non traditional machining

38
Department of Mechanical Engineering, The Ohio State University Sl. #1 GATEWAY GATEWAY Traditional Machining

Transcript of non traditional machining

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Traditional Machining

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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

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Chip TypesContinuous Built Up Edge (BUE)

DiscontinuousSegmented

BUE

Ref: Manufacturing Processes for Engineering Materials Fig 8.4, p 478.

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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

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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

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Tool Wear

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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

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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

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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

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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

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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

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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=

=

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

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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

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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)

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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

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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

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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

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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.

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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

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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

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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

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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.

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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

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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

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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.

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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

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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

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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

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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

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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.

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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

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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)

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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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