Tamkang Journal of Science and Engineering, Vol. 8, No 1, pp. 23
-
28
(
2005
)
23
S. K. Mukherjee
1
, S. Kumar
1 and P. K. Srivastava
2
*
1
Department of Production Engineering,
2
Department of Applied Chemistry, Birla Institute of Technology,
Mesra, Ranchi 835215, India
Material removal rate in electrochemical machining is analyzed in context of over voltage and conductivity of the electrolyte solution. It is observed that over voltage is very sensitive to equilibrium gap and tool feed rate. Material removal rate decreases due to increase in over voltage and decrease in current efficiency, which is directly related to the conductivity of the electrolyte solution. It is observed that the corrected current density is always lower than the actual current. The calculated material removal rate efficiency is found to be 57%.
Key Words : Electrochemical Machining, Over-voltage, Material Removal Rate, Conductivity
Advanced materials are known for their improved strength, thermal resistance, wear resistance and corrosion resistance, which are machined by non-conventional energy sources. Among several non-conventional processes
[1
-
4] electrochemical machining is interesting because the removal of material is by an atom to an atom resulting in higher finish with stressed crack free surface and independent of the hardness of the work materials. Advance manufacturing technology has evolved thrust areas like automation of manufacture with high precession[5
-
7].
Recently, the product size ranging from 50 to 500 m m have been prepared by Micro-electrochemical machining and Micro-electrochemical Grinding [
8-11
]. Electrochemical Machining (ECM) is good for steel and super alloys and most often used when machining either shaped holes or cavities into electrically conductive materials [12,13].
At high concentration of electrolyte, electrolytes do not behave ideally and resistance of the solution [14] increases which may cause deviation from Faraday’s law and Ohm’s law. Further, it has been assumed that the pro-
*Corresponding author. E-mail: pk_srivastavapk@sancharnet.in
cess of ECM to be ideal in nature till it obeys Ohm’s law and Faraday’s law [2,15]. But there have been no report on the applicability of these laws for electrochemical machining.
The process of Electrochemical Machining is developed on the principle of Faraday’s law and Ohm’s law. In this process an electrolytic cell is formed by the anode
(work piece) and the cathode (tool) in the midst of a flowing electrolyte. The metal is removed by the controlled dissolution of the anode according to the well known Faraday’s law of electrolysis. When the electrodes are connected to about 20 V electric supply source, flow of current in the electrolyte is established due to positively charged ions being attracted towards the cathode and vice versa. Current density depends on the rate at which ions arrive at respective electrodes which is proportional to the applied voltage, concentration of electrolyte, the gap between the electrodes and tool feed rate. Due to electrolysis process at the cathode, hydroxyl ions are released which combine with the metal ions of anode to form insoluble metal hydroxides. Thus the metal is mainly removed in the form of sludges and

24 S. K. Mukherjee et al.
precipitates by electrochemical and chemical reactions occurring in the electrolyte cell. In this way even hardest possible material can be given a complicated profile in a single machining operation.
In aqueous solution of NaCl following reaction occurs
NaCl
ƒ
Na
H
2
O
ƒ
H
+
+
+ Cl
+ OH
-
-
On passing the electric current through the solution positive ions moves towards cathode and negative ions moves towards anode. Each Na
+ ions gain an electron and is converted to Na. Hence Na
+ ions are reduced at the cathode by means of electrons.
Cathode reactions
Following reaction takes place at cathode
2
.
Na
+
+ e
ƒ
Na
Na + H
2
O
ƒ
Na (OH) + H
+
2H
+
+ 2e
ƒ
H
2
­
It shows that only hydrogen gas will evolve at cathode and there will be no deposition.
Anode reaction
Fe
ƒ
Fe
2+
Fe
2+
+ 2Cl
-
Fe
2+
FeCl
+ 2OH
-
2
+ 2e
ƒ
FeCl
2
ƒ
+ 2 OH
-
Fe (OH)
ƒ
2
Fe(OH)
2
2Cl
®
Cl
2
(g) + 2e
+ 2 Cl
-
2FeCl
2
+ Cl
2
ƒ
2FeCl
3
H
+
+ Cl
ƒ
HCl
2Fe (OH)
2
+ H
2
O + O
2
ƒ
2Fe(OH)
3
¯
Fe(OH)
3
+ 3HCl
ƒ
FeCl
3
+ 3H
2
O
FeCl
3
Cl
-
+ 3 NaOH
ƒ
Fe(OH)
3
¯
+ 3NaCl ions may loose an electron and hence undergoes oxidation at anode leading to evolution of chlorine gas at anode. First and second ionization potential of iron are 182.2 kcal atom
-
1 and 373.1 kcal atom
-
1 respectively are not high and iron atom can easily loose two electrons forming Fe
2+ ions. The structure of Fe
2+ ion is not stable and easily loses one electron by the action of air or an oxidizing agent to form Fe
3+ ion (ionization potential 703 kcal atom
-
1
) having stable electronic configuration. Therefore, iron may react with scheme given above to form heavy flock of Fe(OH)
3 as a sludge in addition to Fe(OH)
2
.
Table 1.
Effect of penetration rate on machining gap and current density
Current density
A/cm
2
Equilibrium gap
(cm)
Penetration rate
(cm/sec)
480
290
190
140
60
0.0025
0.0050
0.0075
0.0100
0.0150
0.0100
0.0058
0.0038
0.0030
0.0017
When sufficient electrical energy (about 6 eV) is available between tool and work piece, a metallic ions may be pulled out of the work piece surface. The positive metallic ions will react with negative ions present in the electrolyte solution forming metallic hydroxides and other compounds, and thus the metal will be anodically dissoluted with the formation of sludges and precipitates.
The material removal rate depends chiefly on feed rates. The feed rate determines the current passed between the work piece and the tool. As the tool approaches the work, the length of the conductive current path decreases and the magnitudes of current increases. This lessening of the gap and increase in the current continues until the current is just sufficient to remove the metal at a rate corresponding to the rate of tool advance. A stable cut is then established with a fixed spacing between the work and the tool, termed as the equilibrium machining gap. If the tool feed rate is reduced, the tool advance will momentarily lag behind, increasing the gap and thus resulting in a reduction of current. This happens until a stable gap is once again established. Current density value is based on a fixed feed rate for one cm
2 of work piece considering an efficiency of 100%. The total amperage required for machining of work piece can be calculated by multiplying the current density and the surface area being machined. The effect of penetration rate on machining gap and current density is given in Table 1 [15].
Over-voltage have been calculated with varying equilibrium gap and tool feed rate.
Over voltage was calculated by utilizing the Eq. (1)
D
V =
V
- r
Z F
K A
Y e f (1)

Effect of Over Voltage on Material Removal Rate During Electrochemical Machining 25 where
D
V = over voltage, V = applied voltage (10 V), r
= density of work piece, F = Faraday constant, K = conductivity / specific conductance of electrolyte solution (taken as constant 0.20 ohm
-
1 cm
-
1
), A = atomic number of work piece metal, Y e
= equilibrium gap and f = tool feed rate. The variation of over voltage with equilibrium gap is shown in Figure 1 which indicate that over-voltage decreases linearity with increase in equilibrium gap. When equilibrium gap approaches to zero, over voltage approaches to applied voltage. Figure 2 shows variation of tool feed rate with overvoltage, which shows that over voltage decreases sharply with penetration rate and goes to negative side after a certain tool feed rate. Negative value of
D
V, seems to be unreal because un-matching long range values of penetration rate for single fixed value of equilibrium gap.
The variation of over voltage with equilibrium gap is shown in Figure 3, when equilibrium machining gap (Y e
) and tool feed rate (f) both are varied in equation (1), which shows that the over voltage is always high and is above or around 6 V to the total applied voltage 10 V. The corresponding variation in current densities shown in
Figure 4. It is clear from the Figure 4 that the corrected current density (I c
) is significantly lower than the actual current density. The current efficiency against equilibrium gap is shown in Figure 5 which indicate that there is a maxima for a particular equilibrium gap i.e. maximum efficiency can be obtained at this maxima. The plot of current density against current efficiency is shown in
Figure 6 which also shows a maxima at a current density of 104 Amp/cm
2
. The plot of corrected current density
Figure 2.
Variation of over-voltage with tool feed rate (f), when equilibrium machining gap Y e
= 0.015 cm is fixed.
Other data are same as Figure 1.
Figure 1.
Variation of over-voltage with equilibrium machining gap when tool feed rate (f) = 0.00167 cm/sec, V
= 10 V, K = 0.2 ohm
55.85, r
= 7.86, Y e
-
1 cm
-
1
, F = 96500, Z = 2, A = are taken from Table 1.
Figure 3.
Variation of over-voltage with equilibrium Machining gap. When tool feed rate (f) is varied as equilibrium machining gap. Other data are same as in Figure 1.

26 S. K. Mukherjee et al.
(I c
) and electrolyte solution resistance is shown in Figure
7. The resistance of the electrolyte solution (R) is calculated by Eq. (2).
V c
= I c
R (2) where V c
= corrected voltage, and I c
= corrected current density and which shows that resistance of the solution decreases omically upto current density 104 Amp/cm
2 after that variations is seems to be non-omic. The actual corrected material removal rate (MRR c
) calculated and theoretical material removal rate MRR th obtained by Eq. (3)
MRR = AI c
/ZF (3) are shown in Figure 8. The efficiency ( h
) of material removal calculated by Eq. 4, h
=
MRR c
MRR th
´
100 (4) indicate that efficiency is about 57%. However the efficiency of maximum material removal is about 72% at optimum condition [15,16]. It appears that this discrepancy in the material removal rate is due to de-
Figure 4.
Variation of current density with equilibrium machining gap. When tool feed rate (f) varies as equilibrium machining gap, other data are same as in Figure
1, (a) for actual current density (b) for corrected current density.
Figure 6.
Variation of current efficiency with current density.
When tool feed rate (f) varies as equilibrium machining gap (Y e
), other data are same as in Figure 1.
Figure 5.
Variation of current efficiency with equilibrium machining gap. When tool feed rate (f) varies as equilibrium machining gap (Y e
), other data are same as in Figure 1.
Figure 7.
Variation of Resistance of electrolyte solution with effective current density (I c
). Other data are same as in Figure 1.

Effect of Over Voltage on Material Removal Rate During Electrochemical Machining 27
Figure 8.
Material removal rate, (a) theoretical, (b) experimental, determined by Eq. (3).
crease in current efficiency, which is directly related to over-voltage, polarization and passivation. It may also be attributed that a fraction of current consumed in side reactions, as previously formed low valency metal ions are oxidized to a higher valency wastefully using current [17,18] The specific conductance (K) of the solution is only parameter which is suppressed by increasing over voltage, polarization and passivation and side reactions.
The over-voltage is the important parameter which restrict the material removal rate and is sensitive to tool feed rate and equilibrium machining gap. If over voltage
D
V = 0, then Eq. (1) reduces to
K = 345.57 Y e f
This indicates that for maximum efficiency specific conductance must be equal to 345.57 Y e f. Increase in over-voltage is associated with decrease in equivalent conductance from its value at infinite dilution due to decrease in ionic mobility which depends on dielectric constant, viscosity and temperature of the electrolyte solution.
Further, researches are underway to test these models by taking the values of appropriate parameters and to reproduce the experimental results for different metals and alloys in electrochemical machining.
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Manuscript Received: May 4, 2004
Revision Received: Jun. 25, 2004
Accepted: Sep. 8, 2004