Formula Sheet: Machininf and Machine Tool Operations | Manufacturing Engineering - Mechanical Engineering PDF Download

 Page 1


Mac hining and Mac hine T o ol Op erations F orm ula
Sheet
Cutting P arameters
• Cutting Sp eed (v
c
) : Sp eed of the w orkpiece or to ol surface.
v
c
=
pDN
1000
(Units: mmin
-1
)
where D is diameter (mm ), N is rotational sp eed ().
• F eed Rate (f ) : Linear or angular adv ance p er rev olution or to oth.
f =
F eed p er to oth× Num b er of teeth×N
1000
(Units: mmin
-1
)
where feed p er to oth is in mm .
• Depth of Cut (d ) : Thic kness of material remo v ed (mm ).
Material Remo v al Rate (MRR)
• T urning :
MRR=v
c
fd (Units: mm
3
min
-1
)
where v
c
is cutting sp eed (mmin
-1
), f is feed (mm ), d is depth of cut (mm ).
• Milling :
MRR=wdf (Units: mm
3
min
-1
)
where w is width of cut (mm ), f is feed rate (mmmin
-1
).
• Drilling :
MRR=
pD
2
fN
4
(Units: mm
3
min
-1
)
where D is drill diameter (mm ), f is feed p er rev olution (mm ), N is .
T o ol Life
• T a ylor’s T o ol Life Equation :
v
c
T
n
=C
where T is to ol life (min ), n is to ol life exp onen t (material-dep enden t, t ypically 0.1–
0.3), C is a constan t.
• Extended T a ylor’s Equation :
v
c
T
n
f
a
d
b
=K
where a,b are exp onen ts for feed and depth of cut, K is a constan t.
• T o ol W ear : Flank w ear, crater w ear, and c hipping affect to ol life.
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Page 2


Mac hining and Mac hine T o ol Op erations F orm ula
Sheet
Cutting P arameters
• Cutting Sp eed (v
c
) : Sp eed of the w orkpiece or to ol surface.
v
c
=
pDN
1000
(Units: mmin
-1
)
where D is diameter (mm ), N is rotational sp eed ().
• F eed Rate (f ) : Linear or angular adv ance p er rev olution or to oth.
f =
F eed p er to oth× Num b er of teeth×N
1000
(Units: mmin
-1
)
where feed p er to oth is in mm .
• Depth of Cut (d ) : Thic kness of material remo v ed (mm ).
Material Remo v al Rate (MRR)
• T urning :
MRR=v
c
fd (Units: mm
3
min
-1
)
where v
c
is cutting sp eed (mmin
-1
), f is feed (mm ), d is depth of cut (mm ).
• Milling :
MRR=wdf (Units: mm
3
min
-1
)
where w is width of cut (mm ), f is feed rate (mmmin
-1
).
• Drilling :
MRR=
pD
2
fN
4
(Units: mm
3
min
-1
)
where D is drill diameter (mm ), f is feed p er rev olution (mm ), N is .
T o ol Life
• T a ylor’s T o ol Life Equation :
v
c
T
n
=C
where T is to ol life (min ), n is to ol life exp onen t (material-dep enden t, t ypically 0.1–
0.3), C is a constan t.
• Extended T a ylor’s Equation :
v
c
T
n
f
a
d
b
=K
where a,b are exp onen ts for feed and depth of cut, K is a constan t.
• T o ol W ear : Flank w ear, crater w ear, and c hipping affect to ol life.
1
Mac hining Time
• T urning (Single P ass) :
t
m
=
L
fN
(Units: min )
where L is length of cut (mm ), f is feed (mm ), N is .
• Milling :
t
m
=
L+L
o
f
(Units: min )
where L
o
is approac h/o v ertra v el length (mm ), f is feed rate (mmmin
-1
).
• Drilling :
t
m
=
L
fN
+t
a
where t
a
is allo w ance time for to ol engagemen t (min ).
Cutting F orces and P o w er
• Cutting F orce (F
c
) : F orce in direction of cutting.
F
c
=k
s
A
where k
s
is sp ecific cutting energy ( Nmm
-2
), A is c hip cross-sectional area (f×d ,
mm
2
).
• P o w er Requiremen t :
P =
F
c
v
c
60×1000
(Units: kW )
where F
c
is in N , v
c
is in mmin
-1
.
• Sp ecific Energy :
u=
P
MRR
(Units: Jmm
-3
)
Mac hining Pro cesses
• T urning : Single-p oin t cutting to ol remo v es material from rotating w orkpiece.
• Milling : Multi-p oin t cutting to ol, t yp es include slab, face, and end milling.
• Drilling : Pro duces holes using a rotating drill bit.
• Grinding : Abrasiv e mac hining for surface finish.
MRR
grinding
=v
w
db
where v
w
is w orkpiece v elo cit y (mmin
-1
), d is depth of cut (mm ), b is wheel width
(mm ).
2
Page 3


Mac hining and Mac hine T o ol Op erations F orm ula
Sheet
Cutting P arameters
• Cutting Sp eed (v
c
) : Sp eed of the w orkpiece or to ol surface.
v
c
=
pDN
1000
(Units: mmin
-1
)
where D is diameter (mm ), N is rotational sp eed ().
• F eed Rate (f ) : Linear or angular adv ance p er rev olution or to oth.
f =
F eed p er to oth× Num b er of teeth×N
1000
(Units: mmin
-1
)
where feed p er to oth is in mm .
• Depth of Cut (d ) : Thic kness of material remo v ed (mm ).
Material Remo v al Rate (MRR)
• T urning :
MRR=v
c
fd (Units: mm
3
min
-1
)
where v
c
is cutting sp eed (mmin
-1
), f is feed (mm ), d is depth of cut (mm ).
• Milling :
MRR=wdf (Units: mm
3
min
-1
)
where w is width of cut (mm ), f is feed rate (mmmin
-1
).
• Drilling :
MRR=
pD
2
fN
4
(Units: mm
3
min
-1
)
where D is drill diameter (mm ), f is feed p er rev olution (mm ), N is .
T o ol Life
• T a ylor’s T o ol Life Equation :
v
c
T
n
=C
where T is to ol life (min ), n is to ol life exp onen t (material-dep enden t, t ypically 0.1–
0.3), C is a constan t.
• Extended T a ylor’s Equation :
v
c
T
n
f
a
d
b
=K
where a,b are exp onen ts for feed and depth of cut, K is a constan t.
• T o ol W ear : Flank w ear, crater w ear, and c hipping affect to ol life.
1
Mac hining Time
• T urning (Single P ass) :
t
m
=
L
fN
(Units: min )
where L is length of cut (mm ), f is feed (mm ), N is .
• Milling :
t
m
=
L+L
o
f
(Units: min )
where L
o
is approac h/o v ertra v el length (mm ), f is feed rate (mmmin
-1
).
• Drilling :
t
m
=
L
fN
+t
a
where t
a
is allo w ance time for to ol engagemen t (min ).
Cutting F orces and P o w er
• Cutting F orce (F
c
) : F orce in direction of cutting.
F
c
=k
s
A
where k
s
is sp ecific cutting energy ( Nmm
-2
), A is c hip cross-sectional area (f×d ,
mm
2
).
• P o w er Requiremen t :
P =
F
c
v
c
60×1000
(Units: kW )
where F
c
is in N , v
c
is in mmin
-1
.
• Sp ecific Energy :
u=
P
MRR
(Units: Jmm
-3
)
Mac hining Pro cesses
• T urning : Single-p oin t cutting to ol remo v es material from rotating w orkpiece.
• Milling : Multi-p oin t cutting to ol, t yp es include slab, face, and end milling.
• Drilling : Pro duces holes using a rotating drill bit.
• Grinding : Abrasiv e mac hining for surface finish.
MRR
grinding
=v
w
db
where v
w
is w orkpiece v elo cit y (mmin
-1
), d is depth of cut (mm ), b is wheel width
(mm ).
2
Key Notes
– Use SI units: v
c
in mmin
-1
, f in mm or mm , d in mm , P in kW .
– T ypical v alues: n˜ 0.2 (HSS to ols), n˜ 0.5 (carbide to ols), k
s
v aries (e.g., 2000–
4000 MPa for steel).
– Optimize v
c
, f , and d for to ol life vs. pro ductivit y (economic mac hining).
– A ccoun t for to ol geometry (ra k e angle, clearance angle) in force calculations.
– Co olan ts reduce to ol w ear a nd impro v e surface finish.
– F or milling, consider cutter diameter and n um b er of teeth for accurate f .
3