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• Friends, our subject is Manufacturing Processes II and module II is still running and subject

• is Mechanics of Machining and today is lecture - 4. The topic today is interrelations among

• the tool angles expressed in different systems and what are the instructional objectives

• or content of lecture today.

• State the purposes of conversion of tool angles from one system to another. Why do we need

• conversion of tool angles from ASA to ORS or ORS to NSA and so on? Name the different

• methods of the conversion of tool angles. There are different methods what are those?

• Convert tool angles by graphical method. Rake angle from ASA to ORS and vice versa, clearance

• angles from ASA to ORS and vice versa. Next convert tool angles from orthogonal rake system

• to normal rake system and last ascertain tool geometry in some specific conditions. Now

• what are the purposes of conversion of tool angles?

• To understand geometry if expressed in a different system. Suppose you are conversant with a

• particular system of tool designation, say orthogonal rake system but you have got a

• book written by a foreign author who dealt the cutting tool geometry in ASA system. You

• may not be able to understand, then what you have to do? You have to learn both ASA system

• and orthogonal system and also convert the tool angles given in the book in ASA system

• in to ORS system for your understanding, your visualization and study. Now next, derive

• benefits of different system. Now there are different tool designative system ASA system,

• orthogonal system, normal rake system, maximum rake system, work reference system, each system

• Now we have to derive the advantages. To derive for example, say ASA system is very convenient

• for tool manufacturing tool inspection and so on. Then orthogonal system, orthogonal

• system is very simple. It is very useful say general study, research, analysis and so on

• but orthogonal system does not provide the exact tool geometry if lambda inclination

• angle is not zero. Thirdly if you want to resharpen the cutting tool then ORS system

• is not that very convenient whereas normal rake system that gives the true picture of

• the cutting tool and it enables very easy resharpening of the tool.

• So if you want to derive the benefits we should convert tool angle from one system to another

• to derive the benefits. Now communicate geometry to others who follow different tool designation

• system. Suppose you do research on a machining process with a cutting tool in ORS system.

• Now you go to a conference and say USA and there people are more conversant in ASA system.

• How will you communicate the tool geometry that you have dealt with to them who are knowledgeable

• about ASA system that means, you have to convert your tool angles from ORS to ASA, and then

• tell them this is the geometry actually in ASA system for there understanding and this

• is mutually true vice versa also. Now what are the different methods of conversion of

• tool angles?

• There are basically four methods. First is analytical method it is geometrical method

• very simple but tedious. It takes lot of time and

• monotonous. Graphical Method based are Masterline principle, it is very simple, quick

• and very popular. So most of the people you know learn this method first. Transformation

• matrix method is a little complex method but very suitable for complex tool

• geometry. Say for example, say geometry of cutting, say drill geometry for horn tools

• then for conversion of tool angles say hob cutters or gear shaping cutters for such complex

• shaped cutters or cutting tools the transmission matrix method is appropriate

• for conversion and vector method is Universal, very strong powerful method as

• well as very simple and quick but it needs concept of vectors and matrix. So our concentration

• will be on graphical method master line principle. So conversion of tool angles

• by graphical method using master lines.

• Now let us start with conversion of rake angles. You know the cutting tools have got three

• important angles. One is rake angle, next is clearance angle and third is cutting angle

• and beside that finally the tool nose radius. So let us start with conversion of rake angles

• from ASA system to ORS and vice versa.

• So first of all say rake angle, we shall deal with conversion of rake angles from ASA to

• ORS and vice versa. So let us start with this. By graphical method, this is based on master

• line principle, then what is master line? First of all you have to understand the master

• line concept. See this is master line, let me show you the master line for rake surface.

• First you draw a cutting tool. This is a top view of the cutting tool. It is drawn in orthogonal

• rake sorry pi r reference plane, then you visualize the other planes. This is machine

• longitudinal plane pi x, this is machine transfers plane pi y, this is cutting plane pi c and

• this is orthogonal plane pi o. Now this is xm, this is ym, this is xo orthogonal, this

• is yo and zo and zm perpendicular to the plane.

• So again I repeat this is pi x plane, this is pi y plane - machine transverse plane,

• this is orthogonal plane and this is cutting plane. Now you show the rake angles in different

• planes. Say first of all, let us take the section of the tool in machine longitudinal

• plane and show the cutting tool section. This is section of the cutting tool and in which

• plane the diagram has been drawn, the section is taken on pi x plane. So this is pi x, machine

• longitudinal plane and what is this axis this is xm, what is this is axis y this is zm.

• So this is zm and this is xm and what is this angle? Angle between the reference plane and

• the rake surface, so this is gamma x that is side rake.

• Now what you have to, this is the bottom surface of the tool and these are rake surface you

• extend the rake surface until it meets the bottom surface suppose it meets at point D

• prime. Say at certain distance, this rake surface meets the bottom surface and if you

• project it on this diagram on the view drawn in reference plane so this is point suppose

• D. So D is situated on the bottom plane which is parallel to the reference plane or it is

• horizontal plane. Now you take the cutting tool section along machine transfer plane

• in this direction. So this is the cutting tool and which plane the diagram has been

• drawn, pi y machine transverse plane by take a section by this machine transverse plane.

• So this is obviously zm and this is ym axis, xm is perpendicular to the plane and what

• is this angle? this is rake angle in which plane? pi y plane, so this is gamma y that

• is back rake. If you extend this rake surface up to the bottom plane of the tool then meets

• at a point say this is point B prime and on this diagram if you project it this is the

• point this is the distance suppose this is o oD this is oB. So B and D both of situated

• on the bottom surface and if I join B and D by a straight line then what is this BD.

• BD is situated on the bottom plane which is also parallel to the reference plane. This

• is reference plane, this surface is reference plane, this plate now what physically what

• is the meaning of this.

• This is the line of intersection between the rake surface of the tool if extended and the

• bottom surface of the tool. So this is the line of intersection between the rake surface

• and the bottom surface if it is extended on this direction it will meet a point D and

• B. Now you can extend it. So this line is called Master Line for rake surface for a

• Master Line for rake surface, similarly Master Line for clearance surface will also appear.

• Now what is this point? Say this is point C. It means if the rake surface is extended

• along this orthogonal plane this will meet the bottom surface at point C and that point

• C will be always situated on the line of intersection.

• Physically it means that if you take the section draw the view of the cutting tool from here extend it. So this

• is orthogonal plane and this is the cutting tool, this is the rake surface, this is rake

• angle orthogonal rake and this axis is zo, this is xo and so on. Now if you extend this

• rake surface then it will meet the bottom surface of the tool at point say C prime and

• if it is extended it meets point C. Now what is the thickness of the tool? This is the

• thickness of the tool say T, here this is the thickness of the tool T. Now look at this

• tool from this side along this direction along xo and now but this view that we will get

• of the tool will be in the cutting plane. So you draw the diagram in the cutting plane.

• So this is yo and this is zo and what is the view?

• Now if this is extended like this, this will also meet certain point and if it is extended

• this will be point, this will be somewhere A prime and this will be extended here. This

• will be A. So we get DCBA were this rake surface if extended meets the bottom surface along

• machine longitudinal plane, machine transverse plane, orthogonal plane and cutting plane.

• Now here you can see, that what this length OD? If we put it here OD equal to this OD

• this intercept. This intercept is equal to this intercept how much is this? This is equal

• T what is this angle same gamma x, so this OD. OD is equal to T multiplied tangent cotangent

• of gamma x so T cotangent gamma x.

• Similarly OB is how much? OB this is OB this equal to T, this is gamma y, so this is equal

• to T cotangent of gamma y, T cot gamma y then what is OC? OC will be T what is this angle?

• gamma O, so this will be T cotangent of gamma O and what is OA? This much this angle is

• lambda for inclination angle of the cutting tool. So OA will be equal to T cotangent lambda.

• So this will be very useful. Now you get the concept of master line. Now this concept will

• be know utilized to convert the tool angles from to one system to another.

• Now say conversion. First you start say convert rake angle from ASA to ORS. Now let us draw

• the diagram again. This is the cutting tool top view drawn in reference plane pi and then

• you visualize the different planes - machine longitudinal plane, machine transverse plane,

• cutting along the cutting edge and orthogonal plane and mind that this is ninety degree

• and this is xm, ym. This is xo, this is yo, and zo zm perpendicular to this point o.

• Now here suppose this is the master line, suppose this is the master line for rake surface

• and this point is D, this point is C, this point B and this point is A. What we observed

• last time that OD is equal to T, the thickness of the tool multiplied by cotangent gamma

• x. If T is one, say unity for T is equal to unity OD is equal to cotangent of gamma x.

• OB is equal cotangent of gamma y. OC is equal to cotangent of gamma O and OA is equal to

• cotangent of lambda we get it now.

• We have to proof now we have to convert from ASA to ORS. Now what is the meaning of conversion

• from ASA to ORS that means if the tool angle the value of the tool angles are given in

• ASA system then what will be the value of the rake angles of the same tool that is the

• question that means, the meaning is determine gamma O and lambda which is also a rake angle

• from the given values of gamma x and gamma y that means, this is a function of gamma

• O and lambda is an this is a ORS system and this is ASA system. So from ASA system to

• ORS we have to convert now how this will be converted. Now we are discussing about conversion

• of cutting tool angles. So first we shall show the conversion of rake angles.

• You know the rake angles, there are side rake, back rake or orthogonal rake even lambda intersecting

• angle is also a rake angle. So first conversion of rake angles from ASA to ORS that means,

• let us write say tangent of gamma o is equal to tangent of gamma x sin phi plus tangent

• of gamma y cosine phi. The other one is tangent of inclination angle lambda is equal to minus

• tangent of gamma x cosine phi plus tangent of gamma y sin phi instead of cosine phi.

• Say equation number one and equation number two.

• Now actually what we are going to do now, what we are going to do that if the values

• of gamma x, the gamma x and gamma y gamma x and gamma y are known to me then and phi

• is also known that is the tool angles are given in ASA system we have to determine the

• rake angles gamma o and lambda in ORS system that means to find out rake angle orthogonal

• rake and lambda that is in ORS system as function of gamma x, gamma y and the cutting angle

• phi. The principle cutting angle phi and we know that principle cutting angle phi is equal

• to ninety degree minus phi s where phi s is approach angle and this approach angle is

• given in ASA system.

• So if phi s know from where you can determine phi and put the values of gamma x gamma y

• and phi in to these equations number one and two we can determine the values of orthogonal

• rake and inclination angle lambda that is from the given values of the rake angles in

• a ASA system, we are determining the rake angles in ORS system. So now, how to proof

• this equation? We have to proof these equations. See equation number one proof of equation

• number one. How shall we do it? Let us take the help of this drawing. Draw this diagram