THEORY OF METAL CUTTING 2

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1) What is tool signature ? And what are the different systems of specifying tool geometry? :

1) What is tool signature ? And what are the different systems of specifying tool geometry? In simple words The numerical code that describes all the key angles of a given cutting tool is called tool signature Convenient way to specify tool angles by use of standardized abbreviated system is known as tool signature or tool nomenclature. The tool signature comprises of seven elements and is specified in different systems .

Cutting tool geometry:

Cutting tool geometry

Slide 3:

There are several systems available, some of the important systems are: American standard system (ASA) Orthogonal rake system (ORS) Maximum rake system (MRS) Normal rake system (NRS) and The system most commonly used is American standard system(ASA)

American standard system:

American standard system

Orthogonal rake system(ors):

Orthogonal rake system(ors)

Orthogonal rake system (ors):

Orthogonal rake system (ors)

Maximum rake system (mrs):

Maximum rake system (mrs)

Maximum rake system (mrs):

Maximum rake system (mrs)

Normal rake system (nrs) :

Normal rake system (nrs)

normal rake system (nrs):

normal rake system (nrs)

2) What is orthogonal cutting and oblique cutting ? List the assumptions in calculating cutting force?:

2) What is orthogonal cutting and oblique cutting ? List the assumptions in calculating cutting force? Orthogonal cutting In orthogonal cutting the tool approaches the work piece with its cutting edge parallel to the uncut surface and at right angle to the direction of cutting. Thus tool approach angle and cutting edge inclination are zero. Here only two component forces are acting cutting force Fc and thrust force Ft. So the metal cutting may be considered as 2 Dimensional cutting. work tool feed

Oblique cutting :

Oblique cutting The cutting edge is inclined at an angle i (known as inclination angle ) with the normal to the direction of tool travel . The cutting edge may are may not clear the width of the work piece. The chip flow on tool face making an angle with the normal on the cutting edge. The chip flows side ways in a long curl. Three components of the forces (mutually perpendicular act at the cutting edge). Oblique cutting occur when the major edge of the cutting tool is presented to the work piece at an angle which is not perpendicular to the direction of feed.

Assumptions in calculating the cutting forces: -:

Assumptions in calculating the cutting forces: -

3) Establish a relation between three velocities in orthogonal cutting ?:

3) Establish a relation between three velocities in orthogonal cutting ? Vc=Chip velocity Vs =Shear velocity V= cutting velocity Φ =Shear angle = Rake angle α

Slide 17:

The cutting velocity V: it is the velocity of the tool relative to the work and directed parallel to Fh. The chip velocity Vc: it is the velocity of the chip relative to the tool and directed along the tool face. The shear velocity Vs: it is the velocity of the chip relative to the work piece and directed along the shear plane. With the help of sine rule we can write V = Vs = Vc Sin (90+ a-f) Sin (90- a) S in f Chip velocity Vc = V sin f Cos ( f-a) Shear velocity Vs = V Cos a Cos ( f-a)

4) List the assumptions made in development of merchant’s circle diagram? :

4) List the assumptions made in development of merchant’s circle diagram? The following are the assumptions listed in merchant’s circle diagram The tool is perfectly sharp and there is no contact along the clearance face The shear surface is plane extending upward from the cutting edge The cutting edge is a straight line, extending perpendicular to the direction of motion and generates a plane surface as the work moves past it. The chip does not flow to either sides. The depth of cut is constant. Width of tool is greater than that of work piece. The work moves relative to the tool with uniform velocity. A continuous chip is produced with no built up edge. Plain strain conditions exist i.e. the width of the chip remains equal to the width of the work piece. Chip is assumed to shear continuously across plane on which the shear stress Reaches the value of shear flow stress .

5) Determine the relationship among the various forces by merchant‘s circle diagram? :

5) Determine the relationship among the various forces by merchant‘s circle diagram? Various cutting forces acting on a single point cutting tool has been shown in the following figure by merchant. He suggested an easy and compact way of representing the various forces in side a circle with diameter R. Fc= C utting force Fv= Thrust force F = Frictional force a = Rake angle of tool f = Shear angle b = Friction angle Ns= Normal force to shear force N= Force normal to friction force

Slide 20:

In the diagram two force triangles has been combined . The resultant R can be resolved into two components Fc and Ft. Fc and Ft can be determined by force dynamometers. R=Fc + Ft The rake angle ( a) can be measured from the tool, and F and N can be determined The shear angle ( f) can be taken from its relation with chip reduction coefficient. And Fs and Fn can be calculated . Tan f = r Cos a 1-r Sin a From the figure Frictional resistance F= Fc Sin a + Fv Cos a And Normal force N= Fc Cos a – Fv Sin f

Slide 22:

But Kinematic coefficient of friction ( m) = F =tan b N m = F = Fc Sin a + Fv Cos a = Fc Tan a + Fv N Fc Cos a - Fv Sin a Fc – Fv Tan a Shear force Fs = Fc Cos f - Fv sin f And Normal force Ns= Fc Sin f + Fv cos f

Slide 23:

6) Derive an expression for the shear angle in orthogonal cutting In terms of rake angle and chip thickness ratio? The out ward flow of the metal causes the chip to be thicker after separation from the parent metal. Metal prior to being cut Is much longer than the chip which is removed. The chip thickness ratio or cutting ratio is the ratio of uncut chip thickness to the cut chip thickness. When metal is cut there is no change in volume of the metal cut therefore t1*b1*L1 = t2*b2*L2 where t1 & t2 are chip thickness before and after cutting L 1 &L2 are length of chip before and after cut. b1 & b2 are width of cut before and after cut it is observed that b1 = b2

Slide 25:

There fore t1 * L1 = t2 * L2 t1 = L2 = r t2 L1 From the triangle ABC BC = Sin f B ut BC =t1 AB AB = t1 ------ (1) Sin f From the triangle ABD BD = Sin 90-( f-a) AB B ut Sin 90- ( f-a) = cos ( f-a) And BD= t2 AB= t2 ----- (2) Cos (f-a) From (1) and(2) t1 = Sin f = r t2 Cos ( f-a)

Slide 26:

r = Sin f Cos f . Cos a + Sin f Sin a r Cos a = 1 – r Sin a Tan f Tan f = r Cos a 1- r Sin a There fore shear angle can be shown from the above equation