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Manufacturing Processes-2 
SUBJECT CODE :4ME04 
SEM 4 
DEPARTMENT OF MECHANICAL ENGINEERING
BY MR.K.P.PAWAR 
LECTURER 
ANURADHA COLLEGE OF ENGINEERING 
*
LECTURE -4 
Objectives of Lecture 
 To understand merchant cutting force diagram 
 To learn various sources of heat in metal cutting
Merchant cutting force diagram 
Assumptions: 
1.The cutting velocity always remains constant 
2. Cutting edge of the tool remain sharp throughout the cutting 
3. There is no side ways of flow of the chip 
4. Only continuous chip is produced 
5.There is no built-up edge 
6. No consideration is made of the inertia force of the chip 
7. The behavior of the chip is like that of a free body which is in 
the state of stable equilibrium under the action of two resultant 
forces which are equal, opposite & collinear
Fs = Shear force, which acts along the 
shear plane, is the resistance to shear of 
the metal in forming the chip 
Fn = Force acting normal to the shear 
plane ,is the backing up force on the 
chip provided by the work piece 
F = Frictional resistance of the tool 
acting against the motion of the chip as 
it moves upward along the tool 
N = Normal to the chip force, is 
provided by the tool 
Fc = Horizontal cutting force exerted by 
the tool on the work piece 
Ft = Vertical force which helps in 
holding the tool in position and acts on 
the tool nose
Lecture 4
1. Merchant circle is useful to determine the relation between the 
various forces & angles. 
2. In the diagram two force triangles have been combined & R & 
R’ together have been replaced by R 
3. The force R can be resolved into two components Fc & Ft 
4. Fc & Ft can be determined by force dynamometers 
5. The rack angle (α ) can be measured from the tool & forces F & 
N can then be determined 
6. The shear angle (Ф) can be obtained from it’s relation with chip 
reduction coefficient 
7. Now Fs & Fn can also be determine
Relationship of various forces 
F=OA=CB=CG+GB 
=ED+GB 
=Fc sin 훼 + Ft cos 훼 
N=AB=OD-CD 
=OD-GE 
=Fc cos 훼 + Ft sinα 
Frictional force diagram
Shear Force System 
Fs = OA=OB-AB 
=OB-CD 
= Fc cosФ – Ft sinФ 
Fn = AE= AD+DE 
=BC + DE 
= Fc sinФ + Ft cosФ
Ф
Sources of Heat in Metal Cutting
Lecture 4
Around shear Plane 
 Region in which actual plastic deformation of the metal occurs 
during machining. 
 Due to this deformation heat is generated. 
 Portion of this heat is carried away by the chip, due to which 
it’s temperature is raised. 
 The rest of the heat is retained by the work piece. 
 Region is known as primary deformation zone.
Tool- chip interface 
 As the chip slides upwards along face of the tool friction occurs 
between their surfaces, due to which heat is generated. 
 A part of this heat carried by the chip, which further raises the 
temperature of the chip and the rest transferred to the tool & the 
coolant. 
 This area is known as secondary deformation zone. 
 The amount of heat generated due to friction increases with the 
increase in cutting speed. 
 It is not appreciably effected with the increase in depth of cut. 
 When the feed rate is increased the amount of frictional heat 
generated is relatively low. But, in that case,the surface finish 
obtained is inferior
Tool- work piece interface 
 That portion of tool flank which rubs against the work surface 
is another source of heat generation due to friction. 
 This heat is also shared by the tool, work piece and the coolant 
used. 
 It is more pronounced when the tool is not sufficiently sharp.
Question & Answer Session 
Q.1 .What are various assumptions assume by merchant for 
cutting force analysis ? 
Q.3.What are various sources of heat in metal cutting ?

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Lecture 4

  • 1. Manufacturing Processes-2 SUBJECT CODE :4ME04 SEM 4 DEPARTMENT OF MECHANICAL ENGINEERING
  • 2. BY MR.K.P.PAWAR LECTURER ANURADHA COLLEGE OF ENGINEERING *
  • 3. LECTURE -4 Objectives of Lecture  To understand merchant cutting force diagram  To learn various sources of heat in metal cutting
  • 4. Merchant cutting force diagram Assumptions: 1.The cutting velocity always remains constant 2. Cutting edge of the tool remain sharp throughout the cutting 3. There is no side ways of flow of the chip 4. Only continuous chip is produced 5.There is no built-up edge 6. No consideration is made of the inertia force of the chip 7. The behavior of the chip is like that of a free body which is in the state of stable equilibrium under the action of two resultant forces which are equal, opposite & collinear
  • 5. Fs = Shear force, which acts along the shear plane, is the resistance to shear of the metal in forming the chip Fn = Force acting normal to the shear plane ,is the backing up force on the chip provided by the work piece F = Frictional resistance of the tool acting against the motion of the chip as it moves upward along the tool N = Normal to the chip force, is provided by the tool Fc = Horizontal cutting force exerted by the tool on the work piece Ft = Vertical force which helps in holding the tool in position and acts on the tool nose
  • 7. 1. Merchant circle is useful to determine the relation between the various forces & angles. 2. In the diagram two force triangles have been combined & R & R’ together have been replaced by R 3. The force R can be resolved into two components Fc & Ft 4. Fc & Ft can be determined by force dynamometers 5. The rack angle (α ) can be measured from the tool & forces F & N can then be determined 6. The shear angle (Ф) can be obtained from it’s relation with chip reduction coefficient 7. Now Fs & Fn can also be determine
  • 8. Relationship of various forces F=OA=CB=CG+GB =ED+GB =Fc sin 훼 + Ft cos 훼 N=AB=OD-CD =OD-GE =Fc cos 훼 + Ft sinα Frictional force diagram
  • 9. Shear Force System Fs = OA=OB-AB =OB-CD = Fc cosФ – Ft sinФ Fn = AE= AD+DE =BC + DE = Fc sinФ + Ft cosФ
  • 10. Ф
  • 11. Sources of Heat in Metal Cutting
  • 13. Around shear Plane  Region in which actual plastic deformation of the metal occurs during machining.  Due to this deformation heat is generated.  Portion of this heat is carried away by the chip, due to which it’s temperature is raised.  The rest of the heat is retained by the work piece.  Region is known as primary deformation zone.
  • 14. Tool- chip interface  As the chip slides upwards along face of the tool friction occurs between their surfaces, due to which heat is generated.  A part of this heat carried by the chip, which further raises the temperature of the chip and the rest transferred to the tool & the coolant.  This area is known as secondary deformation zone.  The amount of heat generated due to friction increases with the increase in cutting speed.  It is not appreciably effected with the increase in depth of cut.  When the feed rate is increased the amount of frictional heat generated is relatively low. But, in that case,the surface finish obtained is inferior
  • 15. Tool- work piece interface  That portion of tool flank which rubs against the work surface is another source of heat generation due to friction.  This heat is also shared by the tool, work piece and the coolant used.  It is more pronounced when the tool is not sufficiently sharp.
  • 16. Question & Answer Session Q.1 .What are various assumptions assume by merchant for cutting force analysis ? Q.3.What are various sources of heat in metal cutting ?