Tool Geometry

Introduction
Tool Geometry Concept of Rake and Clearance Angles

(a)
Fig. Probable forms of early
cutting implements

(b)
Tool Geometry Concept of Rake and Clearance Angles

Fig. Concept of Rake and Clearance Angles

Tool Geometry Concept of Rake and Clearance Angles

Fig. Concept of Rake and Clearance Angles

 Types of Rake Angles
b
a
Tool Geometry

Fig.: a. Positive Rake

b. Negative Rake
c. Zero Rake
 Positive Rake Angle
The use of positive rake
angles is recommended:
 When machining low strength ferrous
Tool Geometry

and non-ferrous materials and work

hardening materials.
 When using low power machines.
 When machining long shafts of small
diameters.
 When the setup lacks strength and
rigidity.
 When cutting at low speeds.
 Negative Rake Angle
The use of negative rake
angles is recommended:
Tool Geometry

When machining high strength alloys.

When there are heavy impact loads
such as in interrupted machining.
For rigid setups and when cutting at
high speeds.
 Basic Features of a Single Point Tool
Auxiliary Cutting Edge
Single Point
Rake
(rake face, principal Face
cutting edge, auxiliary cutting edge, principal flank
Auxiliary Flank Surface
surface, auxiliary flank surface and tool nose)
Base
Tool Geometry

Principal
Shank
Cutting Edge
Tool Nose
Principal Flank Surface
Tool Geometry Left Hand & Right Hand Tools
 Systems of Tool Geometry
 Tool in Hand System: salient features of
the cutting tool point are identified or
visualized
Tool Geometry

 Machine Reference System - ASA

System
 Tool Reference System
 Orthogonal Rake System - ORS
 Normal Rakes System – NRS
 Work Reference System - WRS
Tool Geometry ASA – Planes of Reference

Fig.: Planes and Axes of Reference in ASA System

Tool Geometry ASA – Planes & Axes of Reference

Fig.: Planes and Axes of Reference in ASA System

P
14
15
Tool Geometry Tool Angles in ASA System

Fig.: Tool Angles in ASA System

Tool Geometry Tool Angles in ASA System
Tool Geometry Tool Angles in ASA System
Tool Geometry Tool Angles in ASA System
Tool Geometry ASA – Tool Signature
Tool Geometry ORS – Planes of Reference

Fig.: Planes and Axes of Reference in ORS System

Tool Geometry ORS – Planes & Axes of Reference

Fig.: Planes and Axes of Reference in ORS System

Tool Geometry Tool Angles in ORS System

Fig.: Tool angles in ORS System

Tool Geometry Tool Angles in ORS System
Tool Geometry Tool Angles in ORS System
Tool Geometry Tool Angles in ORS System
Tool Geometry ORS – Tool Signature
Tool Geometry Tool Angles – Sign Convention

Fig.: Sign Convention for Inclination Angle

 Conversion of Rake Angles
C

F
Conversion of Tool Geometry

Rake Plane
A
D

Base Plane
B

E
 ASA to ORS - Conversion
A, B C T
B A
Conversion of Rake Angles

B
T
D D
A

T B C
B

T for T = unity
A
F E A
 ASA to ORS - Conversion
O A, B C
Conversion of Rake Angles

Since triangles
OCE and BCD are similar:
E
Conversion of Rake Angles ASA to ORS - Conversion

unity
 ASA to ORS - Conversion
O A, B G C
Conversion of Rake Angles

Similarly by considering
similar triangles BDC and GFC:
Conversion of Rake Angles ASA to ORS - Conversion

unity
Conversion of Rake Angles ASA to ORS - Conversion

Both the above equations can be written

in matrix form :

Transformation
Matrix
 ORS to ASA - Conversion

It has been already proven that:

Conversion of Rake Angles

From the above, it can be written as:

 ORS to ASA - Conversion

= ?
Conversion of Rake Angles
Conversion of Rake Angles

=
ORS to ASA - Conversion
Conversion of Rake Angles ORS to ASA - Conversion

Transformation
Matrix
Conversion of Clearance Angles Principal Flank Angles

C
D λ
O B A

Principal Flank Surface

 Principal Flank Angles
Auxiliary Flank
Principal Flank P, O O P
D
C
B B
Classification

P
O D
O A
P
P C

A
 ASA to ORS - Conversion
E P, O D
Conversion of Clearance Angles

Since triangles
AED and BOD are similar:
A
Conversion of Clearance Angles

unity
ASA to ORS - Conversion
 ASA to ORS - Conversion
E P, O F D
Conversion of Clearance Angles

Similarly by considering
similar triangles OBD and FCD :
Conversion of Clearance Angles

unity
ASA to ORS - Conversion
Conversion of Clearance Angles ASA to ORS - Conversion

Both the above equations can be written

in matrix form :

Transformation
Matrix
 ORS to ASA - Conversion

It has been already proven that:

Conversion of Clearance Angles

From the above, it can be written as:

Conversion of Clearance Angles

=
?
ORS to ASA - Conversion
Conversion of Clearance Angles

=
ORS to ASA - Conversion
Conversion of Clearance Angles ORS to ASA - Conversion

Transformation
Matrix
Tool geometry ASA&ORS - Designation
 NRS system- Planes of Reference
Normal Rake System (NRS) utilizes three
reference planes in order to measure various
tool angles.

Reference Plane (πR): It is a plane

perpendicular to the cutting velocity vector
(Vc).
Tool geometry

Cutting Plane (πC): It is a plane

perpendicular to reference plane (πR) and
contains the principal cutting edge of the tool.

Normal Plane (πN): It is a plane

perpendicular to the principal cutting edge of
the tool. Normal plane may not be
perpendicular to the reference plane (πR) and
Cutting Plane (πC). However, normal plane is
always perpendicular to the principal cutting
edge.
 Tool angles in NRS system
Normal Rake Angle (γN):
It is the angle of orientation of tool’s rake
surface from the reference plane (πR) and
measured on normal plane (πN).

Normal Clearance Angle (αN):

Tool Geometry

It is the angle of orientation of tool’s

principal flank surface from the cutting
plane (πC) and measured on normal plane
(πN).

Auxiliary Normal Clearance Angle (αN’):

It is the angle of orientation of tool’s
auxiliary flank surface from the auxiliary
cutting plane (πC’) and measured on
auxiliary normal plane (πN’).
Tool Geometry Tool Designation in NRS system

Maximum Rake System (MRS):

it consists of one rake angle, known as maximum rake angle; one
clearance angle, known as minimum clearance angle.
 ORS TO NRS SYSTEM
Tool representation in NRS system
ORS TO NRS SYSTEM
Sectional view in NRS system
ORS TO NRS SYSTEM
Relation between rake angles
 ORS TO NRS SYSTEM

∠AOB = γo
∠AOC = γn
∠BAC = λ

Now,
AC = ABcosλ
OAtanγn= (OAtanγo)cosλ
Hence, tanγn= tanγocosλ
 ORS TO NRS SYSTEM
Relation between clearance angles
 ORS TO NRS SYSTEM

∠ABA’ = αo
∠ACA’ = αn
∠BAC = λ

AC = ABcosλ
AA’cotαn= AA’cotαocosλ
Hence, cotαn= cotαocosλ

Similarly it can be proved,

cotαn’= cotαo’cosλ’
 Master line
Master line is the line of intersection
between the Reference Plane (πR) and any
one of the three tool point surfaces.

Master Line for Rake Surface:

It is the line of intersection between the
Tool Geometry

Reference Plane (πR) and Rake surface of

the cutting tool.

Master Line for Principal Flank Surface:

It is the line of intersection between the
Reference Plane (πR) and Principal Flank
surface of the cutting tool.

Master Line for Auxiliary Flank Surface:

It is the line of intersection between the
Reference Plane (πR) and Auxiliary flank
surface of the cutting tool.
 Maximum Rake Angle (ASA)
O A, B C
Conversion of Rake Angles

F
M

D in triangle BDC

E
 Maximum Rake Angle (ORS)
O A, B C
Conversion of Rake Angles

F
M similarly
D in triangle BFE

E
 Minimum Clearance Angle (ASA)
E P, O D
Conversion of Clearance Angles

C
M

B in triangle OBD

A
 Minimum Clearance Angle (ORS)
E P, O D
Conversion of Clearance Angles

C
M Similarly
B in triangle OCA

A
 References

• Metal Cutting Principles, M.C. Shaw, Oxford

University Press
• Machining & Machine Tools,
AB Chattopadhyay, Wiley
• Principles of Metal Cutting, GC Sen and A
Bhattacharya, New Central Book Agency
• Principles of Metal Cutting, G Kuppuswamy,
Universities Press