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Welcome to the course on Advanced Machining
Processes we are going today to the theory
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of electrochemical machining part 2 The outline
of the todays lecture is as follows material
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removal in electrochemical machining inter
electrode gap evaluation in electrochemical
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machining single equation for inter electrode
gap evaluation in ECM self regulating feature
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of ECM process chemical equivalent of an alloy
maximum permissible feed rate in ECM temperature
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gradient and electrical conductivity evaluation
in ECM then some numerical problems will be
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solved related to electrochemical machining
process
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Let us see how to evaluate or calculate material
removal and material removal rate in electrochemical
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machining process Material removal is abbreviated
as small m in electrochemical machining as
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I mentioned in the earlier lecture that is
in part one electrochemical machining follows
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faraday's laws of electrolysis which clearly
tells that mass of material removed is equal
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to ItE divided by F where I is the current
flowing in the circuit or in this particular
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case through the inter electrode gap t is
the time of flow of the electric current or
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electrochemical machining E is the chemical
equivalent of the anode material and F is
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the Faraday's constant which has 96500 coulombs
as its value which is constant
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Material removal rate in ECM can be calculated
when we divide m by time t of machining that
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becomes m by t as you can see here which is
indicated as m dot which becomes equal to
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IE over F now here m is the amount of material
removed in grams I is current flowing through
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the inter electrode gap in amperes t is time
of current flow or electrochemical machining
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E is gram equivalent or gram chemical equivalent
of anode material that is the work piece material
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F is Faraday's constant given in coulombs
or ampere seconds and m dot is material removal
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rate in grams per second
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Note it that here I have mentioned material
removal rate in grams per second it can also
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be represented as MRRg where the suffix g
indicates that it is in grams per second there
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are other ways also of representing the material
removal rate which we will see
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Material removal rate can be obtained as rho
a v a over t and volume of anode removed v
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a let us see it is given by A a cross-sectional
area the inter electrode gap y a that is the
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gap divided by t is the time and rho a is
the density of the anode material
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Now as I have written here rho a is density
of anode v a is the volume of material removed
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this v a and this v a they are the same and
A a is the cross-sectional area on the anode
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from which material is being removed or in
other better way we can say through which
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the current is flowing in time t y a is the
thickness of the material removed in time
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t and delta V is over potential which will
be shown in the following equations and k
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is electrolytes electrical conductivity that
will be used in the following equation
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From above equation we can write MRRl where
MRR suffix l indicates linear material removal
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rate whose units will be millimeter per second
and that is y a over t y a is the thickness
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of the material that has been removed and
it is given by y a over t is given by IE over
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F rho a A a So we write this MRRL that is
the linear material removal rate is equal
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to JE over F rho a because I over Aa can be
written as J as has been done in this particular
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equation rest of the terms remains the same
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Current density J this above equation can
be written as MRRl is equal to V minus delta
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V over A a multiplied by K A a divided by
A into E over F rho A Now here you can see
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J has been replaced we know I is equal to
voltage divided by cross-sectional area and
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here delta V as I mentioned in the earlier
slide is over potential so V minus delta V
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becomes the effective voltage which is working
across the inter electrode gap so this particular
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equation can be used for evaluating linear
material removal rate from the work piece
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material I have already shown in the last
lecture what this MRRl means
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So MRRl again written in the same form now
let us understand it like this that y is the
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amount of material that has been removed in
time t from the work piece now this is the
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front view of the work piece and tool combination
showing the inter electrode gap that is the
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or the gap that is shown over here now here
MRRl is in front gap only side gap are not
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considered here we are considering only this
front gap that is this one the gap that is
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in the sides is not considered in this particular
equation however you can evaluate MRRl from
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the side gap also by developing an equation
on the same lines
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Now if you see this assembly from the top
you will find that the cross-sectional area
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through which current is flowing is shown
over here and this is the one which is the
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diameter of the tool tool diameter and this
is the one which is the diameter of the cavity
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that has been formed on the work piece
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Now dy dt is the rate of change of inter electrode
gap what is this rate of change of inter electrode
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gap here let us see we are giving the feed
to the tool that is moving downwards and due
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to the removal of the material the surface
of the work piece is also moving downward
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so both are moving in the same direction
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Now if we see here if the movement of the
surface top surface of the work piece is say
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y here then at which rate the gap between
the bottom surface of the tool and top surface
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of the work piece is changing with time we
have to find it out here this becomes Y in
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place this is the surface that has been removed
from here this becomes Y then rate of change
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of the gap between the bottom surface of the
tool and the top surface of the work piece
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that is given by dy over dt and since this
is the inter electrode gap so it say the rate
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of change of inter electrode gap that is this
particular gap
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So we have to find out this and this is given
by dy over dt is equal to y over t the rate
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the inter electrode gap remove or the material
removed from there in time t now this f because
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both are moving in the same direction so effective
inter electrode gap becomes the difference
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between the amount linear material removal
rate and feed rate that is f
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And this you can find out like this we have
already found dy over dt that is E into V
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minus delta V k over F rho A over Y and this
is the minus f that is there so we add it
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here so this will give you the rate at which
the inter electrode gap is changing with time
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now the question is how to evaluate this inter
electrode gap in ECM
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Now the two cases are there one is the case
of zero feed rate that is when the value of
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f is 0 that means no feed or no movement of
the tool only the surface of the work piece
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is recessing downwards another case is that
where the feed rate is not zero that means
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tool is moving and work piece is also recessing
downwards work piece surface is recessing
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downwards
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So let us see for the first case from the
previous equation we can write down dy over
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dt is equal to c over y minus f where C is
given by E into V minus delta V k over F into
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rho a now we are writing here V minus delta
V as V effective V e now one thing is to be
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seen over here that whole of this term has
been represented as C and it is varying with
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y that is the inter electrode gap so this
is nothing but this represented by V e k is
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there and F rho a is there and this is given
by V e is equal to V minus delta V
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Now in this particular figure we can clearly
see that tool is feeding is being fed downward
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there is the flow of the electrolyte in this
particular direction with a certain velocity
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and work piece and tool both are connected
to the power supply tool being cathode and
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work piece being anode Now here as I have
mentioned earlier two cases arise one is the
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case where feed rate f is equal to 0 and another
is the case where feed rate is not equal to
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0
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Let us evaluate the inter electrode gap in
ECM for zero feed rate when feed rate of the
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tool towards the work piece is 0 that means
tool is stationary now substitute in earlier
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equation f is equal to 0 then we will get
that dY as function of Y here is equal to
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C into dt Integrate both sides of this particular
equation it will give Y is equal to Y 0 square
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plus 2 C t under the root whole
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Now this equation has been derived taking
the initial condition to evaluate the constant
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of integration for Y is equal to Y 0 at time
t is equal to 0 that is the initial inter
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electrode gap if at t time whatever inter
electrode gap we maintain in the beginning
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that is indicated by Y over here and that
is the initial condition this equation is
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well represented by the figure in the next
slide I will show you here there are certain
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assumptions in deriving this particular equation
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Here K is taken constant that is the electrical
conductivity of the electrolyte in the inter
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electrode gap Delta V is a small fraction
of V delta V is the over potential which is
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a very small fraction of the voltage being
applied and K of work piece and tool are very
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very large compared to the electrolyte k is
the electrical conductivity of the work piece
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and the tool
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Let us take the case of plain parallel electrodes
machining that is normal to the feed direction
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as you can see over here here is the plain
parallel machining Electrolyte properties
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are change in Z direction that means we are
considering 2D problems third direction that
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is the Z direction we are assuming that the
electrolyte properties are the same along
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the Z direction there is no variation
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Now this equation yields the relationship
between inter electrode gap and machining
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time any time t Now you can see here that
as the time t is increasing inter electrode
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gap is increasing according to the equation
which we derive in the earlier slide now here
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you can see the time t is equal to 0 There
is a certain inter electrode gap that is represented
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by Y0 and that is what we have used in the
earlier equation for as the initial condition
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So the relationship Y is equal to Y0 follow
a parabolic this relationship follow a parabolic
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curve that is shown over here Now most of
the time in electrochemical machining feed
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rate is not equal to zero rather there is
a finite feed rate so that means F is not
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equal to 0 and let us see how to evaluate
the inter electrode gap when feed rate is
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not equal to zero that is the finite feed
rate
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Case two now when constant feed is given to
the tool that is f not equal to 0 for better
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performance of the process it is desirable
to machine under equilibrium condition that
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is dy over dt is equal to zero constant inter
electrode gap is maintained Now this is very
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important to understand that here in this
particular case when dy over dt is equal to
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zero that simply means that this gap is maintained
constant and this gap is nothing but equal
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to equilibrium gap and this can be maintained
only when the condition that linear material
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removal rate is equal to the feed rate then
only the gap between the bottom face of the
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tool and top face of the surface being machined
will remain constant
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So y that is the inter electrode gap is equal
to y e that is the inter electrode gap under
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equilibrium condition and this is given by
c by f as we have seen earlier for the case
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dy over dt is equal to 0 Here ye is inter
electrode gap under the equilibrium condition
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For the generalized analysis it is always
better to go for non dimensionalization of
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the parameter hence here the parameters have
been non dimensionalized as you can see y
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dash is equal to y over y e where y is the
inter electrode gap and y e is the inter electrode
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gap under equilibrium condition and this can
be shown is equal to y f over C because we
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have shown in the earlier slides that y e
is equal to C over f
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Now t dash is equal to the t multiplied by
f square over C and this becomes non-dimensional
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so we can write the equation earlier equation
of dy dt can be written as dy dash over dt
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dash is equal to 1 over y dash minus 1 Now
we can evaluate this equation or we can simplify
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this equation by taking integration on both
sides and we will find finally this equation
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as t dash is equal to y 0 dash minus y dash
plus ln that is natural log of y 0 dash minus
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1 divided by y dash minus 1
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Now how to get this particular equation we
will see in the following slides this equation
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is valid for the case when y dash is greater
than zero this is very important condition
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one should note down if y dash is less than
zero then it will indicate that short circuit
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has taken place between the tool and the work
piece and this is highly undesirable condition
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no short circuit should take place between
the tool and the work piece otherwise both
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will get damaged
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Now this equation can be written as dt dash
over dy dash the earlier equation which I
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wrote there is equal to y dash over 1 minus
y dash this becomes equal to if we add minus
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1 and plus 1 then it becomes 0 so we get the
same equation so we can write it as minus
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1 plus y dash plus 1 divided by 1 minus y
dash and this can be written like this that
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is minus 1 minus y dash plus 1 over 1 minus
y dash we can simplify it and write it as
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minus 1 plus 1 over 1 minus y dash because
this term we separate out this term and this
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term and 1 minus y dash and 1 minus y dash
of this term will get cancel so you will get
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minus 1 over there plus 1 over 1 minus y dash
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Now if you simplify the earlier equation or
rewrite the earlier equation you will get
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dt dash is equal to minus 1 plus 1 over 1
minus y dash dy dash Integrate both sides
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of this particular equation that is you can
integrate it you will get the after integration
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and simplifying it you will get this becomes
0 to t dash and you can integrate this particular
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part also and you get finally t dash is equal
to minus y dash minus ln y dash minus 1 plus
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K
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Now we have to evaluate the constant of integration
K now for this particular purpose substitute
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the initial condition as y dash is equal to
y 0 dash where we have already seen that initial
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inter electrode gap is given by y 0 and if
initial inter electrode gap is y 0 then you
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non dimensionalize this by dividing by y then
you get y 0 dash and this true at t dash is
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equal to 0 It gives the following relationship
as 0 is equal to minus y dash 0 minus ln y
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0 dash minus 1 plus K from this you get if
you substitute this value and simplify this
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particular equation then you get K is equal
to y 0 dash plus ln y 0 dash minus 1
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Substitute the value of K in above equation
you get t dash is equal to minus y dash minus
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ln y dash minus 1 plus y 0 dash plus ln y
0 dash minus 1 Now you can simplify this equation
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then you will get this as y 0 dash minus y
dash plus ln y 0 dash minus 1 over divided
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by y dash minus 1 You can take this and this
together they will give this equation divide
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this by this because this has the minus term
you will get this particular term
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In this equation only positive values of y
dash are possible y dash is equal to 0 implies
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a short circuit between the tool and work
piece that I have already mentioned and for
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negative value of negative value it will not
work this particular equation will not work
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When the parameters are not non-dimensionalised
the solution obtained can be written as t
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is equal to 1 over f within bracket y 0 minus
y t plus y e ln y 0 minus y e divided by y
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t minus y e this bracket Now this equation
is an implicit equation when you want to evaluate
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the inter electrode gap y t right So this
equation is given in the book on electrochemical
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machining by J A McGeough published by Chapman
and Hall London
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Solving this particular equation takes lot
of time because this is an implicit equation
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and with the help of computer if you want
to solve it for one particular value of inter
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electrode gap it may take 30 to 40 iterations
which takes lot of computer time because solving
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the ECM problem with the help of electrochemical
machine with the help of finite element method
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or boundary element method or any other finite
difference method then there are thousands
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of node and at each node you have to iterate
it for 30 to 40 time
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Total time taken by computer will be too large
so it is quite cumbersome and difficult to
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solve by the help of even difficult in the
sense a lot of time it will be taking on the
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computer
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Now most of the time you find that the feed
rate is inclined to the surface of the work
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piece as I can see here in that particular
case you have to take the component of the
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feed rate which is normal to the work piece
surface and that becomes f cos theta so in
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00:24:39,649 --> 00:24:46,799
place of f you have to use f cos theta at
appropriate places wherever feed rate term
201
00:24:46,799 --> 00:24:48,659
f appears
202
00:24:48,659 --> 00:24:58,440
Now iterative procedure for solution of this
equation can be followed because it has Y
203
00:24:58,440 --> 00:25:03,769
on both sides when you are evolving Y or inter
electrode gap with the help of this particular
204
00:25:03,769 --> 00:25:10,159
equation so it takes 30 to 40 iterations for
solution at each point Computer time when
205
00:25:10,159 --> 00:25:17,460
solve say for 1000 points will be enormous
specially when using finite difference method
206
00:25:17,460 --> 00:25:20,019
finite element method or boundary element
method
207
00:25:20,019 --> 00:25:29,309
Hence an explicit equation to evaluate inter
electrode gap for both the cases that is feed
208
00:25:29,309 --> 00:25:39,490
rate is equal to 0 and finite feed rate without
requiring iterative procedure has been proposed
209
00:25:39,490 --> 00:25:46,669
Now let us see how to evaluate this single
equation for inter electrode gap evaluation
210
00:25:46,669 --> 00:25:56,480
in case of electrochemical machining equation
for evaluating inter electrode gap for numerical
211
00:25:56,480 --> 00:26:15,739
analysis of electro chemical machining process
We have already derived this particular equation
212
00:26:15,739 --> 00:26:24,659
that is dy over dt is equal to E v minus delta
v k over F rho a y minus f where v is the
213
00:26:24,659 --> 00:26:31,669
applied voltage and delta v is the over potential
and F is the feed rate This can be written
214
00:26:31,669 --> 00:26:45,509
as EJ over F rho a minus f this can be rewritten
as dy is equal to EJ over F rho A minus f
215
00:26:45,509 --> 00:26:50,820
into dt
216
00:26:50,820 --> 00:26:57,779
Let us make the following assumptions J that
is the current density remains almost constant
217
00:26:57,779 --> 00:27:04,859
within a small area of an element when I say
element that means I am talking with reference
218
00:27:04,859 --> 00:27:11,739
to the finite difference method or finite
element method of 2D problem or volume of
219
00:27:11,739 --> 00:27:17,940
an element that means I am talking of 3D problem
220
00:27:17,940 --> 00:27:24,440
Computational machining cycle time delta t
is very small it is normally taken as fraction
221
00:27:24,440 --> 00:27:30,980
of a second such that J that is the current
density during that period of time is more
222
00:27:30,980 --> 00:27:40,229
or less constant important for numerical analysis
of this particular process
223
00:27:40,229 --> 00:27:53,129
Integration of above equation would give y
is equal to c dash minus f into delta t plus
224
00:27:53,129 --> 00:28:06,200
k dash to evaluate the value of integration
constant k dash where C dash is equal to EJ
225
00:28:06,200 --> 00:28:14,129
over F rho a at time t is equal to 0 y is
equal to y 0 I have already mentioned if you
226
00:28:14,129 --> 00:28:19,619
substitute this value T is equal to 0 and
y is equal to y 0 in this particular equation
227
00:28:19,619 --> 00:28:30,269
you will get k dash is equal to y 0 substitute
this value of k in this particular equation
228
00:28:30,269 --> 00:28:37,399
then you will get y is equal to y 0 plus c
dash minus f into delta t here I have written
229
00:28:37,399 --> 00:28:45,529
delta t since t is very small hence t is equal
to delta t which i have already written over
230
00:28:45,529 --> 00:28:46,529
here
231
00:28:46,529 --> 00:28:52,710
This equation can be applied for both cases
f is equal to 0 and f not equal to 0 as if
232
00:28:52,710 --> 00:29:00,679
you see again previous equation here you can
because feed rate is here if you are taking
233
00:29:00,679 --> 00:29:07,359
the case of feed rate is equal to 0 substitute
the value F is equal to 0 if it is not 0 then
234
00:29:07,359 --> 00:29:13,059
you substitute here the value of f whatever
is the feed rate in appropriate units you
235
00:29:13,059 --> 00:29:18,539
will be able to evaluate the inter electrode
gap in both the cases whether zero feed rate
236
00:29:18,539 --> 00:29:22,570
or finite feed rate from the same equation
237
00:29:22,570 --> 00:29:28,869
Now what is this Y 0 you know when you are
beginning the machining then whatever is the
238
00:29:28,869 --> 00:29:36,049
initial inter electrode gap that is Y 0 Now
when we deal with the finite element method
239
00:29:36,049 --> 00:29:45,129
or other procedure then we in place of Y we
can use Y I that is the I S node and Y I is
240
00:29:45,129 --> 00:29:52,659
equal to Y 0 and if it is at time T is equal
to 0 if time T 1 is there then it becomes
241
00:29:52,659 --> 00:29:58,479
Y I is equal to YT1I and so on as I have shown
over here
242
00:29:58,479 --> 00:30:05,479
Y I indicates front gap only not the side
gap as I have mentioned earlier also we are
243
00:30:05,479 --> 00:30:12,190
not considering this side gap over here we
are considering only the front gap as shown
244
00:30:12,190 --> 00:30:19,210
over here this idea can be applied for the
calculation of the anode profile in electrochemical
245
00:30:19,210 --> 00:30:24,580
drilling also so this equation which we have
just derived as single equation for finite
246
00:30:24,580 --> 00:30:30,229
feed rate as well as for zero feed rate is
very very important especially when you are
247
00:30:30,229 --> 00:30:39,350
solving large problems having thousands of
nodes and in a very small machining time delta
248
00:30:39,350 --> 00:30:40,909
t you are taking
249
00:30:40,909 --> 00:30:47,539
Then total computational time will be substantially
reduced if this single equation used in place
250
00:30:47,539 --> 00:30:57,489
of parabolic equation and implicit equation
which requires solution for 30 or 40 iteration
251
00:30:57,489 --> 00:31:05,649
for each point solution Now apart from this
evaluation of inter electrode gap either by
252
00:31:05,649 --> 00:31:11,850
parabolic equation or implicit equation or
by single equation applicable for both there
253
00:31:11,850 --> 00:31:17,840
are certain interesting features with this
electrochemical machining process has got
254
00:31:17,840 --> 00:31:23,700
and this self regulating is one of the very
important feature of electrochemical machining
255
00:31:23,700 --> 00:31:24,700
process
256
00:31:24,700 --> 00:31:34,701
ECM process always attempts to attain an equilibrium
gap condition such that y is equal y 0 it
257
00:31:34,701 --> 00:31:43,840
always attempts to attain this condition or
in other words you can say f is equal to MRRle
258
00:31:43,840 --> 00:31:50,980
here suffix l indicates the linear material
removal rate and e indicates the linear material
259
00:31:50,980 --> 00:31:52,899
removal rate under equilibrium condition
260
00:31:52,899 --> 00:31:59,450
Now one point is to be noted that if f is
equal to MRRle then inter electrode gap will
261
00:31:59,450 --> 00:32:06,499
always remain constant and once inter electrode
gap remains constant we call it as equilibrium
262
00:32:06,499 --> 00:32:14,049
condition in case the equilibrium condition
is disturbed two possibilities exist as discussed
263
00:32:14,049 --> 00:32:20,359
below disturbed means either inter electrode
gap becomes more than equilibrium gap or it
264
00:32:20,359 --> 00:32:22,479
becomes less than equilibrium gap
265
00:32:22,479 --> 00:32:29,909
Now let us see what happens when initial inter
electrode gap is more than equilibrium gap
266
00:32:29,909 --> 00:32:37,879
or less than equilibrium gap Case one if inter
electrode gap y is greater than equilibrium
267
00:32:37,879 --> 00:32:46,169
inter electrode gap y e then MRRl linear material
removal rate will be lower as compared to
268
00:32:46,169 --> 00:32:54,979
MRRle because y is greater than y e as you
can see here that means the current density
269
00:32:54,979 --> 00:33:00,950
will become lower as the inter electrode gap
increases current density becomes lower and
270
00:33:00,950 --> 00:33:07,190
this is greater than equilibrium gap so current
density compared to the case when equilibrium
271
00:33:07,190 --> 00:33:15,649
gap is y e it will become lower or f becomes
greater than MRRl because we can use this
272
00:33:15,649 --> 00:33:21,539
particular equation for this particular purpose
that when y is greater than y e then feed
273
00:33:21,539 --> 00:33:24,850
rate becomes greater than linear material
removal rate
274
00:33:24,850 --> 00:33:32,629
And you can see here this is the equilibrium
gap y e and this is the initial gap or the
275
00:33:32,629 --> 00:33:38,659
gap inter electrode gap y so in this particular
case this one feed rate becomes greater than
276
00:33:38,659 --> 00:33:44,879
MRRl so what will happen also please note
that lower value of inter electrode gap will
277
00:33:44,879 --> 00:33:52,869
result in higher value of J that is current
density that is higher value of MRRl because
278
00:33:52,869 --> 00:33:58,489
once the value of J becomes higher than the
or the current density becomes higher than
279
00:33:58,489 --> 00:34:03,179
the material removal rate increases
280
00:34:03,179 --> 00:34:09,100
As a result of this condition that is the
feed rate greater than MRRl the inter electrode
281
00:34:09,100 --> 00:34:19,149
gap will to decrease hence y tends to decrease
or attempts to be equal to y e because when
282
00:34:19,149 --> 00:34:25,630
this y is trying to reduce then definitely
this y will be tending to move towards the
283
00:34:25,630 --> 00:34:33,710
equilibrium gap y e So we are discussing self
regulating feature of electrochemical machining
284
00:34:33,710 --> 00:34:40,110
case one is the case where inter electrode
gap is greater than equilibrium inter electrode
285
00:34:40,110 --> 00:34:43,790
gap
286
00:34:43,790 --> 00:34:52,330
Now case two is the one where inter electrode
gap or initial inter electrode gap is less
287
00:34:52,330 --> 00:35:00,710
than equilibrium gap then MRRl that is linear
material removal rate will be greater than
288
00:35:00,710 --> 00:35:08,040
the linear material removal rate under the
equilibrium conditions and f is smaller than
289
00:35:08,040 --> 00:35:11,961
MRRl compared to the equilibrium condition
290
00:35:11,961 --> 00:35:19,360
As a result of this inter electrode gap attempts
to attain higher value because linear material
291
00:35:19,360 --> 00:35:29,920
removal rate is greater than feed rate so
gap will continuously keep increasing so y
292
00:35:29,920 --> 00:35:36,110
that is the gap will always try to attain
the equilibrium gap as you can see here this
293
00:35:36,110 --> 00:35:43,360
is the y e and this is the y y is smaller
than y e now since material removal linear
294
00:35:43,360 --> 00:35:49,570
material removal rate in this particular case
is greater so this will try to move faster
295
00:35:49,570 --> 00:35:55,160
this surface will try to move faster than
the feed rate and the gap will try to increase
296
00:35:55,160 --> 00:36:03,990
so that it attains the value of equilibrium
gap that is y e
297
00:36:03,990 --> 00:36:11,890
So in this figure which I am going to show
we have seen earlier that whether the inter
298
00:36:11,890 --> 00:36:17,920
electrode gap was lower than the equilibrium
gap or larger than the equilibrium gap in
299
00:36:17,920 --> 00:36:26,110
both the cases inter electrode gap automatically
was attempting to attain the equilibrium gap
300
00:36:26,110 --> 00:36:31,960
the same thing which we discussed in the or
we saw in the earlier slides is represented
301
00:36:31,960 --> 00:36:42,570
here in the form of the graph as you can see
here here is the Y dash and here is the time
302
00:36:42,570 --> 00:36:50,060
Now you can see here if it is 1 then equilibrium
gap and inter electrode gap both are the same
303
00:36:50,060 --> 00:36:56,260
that means the machining will continue under
equilibrium condition if gap becomes more
304
00:36:56,260 --> 00:37:02,770
than that in this zone then you can see all
the curves they are attempting to attempt
305
00:37:02,770 --> 00:37:08,100
asymptotic condition where the inter electrode
gap becomes equal to the equilibrium gap
306
00:37:08,100 --> 00:37:14,280
If it is lesser than that then also it will
be it is trying to attempt to get the asymptotic
307
00:37:14,280 --> 00:37:20,540
condition and to attain the equilibrium condition
even if it is less than and so it is very
308
00:37:20,540 --> 00:37:28,110
clearly visible here that in both the cases
inter electrode gap attempts to attain equilibrium
309
00:37:28,110 --> 00:37:33,440
inter electrode gap the same thing is written
here that in this figure y dash is equal to
310
00:37:33,440 --> 00:37:38,530
1 indicates equilibrium condition that is
this one dash dash condition
311
00:37:38,530 --> 00:37:46,810
If its value is not equal to 1 then in both
cases it that is y dash less than 1and y dash
312
00:37:46,810 --> 00:37:52,540
greater than 1 becomes asymptotic in nature
that you can see here that means it attempts
313
00:37:52,540 --> 00:38:01,151
to attain an equilibrium condition and that
condition is represented by 1 over here and
314
00:38:01,151 --> 00:38:11,970
we all know already that MRRl is given by
this particular equation
315
00:38:11,970 --> 00:38:20,160
Now we know that electrochemical machining
process is applicable only for electrically
316
00:38:20,160 --> 00:38:27,120
conducting material now electrically conducting
materials they can be they are the metals
317
00:38:27,120 --> 00:38:34,010
only they can be mostly they are the metals
they can be pure metal that means iron there
318
00:38:34,010 --> 00:38:36,270
are no other constituent
319
00:38:36,270 --> 00:38:44,350
Or second case is where other constituents
are there that means alloy more than one metals
320
00:38:44,350 --> 00:38:51,930
are there and they form the alloy now the
question arises especially when alloy is there
321
00:38:51,930 --> 00:38:59,890
what is going to be the value of the chemical
equivalent that is E because E is different
322
00:38:59,890 --> 00:39:05,460
for different metals when more than one metals
are there in the alloy how to evaluate this?
323
00:39:05,460 --> 00:39:11,040
So there are two methods to evaluate chemical
equivalent of an alloy
324
00:39:11,040 --> 00:39:21,830
Let us see a large number of the materials
being machined by ECM process are alloys not
325
00:39:21,830 --> 00:39:31,920
only pure metals the value of chemical equivalent
E of an alloy can be evaluated by one of the
326
00:39:31,920 --> 00:39:41,980
following two methods first one is known as
percentage by weight method and here I will
327
00:39:41,980 --> 00:39:44,910
like to emphasis what this percentage means
328
00:39:44,910 --> 00:39:49,910
Say suppose an alloy is there and five constituents
are there then each constituent will be in
329
00:39:49,910 --> 00:39:57,070
different weight percent someone may be 80
weight percent another maybe 5 percent third
330
00:39:57,070 --> 00:40:04,510
may be 2 percent something like that So that
percentage by weight method is the one and
331
00:40:04,510 --> 00:40:10,320
second is known as super position of charge
method we will discuss both of them
332
00:40:10,320 --> 00:40:24,520
Percentage by weight method now in this particular
case the sum of the chemical equivalent AI
333
00:40:24,520 --> 00:40:35,770
divided by ZI I indicates the IS element maybe
written as A1 over Z1 plus A2 over Z2 and
334
00:40:35,770 --> 00:40:44,660
so on for different elements of each element
I in the alloy is multiplied by its percentage
335
00:40:44,660 --> 00:40:53,310
respective proportion by weight that is XI
in the alloy It gives a value for the chemical
336
00:40:53,310 --> 00:41:03,870
equivalent of the alloy that is abbreviated
as A over Z with suffix small a
337
00:41:03,870 --> 00:41:10,980
It can be written the equation is written
like A over Z A over Z is nothing but E that
338
00:41:10,980 --> 00:41:18,960
is the chemical equivalent where A is the
atomic mass of the element and Z is the valency
339
00:41:18,960 --> 00:41:24,400
at which it is dissolving please note here
I have mentioned earlier lecture also that
340
00:41:24,400 --> 00:41:30,720
some elements have more than 1 valencies say
2 valencies 3 valency then you should clearly
341
00:41:30,720 --> 00:41:38,560
know at which valency it is dissolving then
only you will get the correct value of E otherwise
342
00:41:38,560 --> 00:41:46,400
it will be a misleading value of E then calculated
MRR as well as predicted anode shape or design
343
00:41:46,400 --> 00:41:49,760
tool shape all will be erroneous
344
00:41:49,760 --> 00:41:57,040
So A by Z a is equal to 1 upon 100 summation
I is equal to 1 to n where n is the number
345
00:41:57,040 --> 00:42:04,900
of the elements in the alloy A i over Z i
X i where X i as mentioned over here is the
346
00:42:04,900 --> 00:42:15,660
weight percent of a particular element i n
is the number of constituent elements Use
347
00:42:15,660 --> 00:42:24,590
this value of E that is equal to A over Z
a in the equation of MRRl this is useful for
348
00:42:24,590 --> 00:42:37,080
the equation whether it is for MRRl or MRRg
or MRRv or even MRRa if it is being used
349
00:42:37,080 --> 00:42:47,830
Now super position of charge method the basic
philosophy of super position of charge method
350
00:42:47,830 --> 00:42:56,480
is for the dissolution of 1 gram of alloy
the total amount of electric charge required
351
00:42:56,480 --> 00:43:07,350
for dissolution by individual element is equated
to Z over A suffix small a multiplied by F
352
00:43:07,350 --> 00:43:11,100
that is the Faraday’s constant
353
00:43:11,100 --> 00:43:18,960
And it is written like this Z over A F is
equal to F summation i is equal to 1 to N
354
00:43:18,960 --> 00:43:27,980
X i over 100 Z i over A i where Z i is the
valency of highest element A i is the atomic
355
00:43:27,980 --> 00:43:35,610
mass of the highest element and X i represents
the percentage by weight of that particular
356
00:43:35,610 --> 00:43:39,170
highest element in the alloy
357
00:43:39,170 --> 00:43:44,640
This can be simplified like A by because in
the earlier equation we try to find out A
358
00:43:44,640 --> 00:43:51,580
by Z that is the E so we can write this equation
this particular equation in this particular
359
00:43:51,580 --> 00:43:59,450
form so that we directly get the value of
E and A by Z a is equal to 100 divided by
360
00:43:59,450 --> 00:44:06,990
summation i is equal to 1 to n X i Z i over
A i so whatever value of E you get from here
361
00:44:06,990 --> 00:44:11,800
this value can substitute in the equation
of MRR
362
00:44:11,800 --> 00:44:21,710
Comparison of two methods for evaluation of
E mass removal rate can be obtained from this
363
00:44:21,710 --> 00:44:30,290
particular equation m dot is equal to A over
Z a I over F A over Z a represents for alloy
364
00:44:30,290 --> 00:44:37,010
and we are able to calculate from one of the
two methods the value of A over Z a for the
365
00:44:37,010 --> 00:44:38,010
alloy
366
00:44:38,010 --> 00:44:45,840
Current we already know Faraday’s constant
we already know we can find out the mass material
367
00:44:45,840 --> 00:44:54,980
removal rate that is also represent it as
MRRg These two methods give different values
368
00:44:54,980 --> 00:45:01,840
of A by Z a that is the chemical equivalent
of the alloy now some values that have been
369
00:45:01,840 --> 00:45:09,690
calculated for a particular case and you can
see from case one for case one or for one
370
00:45:09,690 --> 00:45:17,040
particular alloy method one gives the 26.8
value while method two gives you the 25.1
371
00:45:17,040 --> 00:45:26,360
While second case method one gives you 39.9
and method two gives 34.7 so you can see clearly
372
00:45:26,360 --> 00:45:32,830
there is a difference in the value of E now
if the value of E is different as you can
373
00:45:32,830 --> 00:45:39,990
see over here then definitely material removal
rate either in gram or linear or volume these
374
00:45:39,990 --> 00:45:46,760
also going to be different so you have to
be careful which method gives better results
375
00:45:46,760 --> 00:45:51,160
as compared to the experimental results you
should use that particular method for the
376
00:45:51,160 --> 00:46:00,830
case that applies in your industry or research
work
377
00:46:00,830 --> 00:46:07,910
Now as I have mentioned already that when
material is being removed the tool is being
378
00:46:07,910 --> 00:46:14,780
fed continuously towards the work piece so
that you can maintain the constant inter electrode
379
00:46:14,780 --> 00:46:20,610
gap during machining and if inter electrode
gap is constant then other parameters are
380
00:46:20,610 --> 00:46:28,250
constant then material removal rate also becomes
constant but what is that maximum value which
381
00:46:28,250 --> 00:46:36,340
you can use during ECM because larger the
value of feed rate larger becomes the material
382
00:46:36,340 --> 00:46:39,170
removal rate
383
00:46:39,170 --> 00:46:46,370
Theoretically there is no upper limit for
feed rate in ECM however there are certain
384
00:46:46,370 --> 00:46:51,960
practical constraints because of which we
have to limit the feed rate because if feed
385
00:46:51,960 --> 00:46:56,010
rate is very very high then what will happen
the tool will move very fast towards the work
386
00:46:56,010 --> 00:47:02,060
piece and it will touch the work piece and
short circuit will take place and in any case
387
00:47:02,060 --> 00:47:10,220
we do not want short circuit to take place
for this during actual ECM electrolyte flow
388
00:47:10,220 --> 00:47:19,030
rate should be such that it is able to carry
away the heat produced during ECM and electrolyte
389
00:47:19,030 --> 00:47:21,290
boiling does not take place
390
00:47:21,290 --> 00:47:27,450
This is very important first thing is it should
be able to take away the heat carry away the
391
00:47:27,450 --> 00:47:34,180
heat produced during the ECM process because
we all know that this is the tool and this
392
00:47:34,180 --> 00:47:41,610
is the work piece and here is the electrolyte
it is flowing these two are connected to the
393
00:47:41,610 --> 00:47:48,120
positive and negative terminal so this is
working as the electrical resistance and in
394
00:47:48,120 --> 00:47:54,190
this resistance or inter electrode gap heat
is being generated and this heat should be
395
00:47:54,190 --> 00:47:57,170
taken away out of the machining zone
396
00:47:57,170 --> 00:48:04,150
If it remains there then electrolyte temperature
will keep increasing and once electrolyte
397
00:48:04,150 --> 00:48:08,420
temperature is increasing as we have seen
earlier electrolyte conductivity will keep
398
00:48:08,420 --> 00:48:13,320
changing and once electrolyte conductivity
changes then material removal rate will keep
399
00:48:13,320 --> 00:48:16,800
changing continuously this is one which we
do not want
400
00:48:16,800 --> 00:48:24,140
Second thing is the electrolyte boiling we
do not want that electrolyte should boil in
401
00:48:24,140 --> 00:48:32,170
the inter electrode gap first thing is once
it starts boiling it will create or generate
402
00:48:32,170 --> 00:48:39,550
the water vapour which will change the electrical
conductivity of the electrolyte Second thing
403
00:48:39,550 --> 00:48:46,620
the rise in the temperature will be quite
high this will also affect the conductivity
404
00:48:46,620 --> 00:48:52,710
of the electrolyte which will affect the material
removal rate as well as the shape of the work
405
00:48:52,710 --> 00:48:56,150
piece that you are going to get on the work
piece