Metal

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Metal Machining
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• Objectives
• Introduce cutting terminology and principles
• Review modern machining technologies and new
  methods (papers)
• Introduce cutting parameters
• Develop cutting models
• Analyze a cutting example

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• Machining types
• Turning
• Drilling
• Milling
• Shaping
• Planing
• Broaching

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• Machining tools
• Single point
• Multiple point

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Machining tool materials Most modern cutting
tool materials are a matrix of materials designed
to be very hard. These materials will be covered
in the next chapter.
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Machining surface finish
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Machining terminology Speed surface cutting
speed (v) Feed advance of tool through the part
(f) Depth of cut depth of tool into part
(d) Rake face tools leading edge Rake angle
slant angle of tools
leading edge (a) Flank following edge of
cutting tool Relief angle angle of tools
following edge above part surface
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Machining terminology (cont.) Chip
thickness thickness of machined chip (tc
) Depth of cut to Shear plane length
measured along shear plane chip (ls ) Chip width
(not shown) width of machined chip (w ) Shear
angle angle of shearing surface measured from
tool direction (f)
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Cutting conditions Note - Primary cutting due to
speed - Lateral motion of tool is feed - Tool
penetration is depth of cut The three together
form the material removal rate (MRR) MRR v f
d with units of (in/min)(in/rev)(in)
in3/min/rev (or vol/min-rev) Types of
cuts Roughing feeds of 0.015 0.05
in/rev depths of 0.1 0.75 in
Finishing feeds of 0.005 0.015 in/rev depths
of 0.03 0.075 in
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Cutting geometry
Obviously, the assumed failure mode is shearing
of the work along the shear plane.
Chip thickness ratio r to / tc From the
shear plane geometry r ls sinf/ls cos(f -
a) which can be arranged to get tan f r
cos a /1 r sin a
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Cutting geometry
Note from the triangles in (c) that the shear
strain (g) can be estimated as g AC/BD (DC
AD)/BD tan(f - a) cot f
Thus, if know r and a, can determine f, and given
f and a, can determine g.
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Cutting forces
Since R R R, we can get the force balance
equations F Fc sin a Ft cos a F friction
force N normal to chip force N Fc cos a -
Ft sin a Fc cutting force Ft thrust
force Fs Fc cos f - Ft sin f Fs shear force
Fn normal to shear plane force Fn Fc sin f
Ft cos f
Forces are presented as function of Fc and Ft
because these can be measured.
Friction angle b tan b m F/N Shear
plane stress t Fs/As where As to
w/sin f
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Cutting forces given shear strength
Letting S shear strength, we can derive the
following equations for the cutting and thrust
forces Fs S As Fc Fs cos ( b - a)/cos (
f b - a) Ft Fs sin ( b - a)/cos ( f b -
a) The other forces can be determined from
the equations on the previous slide.
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Merchant equations
Combining the equations from the previous
slides t (Fc cos f - Ft sin f)/(tow/sin f
) Merchant eqn The most likely shear angle will
minimize the energy. Applying dt/df 0 gives f
45 a/2 - b/2 Merchant reln What does the
Merchant relation indicate?
The Merchant reln is a function of a and b. Where
did these variables come from? Answer -
Although the Merchant eqn is not shown as a
direct function of a and b, these enter from the
equations for Fc and Ft from the previous slide!
If we increase the shear angle, we decrease the
tool force and power requirements!

• increase in friction angle decreases shear angle
• increase in rake angle increases shear angle

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Cutting models The orthogonal model for turning
approximates the complex shearing process
to feed (f) w depth of cut (d)
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Cutting power
Power is force times speed P Fc
v (ft-lb/min) The cutting horsepower is hpc Fc
v/33,000 (hp) The unit horsepower is hpu
hpc/MRR units? Due to efficiency losses (E about
90), the gross hp is hpg hpc/E
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Cutting energy
Specific energy is U Fc v/(v tow) Fc /(tow)
(in-lb/in3) The table shown contains power and
specific energy ratings for several work
materials at a chip thickness of 0.01 in. For
other chip thicknesses, apply the figure to get a
correction factor multiply U by correction
factor for thickness different than 0.01).
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Machining example
In orthogonal machining the tool has rake angle
10, chip thickness before cut is to 0.02 in,
and chip thickness after cut is tc 0.045 in.
The cutting and thrust forces are measured at Fc
350 lb and Ft 285 lb while at a cutting speed
of 200 ft/min. Determine the machining shear
strain, shear stress, and cutting
horsepower. Solution (shear strain) Determine r
0.02/0.045 0.444 Determine shear plane angle
from tan f r cos a /1 r sin a tan f
0.444 cos 10 /1 0.444 sin 10 gt f 25.4 Now
calculate shear strain from g tan(f - a) cot
f g tan(25.4 - 10) cot 25.4 2.386
in/in answer!
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Machining example (cont.)
In orthogonal machining the tool has rake angle
10, chip thickness before cut is to 0.02 in,
and chip thickness after cut is tc 0.045 in.
The cutting and thrust forces are measured at Fc
350 lb and Ft 285 lb while at a cutting speed
of 200 ft/min. Determine the machining shear
strain, shear stress, and cutting
horsepower. Solution (shear stress) Determine
shear force from Fs Fc cos f - Ft sin f Fs
350 cos 25.4 - 285 sin 25.4 194 lb Determine
shear plane area from As to w/sin f As
(0.02) (0.125)/sin 25.4 0.00583 in2 The shear
stress is t
194/0.00583 33,276 lb/in2 answer!
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Machining example (cont.)
In orthogonal machining the tool has rake angle
10, chip thickness before cut is to 0.02 in,
and chip thickness after cut is tc 0.045 in.
The cutting and thrust forces are measured at Fc
350 lb and Ft 285 lb while at a cutting speed
of 200 ft/min. Determine the machining shear
strain, shear stress, and cutting
horsepower. Solution (cutting
horsepower) Determine cutting hp from hpc Fc
v/33,000 hpc (350) (200)/33,000 2.12
hp answer!
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Cutting temperatures
In machining 98 of the cutting energy is
converted into heat. This energy flows into the
work part, chip, and tool. Cook determined an
experimental equation for predicting the
temperature rise at the tool-chip interface
during machining DT 0.4 U (v
to/K)0.333/(rc) where DT mean temperature rise
(F) U specific energy (in-lb/in3) v
cutting speed (in/s) to chip thickness before
cut (in) rc volumetric specific heat of the
work material (in-lb/(in3-F)) K thermal
diffusivity of the work material (in2/s) Note -
To get total temperature at tool-chip interface,
must add in ambient
temperature!
Example in text calculates DT 936 total tool
temperature, given v 200 ft/min, rc 120
in-lb/(in3- F) and K 0.125 in2/s
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Cutters
Toroid
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Cutters
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Machining
What did we learn?