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LECTURE-08THEORY OF METAL CUTTING
- Theory of Chip Formation
NIKHIL R. DHAR, Ph. D.DEPARTMENT OF INDUSTRIAL & PRODUCTION
ENGINEERINGBUET
22/2Department of Industrial & Production Engineering
Chip Formation
Every Machining operation involves the formation of chips. The nature of which differs from operation to operation, properties of work piece material and the cutting condition. Chips are formed due to cutting tool, which is harder and more wearer-resistant than the work piece and the force and power to overcome the resistance of work material. The chip is formed by the deformation of the metal lying ahead of the cutting edge by a process of shear. Four main categories of chips are:
Discontinuous ChipsContinuous or Ribbon Type ChipsContinuous Chip Built-up-Edge (BUE)Serrated Chips
22/3Department of Industrial & Production Engineering
Types of Chips
Discontinuous Chips: These chips are small segments, which adhere loosely to each other. They are formed when the amount of deformation to which chips undergo is limited by repeated fracturing. Hard and brittle materials like bronze, brass and cast iron will produce such chips.
Continuous or Ribbon Type Chips: In continuous chip formation, the pressure of the work piece builds until the material fails by slip along the plane. The inside on the chip displays steps produced by the intermittent slip, but the outside is very smooth. It has its elements bonded together in the form of long coils and is formed by the continuous plastic deformation of material without fracture ahead of the cutting edge of the tool and is followed by the smooth flow of chip up the tool face.
22/4Department of Industrial & Production Engineering
Continuous Chip Built Up Edge: This type of chip is very similar to that of continuous type, with the difference that it is not as smooth as the previous one. This type of chip is associated with poor surface finish, but protects the cutting edge from wear due to movement of chips and the action of heat causing the increase in tool life.
Serrated Chips: These chips are semicontinuous in the sense that they possess a saw-tooth appearance that is produced by a cyclical chip formation of alternating high shear strain followed by low shear strain. This chip is most closely associated with certain difficult-to-machine metals such as titanium alloys, nickel-base superalloys, and austenitic stainless steels when they are machined at higher cutting speeds. However, the phenomenon is also found with more common work metals (e.g., steels), when they are cut at high speeds.
22/5Department of Industrial & Production Engineering
Actual Chip Forms and Classifications
C-type and ε-type broken chips
Short helical broken chips
Medium helical broken chips
Long helical broken chips
Long helical unbroken chips
Long and snarled unbroken chips
Desired
Not Desired
22/6Department of Industrial & Production Engineering
Chip Formation in Metal Machining
Since the practical machining is complex we use orthogonal cutting model to explain the mechanics.In this model we used wedge shaped tool. As the tool forced into the material the chip is formed by shear deformation.
Rake angle (γ)
ToolWorkpiece
Chip
Roughsurface
Shinysurface
Uncut chipThicknessa1=So sin φ
Chip Thickness
(a2)
Shear Angle
(β)
Clearance angle (α)
Shear plane
Rakesurface
Flanksurface
Negative rake
Positive rake
22/7Department of Industrial & Production Engineering
Deformation of Uncut Layer
The problem in the study of the mechanism of chip formation is the deformation process of the chip ahead of the cutting tool. It is difficult to apply equation of plasticity as the deformations in metal cutting are very large. Experimental techniques have always been resorted to for analyzing the deformation process of chips. Several methods have been used:
Taking photographs of the side surface of the chip with a high speed movie camera fitted with microscope.
Observing the grid deformation (directly) on the side surface of the work piece and on the inner surface of a compound work piece.
Examination of frozen chip samples taken by drop tool apparatus and quick stop apparatus,
22/8Department of Industrial & Production Engineering
Grid Deformation Methods
The type of stress-state conditions is evaluated by means of an angle index e obtainable from Levy-Lode’s theorem,
-[1]-----otan30e)o(30tan
2e1e32e2e1e
where,e = deformation criteria
= 00 for pure tension= 300 for pure shear= 600 for pure compression
ro = radius of circles marked on the workpiece r1 & r2 = semi-axes of the ellipse after deformation.
-[2]---o3e2e1e andor2rln2e ,
or1rln1e
ToolWorkpiece
Chip
ro
r2
r1
Schematic representation of the translocation of circles into ellipses during chip formation.
22/9Department of Industrial & Production Engineering
From Equation [1] and Equation [2]
]3[
2r1r
ln
3
2or
2r
1r
ln otan30e)otan(30
Case-1: For Pure Tension [e=0]
-[5]--- ε)(1 )4
2ε2ε2.(1
2
0r2r and
2ε1
0r2r ε,1
or1r
[4] ----------με)(1or2r and ε)(1or 1r
Where, ε = cutting strengthμ = frictional coefficient=½
since ε is very very small so neglecting ε2
22/10Department of Industrial & Production Engineering
Now, from equation [5]
[6]-----1ε)(1ε)(12
0r
22r1r
2
0r2r
0r1r
From Equation [3] and Equation [6]
Tension Purefor o0e or,
0tan30e)0 tan(30or,
-[7]---1
2r1rln
2r1r.
60r
42r
21rln
)2r1rln(
3)2
0r2r1rln(
0tan30
e)0tan(30
22/11Department of Industrial & Production Engineering
Case-2: For Pure Shear [e=300]
-[9]--- 1 ε)2
3(1 ε)
2
3(1
0r2r
0r1r and ε
231
0r2r ε,
2
31
or1r
[8] ----------με)-ε-(1or2r and με)ε(1or 1r
From Equation [3] and Equation [9]
Tension Purefor o30e or,
tan(0)0e)0 tan(30or,
[10]-----0
2r1rln
31ln
2r1rln
3
20r
2r1rln
0tan30
e)0tan(30
22/12Department of Industrial & Production Engineering
Case-3: For Pure Compression [e=60o]
]13[---------1ε-1 ε1or2r
2
or1r
-[12]--- ε)(1 )4
2ε2ε2.(1
2
0r1r and ε1
0r2r ,
2ε1
or1r
[11] ----------ε)(1or2r and με)(1or 1r
From Equation [3] and Equation [13]
nCompressio Purefor 60e or,
)30tan(tan30e) tan(30or, 1
rr
ln
rr
r
rrln
tan30
e)tan(30
o
000
2
1
1
2
2
30
22
1
0
0
22/13Department of Industrial & Production Engineering
Chip Reduction Coefficient (ξ)
Chip reduction coefficient (ξ) is defined as the ratio of chip thickness (a2) to the uncut chip thickness (a1). This factor, ξ, is an index of the degree of deformation involved in chip formation process during which the thickness of layer increases and the length shrinks. In the USA, the inverse of ξ is denoted by rc and is known as cutting ratio. The following Figure shows the formation of flat chips under orthogonal cutting conditions. From the geometry of the following Figure.
γo
β
ToolWorkpiece
O
AB
C
a1
a2
Chip
]1[sinβ
sinγsinβcosγcosβ
sinβOA
)γcos(βOA
AB
AC
a
aξ 000
1
2
22/14Department of Industrial & Production Engineering
Shear Angle (β)
From Equation [1]
angleShear o
sinγξo
cosγ1tanβ
osinγξ
0cosγ
tanβ
0sinγ
tanβ0
cosγ
sinβ0
sinγsinβ0
cosγcosβξ
22/15Department of Industrial & Production Engineering
Condition for maximum chip reduction coefficient (ξ) from Equation [1]
angleShear 0
γ2
π
2
1β
2
πcosβ)
0γcos(β
2
πcos0sinβ)
0γsin(βcosβ)
0γcos(β
0β2sin
)cosβ0
γcos(β)0
γsin(βsinβ
0sinβ
)0
γcos(β
dβ
dor 0
dβ
dξ
22/16Department of Industrial & Production Engineering
Velocity Relationships
The following Figure shows the velocity relation in metal cutting. As the tool advances, the metal gets cut and chip is formed. The chip glides over the rake surface of the tool. With the advancement of the tool, the shear plane also moves. There are three velocities of interest in the cutting process which include:
γo
β
ToolWorkpiece
ChipVs
Vf
Vc
γo
β
Vc
Vf
Vs
90o -γo
90o -β+γo
γo -β
VC = velocity of the tool
relative to the workpiece. It is called cutting velocity
Vf = velocity of the chip
(over the tool rake) relative to the tool. It is called chip flow velocity
Vs= velocity of
displacement of formation of the newly cut chip elements, relative to the workpiece along the shear plane. It is called velocity of shear
22/17Department of Industrial & Production Engineering
According to principles of kinematics, these three velocities, i.e. their vectors must form a closed velocity diagram. The vector sum of the cutting velocity, Vc, and the chip velocity, Vf, is equal to the shear velocity, Vs. Thus,
fV
cV
sV
sinβf
V
oγ(βo90sin
cV
)o
γosin(90
sV
ξV
V or,
ξc
V
)o
γcos(β
sinβc
V
)o
γ(β090sin
sinβc
Vf
V
f
c
γo
β
Vc
Vf
Vs
90o -γo
90o -β+γo
γo -β
22/18Department of Industrial & Production Engineering
Kronenberg derived an interesting relation for chip reduction coefficient (ξ) which is of considerable physical significance. Considering the motion of any chip particle as shown in the following Figure to which principles of momentum change are applied:
dθμv
dv
dθv
dv
N
Fμ
dt
dθmvr2mωN
dt
dvmF
Vf
Vc
FN
γo
)γ2
π( 0
22/19Department of Industrial & Production Engineering
As the velocity changes from Vc to Vf, hence
0γ
2
πμ
eξ
0γ
2
πμ
ef
Vc
V
oγ
2
πμ
cV
fV
ln
fV
cV
πdθv
dv)γ-
2
π(
0
o
This equation demonstrates that the chip reduction coefficient and chip flow velocity is dependant on the frictional aspects at the interface as
well as the orthogonal rake angle (γ0). If γ0 is increased, chip reduction
coefficient decreases.
Vf
Vc
FN
γo
)γ2
π( 0
22/20Department of Industrial & Production Engineering
Shear Strain (ε)
The value of the shear strain (ε) is an indication of the amount of deformation that the metal undergoes during the process of chip formation. The shear strain that occurs along the shear plane can be estimated by examining the following Figure. The shear strain can be expressed as follows:
AMagnitude of strained material
CB
Plate thickness γo
A
B
C
D
β
β-γo
Shear strain during chip formation (a) chip formation depicted as a series of parallel sliding relative to each other (b) one of the plates isolated to illustrate the definition of shear strain based on this parallel plate model (c) shear strain triangle
-[1]-)o
γtan(ββcot BD
CD
BD
AD
BD
CDAD
BD
ACε
γo
β
ToolWorkpiece
Shear plane
Chip=parallel shear plates
acb
22/21Department of Industrial & Production Engineering
From equation [1]
strainShear βsin
cV
sV
ε
[3]equation and [2]equation From
[3])
oγ-(β coso
γcos
cV
sV
iprelationsh velocity From
[2])
oγ-(β cos β.sin
o γcos
)o
γtan(ββcot ε
22/22Department of Industrial & Production Engineering
Any questions or comments?