolerances and complex shapes in advanced materials by conventional machining methods.To machine the advanced dif?cult-to-machine materials,

newer machining processes have come forward.Instead of removing the material by the hard cutting tool,the material is removed by the innovative energy utilization [1,2].Newer Machining Processes (NMPs)uses different forms of energies to remove the excess amount of material.Recently,a new trend has been introduced to combine the features of two or more than two machining processes to exploit the potential of each constituent process and diminish their disadvantages.Such machining processes with combined features are called as hybrid machining processes (HMPs).Electro-chemical spark machining (ECSM)is one of them,which combines the features of electrochemical machining (ECM)and electrodischarge machining (EDM).Material removal rate (MRR)in ECSM is close to EDM but much lower than ECM under the same parameter settings.

ECSM is a new innovative HMP for which scarce literatures are available.Yet it has not been commercia-lized and is still under laboratory study stage.Basak and Ghosh [3]have developed a theoretical model of the ECSM process.Crichton et al.[5]gave theoretical analysis with its

https://www.sodocs.net/doc/9b10108272.html,/locate/ijmactool

0890-6955/$-see front matter r 2006Elsevier Ltd.All rights reserved.doi:10.1016/j.ijmachtools.2005.12.005

?Corresponding author.Tel.:+9105322271812;

fax:+9105322445101.

E-mail address:vinody@mnnit.ac.in (V.Yadava).

experimental veri?cation of effects of the pulsed voltage and phase angle and amplitude of vibrating tool electrode waveform,for the study of metal machining rates. McGeough et al.[6]experimentally observed that the sparking occurs at the tool electrode interface.Khayry and McGeough[7]have discussed metal removal in the leading and side-gaps of ECA drilling.Jain et al.[8]carried out experimental study of ECSM on Kevlar-?ber-epoxy and Glass-?ber-epoxy composites to?nd the effect of change in voltage and speci?c conductance of the electrolyte on the MRR,relative tool wear rate and overcut.Gautam and Jain[9]carried out experiments with the different tool kinematics in electro-chemical spark drilling(ECSD)to enhance the process capabilities.Authors carried out the parametric study of tool rotation speed,limiting depth of cut,tool eccentricity,MRR,surface integrity.Jain et al.

[10]solved the ECSM problem as3D unsteady state problem using the FEA technique and carried out the MRR,overcut and limited depth of cut analysis during the machining with respect to the supply voltage.They assumed the nature of the spark as prismatic column with square cross-section.Kulkarni et al.[11]have carried out the experiments to explain the mechanism of the spark generation.

From the literature survey it is found that ECSM is at the research level only and most of the works are experimental.Few theoretical papers are available related to determination of MRR.Basak et al.[4]have given analytical model of MRR with the experimental validation, but the basic theory of spark generation proposed by them does not match with the actual situation.Jain et al.[10] have carried out the3D FE analysis but they have neglected the effect of the concentration.Most of the researchers have considered uniformly distributed heat source within a spark.This assumption is far from reality. This factor is evidenced from the actual shape of a crater found by Kulkarni et al.[11].Heat?ux distribution within a spark is assumed as Gaussian.

In the present work FEM based model has been developed for the determination of transient temperature distribution due to single spark within the zone of in?uence of single spark.It is further used to determine MRR using the temperature plots in the zone of in?uence of single spark and number of sparks per unit time.

2.Mathematical modeling

Physical laws governing the material removal during ECSM process are yet to be understood.Since ECSM is a complex machining process hence its modeling requires certain assumptions.To make the analysis of ECSM tractable,following assumptions are considered:

1.Workpiece material is assumed to be homogeneous and

isotropic.

2.At a time only one spark is produced at the workpiece

top surface(single Spark phenomenon).The zone of in?uence due to single spark is assumed to be axisym-metric in natureeq T=q y?0T.

3.The boundaries(S2and S3)of the domain(Fig.1),away

from the heat?ux are chosen at such a distance that there is no heat transfer across those boundaries.i.e.

q T=q n?0.

4.Only a fraction of total sparking heat?ux is dissipated

into the workpiece.Shape of heat?ux is assumed to be Gaussian distributed.From the experimental studies of Kulkarni et al.[11]for single spark,the heat-affected zone is circular and the crater is dome shaped.So re?ecting the shape of crater,we can approximate the nature of the heat?ux as Gaussian.

5.All sparks are considered to be identical during the

whole machining period.

6.Ejection ef?ciency is assumed to be100%.Also,there is

no deposition of recast layer on the machined surface.

7.Material removal by cavitation effect is neglected.

Nomenclature

C electrolyte concentration,%by wt

R radius of spark,m m

T temperature,K

I c critical current,A

R w energy partition to workpiece

T0ambient temperature,K

T m melting temperature,K

V c critical voltage,V

c speci?c heat capacity of workpiece,J/kg K h c convective heat transfer coef?cient,W/m2K k thermal conductivity,W/m K

t time,s

r;z coordinates along r-and z-axis,respectively df duty factor t on on-time,s

t off off-time,s

q w heat?ux,W/m2

D T change in temperature,K r Density,kg/m3 Subscript

i initial

w workpiece

Superscript

b boundary element

e area element

T transpose

K.L.Bhondwe et al./International Journal of Machine Tools&Manufacture46(2006)1699–1706 1700

Governing equation for calculation of transient tempera-ture distribution within the workpiece for the present problem which is assumed to be axisymmetric is given by

k

1

r

r

q T

q r

t

q2T

q z2

?r c

q T

q t

,(1)

where,k;c and r are thermal conductivity,speci?c heat capacity and density of the workpiece material,respec-tively.

The initial and boundary conditions for the present case are as given below.

Initial condition:At the start of the ECSM process et?0T,the workpiece is immersed in the electrolyte and the temperature of the whole domain is assumed to be at room temperatureeT0T.

i.e.T?T0in the workpiece domain ABCD at t?0 (Fig.1(b)).

Boundary conditions:

(i)Boundary S2and S3are considered to be insulated. q T=q n?0,where n indicates normal direction to S2 or S3.

(ii)Heating process is taken to be axisymmetric about the axis of a spark,so heat?owing from the counterpart of the domain is equal to the heat?owing to the counterpart. Therefore,the net heat loss or gain is absolutely zero on surface S1.q T=q r?0,at r?0.

(iii)On surface S4,where a spark occurs(AE),heat?ux boundary condition is applied.For rest of the part(EB),convective boundary condition is employed.Thus,

àk

q T

q z

?h ceTàT0Tif r4R

?q w if r p R

?0for off-time.e2TBased on shape of machined surface found by Kulkarni et al.[11],in the present work a Gaussian heat?ux distribution is taken and heat?ux calculation expression is derived[12]

q WerT?

4:45R w V C I C

p R2

expà4:5

r

R

2

,(3) where,r is the radial distance from the axis of the spark,R is spark radius,V C is critical voltage and I C is critical current.

Both V C and I C are the functions of the electrolyte concentrationeCTand their values are obtained from the graphs of critical voltage verses electrolyte concentration eCTand critical current verses electrolyte concentration[4]. These values are?tted using MS-ORIGIN software to obtain following mathematical relationship between V C and C and I C and C,respectively.

V C?0:02381C2à1:6095Ct43:536,(4a) I C?3:2323?10à5C3à0:0027056C2

t0:091378Ct0:71429.e4bTOne of the important parameters required for computa-tional analysis of ECSM process is the percentage of heat ?ux distributed between cathode,anode,workpiece and electrolyte.No comprehensive method has so far been proposed to calculate the value of energy partition to workpieceeR wTduring ECSM process.In the present work R w is taken as0.20[4].Basak and Ghosh[4]have taken spark diameter2a?10à6I b,where2a is spark diameter in meters and I b is the current in amperes at the instant of the circuit opening.But they have assumed that spark channel is cylindrical in shape.Also Jain et al.[10]assumed prismatic nature of spark with square cross section,which is far from real life situation.Kulkarni et al.[11]have given the crater diameter for different workpiece materials as 300m m based on their experiments.So this diameter is taken as spark diameter,which gives spark radiuseRTto be150m m.

2.1.Calculation of MRR

The material removal in ECSM is mainly caused by the melting and vaporization.It is considered as thermal phenomenon and temperature distribution is evaluated from the Fourier heat conduction equation.In ECSM,the discharge takes place due to high electric?eld across the hydrogen bubble generated in the electrolysis reaction. However,the problem arises in locating the nucleation of the hydrogen bubble over the tool surface.Actually,

Fig.1.ECSM:(a)line sketch of experimental setup;(b)thermal model.

K.L.Bhondwe et al./International Journal of Machine Tools&Manufacture46(2006)1699–17061701

bubble generation is complex and random phenomenon. To simplify the situation,the analysis of the material removal due to single pulse is carried out.Assuming that the energy is equally distributed among the spark,the material removed per unit time is calculated from material removed by one spark and total number of sparks per unit time.

Using basic heat transfer laws of conduction and convection,temperature distribution among the different nodes of domain is calculated.The amount of molten material can be determined by the volume limited by the iso-temperature plane of the melting temperature at the end of the pulse.The mathematical expression for calculating the volume is given as[13]

V?

ZZZ

D

fer;z;yTd r d z d y.(5) Since,the3-D problem is approximated to2-D problem by considering q T=q y?0,amount of material removed is calculated by integrating the area Aer;zTbounded by the isothermal line of melting temperature,obtained in the r–z plane.This area Aer;zTis integrated in y direction over 2p rad angle

V?

Z2p

Aer;zTd y?Aer;zT?2p.(6) During machining,spark takes place between tool and electrolyte.And since workpiece is close to the tool,part of energy is utilized for the machining.The volume obtained by Eq.(6)is for one spark.The volume of material per unit time is calculated by

MRR v?V?number of sparks per unit time,

where,number of sparks per unit time will depend upon the pulse duration.

The mass MRR is given by

MRR m?MRR v?r,

where r is density of the workpiece material.

3.Finite element formulation

The following expressions are obtained for elemental stiffness matrix?K e,capacitance matrix?C e,and right side vector f f g e when Galerkin’s FEM[14]is applied to Eqs.(1) and(2),for the workpiece domain ABCD(Fig.1)

?K e?

Z

D e k?B eT?B e r d r d zt

Z

S

h c f N g b f N g bT r d s,(7)

?C e?

Z

D e

r c f N g e f N g eT r d r d z,(8)

f f

g e?

Z

S T0h c f N g b r d st

Z

S q

f N

g b f q w g r d s.(9)

Here,the matrix?B e relates the temperature derivatives with its nodal values.S is the convective-boundary(EB)and S q is boundary of input heat?ux(AE).The assembled equations after assembly of above Eqs.(7)–(9)are:

?GC nnm?nnm f T

g nnm?1t?GK nnm?nnm f T g nnm?1?f GF g nnm?1,

(10)?GK ?

P nem

e?1

?K e

nne?nne

;

?GC ?

P nem

e?1

?C e

nne?nne

;

f GF g?

P nbm

b?1

f f

g e

nnbe?1

;

(11)

where nnm is number of nodes in the mesh,nne is number of nodes in the element,nem is number of elements in the mesh,nbm is the number of boundary elements in the mesh,nnbe is the number of nodes in a boundary element, [GC]is global heat capacitance matrix,[GK]is global coef?cient matrix,f T g is global nodal temperature,and f GF g is global right side vector,and f T

g is time derivative of f T g.Eq.(10)is converted into algebraic equations after application of implicit?nite difference method(FDM)as follows:

?~

GK f T g st1??~G~K ;f T g stf~

GF g s;st1,(12) where

?~

GK ??GC ta D t st1?GK st1;

?~G~K s??GC àe1àaTD t st1?GK s;

f~

GF g s;st1?D t st1?a f GF g st1te1àaTf GF g s ;

(13)

where f g s refers to the value of the enclosed quantity at time,t?t s?

P n

i?1

D t i,n is the number of time steps and D t s is the time interval,i.e.D t s?t sàt sà1.Eq.(12)is then solved using Gauss elimination method to get the tempera-tures after each time step s.

4.Results and discussion

4.1.Validation

In order to assess the accuracy and ef?ciency of the present?nite element formulation,the numerical proce-dure and developed FEM based code using Matlab6.1,a heat transfer problem with various boundary conditions (speci?ed boundary,insulated boundary,convective boundary and incoming heat?ux boundary)is simulated. The temperature distribution using present FEM based code is compared with analytical solution in the literature [14].The results using present FEM based code are matching well with the values given in the literature.

The workpiece domain of size600m m?600m m is discretized into eight noded quadratic serendipity ele-ments(Fig.1).Convergence conditions were carried out by increasing the number of elements in the mesh. The simulation showed that the nodal temperature of

K.L.Bhondwe et al./International Journal of Machine Tools&Manufacture46(2006)1699–1706 1702

workpiece domain obtained were essentially unchanged,when the mesh size is in excess of 256elements.The mesh of 256elements is thus found to be the smallest number,which is adequate for convergence.Hence the mesh consisting of 256number of elements (nem)having element length of 75m m with 833number of nodes in the mesh (nnm)is used for further analysis.The nodal temperature distribution of the workpiece domain is found using computer with Pentium 4processor.

Fig.2(a)shows the temperature distribution along the radial distance from the center and Fig.2(b)shows the temperature distribution along the depth from the top surface in soda lime glass and alumina workpiece.The temperature distribution is obtained with eight noded quadratic serendipity elements having element length of 75m m eR =2;R ?spark radius T.The spark radius is kept whole number multiple of element length used in ?nite element analysis from the computational point of view.The temperature on the top surface registers the change in values upto the distance 225m m,after that temperature remains equal to the room temperature.The nature of temperature distribution (Fig.2),it is clear that highest

temperature is at the point where the spark strikes the workpiece and decreases with increase in the distance from this point.Since,speci?c heat of alumina is higher than speci?c heat of soda lime glass.Hence more heat content is stored in alumina workpiece in comparison to sodalime glass for the same heat ?ux input from the spark causing more temperature rise in alumina.

Once the temperature distribution is known,the nodes possessing the temperature more or equal to melting point temperature of the workpiece material are identi?ed and used to plot temperature isotherms.The area enclosed by isomelt is found out which is further used to ?nd MRR as discussed in Section 2.1.The methodology is applied for the soda lime glass as well as for alumina (Al 2O 3)workpiece material.The cutting conditions for soda lime glass and alumina are given in Tables 1and 2,respectively [4,15].The details of duty factor are given in Table 3.The relationship between critical voltage eV c Tand critical current eI c Twith electrolyte concentration are given by Eq.(4).

T o p s u r f a c e t e m p e r a t u r e (K )

Radial distance from center (mm)

(a)

T e m p e r a t u r e (K )

Depth from the top surface (mm)

(b)Fig.2.Variations of temperature distribution in the workpiece:(a)on top surface along radial direction from the center of spark;(b)along depth from top surface at the center of spark.The machining data are taken as t on ?10?10à4s ;t off ?5?10à4s ;df ?67%;R w ?0:20;C ?25%.

Table 1

Values taken for analysis of soda lime glass c (J/kg K)670h c (W/m 2K)10000I c (A) 2.3k (W/mK) 1.60R em m T150R w

0.2T m (K)1673T 0(K)298V c (V)21r (kg/m 3)

2170

Table 2

Values taken for analysis of alumina (Al 2O 3)c eJ =kg K T875h c (W/m 2K)10000I c (A) 2.3k (W/mK)26R em m T150R w

0.2T m (K)2100T 0(K)298V c eV T21r ekg =m 3T

3.9

Table 3

Details of on-time,off-time and pulse duration for different duty factor

Duty factor et on

t on tt

off

?100T(%)On-time (s)Off-time (s)

Pulse

duration (s)6710?10à45?10à415?10à47515?10à45?10à420?10à480

20?10à45?10à4

25?10à4

K.L.Bhondwe et al./International Journal of Machine Tools &Manufacture 46(2006)1699–1706

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Fig.3shows the variation of MRR with concentration of electrolyte (NaOH)due to ECSM of soda lime glass workpiece using the present model and the MRR experimentally found by Basak et al.[4].The values of the calculated MRR using present model have some difference from the experimental values.The difference between the results is due to the assumptions taken in the present analysis for ejection ef?ciency,energy partition and spark radius (Section 2).But the trend in variation of MRR with electrolyte concentration using present model are approximately same.

Fig.3shows that calculated MRR using present model goes on increasing from 10%concentration to 30%concentration signi?cantly and thereafter the concentration does not play any role to enhance the MRR.This can be explained from the fact that as the concentration is increased,the critical voltage and critical current increases.An increase in electrolyte current would mean the accelerated electrolysis process.It would result in greater rate of hydrogen bubbles at the cathode tool.The increased rate of hydrogen bubbles at the cathode implies an enhanced rate of sparking and hence higher MRR.When the concentration is increased beyond 30%,speci?c conductance of the electrolyte decreases and the change in the voltage and current across the electrolyte is almost negligible.Since,the heat energy developed from the spark is proportional to the critical voltage and current,the material removal will be less at higher values of concentra-tion.Similar trend is observed with experimental results of Basak et al.[4].

Fig.4shows the results obtained for alumina using present model and experimentally calculated MRR [15].MRR increases with increase in electrolyte concentration.Again the variation in MRR using present model is similar to the experimental results.As discussed for soda lime glass,the difference in values of MRR in alumina workpiece using present model and the experimental values are due to the assumptions taken in the present analysis.Unlike soda lime glass,the mobility of ions and corre-spondingly the speci?c conductance does not get affected while machining ceramics.It is because the potential difference applied in machining ceramics is high which

has prominent role in material removal.It is evident from Figs.3and 4that the change in value of MRR for soda lime glass with concentration is more than that of alumina.4.2.Material removal rate (MRR)

In this section study on MRR is presented for two types of material,soda lime glass and alumina workpiece.The effect of duty factor (df)and energy partition eR w Thas been observed on both types of material.

4.2.1.Soda lime glass

Fig.5shows the variation of MRR with duty factor due to ECSM of soda lime glass workpiece.Here,the duty factor is increased by increasing the spark on time et on Tand keeping off time et off Tconstant (Table 3).Thus for the larger duty factor,spark energy will be transferred to the workpiece for more time.Therefore,it is clear that with the increase in duty factor there is increase in the nodal temperature and area having temperature above the melting temperature of workpiece material.Hence,volume of the material removed by single spark is increased which leads to higher MRR.

M R R (m g /m i n

)Electrolyte concentration (wt%)

Fig.3.Variation of MRR during ECSM of soda lime glass workpiece.

M R

R (10-1m g /m i n )

Electrolyte concentration(wt%)

Fig.4.Variation of MRR during ECSM of alumina (Al 2O 3)workpiece.

M R R (m g /m i n )

Duty Factor (df)

Fig.5.Effect of duty factor on MRR due to ECSM of soda lime glass workpiece with R w ?0:20;C ?20%.Other data are taken from Table 1.

K.L.Bhondwe et al./International Journal of Machine Tools &Manufacture 46(2006)1699–1706

1704

Fig.6shows that MRR due to ECSM of soda lime glass workpiece increases with increase in energy partition.Increase in the energy partition means the amount of heat going to the workpiece is more,which is responsible to increase the temperature at the nodes in the workpiece domain.Hence,volume of material having temperature above the melting temperature of soda lime glass is also increased.It increases the amount of material removed from the workpiece.

4.2.2.Alumina (Al 2O 3)

Alumina (Al 2O 3)workpiece is undertaken with the same on time et on Tand off time et off Tas those used for the soda lime glass (corresponding details are given in Table 3).Fig.7shows the effect of variation in MRR with increase in duty factor on alumina workpiece due to ECSM.The highest temperature goes on increasing with increase in duty factor.The reason is again same that with the increase in duty factor there is increase in pulse on time and correspondingly in MRR also.However,increase in the MRR with the duty factor for ceramics (alumina)is evident to be less as compared with the soda lime glass because of its high melting point.Also it is not advised to treat ceramic (alumina)workpieces with high duty factor,since at higher duty factor heat transferred will be more and there is danger of formation of crack,which further results in complete rupture [15].

Fig.8shows the effect of energy partition eR w Ton MRR due to single spark in ECSM.With the increase in energy partition,material removal rate increases.The reason is same as discussed for soda lime glass.But for ceramics high-energy partition is not preferred as it is crack sensitive at higher temperatures.5.Conclusions

In the present work,a FEM based model has been developed to study the temperature distribution in the

workpiece and MRR with respect to change in the input parameter like electrolyte concentration,duty factor and energy partition.The present model is applied to two types of material,soda lime glass and alumina (Al 2O 3).Some of the conclusions from the study are summarized below:

The developed model used for the analysis for ECSM is matching with the experimental results under the same machining conditions as used in the literature,within the acceptable range.

For soda lime glass workpiece material MRR goes on increasing from 10%to 30%electrolyte concentration signi?cantly.Thereafter the concentration does not play any role to enhance the MRR.However,for alumina MRR increases with increase in electrolyte concentra-tion.The change in value of MRR for soda lime glass with concentration is more than that of alumina.

M R R (m g /m i n )

Energy Partition (R w )

Fig.6.Effect of energy partition on MRR due to ECSM of soda lime glass workpiece with t on ?10?10à4s ;t off ?5?10à4s ;df ?67%

;C ?25%.Other data are taken from Table 1.

M R R (10-1m g /m i n )

Duty factor df (%)

Fig.7.Effect of duty factor on MRR due to ECSM of alumina (Al 2O 3)workpiece with eR w ?0:20

;C ?25%.Other data are taken from Table 2.

0123456M R R (10-1m g /m i n )

Energy partition (R w )

Fig.8.Effect of energy partition on MRR due to ECSM of alumina (Al 2O 3)workpiece with t on ?10?10à4s ;t off ?5?10à4s ;df ?67%;C ?25%.Other data are taken from Table 2.

K.L.Bhondwe et al./International Journal of Machine Tools &Manufacture 46(2006)1699–1706

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With increase in duty factor MRR increases for both soda lime glass and alumina workpiece material.

However,the variation of MRR with duty factor in alumina is found less than that of soda lime glass.

MRR increases with the increase in energy partition eR wTdue to ECSM for both soda lime glass and alumina.

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