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Metal CuttingS. Mukhopadhyay
Reference Books▪ A. B. Chattopadhyay, Machining and Machine Tools,
Wiley.
▪ A. Ghosh and A.K. Mallick, Manufacturing Science,
EastWest Press.
▪ G. K. Lal, Introduction to Machining Science, New Age
International Publishers.
▪ A Bhattacharya, Metal Cutting Theory and Practice,
New Central Book Agency (P) Ltd.
▪ Web: Manufacturing Processes II by NPTEL
(https://nptel.ac.in/courses/112105127/)
Metal CuttingS. Mukhopadhyay
Single point vs. Multipoint cutting tools1
Tool geometry plays a crucial role on the performance of cutting tool, efficiency and
economy of machining.
▪ Single point cutting tools → Only one cutting edge
e.g. Turning, shaping, planing, boring, slotting tools
▪ Double (two) point cutting tool → Two cutting edges
e.g. Drills
▪ Multipoint cutting tool → Multiple cutting edges
e.g. Milling cutters, broaching tools, hobs,Gear shaping cutters, grinding wheels
turning boring
drilling
milling broaching
Metal CuttingS. Mukhopadhyay
Geometry of single point cutting tools
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Metal CuttingS. Mukhopadhyay
Concept of rake and clearance angles▪ Tool geometry basically refers to some specific angles and slope of salient faces
and edges of the tool at their cutting point.
▪ The most important ones are rake angle and clearance angle.
▪ Rake angle (𝜸): Angle made by the rake face with the reference plane 𝜋R (plane ⊥
to cutting velocity vector 𝑉C).
▪ Clearance angle (𝜶): Angle made by the tool flank surface with the finished surface
(or cutting plane 𝜋C which is ⊥ to 𝜋R and containing the cutting edge). Always +ve
to prevent rubbing of tool against workpeice.
Chattopadhyay, Machining and Machine tools
Types of rake angle and function
S. Mukhopadhyay
▪ Positive rake: Reduces cutting force and power.
▪ Negative rake: To increase strength and life of cutting edge.
▪ Zero rake: To simplify design and manufacture.
Apart from rake and clearance , there is wedge angle 𝛿 to provide mechanical
strength to the tool at the cutting edge.
𝛾 + 𝛿 + 𝛼 = 90°
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Metal Cutting
System of description of tool geometry
S. Mukhopadhyay
5
Tool geometry can be specified in various standard systems. Each has it’s own merits
and demerits.
▪ Tool-in-hand system: Only the principal surfaces and the cutting edges identified.
No quantitative information provided.
▪ Machine reference (ASA) system: Established by American Standards Association.
The various planes (where tool angles are evaluated) and the corresponding axes
are oriented based on the configuration and orientation of the machine tool.
▪ Tool reference systems: A family of systems where the axes and planes are based
on the configuration of the cutting tool. This provides more accurate and detailed
estimate of various tool angles , and hence more suitable for research purpose.
– Orthogonal Rake System (ORS)
– Normal Rake System (NRS)
Metal Cutting
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S. Mukhopadhyay
Tool-in-hand system
Principal surfaces and edges of a cutting tool identified by tool-in-hand system
Chattopadhyay, Machining and Machine tools
Metal Cutting
S. Mukhopadhyay
Machine reference system (ASA)
▪ Reference plane (𝝅𝐑): Plane perpendicular to the cutting velocity vector 𝑉C.
▪ Machine longitudinal plane (𝝅𝐗): Taken upright (normal) on 𝜋R and in the
direction of machine longitudinal feed.
▪ Machine transverse plane (𝝅𝐘): Also upright on 𝜋R and along machine
transverse feed (perpendicular to 𝜋X)
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The planes of reference are 𝜋X − 𝜋Y − 𝜋R and coordinates system Xm − Ym − Zm
Metal Cutting
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S. Mukhopadhyay
ASA system cont’d…▪ Side rake (𝜸𝐗): Angle of inclination of rake surface from
reference plane, measured on 𝜋X.
▪ Back rake (𝜸𝐘): Angle of inclination of rake surface from
reference plane, measured on 𝜋Y.
▪ Side clearance (𝜶𝐗): Angle of inclination of principal
flank from machined surface, measured on 𝜋X.
▪ Back clearance (𝜶𝐘): Same as 𝜋X, but measured on 𝜋Y.
▪ Approach angle (𝛗𝐒): Angle between the principal
cutting edge (it’s projection on 𝜋R) and 𝜋Y and
measured on 𝜋R).
▪ End cutting edge angle (𝛗𝒆): Angle between the
auxiliary cutting edge (it’s projection on 𝜋R) and 𝜋X and
measured on 𝜋R.
Metal Cutting
S. Mukhopadhyay
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ASA system cont’d…
Tool signature in ASA
𝛾Y − 𝛾X − 𝛼Y − 𝛼X − φ𝑒 − φ𝑆 − 𝑟
▪ Nose radius (r): Radius (inch) given to the tool tip,
it provides strength to the tool tip and results in
better surface finish.
Metal Cutting
S. Mukhopadhyay
Orthogonal rake system (ORS)10
Apart from 𝜋R which is common between ASA and ORS , there are new definition
of planes in ORS which are associated with the tool (rather than the machine).
▪ Cutting plane (𝝅𝐂): Plane upright (perpendicular) on 𝜋R and containing the
principal cutting edge.
▪ Orthogonal plane (𝝅𝐎): Plane perpendicular to both 𝜋R and 𝜋C, hence is
perpendicular to th projection of principal cutting edge on 𝜋R.
The planes of reference are 𝜋C − 𝜋O − 𝜋R and coordinates system XO − YO − ZO
Metal Cutting
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S. Mukhopadhyay
ORS system cont’d…
▪ Orthogonal rake (𝜸𝒐): Angle of inclination of rake
surface from reference plane, measured on orthogonal
plane 𝜋o.
▪ Inclination angle (𝝀): Angle of inclination of principal
cutting edge from reference plane 𝜋R , measured on
𝜋C.
▪ Orthogonal clearance (𝜶𝐎): Angle of inclination of
principal flank from 𝜋C, measured on 𝜋o.
▪ Auxiliary orthogonal clearance (𝜶𝐎′ ): Angle of
inclination of auxiliary flank from auxiliary cutting plane
𝜋C′ , measured on auxiliary orthogonal plane 𝜋O
′ .
Metal Cutting
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ORS system cont’d…
S. Mukhopadhyay
▪ Principal cutting edge angle (𝛗): Angle between 𝜋C and
the direction of longitudinal feed, measured on 𝜋R.
▪ Auxiliary cutting edge angle (𝛗𝟏): Angle between 𝜋C′
(𝜋C equivalent of auxiliary cutting edge, shown in
figure) and the direction of longitudinal feed ,
measured on 𝜋R.
▪ Nose radius (r): Radius of the tool tip (mm).
Tool signature in ORS
𝜆 − 𝛾o − 𝛼o − 𝛼o′ − φ1 − φ − 𝑟
Metal Cutting
S. Mukhopadhyay
Normal rake system (NRS) 13
ORS does not reveal the true rake angle when 𝜆 ≠ 0. Hence the Normal rake system
(NRS) is introduced which brings out the true geometrical features of the cutting tool.
Cutting plane 𝜋C is common between ORS and NRS.
Here the new plane definitions are:
▪ Normal plane (𝝅𝐍): Plane perpendicular to the principal cutting edge, hence
rotated from orthogonal plane by inclination angle 𝜆.
▪ Normal reference plane (𝝅𝐑𝐍): This is perpendicular to both 𝜋C and 𝜋N.
The planes of reference are 𝜋C − 𝜋N − 𝜋RN and coordinates system Xn − Yn − Zn
Metal Cutting
NRS system cont’d…
S. Mukhopadhyay
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▪ Normal rake (𝜸𝒏): Angle of inclination of rake surface
from reference plane 𝜋R, measured on normal plane
𝜋N.
▪ Normal clearance angle (𝜶𝒏): Angle of inclination of
the principal cutting edge from 𝜋C, measured on 𝜋N.
▪ Auxiliary normal clearance (𝜶𝒏′ ): Angle of inclination of
the auxiliary cutting edge from 𝜋C′ , measured on 𝜋N
′
(plane perpendicular to auxiliary cutting edge).
▪ The angles φ, φ1 and 𝑟 are same in ORS and NRS.
Chattopadhyay, Machining and Machine tools
Tool signature in NRS
𝜆 − 𝛾n − 𝛼n − 𝛼n′ − φ1 − φ − 𝑟
Metal Cutting
Concept of Work Reference System (WRS)
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The ratio of feed velocity 𝑉fd to cutting velocity 𝑉c :
Normally, →
𝑉fd𝑉C
=𝑠ON
𝜋𝐷N𝑠O ≪ 𝜋𝐷 𝑉fd ≪ 𝑉C
A number of tool angles are defined based on 𝜋R, which is
based on (⊥ to) 𝑉C.
Normally 𝑉fd is ignored, but there are cases (e.g. thread
cutting in lathe, drilling) where 𝑉fd is significant with
respect to 𝑉C.
In the above cases, 𝜋R is defined not in terms of 𝑉C , but
in terms of resultant velocity 𝑉R of 𝑉C and 𝑉fd, otherwise
significant errors creep into the effective values of tool
angles under cutting condition. This system of reference is
knows as Work reference system (WRS). Chattopadhyay, Machining and Machine tools
Metal Cutting
