Lecture 12

[Music] [Music] hello and welcome back to this uh Microsystems for advanced manufacturing processes A Brief Review of the previous lecture what uh we had tried to do last time was to design the electrolyte velocity and pressure uh between electrodes uh du during eum operation and we saw that the velocity is uh actually um limited by the fact that the amount of heat that is translated by the electrical power coming into the electrolyte is uh carried away assuming that there is no conductance across the the tool workpiece surface and uh the velocity should be designed in a manner so that the overall temperature of the electrolyte doesn't cross the boiling point also what is important is that the velocity is also limited by the pressure scale where the pressure comes due to two factors one is the inertial component which is relatively a lower term particularly because of um creepy flows or you know low renold number flows which are uh executed in the small equilibrium Gap that is in question and so therefore the pressure component given by the surface forces the viscous forces have to be matched with the ultimate stress of the material on one side so that's what limits the velocity the design velocity of the electro uh light so uh what augments the velocity is the fact that the temperature should not go below the uh the boiling point and what limits the velocity is the fact that the pressure which is generated because of the viscous effect of this velocity okay uh should not go above the ultimate e stress of the material so we also sort of tried to investigate various effects of uh the Heat and hydrogen generation on E M process between the electrodes on the electrolyte and we were looking at some of the causes of surface finish due to the ACM operation including selective dissolution sporadic uh breakdown of anodic film flow separation formulation of edes evolution of hydrogen gas so on so forth so we had already seen how two phases in an alloy A and B with different dissolution potentials would have a self- roughening effect as opposed to the general self-leveling effect of an ECM process just because of the fact that the potential of one phase may be slightly higher over the potential of the other phase so it was a very interesting uh case that we analyzed where roughness automatically gets generated because of difference in the dissolution potentials of the two phases uh the other uh F fact is about you know uh the sporadic breakdown of uh anodic film which we will just about see today and all these different causes varying from 2 to 4 we'll try to evaluate today today uh after going through a brief recap of the selective dissolution potential so here you can see that there are two phases b and a where there is a difference in the potential resolution potential vda resolution potential of a is lower in comparison to VDB and therefore there is a self- roughening where the B phase only gets dissolved when it hits this particular plane this is just for the sake of repetion that I'm doing so if we really compare both uh the cases so the electric field which is also propor to the current density because electric field times the conductivity becomes the current density uh actually if you look at this Gap is y between tool and the uh the surface a and the available dissolution potential for a is vda so V minus vda by Y is the electric field across this particular Gap if we consider V potential or dissolution potential of a and if we consider that of B then the Gap reduces to Yus Delta thereby the field becomes equal to V minus V DB by Yus Delta and uh typically uh these electric Fields should be similar to each other because they are uh with two equip potential surfaces in question and there should not be really much variation uh at least at the flat face of this B surface and the flat face of the a surface we are not considering Corners here where the field lines would automatically coil and would produce a considerably variated density here okay so this is how the electric fields of the a part of the surface and the B part of the surface would compare and from this expression we really can get a value for this Delta so the Delta uh th can be found out by this expression 1us V minus V DB okay by V minus vda times of Y okay just algebraic manipulation from this particular equation here and so you can really find out what is the surface roughness if you knew the dissolution potentials of the phase A and B excuse me and you are aware of the Gap uh when the two surfaces in an equilibrium so this can be the equilibrium Gap so that is what selective dissolution would mean the other very interesting factor which affects the surface roughness is the sporadic breakdown of anodic film let's see how it happens so the main reason for the sporadic breakdown of the anodic film is the gradual fall fall in the potential difference between the the work surface and the electrolyte in a region away from the Machining area obviously uh because let's say this is the electrode here and there is a certain field which is created in this particular Gap okay which is represented by these lines of forces the fields slightly uh curl around the corners and uh it is also reasonable to assume that this field here can extend farther away from the tool surface as well because field is actually uh as it goes away from the tool it varies as a or it falls down as a uh inverse square of the distance R okay so the field varies as a square of distance from the electrode onwards towards the remaining part of the surface but there does exist a field right so for example if this is the particular potential function which is available to this surface it slowly goes down as the distance increases as a square of R but uh there does exist some value here okay like for example at the point P1 it may be vp1 at the point P2 it may be vp2 so on so forth so there are some finitely existing values of the fields which Escape even though the tool is placed at some distance away from the surface right this is all covered with electrolyte because naturally the electrolyte flows around this Gap and flows over the surface and everywhere else and it flows into the tool from this entry point here in the center so supposing if there is an alloy in this particular region and particularly in the region P1 there may be a phase where the potential which is available here is greater than the dissolution potential of that particular phase available at P1 so there would be selective dissolution at P1 by obviously by the reasons shown before and so dissolution potential of one phase would ensure that only only one phase comes out so you can see here this roughness which is created is because maybe one of the phases here in this particular zone or in this particular Zone maybe had the avilable potential vp1 to be greater than their own dissolution potential okay so you can call it VD of a phase maybe at P1 okay and that came off and because of coming off you have this roughness or tethered surface which results because of that obviously if there are corners and bends which are represented by The Selective removal of one of the phases these Corners would further lead to the coiling and the curling of the fields and so the line density in these points would increase tremendously and because of that there would be more dissolution which is available because of increased line density so the field concentration causes the phases to dissolve very rapidly uh further because of selective dissolution and formulation of these Corners the sharp Corners okay so certainly this is something which is highly undesirable for an ECM process and this can be one of the main mechanisms for uh introducing surface roughness in an ECM uh although the ECM is supposed to be a self-leveling and a very smooth operation the other important factor which is uh uh responsible for the creation of surface roughness is the formulation of edes and the separation of the flows if supposing there is a rough surface which has been created because of the selective dissolution of the field due to an electric electrochemical tool it is always um proper to assume that there may be a case of local circulation particularly when the electrolyte is flown in all both the directions like this so the electrolyte flows over the surface and there are these cases of local circulations which would exist over such crevices and Corners meaning thereby that there are these edies and vortices which are created close to these Corners because of the surface perturbations which the surface no longer a plain surface there are selective dissolutions because of which there is a lot of this cornering effect chamfering effect which is present at various points here okay so these local circulations are a cause for the debris particles which come out of this Zone to keep circulating here without going further okay and that may change the local conductivity because precipitates are one of again the responsible causes for change of the conductivity of the uh the medium electrolyte and edes and vortices are something that you really don't want in ECM the more streamlined operation the ECM would have in terms of electrolyte flow the better it is in terms of uh surface finish okay but the more there is localization of flows and edes and separation of Flows at certain areas there may be local precipitate World Pools which are formulated which have much more conductivity and therefore uh more disolution and that may create a pitting effect in some of the local zones so a great care needs to be designed uh to be taken in designing uh the tool surface particularly uh the same thing may happen to the selective dissolution of the tool as well okay the surface may turn out to be rough with uh operations if there is an alloy tool which is used and one needs to be very careful about these edies and flow separations so this is another third reason for the surface roughness finally as I already have mentioned before the evolution of hydrogen gas is pretty critical and if you can consider this Tool Work piece surface supposing the electrolyte starts flowing from this end into the Gap okay at a certain velocity and by the time it reaches at at the other end here okay uh there is always an increase in the temperature and uh let's say if hydrogen emanates as bubbles into this electrolyte the concentration local concentration of hydrogen in the electrolyte increases because of which there is a change in conductivity and the hydrogen may be concentration may be lesser here but by the time this goes ahead and the hydrogen gets cared away more and more hydrogen packs off you know to this electrolyte so hydrogen concentration is greater here there is a density gradient uh which is created for the gas which is dissolved and therefore the conductivity is varied across the length of the work PC and because of that again there is a tendency of the conductivity to vary uh and also simultaneously the current density to vary so at one point where the current density may be more because of uh reduced hydrogen may have a slightly greater disolution rate in comparison to the point where the current density is lower okay and so therefore again this can also result in some kind of a roughness where some points may be moved uh or dissolved in a greater Pace in comparison to the other points so there are two major aspects when we talk about ECM one is of course the the tool design okay uh and another is the Flow Design the the system of flow you know and the tool design is important because of two reasons one is uh that the tool shape so desired is exactly the negative replica of the shape that you are wanting to embed or imprint onto a surface that is the basic principle of an ECM operation so particularly in Microsystems technology when we are talking about uh some embedment uh some small feature which has to be created on the surface the exact contouring of the tool is very much needed so that the exact negative replic can be produced on the surface at that particular scale and uh the other reason is that you know the El electroly flow that the tool would have would really be uh creating a lot of effects on the overall material removal rate so therefore the way that the electrolyte is flown the way that the sides of the tool are insulated the strengths and fixing Arrangements of the insulations onto the tool they would be of great concern when we want to develop a good ECM process so we will look at the first aspect now that is determining a tool shape so that the desired shape of the job can be achieved for a micro Machining or for a machining condition and in that respect I would like to sort of propose a theory uh where uh we want to theoretically determine what is the tool shape based on a certain function which is uh uh known to be the final shape of the work piece that you would like to uh generate using ECM so when a desired shape of the machined workpiece surface is known and uh we want to somehow map the surface into a tool surface and which is possible actually theoretically I'll just show you an approach where theoretically you can determine uh and so the required geometry of the tool surface for a given set of Machining conditions can be achieved very fast based on that and um the first thing that we need to know here is that the equilibrium Gap between the anode and cathode surfaces can be expressed as G Das is equal to the conductivity times of atomic weight of the material which is dissolved times of the voltage minus over voltage potential which is available for the electrochemical process divided by the density of the material to be removed the lowest valency state of the material and some other parameters like The Fad constant the feed rate supposing it is going at an angle Theta so if Theta is the inclination angle of the tool wrt with respect to the workpiece this can be called f cos Theta okay so that's how you find out the equilibrium Gap as we have seen before and let's actually now assume a certain uh random tool surface and work workpiece surface as represented here let's say this is the XY plane and we're talking about a certain shape here of the work piece okay let's say this is the shape of the work piece which we are kind of aware what this shape would result uh or what what would be the final shape which is desirable so this is given by the design uh design team for the component and uh we also are aware that this workpiece is being fed towards the tool at a feed rate of F and this is automatically the shape of the tool which is gener ated by the requirement of this work piece surface which is known to you so if we select the you know in the two- dimensional sense a point here on the work piece surface let's say PW which is again a function of xw and YW okay and uh try to map a corresponding point on this particular surface the tool surface PT XT YT we should be able to somehow find out the functional relationship that exists between this point and this point given the constraints or conditions of the ECM process like the feed the direction of the feed so on so forth so the feed as you know is in this direction meaning thereby that if you look at uh a tangent to this particular point it would assume to have moved at an angle Theta with respect to the direction of the feied okay so we are already aware of the workpiece surface so let it be defined by a function y equal to 5x so there is a relationship between these two coordinates X and Y and uh it is a sort of uh uh non-parametric representation of uh the surface uh y = to 5x and we want to determine what this would mean when it gets translated into the tool surface to provide the tool shape so when a steady state condition is reached the gap between a point on the workpiece let's say this x w YW Point PW and the point on the tool surface be given by a steady state equilibrium Gap G okay where G has already been calculated before we know what G is it's a function of many things like where the equilibrium Gap is a function of many things as you know the atomic weight the available voltage uh which is there the conductivity the density of the workpiece which uh material maybe iron or copper whatever is being removed or machine so on so forth so if you look at the positional relationship between these coordinates xw YW and XT YT so the XT is displaced forward displaced uh from the xw by an amount G sin Theta where G is this Gap here between PW and PT right and uh if you compare the position coordinates YW and YT the YW is forward displaced from the YT by a Gap g cos Theta meaning thereby we have two equations here XT minus x w which is G sin Theta let's call it equation 1 and YT minus or YW minus YT which is G cos Theta let call it equation 2 we already know the value of g g is actually k a v minus Delta V divided by row z f COS of theta where we assume that the surface is moving along this line PW PT towards the tool surface at an angle Theta so this are very generic form of uh a surface of a mult uh a certain functional shape uh to be replicated in terms of the tool surface so we are mapping from the workpiece surface to the tool Surface by using simple mathematics so here let us say if we wanted to uh just write everything in terms of the new value of G that we had obtained so YT becomes equal to y w minus Ka a v eus Delta V by row ZF time of small F the COS Theta goes away uh which is actually nothing but y wus Lambda by F if you may remember this term here was actually equivalent to the Lambda okay when we did the kinematics and dynamics of the ECM process and the XT here can be related to the xw by the term k a v minus Delta V divided by r z f * of f * of tan of theta right because this was cos Theta and then uh the xw was displaced the xw was displaced um backwards from the XT by the term G sin Theta so therefore uh if you just convert everything here in terms of Lambda you can get x w + Lambda by F tan Theta okay so we make this equation three and this equation four so you already know that there is a functional relationship between the x w and the YW which exists okay so YW is function f of x w and the work P side and tan Theta can be estimated as the slope dyw by DX w at the point PW xw YW okay where XT = x w + Lambda by F time of tan Theta which is dyw by dxw since the work surface geometry is given by uh this relationship the D YW by xw actually equals to [Music] DF x w by dxw so a little bit looking at a little more fundamental way if this is the surface that we are trying to interrogate which is actually the the work piece surface and this is the point PW that we are trying to use to find the or or trying to map into the tool surface at this particular point the tangent which happens here okay is really in this direction right this is the tangent at this point and uh we already know that the way that the surface would move is at an angle of theta with respect to the vertical Direction so if I were to just uh find out whether tan Theta is DW by dyw by dxw here you see if this is Theta this becomes 90 minus Theta okay and this becomes Theta right so this tan of theta is actually dyw by DX W right and so therefore we can safely assume that uh G tan Theta can be expressed as xtal to xw + Lambda by F dyw by dxw right tan Theta this is the g g tan Theta similarly we already have the equation 3s uh oted earlier where we are trying to say YW is a function of xw is nothing but YT + Lambda by F so if this functional relationship exists between the YW and the X W and we have a relationship of YW with YT and XT with xw we can actually write down that y w which is YT + Lambda by f is functionally connected in the same manner to X W's value here which is XT minus Lambda by f * of dyw by dxw so if you really know the slope here then it should not be a problem to map the x w y W to XT YT as available here in this functional relationship so therefore the whole uh Essence that is involved in all this is to somehow be able to write this D YW by dxw meaning thereby this is d 5xw by D xw in terms of of XT and YT so then this whole equation can be converted into all XTS and yts and the function therein which would be plotted would be a map of x w into y xw YW into XT YT so therefore the overall representation of a tool surface provided we already have a functional relationship between the work piece surfaces YW is 5 of x w is given by 5 x - Lambda by F some function okay in terms of XT and YT of XY these are all tool sides minus Lambda by F so this is the whole mapping equation from the workpiece surface to the tool surface now supposing if we assume a functional relationship of the type y equal to let's say a + b x + C x² for the work piece surface and we want to find out what is the mapping into the tool surface as we already know the map is provided by YT = to 5 XT minus Lambda by F some function of XT YT which is nothing but the slope dyw by dxw right minus of Lambda by f so let's try to determine this and try to find out how this is related to uh some function of XT and YT so we already know that dyw by DX W is actually equal to B+ cxw right and uh we are aware that the x w or XT actually is equal to the xw + Lambda by F times of dyw by DX W which means it is equal to x w + Lambda by f time of b + CX W okay so therefore we can either substitute the value of x w in this equation to find out what XT would be in terms or what this would be in terms of XT Standalone so let's suppose that there is a function y on the workpiece surface which is related to X on the tool Sur uh tool Surface by the quadratic equation a + b xw + c x w² now we want to find out how to map it from The Tool uh from the workpiece surface into the tool surface so we first find out what dyw by dxw is let this be equal to some value I right and this is actually it can be represented as b + tce cxw we already from our previous formulation for XT and xw are very well aware that XT is related to xw by the relation x t = x w + Lambda by F times of dyw by dxw so the whole uh effort some some somehow should be to actually convert this whole thing in terms of tools I mean tool side coordinates XT and YT so we can write this as X W + Lambda by f * of I remember we have taken this DW Dy W by DX W as I and so very easily we can see here that uh if supposing we write xw in terms of I it becomes twice cxw is IUS b or x w becomes equal to I by 2 c - B by 2 C right and if we put this value here we get the value of XT as XT equal to I by 2 C minus B by 2 C plus Lambda by F times y okay obviously this would mean that uh if we multiply the whole thing by 2 C we have 2 cxt = i - b + Lambda by f * of 2 C * of I or the value of I in terms of all XT comes out to be b + T cxt ided by 1 + tce C Lambda by F okay so that's how you can formulate dxw by dyw by dxw so if I were to represent this I back into uh the formulation for uh y you already know that YT in this particular case is related to the XT as YT equal to F function 5 of XT minus Lambda LDA by ftimes of IUS Lambda by F okay and uh this really means that this coefficient XT becomes equal to XT minus Lambda by F times of the I value that has been deciphered before as b + twice cxt divided 1 + tce C Lambda by F okay so minus Lambda by F and then of course you already know that YT therefore is written as a function of F here which means it is A + B * of this argument which has been formulated so we are mapping now the function okay plus C * of XT minus Lambda by f b + tce cxt / 1 + tce C Lambda by f s minus Lambda by F in other words if you simplify this expression here this would be coming out as a + bxt + cxt - Lambda by f - Lambda by ftimes of b + T CX t² divid 1 + T C Lambda by F okay so that's how you can map a quadratic function on the workpiece surface to a tool surface so in this is just a generic representation of if suppose the surface is defined by a function what would happen now if you you look at uh the theory that uh is associated with the cad designing process the cad designing also looks into local functions like this and tries to fit some of the uh formulations like basier curve or uh let's say you know spline fits between either two points or many points and this somehow has to be topologically mapped into the corresponding negative workpiece surface so the best way to do it is to keep in mind the equilibrium Gap keep in mind that this surface is going at a certain angle to this uh uh you know tool surface and topologically map it by a function mapping from of the XY on the workpiece surface to the tool surface for a certain simple equation like a quadratic equation it has been demonstrated here but then if there is a complex uh function which is used for fitting Contours or you know uh complex Contours or topologies that function can also be mapped okay so the idea is that the whole design that is there uh of the work piece as per the requirement of the work piece have to be designed in bits and pieces and this each uh can be represented by either a group of functions or just a function or some of them are just linear and then you simply map those points uh onto the corresponding tool surface and obtain that way the tool surface so the tool design can be arrived at theoretically so that's a uh pretty good aspect of the ECM process that you can actually develop a tool surface exact negative of what is there on a uh complex design uh of the requirement of the work piece so with uh this in mind we just Tred to do a numerical problem try to solve a numerical problem here as you see here uh the geometry of a work piece with single curvature is given okay and this uh geometry is given by the equation y + 10 y = 10 + 0.3x - 0.05 x² uh you know that these are values in centimet and the process data is uh that the applied potential is 15 volts over voltage which is needed is 67 volts a feed velocity of 75 mm per minute and um it's given in typically the minus y direction and the work material is copper electrolyte conductivity is about 0.2 ohm inverse CM inverse and we have to determine the equation of the required tool surface uh geometry so uh once again I would like for the sake of reputation to to reiterate this point that a cad geometry is a complex uh system which is created out of many such functions which are standard functions either representing represented by non-parametric or parametric equations uh some linear connections between the many complex functions and then some fits the fits are because sometimes you need to really Express uh very closely a complex topology and there is uh no other choice but to force fit a sort of function like maybe the basier function or the um uh the beastline function or just a normal cubic Herm Mission uh function uh polinomial uh to in a manner that by knowing just by slopes on both or the or the different or maybe one or two points or maybe all the points you can try to develop a fit that way okay so that fit then uh the standard functions which are already there representing the surface and the linear functions may very safely be mapped topologically to develop the exact negative replica so the purpose of all this theoretical analysis is to ultimately arrive at a tool surface given a split up CAD model of a workpiece surface so let's look at this this is a very simplistic case you have already defined the single curvature uh of the equation uh given by this quadratic form and uh we want to find out that for copper uh we assume let's say a monovalent state which is coming out okay so we are assuming Z to be+ one the atomic weight of Copper the work material is 6 3.7 57 G and uh the row here the density function here is actually 8.96 G per CM cub and the value of f here is 96,500 Kum okay and we want to find out provided the feed is given to be 0.75 mm per minute or in other words 0.001 1 to5 cm/s we want to find out what the u g value is which is Lambda by F and Lambda uh can be represented as k a v minus Delta V divided by row ZF uh where these terms are all uh as you have done many times meaning their own uh you know they are encompassing their own definitions so the case the conductivity is given to be for the electrolyte 0.2 ohm inverse CM inverse so we have 0.2 * of the atomic weight of Copper 63.5 7times of um the total potential which is available minus the over voltage which is 15 minus 0.67 divided by the row value which in this particular case um is about uh 8.96 it's copper times of monovalent state so plus 1 * of 96,500 kums okay so that's how the Lambda is and uh this would come out to be about 2.11 10 ^ -4 cm square per second of course the Lambda by F uh can be 21110 the^ -4 by 12.5 10 ^ -4 CM this uh1 169 CM then comes out to be the equilibrium Gap y or g whatever you may think appropriate and this gives us a basis of plotting this functional relationship between y w and x w into YT and XT so that uh let's now have a look uh at uh the final formulation so for the work piece side you know that 5x W is related to the YW by the equation 10 + 0.3 x wus 0 05 X w² and uh we know that the final tool surface geometry as we have already derived before for a quadratic equation can be represented as YT = to 10 + 0.3 * of x - 0.169 times of 0.3 * of 0.1x divided by 1 - 0.1 * of 1. 0.169 okay minus of 0.05 * of square of this argument so this is that argument value if you may remember which was including the slope and uh which was you know uh including the slope in terms of the XT and the YT value okay and uh so this minus 0.05 to the same argument 0.169 9 0.3 - 0.1x / 1 - 0.1 * of 0.169 okay square of that value minus 0.169 which is the Lambda by F or the equilibrium Gap term uh in this expression and so if you solve all this you get a relationship between the uh XT and the YT as X YT is a 9.81 5times plus 0 Point 315 x t minus 0.0 51 XT squ where both XT and YT are in centim okay so basically this is a very good uh methodology of U giving a sort of uh Optimum tool shape for a single curvature uh which is already given by a quadratic equation for the work piece shape so I think today we are kind of at the end of uh the lecture we have uh learned how to derive uh some of the very fundamental aspects of uh velocity uh of uh the electrolyte while moving through the Gap and we have also learned that how critical it is because you know it will essentially be related to the pressure which would be a determinant of the maximum level of the velocity and on the minimum level of the Velocity would be determined by the temperature requirements uh which would ensure that there is no boiling action we tried to apply uh this uh fundamental problem to see what are the surface finish related defects which come in an ECM process thereby we learned a lot of uh you know different corollaries of the ACM process which happens like for example sporadic breakdown of the anotic film or for example um the uh the flow separation of the edes or the hydrogen gas generation which changes local conductivities and it's always a problem with the ECM because the local roughnesses would tend to change and the local current densities because of that would be uh higher and you can have selective dissolution which creates further Problems by coiling the electric Fields you can have uh a case where more hydrogen is generated because of which the conductivity goes up or the SE the the flow separation or the Ed is there by meaning the local precipitates can deposited at different uh places where the local conductivity changes would result in more or less current densities okay so these are some of the very prominent uh problems which are available with the ECM system and the prominence goes high as you do microsystem fabrication with such ECM processes uh we also tried to determine the tool shape where uh uh we investigated how uh you can topologically map one tool surface to other the other aspect of tool is the electrolyte Flow Design which we'll of course try to complete in the next lecture because uh the way that you insulate tools edges the way that you create uh a conduit for the flow of the electrolyte from the tool onto the workpiece Zone decides a lot of uh Machining parameters for the electrochemical process as such and so I would like to investigate these one by one in the next lecture thank [Music] you [Music] [Music] [Music]