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Department of Mechanical Engineering, The Ohio State UniversitySl. #1
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Traditional Machining
Department of Mechanical Engineering, The Ohio State UniversitySl. #2
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Chip Formation (Traditional Machining)
In any traditional machining process, chips are formed by a shearing process
ShearPlane
ShearPlane
ShearPlane
Ref: Manufacturing Processes for Engineering Materials by S. Kalpakjian, Addison Wesley, 2nd Ed., 1991
Department of Mechanical Engineering, The Ohio State UniversitySl. #3
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Chip TypesContinuous Built Up Edge (BUE)
DiscontinuousSegmented
BUE
Ref: Manufacturing Processes for Engineering Materials Fig 8.4, p 478.
Department of Mechanical Engineering, The Ohio State UniversitySl. #4
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Tool GeometryThe shape and orientation of the cutting tool greatly affects the chip formation mechanics
θβ
α
2 1
3
tc
to
Rake Angle
Shear Angle
Clearance Angle
Department of Mechanical Engineering, The Ohio State UniversitySl. #5
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Rake Angle
Of particular importance is the rake angle that the tool makes with the workpiece normal
Positive Rake Neutral Rake Negative Rake
WorkpieceNormal
++
CutterVelocity
WorkpieceNormal
0
CutterVelocity
-
CutterVelocity
WorkpieceNormal
Department of Mechanical Engineering, The Ohio State UniversitySl. #7
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Cutting Parameters (Vertical Milling)Depth of Cut- measured along workpiece normalStep over Distance- (also called radial depth of cut)- Measured
in tangent plane of workpiece and perpendicular tocutter travel or workpiece feed
s is step over distanced is depth of cutf is feed direction of workpiece
s
wf
Department of Mechanical Engineering, The Ohio State UniversitySl. #8
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Feeds/SpeedsMilling Maching Cutting Speeds- Terminology of Machine Tools (Krar, Oswald) Table 61-1
High Speed Steel Cutter Carbide CutterMaterial sfm m/min sfm m/minMachine Steel 70-100 21-30 150-250 45-75Tool Steel 60-70 18-20 125-200 40-60Cast Iron 50-80 15-25 125-200 40-60Bronze 65-120 20-35 200-400 60-120Aluminum 500-1000 150-300 1000-2000 300-600
Recommended Feed per Tooth High Speed Steel Cutters- Terminology of Machine Tools (Krar, Oswald) Table 61-2 Helical Slotting & Form Circular
Face Mills Mills Side Mills End Mills Relieved SawsMaterial in. mm in. mm in. mm in. mm in. mm in. mmAluminum .022 .55 .018 .45 .013 .33 .011 .28 .007 .18 .005 .13Brass & bronze .014 .35 .011 .28 .008 .20 .007 .18 .004 .10 .003 .08 (medium) Cast iron .013 .33 .010 .25 .007 .18 .007 .18 .004 .10 .003 .08 (medium)Machine steel .012 .30 .010 .25 .007 .18 .006 .15 .004 .10 .003 .08Tool steel .010 .25 .008 .20 .006 .15 .005 .13 .003 .08 .003 .08 (medium) Stainless steel .006 .15 .005 .13 .004 .10 .003 .08 .002 .05 .002 .05
Department of Mechanical Engineering, The Ohio State UniversitySl. #9
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Feeds & SpeedsRecommended Feed per Tooth Cem. Carbide Tip Cutters- Terminology of Machine Tools (Krar, Oswald) Table 61-3
Helical Slotting & Form CircularFace Mills Mills Side Mills End Mills Relieved Saws
Material in. mm in. mm in. mm in. mm in. mm in. mmAluminum .020 .50 .016 .40 .012 .30 .010 .25 .006 .15 .005 .13Brass & bronze .012 .30 .010 .25 .007 .18 .006 .15 .004 .10 .003 .08 (medium) Cast iron .016 .40 .013 .33 .010 .25 .008 .20 .005 .13 .004 .10 (medium)Machine steel .016 .40 .013 .33 .009 .23 .008 .20 .005 .13 .004 .10Tool steel .014 .35 .011 .28 .008 .20 .007 .18 .004 .10 .004 .10 (medium) Stainless steel .010 .25 .008 .20 .006 .15 .005 .13 .003 .08 .003 .08
Lathe Feed & Speeds- Machine Tool Practices (Kibbe, et al) Table I-5Low-Carbon High Carbon Alloy Steel Aluminum
Material Steel Steel-anneal Normalized Alloys Cast Iron BronzeSpeed (sfm)
Roughing 90 50 45 200 70 100Finishing 120 65 60 300 80 130
Feed (ipr) Roughing .010-.020 .010-.020 .010-.020 .015-.030 .010-.020 .010-.020Finishing .003-.005 .003-.005 .003-.005 .005-.010 .003-.010 .003-.010
Ref: From Machinery’s Handbook 21st ed
Department of Mechanical Engineering, The Ohio State UniversitySl. #10
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Feeds & Speeds
"For ordinary twist drills (HSS- high speed steel) the feed rate used is... 0.001-0.003 in/rev for drills smaller than 1/8 in. (dia.); 0.002-0.006 in/rev for 1/8 to 1/4 in. dia. drills; 0.004-0.010 in/rev for 1/4 to 1/2 in. dia. drills; 0.007-0.015 in/rev for 1/2 to 1 in. dia. drills; and, 0.010-0.025 in/rev for drills larger than 1 inch. (dia)
The lower values in the feed ranges should be used for hard materials such as tool steels, superalloys, and work hardening stainless steels; the higher values in the feed ranges should be used to drill soft materials such as aluminum and brass."
Ref: From Machinery’s Handbook 21st ed
Cutting Speeds for Drilling (fpm)Material Cutting speed (fpm)Wrought Aluminum Alloys (Cold Drawn) 300
Free Cutting Brass (Cold Drawn) 175
Wrought Magnesium Alloys (Cold Drawn) 350
Mold Steels- P20 & P21 60
1040 Plain Carbon Steel (CD ,Hardness 175-225HB) 75
Department of Mechanical Engineering, The Ohio State UniversitySl. #11
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“Optimal” Feeds & Speeds
• In the “typical operating range”, tool life (T) and cutting speed (V) are related according to Taylor’s Equation VTn =C
where n & C are experimentally determined constants
• FW Taylor studied the effects of the feed, depth of cut, and cutting speed:
1) Cutting Speed is the dominating factor in determining tool life2) Feeds and Depths of Cut are the dominant forces in determining
the force acting on the tool
• Taylor recommended using the maximum allowable feed and depth of cut, then selecting V to balance tool wear with cycle time for the process
Department of Mechanical Engineering, The Ohio State UniversitySl. #12
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Cutting SpeedsCutting Rates- Often given speeds in SFM (surface feet/min), but control spindle rotation in RPM (rev/min).
( )
( ) ( ) ⎥⎦⎤
⎢⎣⎡ ∗=Ω∗=Ω
⎟⎠⎞
⎜⎝⎛∗⎟
⎠⎞
⎜⎝⎛∗
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡ ⎟⎠⎞⎜
⎝⎛
=Ω
Ω=
=
DV
DV
inD
ftV
V
DDRDR
v
Rv
4 as edapproximat sometimes 12
rad 2rev 1
ft 1in 12
)( 2
min
SFMin given minute,per sRevolutionin find To
diametercutter = 2 -inchesin & and
minuteper inchesin minute,per radiansin
π
π
ω
ω
Note: Use the maximum effective cutting diameter of tool
Formula for spindle RPM comes from basic kinematics v= x r
Department of Mechanical Engineering, The Ohio State UniversitySl. #13
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Cutting DiameterTo select the correct radius (or diameter) to use in the formula-- Determine what the spindle is rotating Find the perpendicular distance from the axis of rotation to the furthest point where cutting occurs Double it to get the diameter
Axis ofRevolution
CuttingEdge
d
Lathe- part turns(NOT tool) r is from center to tool if turning down- d is workpiece diameter
Flat Nosed End Mill d=cutter diameter
d
Axis ofRevolution
CuttingEdge
d
Axis
Ball Nosed End Mill if ball is not “buried” in workpiece, then d will be less than cutter diameter i.e. NO cutting occurs at full tool diameter
Department of Mechanical Engineering, The Ohio State UniversitySl. #14
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Feed RatesFeed Rates are commonly given as Advance Per Tooth (APT)To get the feed rate in surface inches per minute use:
f =Ω∗(APT)∗N ⎛ ⎝ ⎜ ⎞
⎠
f /is the feed rate in inches min Ω /is the cutter speed rev min N is the number of teeth on the cutter
More properly one wishes to control the chip load or nominal chip thickness tl. If the cutter is NOT fully loaded, one must increase the feed (APT) to keep the same chip load (tl).
Most tabulated values of the APT assume a fully loaded cutter- they are really listings of the required chip load tl.
Feeds on lathes and drills can be in ipr (inches per revolution): N is no longer required in formula: f =Ω∗(ipr)
Department of Mechanical Engineering, The Ohio State UniversitySl. #15
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Chip Load and Advance Per Tooth
Step over distance (radial depth of cut) at least 1/2 tool diameter chip load (t )= APT
Step over distance (radial depth of cut) less than 1/2 tool diameter chip load (t ) < APT
t l
APT
t l
APT
l l
Department of Mechanical Engineering, The Ohio State UniversitySl. #16
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Shallow Cuts with Ball Nosed End Mill
Decrease in Effective
Cutting DiameterDecrease in Chip Load
Notice how the chip load (tl) is less than the APT for a shallow cut
Rcut Rnom Rnom d= − −⎛⎝⎜
⎞⎠⎟
2 2
d
Rnom
Rcut
t l
APT
Rnom
Department of Mechanical Engineering, The Ohio State UniversitySl. #17
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RCTF- Ball Nose @ Small Depth of Cut
Ref: Figure O-51, Kibbe, et al. Machine Tool Practices 5th Ed, Prentice Hall,1995.
Nominal Tool Diameter0.375 0.5 0.625 0.75 1 1.25 1.5 2 2.5 3
Dia. (Effective Diameter at DOC) / RCTF (Radial Chip Thinning Factor)DOC Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF0.063 0.28 0.7 0.33 0.7 0.38 0.6 0.41 0.5 0.48 0.5 0.54 0.4 0.60 0.4 0.70 0.3 0.78 0.3 0.86 0.30.125 0.35 0.9 0.43 0.9 0.50 0.8 0.56 0.7 0.66 0.6 0.75 0.5 0.83 0.4 0.97 0.4 1.09 0.4 1.20 0.40.188 0.38 1.0 0.48 0.97 0.57 0.9 0.65 0.9 0.78 0.8 0.89 0.7 0.99 0.6 1.17 0.6 1.32 0.5 1.45 0.50.250 0.50 1.0 0.61 0.98 0.71 0.95 0.87 0.9 1.00 0.8 1.12 0.7 1.32 0.7 1.50 0.6 1.66 0.60.313 0.63 1.0 0.74 1.0 0.93 0.95 1.08 0.9 1.22 0.7 1.45 0.7 1.65 0.7 1.83 0.60.375 0.75 1.0 0.97 0.95 1.15 0.95 1.30 0.8 1.56 0.8 1.79 0.7 1.98 0.70.438 0.99 1.0 1.19 0.95 1.36 0.8 1.65 0.8 1.90 0.8 2.12 0.70.500 1.00 1.0 1.22 0.95 1.41 0.9 1.73 0.8 2.00 0.8 2.24 0.70.563 1.24 1.0 1.45 0.9 1.80 0.9 2.09 0.8 2.34 0.80.625 1.25 1.0 1.48 0.95 1.85 0.9 2.17 0.9 2.44 0.80.688 1.49 0.95 1.90 0.95 2.23 0.9 2.52 0.80.750 1.50 1.0 1.94 0.95 2.29 0.9 2.60 0.90.813 1.96 0.95 2.34 0.9 2.67 0.90.875 1.98 0.95 2.38 0.95 2.73 0.90.938 2.00 1.0 2.42 0.95 2.78 0.91.000 2.00 1.0 2.45 0.95 2.83 0.91.250 2.50 1.0 2.96 0.951.500 3.00 1.0
Department of Mechanical Engineering, The Ohio State UniversitySl. #18
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RCTF- Peripheral Milling w/ Flat Nose
.06
.05 .08
.10
.12
.14
.16
.18
.20
.25
.3
.4
.5
.6
.7
.8
.9.95
1.0
Ref: Figure O-49, Kibbe, et al. Machine Tool Practices 5th Ed, Prentice Hall,1995.
Department of Mechanical Engineering, The Ohio State UniversitySl. #19
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Feeds w/ Radial Chip Thinning FactorProper feeds come from finding the required advance per tooth (APT) to get correct chip load (feed value commonly given in books)
let
Radial Chip Thinning Factor
APTt
R
R
f APT N
l
CTF
CTF
=
== ∗ ∗
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
⎡
⎣⎢
⎤
⎦⎥Ω ( )
As we use it, the RCTF is a “first pass” improvement 1) RCTFs for FLAT end mill with small step over distance 2) RCTFs for BALL end mill with small depth of cut 3) Anything over tool radius is assumed to be fully loaded
In some cases tables incorporate RCTFs and give true APTBut usually what you look up in a table is really tl
Department of Mechanical Engineering, The Ohio State UniversitySl. #20
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Feeds/SpeedsMilling Maching Cutting Speeds- Terminology of Machine Tools (Krar, Oswald) Table 61-1
High Speed Steel Cutter Carbide CutterMaterial sfm m/min sfm m/minMachine Steel 70-100 21-30 150-250 45-75Tool Steel 60-70 18-20 125-200 40-60Cast Iron 50-80 15-25 125-200 40-60Bronze 65-120 20-35 200-400 60-120Aluminum 500-1000 150-300 1000-2000 300-600
Recommended Feed per Tooth High Speed Steel Cutters- Terminology of Machine Tools (Krar, Oswald) Table 61-2 Helical Slotting & Form Circular
Face Mills Mills Side Mills End Mills Relieved SawsMaterial in. mm in. mm in. mm in. mm in. mm in. mmAluminum .022 .55 .018 .45 .013 .33 .011 .28 .007 .18 .005 .13Brass & bronze .014 .35 .011 .28 .008 .20 .007 .18 .004 .10 .003 .08 (medium) Cast iron .013 .33 .010 .25 .007 .18 .007 .18 .004 .10 .003 .08 (medium)Machine steel .012 .30 .010 .25 .007 .18 .006 .15 .004 .10 .003 .08Tool steel .010 .25 .008 .20 .006 .15 .005 .13 .003 .08 .003 .08 (medium) Stainless steel .006 .15 .005 .13 .004 .10 .003 .08 .002 .05 .002 .05
Department of Mechanical Engineering, The Ohio State UniversitySl. #21
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Feeds & Speeds - Example 1
Estimate the cutting speed and feed rate required for a 3/4” diameter 2 flute HSS end mill in Cast Iron, with a depth of cut of 0.375” and a step over distance of 0.375.”
The spindle rotational speed is given by:
Ω=V D
⎛
⎝ ⎜
⎞
⎠ ⎟ ∗12π
⎛ ⎝ ⎜
⎞ ⎠ ⎟ =50
0.75⎛ ⎝ ⎜
⎞ ⎠ ⎟ ∗12π
⎛ ⎝ ⎜
⎞ ⎠ ⎟ =250 RPM
The machine feed rate is given by:
f =Ω∗(APT)∗N( )=250∗0.007( )∗2[ ]=1.75 ipm
Department of Mechanical Engineering, The Ohio State UniversitySl. #22
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Feeds & Speeds - Example 2
Estimate the depth of cut, the cutting speed, and feed rate required when rough turning a bronze shaft, from a diameter of 2.000” to 1.800.”
Depth of cut =12*(DO −Di )=12*(2.000−1.800)=0.100"
Refer to tables to get recommended speed and feed.
Department of Mechanical Engineering, The Ohio State UniversitySl. #23
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Feeds/Speeds for Example 2
Lathe Feed & Speeds- Machine Tool Practices (Kibbe, et al) Table I-5Low-Carbon High Carbon Alloy Steel Aluminum
Material Steel Steel-anneal Normalized Alloys Cast Iron BronzeSpeed (sfm)
Roughing 90 50 45 200 70 100Finishing 120 65 60 300 80 130
Feed (ipr) Roughing .010-.020 .010-.020 .010-.020 .015-.030 .010-.020 .010-.020Finishing .003-.005 .003-.005 .003-.005 .005-.010 .003-.010 .003-.010
Department of Mechanical Engineering, The Ohio State UniversitySl. #24
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Feeds & Speeds - Example 2 (Cont’d)Estimate the depth of cut, the cutting speed, and feed rate required when rough turning a bronze shaft, from a diameter of 2.000” to 1.800.”
Depth of cut =12*(DO −Di )=12*(2.000−1.800)=0.100"
Recommended rates- cutting=100 sfm, feed=0.010 ipr
The recommended speed is
Ω=V D
⎛
⎝ ⎜
⎞
⎠ ⎟ ∗12π
⎛ ⎝ ⎜
⎞ ⎠ ⎟ =100∗12
2∗π⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥ =190 RPM
The recommended feed is
f =Ω∗(APT)=190*(0.010)=1.9 ipm
Department of Mechanical Engineering, The Ohio State UniversitySl. #25
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Feeds & Speeds - Example 3Estimate the cutting speed and feed rate required for a 1/2” diameter HSS 2 flute ball nose end mill in “medium” tool steel, with a depth of cut of 0.0625” and a step over distance of 0.250.”
The ball end mill depth of cut is less than the radius. Therefore the effective diameter must be computed:
D=2* Rnom2 −Rnom−d( )2
=2∗ 0.5002
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2−0.500
2 −0.0625⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2=0.33 in
Find speeds and feeds from table.
Department of Mechanical Engineering, The Ohio State UniversitySl. #26
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Feeds/Speeds for Example 3Milling Maching Cutting Speeds- Terminology of Machine Tools (Krar, Oswald) Table 61-1
High Speed Steel Cutter Carbide CutterMaterial sfm m/min sfm m/minMachine Steel 70-100 21-30 150-250 45-75Tool Steel 60-70 18-20 125-200 40-60Cast Iron 50-80 15-25 125-200 40-60Bronze 65-120 20-35 200-400 60-120Aluminum 500-1000 150-300 1000-2000 300-600
Recommended Feed per Tooth High Speed Steel Cutters- Terminology of Machine Tools (Krar, Oswald) Table 61-2 Helical Slotting & Form Circular
Face Mills Mills Side Mills End Mills Relieved SawsMaterial in. mm in. mm in. mm in. mm in. mm in. mmAluminum .022 .55 .018 .45 .013 .33 .011 .28 .007 .18 .005 .13Brass & bronze .014 .35 .011 .28 .008 .20 .007 .18 .004 .10 .003 .08 (medium) Cast iron .013 .33 .010 .25 .007 .18 .007 .18 .004 .10 .003 .08 (medium)Machine steel .012 .30 .010 .25 .007 .18 .006 .15 .004 .10 .003 .08Tool steel .010 .25 .008 .20 .006 .15 .005 .13 .003 .08 .003 .08 (medium) Stainless steel .006 .15 .005 .13 .004 .10 .003 .08 .002 .05 .002 .05
Department of Mechanical Engineering, The Ohio State UniversitySl. #27
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Feeds & Speeds - Example 3 (Cont’d)Estimate the cutting speed and feed rate required for a 1/2” diameter HSS 2 flute ball nose end mill in “medium” tool steel, with a depth of cut of 0.0625” and a step over distance of 0.250.”
Ω=V D
⎛
⎝ ⎜
⎞
⎠ ⎟ ∗12π
⎛ ⎝ ⎜
⎞ ⎠ ⎟ =60
0.33⎛ ⎝ ⎜
⎞ ⎠ ⎟ ∗12π
⎛ ⎝ ⎜
⎞ ⎠ ⎟ =690 RPM
The recommended speed is:
Find the chip reduction factor from table.
D=0.33 inV =60 sfmand APT=0.005in
Department of Mechanical Engineering, The Ohio State UniversitySl. #28
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RCTF- Ball Nose @ Small Depth of Cut for Ex 3
Ref: Figure O-51, Kibbe, et al. Machine Tool Practices 5th Ed, Prentice Hall,1995.
Nominal Tool Diameter0.375 0.5 0.625 0.75 1 1.25 1.5 2 2.5 3
Dia. (Effective Diameter at DOC) / RCTF (Radial Chip Thinning Factor)DOC Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF Dia. RCTF0.063 0.28 0.7 0.33 0.7 0.38 0.6 0.41 0.5 0.48 0.5 0.54 0.4 0.60 0.4 0.70 0.3 0.78 0.3 0.86 0.30.125 0.35 0.9 0.43 0.9 0.50 0.8 0.56 0.7 0.66 0.6 0.75 0.5 0.83 0.4 0.97 0.4 1.09 0.4 1.20 0.40.188 0.38 1.0 0.48 0.97 0.57 0.9 0.65 0.9 0.78 0.8 0.89 0.7 0.99 0.6 1.17 0.6 1.32 0.5 1.45 0.50.250 0.50 1.0 0.61 0.98 0.71 0.95 0.87 0.9 1.00 0.8 1.12 0.7 1.32 0.7 1.50 0.6 1.66 0.60.313 0.63 1.0 0.74 1.0 0.93 0.95 1.08 0.9 1.22 0.7 1.45 0.7 1.65 0.7 1.83 0.60.375 0.75 1.0 0.97 0.95 1.15 0.95 1.30 0.8 1.56 0.8 1.79 0.7 1.98 0.70.438 0.99 1.0 1.19 0.95 1.36 0.8 1.65 0.8 1.90 0.8 2.12 0.70.500 1.00 1.0 1.22 0.95 1.41 0.9 1.73 0.8 2.00 0.8 2.24 0.70.563 1.24 1.0 1.45 0.9 1.80 0.9 2.09 0.8 2.34 0.80.625 1.25 1.0 1.48 0.95 1.85 0.9 2.17 0.9 2.44 0.80.688 1.49 0.95 1.90 0.95 2.23 0.9 2.52 0.80.750 1.50 1.0 1.94 0.95 2.29 0.9 2.60 0.90.813 1.96 0.95 2.34 0.9 2.67 0.90.875 1.98 0.95 2.38 0.95 2.73 0.90.938 2.00 1.0 2.42 0.95 2.78 0.91.000 2.00 1.0 2.45 0.95 2.83 0.91.250 2.50 1.0 2.96 0.951.500 3.00 1.0
Department of Mechanical Engineering, The Ohio State UniversitySl. #29
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Feeds & Speeds - Example 3 (Cont’d)Estimate the cutting speed and feed rate required for a 1/2” diameter HSS 2 flute ball nose end mill in “medium” tool steel, with a depth of cut of 0.0625” and a step over distance of 0.250.”
Look up tables give RCTF =0.7
The recommended feed rate is:
f =Ω∗(APT)∗N( )=690∗0.0050.7
⎛ ⎝ ⎜
⎞ ⎠ ⎟ ∗2⎡
⎣ ⎢ ⎤ ⎦ ⎥ =9.9 ipm
D=0.33 inV =60 sfmand APT=0.005inΩ=690 RPM
Department of Mechanical Engineering, The Ohio State UniversitySl. #30
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MachinabilityMachinability generally involves three factors
1) Surface Finish2) Tool Life3) Force and Power Requirements
Machinability Ratings are the cutting speeds required to obtain a tool life of T=60 min-- (in general, for a given material, higher speeds decrease the tool life, & slower speeds increase it
Standard is AISI 1112 steel- rating of 100 for a tool life of 60 min, use cutting speed of 100 SFM (AISI 1112)
Machinability of Various Materials Free Cutting Brass 300 Pearlitic Gray Iron 702011 wrought Al 200 3140 steel 55Nickel 200 Inconel 30AISI 1112 Steel 100 Precip-Harden'g Steel 20
From example 8.5, Kalpakjian. Manufacturing Processes for Engineering Materials 2nd Ed, Addison-Wesley 1991.
Department of Mechanical Engineering, The Ohio State UniversitySl. #31
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Power & Force Estimation
Power, P, requirements can then be determined as...
P =u⋅MRR where MRR is the Material Removal Rate
Torque, , is found from
Τ =u ⋅MRR
ω
P =ΤΤ where is the spindle speed
Fp, the force in the direction of the cutting velocity, V, is
Fp =PV=
u⋅MRRV
Department of Mechanical Engineering, The Ohio State UniversitySl. #32
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Specific Energies of Machining
Ref: Shaw. Metal Cutting Principles, Clarendon Press 1984, p. 43
Material
Aluminum Alloys 100,000Gray Cast Iron 150,000Free Machining Brass 150,000Free Machining Steel (AISI 1213) 250,000“Mild” Steel (AISI 1018) 300,000Titanium Alloys 500,000Stainless Steels 700,000High Temp. Alloys 700,000
⎟⎠⎞
⎜⎝⎛ ⋅
3f
in
inlb ou
2.0in 010.0
1001 ⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −=
loo t
uu αu can be determined from
where α is the effective rake angle (in degrees) & tl is the undeformed (nominal) chip thickness (in inches)
Department of Mechanical Engineering, The Ohio State UniversitySl. #33
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Cutting Power - Example 1Find the power for an 8” HSS face mill (10 teeth, αe=30o) to remove 0.1” from Cold Drawn, Wrought Aluminum, with a step over distance of 4.0” at a speed of 600 fpm and an APT 0.022.”
MRR= f ⋅w⋅d=64⋅0.1⋅4=25.6in3
min⎛ ⎝ ⎜
⎞ ⎠ ⎟
Ω =V D
⎛ ⎝ ⎜
⎞ ⎠ ⎟
12π
⎛ ⎝ ⎜ ⎞
⎠ ⎟ =
6008
⎛ ⎝ ⎜ ⎞
⎠ ⎟ 12
π⎛ ⎝ ⎜ ⎞
⎠ ⎟ =290RPM
Compute the speed and feed.
f =Ω(APT)N =290(0.022)(10)=64inmin
The material removal rate is:
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Cutting Power - Example 1(cont’d)Find the power for an 8” HSS face mill (10 teeth, αe=30o) to remove 0.1” from Cold Drawn, Wrought Aluminum, with a step over distance of 4.0” at a speed of 600 fpm and an APT 0.022.”
t1=APT=0.022in u0 =105 lbf inin3
u=u0 1−α
100⎛ ⎝ ⎜ ⎞
⎠ ⎟ 0.010in
t1
⎛ ⎝ ⎜
⎞ ⎠ ⎟
0.2
u=u0 1− α100̊
⎛ ⎝ ⎜ ⎞
⎠ ⎟ 0.010in
t1
⎛ ⎝ ⎜
⎞ ⎠ ⎟
0.2
=105lbf inin3 1− 30̊
100̊⎛ ⎝ ⎜ ⎞
⎠ ⎟ 0.010in
0.22⎛ ⎝ ⎜ ⎞
⎠ ⎟
0.2 1hp⋅min395950lbf in
⎛
⎝ ⎜
⎞
⎠ ⎟
Powerat spindle=PS =u⋅MRR=0.151⋅25.6=3.86hp
Ω =290RPM
f =64inmin
MRR=25.6 in3
min
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Cutting Power - Example 2Estimate the work required to turn down an annealed 304 stainless rod 6 in long from a diameter of 0.500” to a diameter of 0.480.” (Assume αe=13o, & ipr=0.003”)
u0 =7*105 lbf inin3 & t1=ipr=0.003"
u=u0 1− α100̊
⎛ ⎝ ⎜ ⎞
⎠ ⎟ 0.010in
t1
⎛ ⎝ ⎜
⎞ ⎠ ⎟
0.2
=7*105 lbf inin3 1−
13̊100̊
⎛ ⎝ ⎜ ⎞
⎠ ⎟ 0.010in
0.003⎛ ⎝ ⎜ ⎞
⎠ ⎟
0.2
=775*103 lbf inin3
E =u⋅V = 775*103 lbfinin3
⎛ ⎝ ⎜
⎞ ⎠ ⎟ 0.092in3( )=71,300lbf in
VolumeRemoved=V =π4
do2 −di
2[ ](L)
=π4(0.5)2 −(0.480)2[ ](6)=0.092in3
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Summary
Factors for Chip production: • rake angle• clearance angle• shear angle
Factors that affect machining parameters:• effective diameter• depth of cut• radial depth of cut (if applicable)• speeds (tip and spindle)• feed rate• material• tool material
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Credits This module is intended as a supplement to design classes in mechanical
engineering. It was developed at The Ohio State University under the NSF sponsored Gateway Coalition (grant EEC-9109794). Contributing members include:
Gary Kinzel …………………………………….. Project supervisor Chris Hubert and Alan Bonifas ..……………... Primary authors Phuong Pham and Matt Detrick ……….…….. Module revisions L. Pham …………………………………….….. Audio voice
References: Machinery’s Handbook 21st edKalpakjian, S. and Addison Wesley, Manufacturing Processes for Engineering Materials , 2nd
Ed., 1991Kibbe, et al. Machine Tool Practices 5th Ed, Prentice Hall,1995Shaw. Metal Cutting Principles, Clarendon Press
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Disclaimer
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