Module 2 Mechanics of Machining Lesson 8 Machining forces and Merchant’s Circle Diagram (MCD) - Mechanical Engineering PDF Download

 Page 1


 
 
 
 
 
 
 
 
 
Module  
2    
Mechanics of 
Machining 
 
   
Version 2 ME IIT, Kharagpur 
Page 2


 
 
 
 
 
 
 
 
 
Module  
2    
Mechanics of 
Machining 
 
   
Version 2 ME IIT, Kharagpur 
 
 
 
 
 
 
 
Lesson  
 8    
Machining forces and 
Merchant’s Circle 
Diagram (MCD) 
 
 
Version 2 ME IIT, Kharagpur 
Page 3


 
 
 
 
 
 
 
 
 
Module  
2    
Mechanics of 
Machining 
 
   
Version 2 ME IIT, Kharagpur 
 
 
 
 
 
 
 
Lesson  
 8    
Machining forces and 
Merchant’s Circle 
Diagram (MCD) 
 
 
Version 2 ME IIT, Kharagpur 
Instructional Objectives  
 
At the end of this lesson, the student would be able to  
 
(i)  Ascertain the benefits and state the purposes of determining cutting 
forces 
(ii)  Identify the cutting force components and conceive their 
significance and role 
(iii)  Develop Merchant’s Circle Diagram and show the forces and their 
relations 
(iv)  Illustrate advantageous use of Merchant’s Circle Diagram 
 
 
(i)  Benefit of knowing and purpose of determining cutting 
forces. 
 
The aspects of the cutting forces concerned : 
• Magnitude of the cutting forces and their components 
• Directions and locations of action of those forces 
• Pattern of the forces : static and / or dynamic. 
Knowing or determination of the cutting forces facilitate or are required for : 
• Estimation of cutting power consumption, which also enables 
selection of the power source(s) during design of the machine tools 
• Structural design of the machine – fixture – tool system 
• Evaluation of role of the various machining parameters ( process – 
V
C
, s
o
, t, tool – material and geometry, environment – cutting fluid) 
on cutting forces 
• Study of behaviour and machinability characterisation of the work 
materials 
• Condition monitoring of the cutting tools and machine tools. 
 
(ii)  Cutting force components and their significances 
 
The single point cutting tools being used for turning, shaping, planing, slotting, 
boring etc. are characterised by having only one cutting force during 
machining. But that force is resolved into two or three components for ease of 
analysis and exploitation. Fig. 8.1 visualises how the single cutting force in 
turning is resolved into three components along the three orthogonal 
directions; X, Y and Z. 
The resolution of the force components in turning can be more conveniently 
understood from their display in 2-D as shown in Fig. 8.2. 
 
 
 
Version 2 ME IIT, Kharagpur 
Page 4


 
 
 
 
 
 
 
 
 
Module  
2    
Mechanics of 
Machining 
 
   
Version 2 ME IIT, Kharagpur 
 
 
 
 
 
 
 
Lesson  
 8    
Machining forces and 
Merchant’s Circle 
Diagram (MCD) 
 
 
Version 2 ME IIT, Kharagpur 
Instructional Objectives  
 
At the end of this lesson, the student would be able to  
 
(i)  Ascertain the benefits and state the purposes of determining cutting 
forces 
(ii)  Identify the cutting force components and conceive their 
significance and role 
(iii)  Develop Merchant’s Circle Diagram and show the forces and their 
relations 
(iv)  Illustrate advantageous use of Merchant’s Circle Diagram 
 
 
(i)  Benefit of knowing and purpose of determining cutting 
forces. 
 
The aspects of the cutting forces concerned : 
• Magnitude of the cutting forces and their components 
• Directions and locations of action of those forces 
• Pattern of the forces : static and / or dynamic. 
Knowing or determination of the cutting forces facilitate or are required for : 
• Estimation of cutting power consumption, which also enables 
selection of the power source(s) during design of the machine tools 
• Structural design of the machine – fixture – tool system 
• Evaluation of role of the various machining parameters ( process – 
V
C
, s
o
, t, tool – material and geometry, environment – cutting fluid) 
on cutting forces 
• Study of behaviour and machinability characterisation of the work 
materials 
• Condition monitoring of the cutting tools and machine tools. 
 
(ii)  Cutting force components and their significances 
 
The single point cutting tools being used for turning, shaping, planing, slotting, 
boring etc. are characterised by having only one cutting force during 
machining. But that force is resolved into two or three components for ease of 
analysis and exploitation. Fig. 8.1 visualises how the single cutting force in 
turning is resolved into three components along the three orthogonal 
directions; X, Y and Z. 
The resolution of the force components in turning can be more conveniently 
understood from their display in 2-D as shown in Fig. 8.2. 
 
 
 
Version 2 ME IIT, Kharagpur 
 
R 
P
X
P
Y
P
Z
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 8.1  Cutting force R resolved into P
X
, P
Y
 and P
Z
 
P
X
P
Y
P
XY
P
X
' 
P
Y
' 
P
Z
P
Z
' 
P
XY
P
XY
'
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 8.2  Turning force resolved into P
Z
, P
X
 and P
Y
 
 
 
 
 
The resultant cutting force, R is resolved as, 
Version 2 ME IIT, Kharagpur 
Page 5


 
 
 
 
 
 
 
 
 
Module  
2    
Mechanics of 
Machining 
 
   
Version 2 ME IIT, Kharagpur 
 
 
 
 
 
 
 
Lesson  
 8    
Machining forces and 
Merchant’s Circle 
Diagram (MCD) 
 
 
Version 2 ME IIT, Kharagpur 
Instructional Objectives  
 
At the end of this lesson, the student would be able to  
 
(i)  Ascertain the benefits and state the purposes of determining cutting 
forces 
(ii)  Identify the cutting force components and conceive their 
significance and role 
(iii)  Develop Merchant’s Circle Diagram and show the forces and their 
relations 
(iv)  Illustrate advantageous use of Merchant’s Circle Diagram 
 
 
(i)  Benefit of knowing and purpose of determining cutting 
forces. 
 
The aspects of the cutting forces concerned : 
• Magnitude of the cutting forces and their components 
• Directions and locations of action of those forces 
• Pattern of the forces : static and / or dynamic. 
Knowing or determination of the cutting forces facilitate or are required for : 
• Estimation of cutting power consumption, which also enables 
selection of the power source(s) during design of the machine tools 
• Structural design of the machine – fixture – tool system 
• Evaluation of role of the various machining parameters ( process – 
V
C
, s
o
, t, tool – material and geometry, environment – cutting fluid) 
on cutting forces 
• Study of behaviour and machinability characterisation of the work 
materials 
• Condition monitoring of the cutting tools and machine tools. 
 
(ii)  Cutting force components and their significances 
 
The single point cutting tools being used for turning, shaping, planing, slotting, 
boring etc. are characterised by having only one cutting force during 
machining. But that force is resolved into two or three components for ease of 
analysis and exploitation. Fig. 8.1 visualises how the single cutting force in 
turning is resolved into three components along the three orthogonal 
directions; X, Y and Z. 
The resolution of the force components in turning can be more conveniently 
understood from their display in 2-D as shown in Fig. 8.2. 
 
 
 
Version 2 ME IIT, Kharagpur 
 
R 
P
X
P
Y
P
Z
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 8.1  Cutting force R resolved into P
X
, P
Y
 and P
Z
 
P
X
P
Y
P
XY
P
X
' 
P
Y
' 
P
Z
P
Z
' 
P
XY
P
XY
'
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 8.2  Turning force resolved into P
Z
, P
X
 and P
Y
 
 
 
 
 
The resultant cutting force, R is resolved as, 
Version 2 ME IIT, Kharagpur 
                            XY
Z
P P R + =                        (8.1) 
              and    Y X XY P P P + =                                                                 (8.2) 
              where, P
X
 = P
XY
sin f   and    P
Y 
= P
XY
cos f                                   (8.3) 
              where, P
Z
 = tangential component taken in the direction of Z
m
 axis 
                          P
X
 = axial component taken in the direction of longitudinal  
                                  feed or X
m
 axis 
       P
Y
 = radial or transverse component taken along Y
m
 axis. 
 
In Fig. 8.1 and Fig. 8.2 the force components are shown to be acting on the 
tool. A similar set of forces also act on the job at the cutting point but in 
opposite directions as indicated by P
Z
', P
XY
', P
X
' and P
Y
' in Fig. 8.2 
 
Significance of P
Z
, P
X
 and P
Y 
 
P
Z
  :  called the main or major component as it is the largest in magnitude. 
         It is also called power component as it being acting along and being  
         multiplied by V
C
 decides cutting power (P
Z
.V
C
) consumption. 
P
y
  :  may not be that large in magnitude but is responsible for causing  
        dimensional inaccuracy and vibration. 
P
X
  :  It, even if larger than P
Y
, is least harmful and hence least significant. 
 
Cutting forces in drilling 
 
In a drill there are two main cutting edges and a small chisel edge at the 
centre as shown in Fig. 8.3. 
The force components that develop (Fig. 8.3) during drilling operation are : 
• a pair of tangential forces, P
T1
 and P
T2
 (equivalent to P
Z
 in turning) 
at the main cutting edges 
• axial forces P
X1
 and P
X2
 acting in the same direction 
• a pair of identical radial force components, P
Y1
 and P
Y2
 
• one additional axial force, P
Xe
 at the chisel edge which also 
removes material at the centre and under more stringent condition. 
 
P
T1
 and P
T2
 produce the torque, T and causes power consumption P
C
 as, 
 T = P
T
 x ½ (D)       (8.3) 
and P
C
= 2 pTN        (8.4) 
where, D = diameter of the drill 
and      N = speed of the drill in rpm. 
The total axial force P
XT
 which is normally very large in drilling, is provided by  
 P
XT
 = P
X1
 + P
X2
 + P
Xe
      (8.5) 
But there is no radial or transverse force as P
Y1
 and P
Y2
, being in opposite 
direction, nullify each other if the tool geometry is perfectly symmetrical. 
 
 
 
 
 
 
 
Version 2 ME IIT, Kharagpur