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Forces in Machining

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Video 1: Forces in Orthogonal Metal CuttingSo, now we are moving to forces in machining; normally we have seen the introduction to machining process. So, we deal with only the orthogonal. So first we should know what is the need of studying the forces in machining operation? If you see the knowledge of cutting forces is required to estimation of the power requirements.Normally power requirements, if you see it is F c into V ; so, if you can calculate the cutting force and you know the velocity cutting velocity. So, you can calculate the what is the power required or the energy required. For the machine tool design that is the static and dynamic stiffness; what is the stiffness required and based on that you can design the tool. Normally the tool machine tool aredesigned like a lathe bed and all those things are designed with a material cast iron because the cast iron has a graphite in it . So, graphite will have the damping effect ok; so, you ah in order to have the damping and all those things ok for that purpose also it will beuseful what are the forces that the lathe bed or the cutting tool at the same time tool holder, tool post these are all to be designed. So, if the forces exceeds what will happen? So, in order to be safe the machine tools are designed according to that for that purposeone has to calculate the forces required ok part accuracy and tool work deflections . So, the part accuracy is also important if ah if I can calculate what are the forces that is experienced during the machining by the tool . And if there is any deflection of the tool if the deflection is there then there will be problem; so, the part  accuracy goes back. So, for that purpose one has to calculatethe forces ok. So, to maintain the no deflection or there is minimum deflection one has to do calculate the forces in the machining operation ok. So, there are the forces in orthogonal metal cutting that is a machining processes; force act in three locations one is shearing zone if you see the shearing zone that is nothing, but the shear force and normal to the shear force; this is a shearing zone ok . So, the chip tool interface the other forces that one observes in this region is ah ah chip tool interface. Normally there are two forces one is the frictional force and the normal to the frictional force; these two are there in this . Forces on the cutting tool by the work piece normally F c and F t are what one can experimentally measure is this are the F c and F t ok. These two forces are the forces experienced by the cutting tool ; normally this cutting tool is placed on the dynamometer. So, the dynamometer will give the forces ok . So, this ah the third one this is what the forces that one can measure and the 1 and 2 are calculated from the experimental measured forces which we can see in the upcoming slides ok. So, if you see there are three force components in the metal cutting operation; one is ah cutting force, second is the thrust force and the radial force; these are the three forces. The normally the cutting forces tangential to direction it is also called as a power component, normally this is as I said in a beginning of this forces F c into V gives me the power requirement. That is why it is called power component the and the cutting force normally acts on the tool by the chip ok. So, I will explain onceI explain thrust force and radial force, I will come back to the cutting force how the cutting force ah will act. So, thrust force it acts in the direction of the feed of feed that is axial direction. That means in this picture if you see this is the thrust force ok. So, my feeding direction is this that is nothing, but the work piece axial direction also in this direction. So, this is the feed direction, this is the radial component which is also you can see which has a radial direction; that means, as per the depth of cut is concern it will move in this direction. So, this is called F R and this is called F t and this is called F c; that means, whenever I am cutting with the cutting tool my chip is moving on top it if that is this my chip will kick down the tool that is nothing, but the cutting force; that means, that it will be in the this direction. So, the cutting chip whatever the chip is coming out; it will kick the tool downside that is the cutting force . And along the direction or the axial direction of the work piece that is called the thrust force and or the sometimes some people they call as a feed force also and the radial force is nothing, but as per the depth of cut is concerned it will be radially inside into the work piece ok . So, the forces F that is frictional force normal to the friction force shear force and normal to the shear force. These are all not calculated directly ok, these are all measure from a relation forced relation that is which we will see in the upcoming slides which is nothing, but the Merchant circularrelation ok. The forces acting on the tool that is nothing, but the cutting force and thrust force also other forces if you have a dynamometer of which two components you can measure F c and F t. Nowadays you also get the 3 dimensional measurement of the cutting forces. So, where you can get the third component also that is called radial component also; so, normally if you see how to measure F c and F t ok. So, that ah I will discuss in the next slide these are all can be written in the cutting force . So, only that we can measure is in the dynamometer is F c and F t. So, if we know two forces and different angles tool angle that is a rake angle shearing direction all those things. That is alpha the friction angle beta if you know the shearing angle 5. So, with this relations you can calculate the frictional forces shear force, frictional force normal to the shearforce, normal to the frictional force this all ok. That means these are all measurable ok; from the Merchant relation Merchant circle relation you can calculate all this Fs; frictional force, shear force other things. Now the question is how to measure and how one can measure this cutting force thrust force. Just we are seeing in the orthogonal that is why we are only dealing with the two forces ok .So, the force measurement if you see the force measurement normally this is the dynamometer you can see which is located beneath the tool. This is the tool this is a tool post, this is the tool post or the tool holder ok you can say this the dynamometer.Dynamometer is the beneath the tool . So, this dynamometer inside the dynamometer if you see the anatomy of the dynamometer; normally to explain you there are three piezoelectric sensors will be there. Normally piezoelectric sensors works on if there is a deformation, it will give certain voltage or EMF . If you give the EMF; normally it will default that is the principle of the piezoelectric materials . So, piezoelectric materials are oriented as per the X, Y and Z axises. So, whenever if you mount a tool on top of it normally a tool is mounted and if you are giving some forces in different directions; what will happen? The piezoelectric materials that are there inside it ok this are the inside what will happen? This will deform; whenever this deform this will give certain voltage or the micro volts or nano volts or volts some volts it will give depend on the forces. So these forces if you are measuring in the three directions on the cutting tool. So, the forces that is acting on the cutting tool you are measuring that is means you are going to get only cutting force thrust force and radial force ok . But normally we see only two forces; however, if you have a three sensors you can measure the three forces ok ; this is about the machining process ah the same thing can be represented here also. Normally machining takes place or the work piece like this and the chip will work on this one and the radial force will be in this direction. So, normally it will be in the opposite direction also ok. As you can see clearly note that practically measured forces are F c and ah Ft and Fr; these are the practically measured forces. However from here using the Merchant circle relation you can calculate other values ok. So, now, we will go for the Merchant relation; how to calculate because how much shear force is required to shear the material and all those things is required. Because we are only seeing the cutting force, but we want to calculate what is the frictional force, what is the shear force and all those things . So, that we can say how much is useful energy that we are imparting to the machine and how much is ah going as a waste and all those things can be calculated ok. So, to have the Merchant circle relation; we are going to have some of the assumptionsto measure this forces . This assumptions are cutting edge is too sharp; that means, that sharpness radius is 0 ok . Normally slightly some people will have doubt what is the sharpness radius? And what is the see some people they understand that sharpness radius is nothing, but the nose radius, but there is a slight deviation between the sharpness radius and and nose radius ok. As I already explained normally if you see a 3 dimensional tool the 3 dimension tool looks like this ok. So, the nose radius is this one this is called nose radius which is represented by R this is nothing, but if assume that this is my principle cutting edge ; just for understanding purpose I just erased the nose radius hope you understood. So, now, what I mean to say this is my flank face, this is my rake face which are meeting at the principle cutting edge this is the principle cutting edge . Every cutting edge will have certain radius that is nothing, but the sharpness radius how sharp this is; that means, this is if you meet this is the radius this is nothing, but the sharpness radius ok . So, nothing in this world is 100 percent or 0; that means, the sharpness radius is practically it cannot be 0, but; however, we are assuming that ah this is 0 ok. So, hope you understood the difference the difference is this is nothing, but sharpness radius whatever the radius that is generated on the cutting edge, this is my nose radiusok . So, assuming the this one ; so, the second point is cutting edge is perpendicular to the cutting velocity; that means, that my I am doing orthogonal machining. So, deformation in two dimensions no side flow; that means, that ah only the deformation is taking placein the plane where we are machining. So, there is no side flow or deformation and all those things. Continuous chip without BUE; so, the chip is flowing on the ah rake surface is without BUE . So; that means, that is a continuous and smooth cutting operation , work piece material is rigid perfectly plastic material; that means, that ah the material is removed perfectly ok. So, there is no slip part something the coefficient of the friction is constant along the chiptool interface; that means, the there is no variation in COF; that is cutting friction is constant if some friction is x; that means, that throughout the chip tool interface it is constant because we have the two zones one is the sticking zone, another one is the sliding zone . So, practically speaking there will be a slight difference will be therein the coefficient of fraction between the sticking region as well as the sliding region; however, we are assuming it is constant for the ah this model. So, resulting force on the chip that is R 1 is applied on the shear plane is equal to ah equal to opposite and collinear to the resultant force; that means, that two forces that is acting in the directions; both are opposite in direction and collinear in thesame ah direction ok.
Video 2: Forces Acting on Cutting ToolSo, now we will move to the forces acting in the cutting tool since we have already seen in the previous to previous slide . So, there the forces if you see this is the shear and this is the normal to the shear force; the resultant is this one ok . Similarly if you see here it is in the red color here; so, you may not see properly . So, that this is ah the force act parallel to the my rake face is nothing, but the frictional force perpendicular two will be the normal to the frictional force. At the same time you have the two forces that is nothing, but one is the cutting force, another one is perpendicular to the cutting force that is the thrust force ok; so, this called F t as you can see; this it is red in red. So, you can see the frictional force normally follow as per along the direction of the rake surface or the chip flow direction interface of the chip flow and the tool rake surface and perpendicular two will be the normal force normally. So, at the same time two forces if you see that ah ah cutting force and thrust force; these are the two forces that acts on the tool from the work piece. So, this two can be measured; so, you can see all the forces here the frictional force and a normal to the frictional force and this is called the frictional angle . The shearing angle along the direction of the shear and I will explain u how to draw this Merchant circle; this is the cutting force and the thrust force . So, you can see the resultant and normally this is shearing angel and ah if you drop this is called alpha that is called rake angle ok. This is the forces acting on the cutting tool during the 2 dimensional cutting note that the all the resultants must be R; the resultant force is R which is equivalent to the resultant of all the forces that is fractional force, normal to the frictional force, cutting force, thrust force, shear force, normal to the shear force all boils to be resultant is only R ok that is what the assumption is ok. Vector addition of ah the frictional force normal to the frictional force resulting in R that is the resultant force . So, vector addition of shear force normal to the shear force gives rest to the again R and the force act acting on the chip must be balance for that purpose R is equivalent to R; R must be in opposite direction to the R; so, R dash must be collinear with R. So, this is what ah you can see ; so, now, you can see the same picture here the Merchant circle, where Merchant is the person invented it and all those things. The need for force relations to calculate the coefficient of friction the normal stress and the shear stress as I said in the previous one. So, I will let you know how to draw simply ok. So, the Merchant circle is a circle; so, Merchant circle normally just first you draw a circle. So, normally it should be on the upside; so, normally the tool should be ah above the centre point ok. So, you can take any position you can draw the tool ; so, this is the point. Now your frictional force is parallel to this rake surface and your cutting force is parallel to the cutting direction that is the cutting velocity direction and your shearing in thisdirection ok. So, this is the direction; so, I know frictional force the cutting force and shear force just three directions . So, I can choose any now normally the thrust force is perpendicular to it . So, the resultant is R which you have seen this is nothing, but R this is my thrust force ; so, R will connect to R. So, this is nothing, but my N; so, this is my frictional angle beta, this is the shearing angle that is phi, this is alpha that is rake angle. So, from the geometry or the trigonometry and all those things, you can calculate other angles. If you see like this this is also become alpha as you can see here this two alternative angles and this is the phi; that is the shearing angle this is beta which I am already explained you know that is thefrictional angle . If you take ah this is 90 degrees ; so, 90 degrees equal to, so alpha plus some other things which you can boils out to be beta minus alpha here ok. So, and this will be 90 minus beta ok; so, if alpha plus 90 minus beta this angle is then you can calculate this angle plus x assume that x If you can calculate now your x will be like beta minus alpha is equal to x; so, that is nothing, but this angle ok. So, this is how you can calculate all the things; so, thathow my x which I want to calculate is beta minus alpha.The coefficient of friction; the first thing what we are going to calculate from this one is the coefficient of friction. The coefficient of friction is nothing, but tan beta; so, this is my beta angle, tan beta equal to F by N that is mu this is coefficient of friction that I am going to calculate. So, the normal stress is N s by A s which is ah N s is nothing, but the this normal to the shear force to the area of shearing . So, shear stress is nothing, but my ah shear force by the area of shear. So, this is how you can calculate we are going to calculate this three from the known sources. Because F s we do not know because we know F c and F t ; from this using Merchant circlewe have to calculate F s N s and frictional force as well as N. So, that is why we are going to calculate all these things; the total work done is nothing, but your F c into V ok . So, F c into V equal to shear force into shearing velocity and the chip velocity into the frictional force; these are this is useful energy, this is un useful energy ok assume that I can say it is a energy going as a waste ok. So, now we will calculate all these things. So, what do you need to measure the coefficient why; what is the need? So, if you want to know what is the answer for this one; what is a need of measuring a coefficient of friction . So, if I want to ah if I can measure coefficient of friction that is nothing, but ah my this one F by N so, that I can understand whatis the energy going as a waste that is nothing, but what is the energy that is going here. If I can calculate coefficient of friction normally coefficient of friction is friction forced by normal to frictional force that is proportional directly proportional to my frictional force ok this one . If my coefficient of friction is very high; that means, thatmy unuseful energy is very high. So, the useful energy goes down for the same input energy ok that is why we want to calculate the coefficient of friction. Now, if you see from the geometry tan beta that is nothing, but ah F by N tan beta this is the beta; tan beta is F by N this is opposite side by adjacent side. Now I want to calculatewhat is the F; see what I always said in the previous slides also I do not know what is the F value, what is the N value, but the from the dynamometer; what can I measure is cutting force and thrust force ok. So, whatever I want to calculate; I have to form the triangular notation to the joining to the F c or F t. For that purpose what Ihave did is F equal to AB normally this is A, this is B; F equal to AB, if it is AB which is I am dividing into AC plus BC ok AC plus BC..Now, AC I am connecting like this; this is a triangle that is called ACM triangle; from this triangle I can say that F c sin alpha that is called this is alpha from the trigonometry you can get this is a its comes as alpha ok. So, this is F c sin alpha and F t cos alpha; BC is F t cos alpha now see BC is equal to D N ok D N this is alpha, this is the trianglethat is called MN D or D M , this is the triangle which in this triangle this is my alpha. So, it is called F c cos alpha; so, at the same time in I have to calculate again normal to the frictional force that is called N , this D B which is called B D or D B which is equivalent to NC this is called NC here is N just let me erase. So, that I will come back again now NC equal to MC minus MN; MC is nothing, but this one,MC is this one MC minus MN this is MN ok. So, now MC is connected to my cutting force this force; so, F c cos alpha F c cos alpha which is adjacent to this one that is why it is F c cos alpha minus F t sin alpha ok. Now, F t sin alpha because I am talking aboutMN which is opposite side; so F t sin alpha . So, the now we have known known values that is called F c is known to us rake angle is known to us F t is known to us because Ft and F c are measured and alpha is a rake angle; here also F c and F t are measured and alphais a rake angle of the tool . So, now I can calculate the frictional forceas well as normal to the frictional force; if I know the frictional force and normal to the frictional force I can calculate the coefficient of friction this is the final term that is called F c sin alpha plus F t cos alpha by F c cos alpha minus F t sin alpha; this is the final equation where all are known to me and I can calculate coefficient of friction. As in said if my mu is high my useful energy will goes down that for the same input energy; that means, that my frictional ah force intochip velocity will goes up so; that means, that unwanted or waste of energy will be more ok.
Video 3: Normal and Shear StressSo, now we will see the normal stresses on the chip normal stress is equivalent to N s by A s ok . So, N s if you see the N s N s is nothing, but this is my shear F s is shear force and perpendicular to is N s thisis N s ok . Now, I am dividing N s that is nothing, but the D P is nothing, but normal to shear force. So, I will divide into two things; one is already I have one Q is there if you see in the picture. D P I am dividing into DQ plus QP. So, DQ which is relevant to as I said earlier also I have unknown things I have to correlate with the known things. That is ah F t and F c; so, so that I have to form my triangle triangles, if I can make the triangles that is integral part of oneshould be know that is F c and F t so that I can calculate. So, now I am going to say DQ is equal to now I say DQ, this is DQ and I know this is a phi . So, D; this is a adjacent side to this triangle D M Q; so, that it can become Cos phi; so, F t cos 5 . So, plus at the same time QP now my QP is there, QP is ah equivalent to MO; if you say the MO; then I am forming a triangle A M O; where I know the phi is the shearing angle in this triangle for that purpose MO is equivalent to my QP. So, this is opposite side to this triangle AOM to the phi; that means, F c sin phi . So, area of shear plane if you see b into t c; now if you see the bottom picture this is nothing, but my t c which is not known to me because I have not measured it, but considering the ah two dimensional metal cutting that is orthogonal metal cutting t naught that is called uncut thickness and chip thickness for the after cutting and before cutting. So, after cutting t naught is equal to myfeed ok if I know feed normally I will give whenever the cutting operation is going to start I have to give feed to the machine tool ok . So, this t naught is known to us; t c not known us; that means, that this is unknown to me and b is nothing, but my width of the chip or depth of cut. So, area of thickness is nothing, but b into t naught and now we have to find the relation between t naught and t c that is a uncut thickness to the thickness. As if you form a triangle; so, t naught is this whatever I have drawn here; if you take this as a triangle this is the phi. So, you can calculate from this triangle t naught equal to t c into sin phi ok. From that now we do not know what is the t c and if you put this equation 1 and 2; if you put equation 2 in the 1; normally you will get equation 3 ok. So, now you can put this into the the above equation that is N s equal to this equation ok. So, now you you can calculate sigma equal to this value that is called F c sin phi plus F t cos phi by ah multiplied by sin phi into a where ah this is a is nothing, but your depth of cut multiplied by uncut thickness that is nothing, but feed ok . So, since we know the depth of cut and feed area of uncut thickness can be easily measured or calculated ok. So, now we are going to the shear stress on the chip now the shear stress is nothing, but the F s by A s; I already seen what is A s that is the area of the shear plane ok, now we have to calculate F s. So, F s is nothing, but this one; so, this is about A P ok this is nothing, but my F s ok . Considering this I will I am making a extension to the O and I am saying now considering the AO M triangle ; if you see that one AO minus OP gives me F s that is P A ok AO minus a p. So, now AO which is a shearing angle that is adjacent side, so, you can say F c cos phi minus OP. Now OP is equivalent to this MQ ok MQ I know this phi; so, that is opposite side so; that means, that if this if this is F t this is opposite side sin phi; so, F t sin phi. So, we can from this again in the from the previous slide these are all same, where area  of the shear plane is nothing, but b into t c whi h is where the t c is not known and area of uncut thickness is nothing, but b into t naught, where t naught is a feed bis the width that is depth of cut. So, depth of cut is known and feed is known; so, you can know this value you know this value ok. So, now from this one you can say A s equal to A by sin phi whenever you put back this into the equation that is a shear stress equation; you will get the shear stress is nothing, but this one ok ; that is F ccos phi minus F t sin phi multiplied by sin phi by area of undeformed chip; that is nothing, but which is nothing, but your depth of cut multiplied by feed ok. So, from the orthogonal metal cutting operation; if it is oblique metal cutting normally there will be a some other terms also will come. Because there will be a slightly inclinationwill be there and all those things will come into the picture ok .Since we are studying only the orthogonal metal cutting operation, this is how you can calculate the the shear shear stress . If you know the shear stress normally you have to apply the more energy compared to the shear stress then only the material will shear ok.So; that means, that whenever I want to shear a material I have to put more stress than the required stress then only the plastic deformation ah will takes place severe plastic deformation will takes place . Work done in in specific cutting energy; so, now, work done total work done is F c into V. As I already said the cutting force multiplied by the cutting velocity is the total work that is done during the machining operation or that am imparting that is the energy . Work done in shear that is called useful and work done in friction, as I said coefficient of friction is calculated or frictional forceis calculated and all those things . So, now total work is F c into V and which is divided into useful and as well as waste energy ok this is the main equation. Now, coming to the if my friction is more what will happen? My un useful energy or the waste energy will goes up. So, my whatever the input I am giving; the most of the energygoes as a waste, so I always should think in the sense where how to reduce the friction and for that purpose only the people uses cooling fluids that is what our course also deals about is machining fluids. At the same time tool coatings are done, lubrications is done, different types of lubrication is done like ah minimum quantity lubrication,flood lubrication or ah cryogenic lubrication and all those things. So, that my this factor F; F into V c will go down. So, that my useful energy if I am giving F c into V; so, I have my main aim is to increase this F s into V s. So, these are the alternatives the cooling and all those things. So, that my useful energy goes increases for the same input F c into V ok. So, that is about the useful ok now coming to the specific cutting energy. So, specific cutting energy is nothing, but thetotal work done on the total work done or the energy given to the volume of the work this material removed ok that is nothing, but F c into V. Specific cutting energy normally represent in terms of U basically . So, specific cutting energy is nothing, but energy given to the material removal rate ok; how much is removed per unit time volume ok that is nothing, but my chip thickness; that means, uncut thickness into the this is called my feed, this is called my depth of cut and this is called my cutting velocity ok . So, if I use this is M M; this is also M M and this is M M per minute or second. So, now, you will get is material removal rate ok that is about the specific cutting energy some people will calculate in other way also.
Video 4: Velocity RelationshipsNow, we are moving to the velocity relationships; velocity relationship as we know there are three velocities in the machining one is chip velocity. Now you can see the chip for the betterment of understanding, we have the chips are there assume my chip velocity will be the direction of my frictional force. At the same time cutting velocity, cutting velocity will be like along the direction of this one that is nothing, but V this is nothing, but V c and the shear velocity; shear velocity will be in the direction of shearing ok ok. So, now you can see this velocity V is cutting direction just I am telling you the directions only because my machining is taking place. And the shearing velocity you can see here also shearing velocity is taking place and my chip velocity is moving in this direction ok.