Journal of Materials Processing Technology 147 (2004) 241–246

Mathematical modeling for controlledelectrochemical deburring (ECD)

S. Sarkar∗, S. Mitra, B. BhattacharyyaProduction Engineering Department, Jadavpur University, Kolkata 700032, India

Received 5 September 2003; accepted 7 January 2004

Abstract

Deburring is the finishing technique required for manufacturing of precise components. In industry manual methods are commonlyemployed for burr removal. Deburring operation with high efficiency and full automation is a very difficult task. Further, removal ofinternal burrs of various size and shape sometimes becomes extremely difficult task. In such situation electrochemical deburring (ECD)offers a potential solution to such problem. In case of ECD, burr is removed by electrochemical dissolution, rather than by mechanicalforce. Due to non-contact nature of the process there is no residual stress and thermal effect on the job surface. For successful utilizationof ECD, in present day manufacturing, still demands for more intensive research, including the parametric analysis of the process. In thepresent paper the characteristics of ECD is analyzed through a developed mathematical model and main influencing factors such as time,initial burr height, inter-electrode gap, voltage and base material removal have been examined. The present study proves that predictionsbased on the developed mathematical model are in very good agreement with the experimental results. The paper also highlights the schemeof the developed ECD system designed to operate within the parametric limits. The present paper through various parametric studies willact as a guideline for the operation of an ECD system.© 2004 Elsevier B.V. All rights reserved.

Keywords: Electrochemical deburring; Burr height; Deburring

1. Introduction

Burrs are thin ridges, usually triangular in shape, thatdevelop along the edge of a workpiece from various man-ufacturing operations, e.g. machining, shearing of sheetmaterials, trimming, forging, casting, etc. Burrs can leadto noisy, unsafe operation in assembled machine parts,produce friction and wear in the parts moving relative toeach other, short circuits in electrical components and mayreduce the fatigue life of components. During heat treat-ment, an edge crack into the parts can lead to breakdownwith increasing tensile stress. Burr also increases leakagein hydro-pneumatic system. Furthermore burrs are usuallysharp and as such they can be a safety hazard to personnel.Removal of burrs in the drilling process occupies more than40% of total machining time and reduces production effi-ciency, and increases cost[1]. In the case of the parts mov-ing relatively to each other, friction and wear due to burrsnot only reduce the edge quality but also produce noise and

∗ Corresponding author.E-mail address: soumyasarkar@vsnl.net (S. Sarkar).

vibration. Common existing deburring process requirestime, labor and other associated cost. Efficiency can be real-ized through automation. But achieving a successful debur-ring process into manufacturing system with high efficiencyand full automation is an extremely difficult problem.

There are several conventional procedures to remove burrsof various size, shape and properties. Commonly manualmethods are often employed. But different internal burrs,which are complicated in shape, are difficult to be treatedmanually. For example, because of inaccessibility, it is dif-ficult to remove burrs from an internal cross-hole, which isperpendicular to a main hole[2]. Electrochemical deburring(ECD) technique has been found as a potential solution forsuch an internal burr, which is difficult to access and diffi-cult to remove, by common manual method.

In case of ECM there are interactive, higher-order influ-ences of the various machining parameters, such as elec-trolyte concentration, inter-electrode gap thickness, voltage,etc., on different dominant machining criteria[3]. As the ba-sic principles of material removal are similar for both ECMand ECD, it is apparent that the above machining parame-ters will also play an important role in ECD operation. In thepresent research mathematical models have been developed

0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.matprotec.2004.01.002

242 S. Sarkar et al. / Journal of Materials Processing Technology 147 (2004) 241–246

to show the variation of the burr height with respect to thevarious electrochemical machining parameters. The effectof the different process parameters, i.e. machining voltage,time, initial burr height and inter-electrode gap on debur-ring rate were also analyzed. Furthermore, an ECD systemhas been designed for the purpose of controlled deburringoperation.

2. Fundamentals of the electrochemical deburring(ECD)

Electrochemical deburring is based on the principle ofanodic dissolution process. The machining rate is governedby the Faraday’s laws of electrolysis. ECD does not applyany mechanical force or any thermal effects because of thenon-contact nature of the process. As in the case of electro-chemical machining (ECM), the machining rate can be keptconstant irrespective of the hardness and toughness of thematerial and physical and chemical properties of the ma-chined surface is not changed after the machining process[4]. This is an attractive feature of ECD over other debur-ring process, because there will be no heat affected zone orresidual stress on the job surface. The current density at thepeak of the surface irregularities is higher than that else-where. Burrs are therefore removed preferentially, and theworkpiece become smoothed. The electrolyte can be pumpedrapidly through the inter-electrode gap, which sweeps awaythe waste product from the deburring zone. Electrochemicaldeburring is a very quick process. Owing to its speed andsimplicity of operation, electrochemical deburring can of-ten be performed with a fixed, stationary cathode tool. Theprocess can also be used in many applications.

3. Development of mathematical models for controlledECD operation

The basic principle of ECD can be explained with theaid of Fig. 1. A and B are two points located on the tip ofthe burr and on the base material just adjacent to the burr,

h

yaya

B Flowingh0 A′ Burr after electrolyte

deburringA Burr before y0 y

deburring

Tool electrode ( - )

B′

Workpiece ( + )

∆y

Fig. 1. Mechanism of electrochemical deburring.

respectively, before deburring operation. After deburring op-eration for time t points A and B will be shifted to points A′and B′, respectively. Initial burr height and inter-electrodegap are h0 and y0, respectively. After deburring operationfor time t the reduced burr height is h and �y is the mea-sure of removal of base material or stock material as shownin Fig. 1.

In case of electrochemical dissolution, the rate of changeof gap between an electrode (tool) and a workpiece (burr)changes can be expressed as follows:

dy

dt= λ

y− f (1a)

where y is the inter-electrode gap after time t and f is thetool feed rate.

The constant factor λ is determined by the particular com-bination of electrolyte fluid, the workpiece material, supplyvoltage and can be expressed as

λ = ηAKV

ρZF(1b)

where η is the current efficiency, A the gram atomic weightof the metallic ions, V the applied voltage, K the conductivityof electrolyte, ρ the density of the anode, i.e. workpiecematerial, Z the valency of the cation and F is the Faraday(= 96,500 C).

Now for the case of electrochemical deburring, tool isstationary, i.e. for a stationary tool, f = 0. Hence, Eq. (1)becomes

dy

dt= λ

y(1c)

and after integration

y =√

y20 + 2λt (2)

Again from Fig. 1 it is seen that

y = y0 + �y (3a)

After substituting the value of y from Eq. (2) the expressionfor �y becomes

�y =√

y20 + 2λt − y0 (3b)

As exhibited in Fig. 1, y′a is the distance of the point A′

after deburring from tool electrode surface and ya is thedistance of the point A before deburring operation from thetool electrode surface. Hence,

ya = y0 − h0 (4)

and

y′a =

√y2

a + 2λt (5a)

Substituting the value of ya in Eq. (5)

y′a =

√(y0 − h0)2 + 2λt (5b)

S. Sarkar et al. / Journal of Materials Processing Technology 147 (2004) 241–246 243

Again from Fig. 1 instantaneous burr height can be expressedas follows:

h = y − y′a (6)

Combining Eqs. (2), (5b) and (6) following equation can beobtained:

h =√

y0 + 2λt −√

(y0 − h0)2 + 2λt (7)

Squaring both sides of Eq. (7) and rearranging the followingrelation is obtained:

y20 − h2 + (y0 − h0)

2 + 4λt

= 2√

(y20 + 2λt){(y0 − h0)2 + 2λt} (8)

Again squaring both sides of Eq. (8) and simplifying, thefollowing equation is obtained:

(y20 − h2)2 + (y0 − h0)

4 + 16λ2t2 + 2{(y20 − h2)(y2

0 − h2)2

+ (y0 − h0)24λt + 4λt(y2

0 − h2)}= 4[(y2

0 + 2λt){(y0 − h0)2 + 2λt}] (9)

After rearranging the above equation deburring time can beexpressed as follows:

t ={

h20 − h2

8λh2

}{(h2

0 − h2) + 4y0(y0 − h0)} (10)

From the above expression it may be observed that whenh = 0 deburring time t becomes infinite, i.e. it would takean infinite time to remove the burr completely. It means itis not possible to remove the burr completely. However inpractical situation burr height reaches the desired allowablelimit within few minutes.

Combining Eqs. (3b) and (10) removal of base materialcan be expressed as follows:

�y =√√√√y2

0 +{

h20 − h2

4h2

}{(h2

0 − h2) + 4y0(y0 − h0)}

(11)

From the above expression it is clear that for a specified fi-nal burr height, loss of base material is independent of volt-age, workpiece material and conductivity of the electrolyte.This only depends on initial burr height final burr height andinter-electrode gap. The above set of equations will be uti-lized to determine the burr height, deburring time and loss ofbase material for various parametric combinations in elec-trochemical deburring.

4. Parametric analysis of the ECD process

Based on the developed mathematical model of electro-chemical deburring process a parametric analysis has been

Table 1Machining conditions and material properties for ECD

Parameters Value

Current efficiency (η) 100%Specific removal volume (Fe2+) 2.3 mm3/A minSpecific conductivity (K) 0.02 mho/mmVoltage (V) 30 VElectrolyte fluid NaNO3 (15%)

0

0.5

1

1.5

2

0 1 2 3 4 5 6

Time (min)

Bu

rr h

eig

ht

(mm

)

Initial inter electrode gap= 2mm Initial burr height = 1.5 mm

Fig. 2. Variation of burr height with respect to time.

carried out to evaluate the effect of various process param-eters, e.g. machining time, voltage, etc., on the burr height,removal of base material and deburring time. The machin-ing conditions and workpiece material considered for thispurpose are exhibited in Table 1.

As evident from Fig. 2 that burr height reduces with in-creasing ECD time and theoretically it would take an infinitetime to remove a burr completely. In practice, however, assoon as the burr height goes below a pre-assigned allowablevalue the process is completed. In Fig. 2, slope of the curveindicating the removal rate of the burr and a sharp slope iscorresponding to rapid removal of the burr. From Fig. 2, itis also observed that with increasing time removal rate ofthe burr reduces.

From Figs. 3 and 4, it can be observed that deburring timeas well as base material removal increases sharply with theincrease in inter-electrode gap and both of them is undesir-able. Hence in electrochemical deburring; it is economicalto keep the gap between the workpiece and the tool elec-trode small, but too small a gap should be avoided becausethis causes electric sparks and shorts. Further inter-electrodegap also has significant effect on the surface finish, surfacetopography and tribological characteristics of the workpiecesurface [5].

02.5

57.510

12.5

1.4 1.5 1.6 1.7 1.8 1.9 2Inter electrode gap (mm)

Deb

urr

ing

tim

e (m

in)

Initial inter electrode gap = 1.5 mmInitial burr height = 0.45 mm

Fig. 3. Deburring time with various gaps between the electrode andworkpiece.

244 S. Sarkar et al. / Journal of Materials Processing Technology 147 (2004) 241–246

0

1

2

3

4

5

6

1.7 1.9 2.1 2.3 2.5

Inter electrode gap (mm)

Bas

e m

ater

ial r

emo

val(m

m) Initial burr height =1.5mm

Final burr height = 0.45mm

Fig. 4. Variation of base material removal with respect to inter-electrodegap.

0

5

10

15

20

10 15 20 25 30 35 40

Voltage (V)

Deb

urr

ing

tim

e (m

in)

Initial inter-electrode gap = 2 mmInitial burr height = 1.5 mmFinal burr height=0.45mm

Fig. 5. Influence of voltage on deburring time.

Fig. 5 exhibits the effect of voltage on deburring time.It is observed that with increase in voltage deburring timereduces considerably, but voltage cannot be raised beyonda certain value due to onset of sparking which will damageboth the workpiece and the tool.

Effect of initial burr height on deburring time and basematerial removal are exhibited in Figs. 6 and 7. It is ob-served from the figures that for a specified final burr heightdeburring time as well as base material removal are morewith higher initial burr height. In practice there are limita-tions on base material removal. Due to this constraint it isdifficult to remove heavy burrs by ECD because in such sit-uation major amount of base material will also be removedalong with burr.

0

1

2

3

4

5

6

7

0.6 0.8 1 1.2 1.4 1.6 1.8

Initial burr height (mm)

Deb

urr

ing

tim

e (m

in)

Inter-electrode gap=2mm Final burr height=0.45mm

Fig. 6. Variation of deburring time with various initial burr heights.

0

0.5

1

1.5

2

2.5

3

0.6 0.8 1 1.2 1.4 1.6 1.8

Initial burr height (mm)

Bas

e m

ater

ial r

emo

val (

mm

)

Initial burr height=1.5mm Final burr height=0.45mm

Fig. 7. Variation of base material removal for different initial burr height.

5. Design of the ECD setup

Fig. 8 shows the design of the electrochemical deburringsystem to carry out deburring operations on various jobs.Among the different deburring operation deburring of in-ternal cross-hole, perpendicular to main shaft is particularlyattractive. The operation has been shown schematically.Workpiece and the deburring tool are being securely heldby a three-jaw chuck and a collet chuck, respectively, withgood accuracy. Both the tool and work holding devices areinsulated from the main body in order to focus an electro-chemical reaction between tool and workpiece only.

A sufficient electrolyte flow between the tool and theworkpiece is necessary to carry away the heat and the prod-ucts of machining and to assist the deburring process at therequired rate, producing a satisfactory surface finish. ECDtooling design demands some special consideration [6]. Itis difficult to provide good electrolyte flow around burrsas they always have sharp corners. In the present researchwork the deburring tool is specially designed to supply suf-ficient electrolyte to the burr position through the internalcross-hole as shown in Fig. 9 and cross-holes are drilledin mutually opposite direction to avoid undue deflection oftool during the flow of the electrolyte. Undesired machiningis restrained through partial insulation of the electrode. Theelectrode is made of copper. Both the tool and the workpieceare placed in machining chamber to avoid the electrolytesplashing over other members of the ECD setup. The workholding device is made of titanium to avoid anodic attack.The metal in contact has been chosen in such a way that theydo not differ much in their electrochemical behavior. Theslide ways cannot be protected permanently, and so they areheavily coated with grease.

The electrolyte flow system consists of a filter, pump,electrolyte storage tank, pressure gauge and flow-measuringdevice, etc. The function of this system is to ensure adequateamount of clean electrolyte flow in the deburring zone. Thetank, pipe lines, valves are made of PVC. The pump is cor-rosion resistant centrifugal type pump.

Another important sub-system of this ECD setup is thepower supply system. This power supply system is equipped

S. Sarkar et al. / Journal of Materials Processing Technology 147 (2004) 241–246 245

Fig. 8. Schematic view of the designed electrochemical deburring setup.

Fig. 9. Schematic view of the deburring tool.

to supply different types of power like low voltage highcurrent plain dc, pulse dc of different ranges.

6. Results and discussion

To verify the developed mathematical model, relevant re-sult published by previous researchers Choi and Du Kim [7]has been utilized. The workpiece material used is SCM-4,the tool electrode is made of copper, dc current is suppliedat 30 V and the electrolyte is NaNO3 diluted to 15%. It wasreported that with NaNO3 electrolyte current contributingto electrochemical dissolution remain steady, i.e. current re-main constant with respect to time. Average current densityfor this experiment was 3.5 A/cm2.

From the current efficiency versus current density curvefor NaNO3 electrolyte it is found that current efficiency (η)is only about 2% for a current density of 3.5 A/cm2 [8].Other data required for burr height calculation for SCM-4is available in Table 1. Now from Eq. (1b) the value ofλ becomes 0.0276. This value of λ has been utilized tocalculate the various process criteria yield.

A comparative study of the theoretical and the experimen-tal values of the variation of burr height with respect to timefor different inter-electrode gaps are shown in Table 2. Theresult has also been shown graphically in Figs. 10–13 fordifferent gaps between tool and workpiece. It is observedthat the developed model matches extremely well with theexperimental results. The theoretical curves and experimen-tal curves are almost overlapped to each other.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6

Time (min)

Bu

rr h

eig

ht

(mm

)

Gap=0.5mm,Experimental

Gap=0.5mm,Theoretical

Fig. 10. Theoretical and experimental values of burr height variation withrespect to time (inter-electrode gap = 0.5 mm).

0

0.2

0.4

0.6

0.8

1

0 2 4 6

Time (min)

Bu

rr h

eig

ht

(mm

)

Gap=1mm,ExperimentalGap=1mm,Theoretical

Fig. 11. Theoretical and experimental values of burr height variation withtime (inter-electrode gap = 1 mm).

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6

Time (min)

Bu

rr h

eig

ht

(mm

)

Gap=1.5mm,Experimental

Gap=1.5mm,Theoretical

Fig. 12. Theoretical and experimental values of burr height variation withtime (inter-electrode gap = 1.5 mm).

246 S. Sarkar et al. / Journal of Materials Processing Technology 147 (2004) 241–246

Table 2Comparative study of experimental and theoretical burr height variation with time

Experiment no. Inter-electrodegap (mm)

Initial burrheight (mm)

Experimental burr height (mm) Theoretical burr height (mm)

After 4 min After 6 min After 4 min After 6 min

1 0.5 0.49 0.2 0.15 0.22 0.182 1 0.93 0.62 0.56 0.63 0.573 1.5 0.89 0.8 0.76 0.8 0.774 2 1.3 1.25 1.2 1.21 1.17

0.6

0.8

1

1.2

1.4

0 2 4 6Time (min)

Bu

rr h

eig

ht

(mm

)

Gap=2mm,Experimental

Gap=2mm,Theoretical

Fig. 13. Theoretical and experimental values of burr height variation withtime (inter-electrode gap = 2 mm).

7. Conclusions

The present research studies make it clear that success-ful adaptation of electrochemical deburring system demandsfor development of controlled ECD system. A mathematicalmodel has been developed and verified with the experimen-tal result. The developed mathematical model is quite pow-erful to analyze and determine the deburring time as well asbase material removal for a given parametric combination.This model can be effectively utilized in manufacturing in-dustry for controlled deburring operation through suitablydesigned ECD setup. From the developed model and analy-sis the following observations conclusions can be made:

(1) The rate of deburring is initially high and it reduces grad-ually with respect to time. Theoretically it would takean infinite time to remove the burr completely. Howevera few minutes of deburring operation are sufficient forall practical purpose.

(2) It is desirable to keep the gap between the workpieceand tool as small as possible because it reduces the lossof base material as well as deburring time.

(3) Higher voltage should be used to reduce the deburringtime.

(4) Higher initial burr height means more deburring timethis will also increase the loss of base material. Henceit is difficult to remove thick burr by ECD because itresults in major loss of base material, which is not de-sirable.

(5) Loss of base material is independent of electrolyte type,concentration, voltage and workpiece material. It is onlyfunction of inter-electrode gap setting, initial burr heightand final desired burr height.

(6) The developed mathematical model is quite powerfuland capable of predicting the results with good accuracy.The model can be effectively utilized for controlled, au-tomated ECD operation in modern manufacturing in-dustries.

Future scope of the work includes extensive experimentalinvestigation to study the effect of the electrolyte concentra-tion, type, the tool geometry and other aspects on deburringtime, burr height and base material removal. The present pa-per through various parametric analyses will act as a guide-line to the manufacturing engineers for the application ofECD system more efficiently in actual practice.

Acknowledgements

Authors would like to thank the All India Council forTechnical Education (AICTE), Government of India, fortheir financial support to this work.

References

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