Dynamics of ecm and tool profile correction

Presentation on
Dynamics of
Electrochemical Machining
and
Tool profile correction
by:
PRADEEP KUMAR. T. P
II sem. M.Tech in ME
SOE, CUSAT.

• Electrochemical Machining (ECM) is a non-
traditional machining (NTM) process
belonging to Electrochemical category.
• ECM is opposite of electrochemical or
galvanic coating or deposition process.
• Thus ECM can be thought of a controlled
anodic dissolution at atomic level of the work
piece that is electrically conductive by a
shaped tool due to flow of high current at
relatively low potential difference through an
electrolyte which is quite often water based
neutral salt solution.

Material removal rate(MRR)
• In ECM, material removal takes place due to
atomic dissolution of work material.
Electrochemical dissolution is governed by
Faraday’s laws of electrolysis.
• The first law states that the amount of
electrochemical dissolution or deposition is
proportional to amount of charge passed
through the electrochemical cell.

• The first law may be expressed as:
• m∝Q,
where m = mass of material dissolved or
deposited
Q = amount of charge passed
The second law states that the amount of
material deposited or dissolved further
depends on Electrochemical Equivalence
(ECE) of the material that is again the ratio of
atomic weigh and valency.

v
QA
m
v
A
ECE
m



where F = Faraday’s constant
= 96500 coulombs
I = current (Amp)
ρ= density of the material
(kg/m3)
t=time(s)
A=Atomic weight
v=valency





.
.
.
0
v
F
IA
t
m
MRR
Fv
Ita
m




• η is the current efficiency, that is, the
efficiency of the current in removing metal
from the workpiece.
• It is nearly 100% when NaCl is used as the
electrolyte but for nitrates and sulphates,
somewhat lower.
• Assuming 100% efficiency,the specific MRRis
)
.
/
(
. 3
s
amp
m
v
F
A
MRR
Sp



• The engineering materials are quite often
alloys rather than element consisting of
different elements in a given proportion.
• Let us assume there are ‘n’ elements in an
alloy. The atomic weights are given as A1, A2,
………….., An with valency during
electrochemical dissolution as ν1, ν2, …………, νn.
The weight percentages of different elements
are α1, α2, ………….., αn (in decimal fraction)

• For passing a current of I for a time t, the mass
of material dissolved for any element ‘i’ is
given by
where Γa is the total volume of alloy dissolved(m3). Each
element present in the alloy takes a certain amount of charge
to dissolve.
i
a
i
m 


i
i
i
i
i
i
i
i
A
v
Fm
Q
Fv
A
Q
m




i
i
i
a
i
A
v
F
Q




The total charge passed,










i
i
i
a
i
i
i
a
i
T
A
v
I
F
t
MRR
A
v
F
Q
It
Q




.
1
, and,

• ECM can be undertaken without any feed to
the tool or with a feed to the tool so that a
steady machining gap is maintained.
• Let us first analyse the dynamics with NO
FEED to the tool.
• Fig. in the next slide schematically shows the
machining (ECM) with no feed to the tool and
an instantaneous gap between the tool and
work piece of ‘h’.

dh h
job tool
electrolyte
Schematic representation of the ECM process
with no feed to the tool

• Now over a small time period ‘dt’ a current of
‘I’ is passed through the electrolyte and that
leads to a electrochemical dissolution of the
material of amount ‘dh’ over an area of ‘S’
rh
Vs
s
rh
V
R
V
I 


)
/
(

• Then,
rh
V
v
A
F
s
rh
Vs
v
A
F
dt
dh
x
x
x
x
.
.
1
1
.
.
1











h
c
h
r
v
F
V
A
dt
dh
x
x


1
.

For a given potential difference and alloy,
Where c is a constant.

cdt
hdh
h
c
dt
dh
A
v
r
F
V
c
r
v
F
V
A
c
i
i
i
x
x














At t = 0, h= h0 and at t = t1, h = h1.
ct
h
h
dt
c
hdh
h
h
t
2
2
0
1
0
2
1
0



 
That is, the tool – work piece gap under zero feed
condition grows gradually following a parabolic curve
as shown in the fig in the next slide.

Variation of tool-work piece gap under zero feed
condition
h0
h
t

• As
• Thus dissolution would gradually decrease
with increase in gap as the potential drop
across the electrolyte would increase
• Now generally in ECM a feed (f) is given to
the tool
h
c
dt
dh

f
h
c
dt
dh



• If the feed rate is high as compared to rate of
dissolution, then after some time the gap
would diminish and may even lead to short
circuiting.
• Under steady state condition, the gap is
uniform i.e. the approach of the tool is
compensated by dissolution of the work
material.
• Thus, with respect to the tool, the work piece
is not moving .

• Thus ,
• Or, h* = steady state gap = c/f
• Under practical ECM condition s, it is not
possible to set exactly the value of h* as the
initial gap.
• So, it is required to be analyse whether the
initial gap value has any effect on progress of
the process.
f
h
c
dt
dh

 ;
0

f
h
c
dt
dh
Thus
dt
dh
f
dt
dh
c
f
c
f
dt
dh
c
t
f
h
ft
t
c
hf
h
h
h








,
.
1
.
'
'
2
2
*
'
*
'

'
'
'
'
'
'
'
'
'
'
'
'
'
*
'
'
'
1
1
1
.
.
dh
h
h
dt
h
h
dt
dh
h
h
f
dt
dh
f
f
c
h
cf
f
h
h
c
dt
dh
f







 







 







• Integrating between t’ = 0 to t’ = t’ when h’
changes from ho’ to h1’























1
1
log
)
1
(
1
)
1
(
1
'
1
'
0
'
1
'
0
'
'
'
'
'
'
'
'
'
0
'
'
1
'
0
'
1
'
0
'
1
'
0
h
h
h
h
t
h
d
h
h
d
t
dh
h
h
dt
e
h
h
h
h
h
h
t

Variation in steady state gap with time for
different initial gap
h1’
t1’
h0= 0.5
h0= 0
Simulation for ho'= 0, 0.5, 1, 2, 3, 4, 5
1

s
I
v
F
A
f
ie
rh
V
v
F
A
f
h
r
v
F
V
A
h
c
f
c
f h
h
h
h
x
x
x
x
x
x
.
;
.
1
.
1
1
*
'











= MRR in m/sec.
Thus, irrespective of the initial gap,

It seems from the above equation that ECM is
self regulating as MRR is equal to feed rate.
If the feed rate, voltage and resistivity of the
electrolyte are kept constant, a uniform gap
will exist and absolute conformity to the tool
shape will be obtained.

• In actual practice, it is not possible to maintain
constant resistivity of the electrolyte.
• Temperature due to heat generated during
chemical reaction tends to reduce resistivity.
• The evolution of gas and any flow
disturbances also affect resistivity.
2
H

• The process is further complicated by the
presence of a polarized layer of ions at either
or both of the electrodes.
• Current density and field strength tend to be
higher at sharp edges and corners. This results
in non-uniform gaps because of higher MRR.
• Therefore, it is difficult to machine sharp
corners by this process.

TOOL PROFILE CORRECTION
• The shape of the ECM tool is not just the
inverse or simple envelope of the shape to be
machined.
• The component shape finally obtained depends
on:
o Tool geometry
o Tool feed direction
o Flow path length
o And other process parameters.

• Involvement of several factors make the
problem more complex.
• Therefore empirical relations have been
formulated for the tool shape correction.
• Proper selection of working parameters can
reduce the effects of process phenomena such
as hydrogen formation.
• That simplifies the problem of tool profile
correction and analytical methods can be used
to derive formulae for predicting it.

Example of die sinking ECM tool
Dark lines show the work profile and corrected tool
profile. Dotted line shows uncorrected tool shape.

• Tool correction, x = y-z
• From triangles ABD and BCD,
• Or, z = h sin α cosec γ
• Taking the MRR as being inversely
proportional to gap size, the incremental MRR
at P qnd Q are related as

 sin
sin
z
h

h
y
z
h




• The machining rate in the direction of tool feed
at any point on the work surface would be the
same under equilibrium machining conditions,
and thus PS = QR, and
• or,




sin
sin
z
h





sin
sin

z
h

y =h sin γ cosec α
The tool correction ,
x = h(sin γ cosec α –sin α cosec γ)
In most die sinking operations, γ = 90 as the
tool is fed orthogonally to some area of the
work surface, therefore,
x = h(cosec α - sin α


sin
sin

h
y

Dynamics of ecm and tool profile correction

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