Mechanics of metal cutting
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Transcript of Mechanics of metal cutting
Topics to be covered
Inroduction to Machining Technology Cutting Models Turning Forces Merchants Circle Power & Energies
Tool
Workpiece
Chip
Heat Generation Zones
(Dependent on sharpnessof tool)
(Dependent on )
(Dependent on
10%
30%
60%
Tool TerminologyTool Terminology
Side relief angle
Side cutting edge angle(SCEA)
Clearance or end relief angle
Back Rake(BR),+
Side Rake (SR), +
End Cuttingedge angle(ECEA)
Nose Radius
TurningCutting edge
FacingCutting edge
Material Removal RateMRR vfd
Roughing(R)
f 0.4 1.25mm / rev
d 2.5 20mm
Finishing(F)
f 0.125 0.4mm / rev
d 0.75 2.0mm
vR vF
Assumptions(Orthogonal Cutting Model)
The cutting edge is a straight line extending perpendicular to the direction of motion, and it generates a plane surface as the work moves past it.
The tool is perfectly sharp (no contact along the clearance face).
The shearing surface is a plane extending upward from the cutting edge.
The chip does not flow to either side The depth of cut/chip thickness is constant uniform
relative velocity between work and tool Continuous chip, no built-up-edge (BUE)
F t
FC
Fr
DIRECTION OF ROTATION
WORKPIECE
CUTTING TOOL
DIRECTION OF FEED
Velocity of Tool relative to workpiece V
Longitudinal 'Thrust' Force (27%)
Radial Force (6%)
Tangential 'Cutting' Force (67%)
‘Turning’ Forces For Orthogonal Model
End view section 'A'-'A'Note: For the 2D Orthogonal Mechanistic Model we will ignore the radial component
Ft
'A' 'A'
cF
FL
FC
Fr
DIRECTION OF ROTATION
WORKPIECE
CUTTING TOOL
DIRECTION OF FEED
Velocity of Tool relative to workpiece V
Longitudinal Force
Radial Force ‘Thrust’ Force
Tangential Force 'Cutting' Force
‘Facing’ Forces For Orthogonal Model
End view
Note: For the 2D Orthogonal Mechanistic Model we will ignore the Longitudinal component
'Turning' Terminology
N is the speed in rpmD is the diameter of the
workpiecef is the feed (linear
distance/rev)d is the depth of cutV is the surface speed
= DN
Standard Terms
Beware, for turning: In the generalized orthogonal model depth of cut (to) is f (the feed), and width of cut (w) is d (the depth of cut)
N
D
d mm
feed (mm/rev)
Tool
Workpiece
rpm
Orthogonal Cutting Model (Simple 2D mechanistic model)
Mechanism: Chips produced by the shearing process along the shear plane
t 0
+
Rake Angle
Chip
Workpiece
Clearance AngleShear Angle
t c
depth of cut
Chip thickness
Tool
Velocity V
tool
tool
Cutting Ratio(or chip thicknes ratio)
As Sin =to
ABand Cos-) =
tc
AB
Chip thickness ratio (r) =t0
tc=
sincos( )
tc
to
A
B
Chip
Workpiece
Experimental Determination ofCutting Ratio
Shear angle may be obtained either from photo-micrographs or assume volume continuity (no chip density change):
Since t0w 0L0 = tcw cLc and w 0=w c (exp. evidence)
Cutting ratio , r = t 0tc
= L cL0
i.e. Measure length of chips (easier than thickness)
w
tL
0
0
0
wc
Lc
ct
Shear Plane Length
and Angle
Shear plane length AB =t0
sinShear plane angle () = Tan
-1 rcos1-rsin
or make an assumption, such as adjusts to minimize cutting force: = 45
0+ /2 - /2 (Merchant)
t c
to
A
B
Chip
tool
Workpiece
Velocities(2D Orthogonal
Model)
Velocity Diagram
From mass continuity: Vto = V ctc
From the Velocity diagram:
V s = Vcos
cos( )
V c = Vr and V c = Vsin
cos( )
(Chip relative to workpiece)
V = Chip Velocity (Chip relative to tool)
Tool
Workpiece
Chip
Vs V = Cutting Velocity
(Tool relative to workpiece)
Shear Velocity
c
Vs
Vc
V
Cutting Forces(2D Orthogonal Cutting)
Free Body Diagram
Generally we know:Tool geometry & typeWorkpiece material
and we wish to know:F = Cutting ForceF = Thrust ForceF = Friction ForceN = Normal ForceF = Shear ForceF = Force Normal
to Shear
c
t
s
n
Tool
Workpiece
Chip
Dynamometer
R
R
R
R
FcFt
sF
FnN
F
Results fromForce Circle Diagram
(Merchant's Circle)
Friction Force F = Fcsin + Ftcos
Normal Force N = Fccos - Ftsin
Shear Force Fs = Fccos - Ftsin
= F/N and = tan typically 0.5 - 2.0)
Force Normal to Shear plane Fn = Fcsin + Ftcos
Forces on the Cutting Tool
and the workpiece
Importance: Stiffness of tool holder, stiffness of machine, and stiffness of workpiece must be sufficient to avoid significant deflections (dimensional accuracy and surface finish)
Primary cause: Friction force of chip up rake face + Shearing force along shear plane
Cutting speed does not effect tool forces much (friction forces decrease slightly as velocity increases; static friction is the greatest)
The greater the depth of cut the greater the forces on the tool Using a coolant reduces the forces slightly but greatly
increases tool life
Stresses On the Shear plane:
Normal Stress = s = Normal Force / Area =Fn
AB w=
Fnsintow
Shear Stress = s = Shear Force / Area =Fs
AB w=
Fssintow
On the tool rake face: = Normal Force / Area = N
tc w(often assume tc = contact length)
= Shear Force / Area = Ftc w
Note: s = y = yield strength of the material in shear
Power
•Power (or energy consumed per unit time) is the product of force and velocity. Power at the cutting spindle:
•Power is dissipated mainly in the shear zone and on the rake face:
•Actual Motor Power requirements will depend on machine efficiency E (%):
Cutting Power Pc = FcV
Power for Shearing Ps = FsVs
Friction Power Pf = FVc
Motor Power Required =Pc
Ex 100
Material Removal Rate (MRR)
Material Removal Rate (MRR) = Volume RemovedTime
Volume Removed = Lwto
Time to move a distance L = L/V
Therefore, MRR =Lwto
L/V= Vwto
MRR = Cutting velocity x width of cut x depth of cut
Specific Cutting Energy(or Unit Power)
Energy required to remove a unit volume of material (often quoted as a function of workpiece material, tool and process:
Ut = EnergyVolume Removed
= Energy per unit timeVolume Removed per unit time
Specific Energy for shearing Us =FsVs
Vwto
Specific Energy for friction Uf =FVc
Vwto= Fr
wto
Ut =Cutting Power (Pc)
Material Removal Rate (MRR)=
FcVVwto
=Fc
wto
Specific Cutting EnergyDecomposition
1. Shear Energy/unit volume (Us)(required for deformation in shear zone)
2. Friction Energy/unit volume (Uf)(expended as chip slides along rake face)
3. Chip curl energy/unit volume (Uc)(expended in curling the chip)
4. Kinetic Energy/unit volume (Um)(required to accelerate chip)
Ut = Us + Uf +Uc +Um
Specific Cutting EnergyRelationship to Shear strength of Material
SHEAR ENERGY / UNIT VOLUME Specific Energy for shearing Us =
FsVs
Vwto
FRICTION ENERGY / UNIT VOLUME
Specific Energy for friction Uf =FVc
Vwto= Fr
wto= F
wtc=
APPROXIMATE TOTAL SPECIFIC CUTTING ENERGY
Ut = Us + Uf = s+ y1+)
U s =scos
sin cos( )= s.
Typical Orthogonal Model Violations
• Geometry and form Violations (i.e. non zero angles of inclination, not sharp - radiused end)
• Shear takes place over a volume (not a line or plane)
• Cutting is never a purely continuous process (cracks develop in chip; material not homogeneous)
• 'Size Effect' - larger stresses are required to produce deformation when the chip thickness is small (statistical probability of imperfection in the shear zone)
• BUE - some workpiece material 'welds' to the tool face (cyclic in nature)