Formula for Turning

Inch
Metric

Inch

Cutting Speed (vc)

vc (SFM) : Cutting Speed
Dm (Inch) : Work Material Diameter
π (3.14) : Pi
n (min^-1) : Main Axis Spindle Speed

(Problem)
What is the cutting speed when main axis spindle speed is 700min^-1and external diameter is Φ2 ?
(Answer)
Substitute π=3.14, Dm=2, n=700 into the formulae.
vc=(π×Dm×n)÷12=(3.14×2×700)÷12
=366.33SFM
Cutting speed is 366.33SFM.

Feed (f)

f (IPR) : Feed per Revolution
I (IPM) : Cutting Length per Min.
n (min^-1) : Main Axis Spindle Speed

(Problem)
What is the feed per revolution when main axis spindle speed is 500min^-1 and cutting length per minute is 120mm/min ?
(Answer)
Substitute n=500, I=4.72 into the formulae.
f=l÷n=4.72÷500=.009IPR
The answer is .009IPR.

Cutting time (Tc)

Tc(min):Cutting Time
lm(Inch):Work Material Length
I (IPM):Cutting Length per Min.

(Problem)
What is the cutting time when 4inch work material is machined at 1000min^-1 with feed = .008IPR ?
(Answer)
First, calculate the cutting length per min. from the feed and spindle speed.
l=f×n=.008×1000=8IPM
Substitute the answer above into the formulae.
Tc=lm÷l=4÷8=0.5(min)
0.5×60=30(sec) The answer is 30 sec.

Theoretical finished surface roughness(h)

h (µinch):Finished Surface Roughness
f (IPR):Feed per Revolution
RE (inch):Insert Corner Radius

(Problem)
What is the theoretical finished surface roughness when the insert corner radius is .031inch and feed is .008 IPR ?
(Answer)
Substitute f=.008IPR, RE=.031 into the formulae.
h=(.008)²÷(8×.031)×1000=.258µinch
The theoretical finished surface roughness is .258µinch.

Metric

Cutting Speed (vc)

※Divide by 1000 to change to m from mm.

vc (m/min) : Cutting Speed
Dm (mm) : Workpiece Diameter
π (3.14) : Pi
n (min^-1) : Main Axis Spindle Speed

(Problem)
What is the cutting speed when main axis spindle speed is 700min^-1and external diameter is Φ50 ?
(Answer)
Substitute π=3.14, Dm=50, n=700 into the formula.
vc=(π×Dm×n)÷1000=(3.14×50×700)÷1000
=110(m/min)
Cutting speed is 110m/min.

Feed (f)

f (mm/rev) : Feed per Revolution
I (mm/min) : Cutting Length per Min.
n (min^-1) : Main Axis Spindle Speed

(Problem)
What is the feed per revolution when main axis spindle speed is 500min^-1 and cutting length per minute is 120mm/min ?
(Answer)
Substitute n=500, I=120 into the formula.
f=l÷n=120÷500=0.24(mm/rev)
The answer is 0.24mm/rev.

Cutting time (Tc)

Tc(min):Cutting Time
lm(mm):Work Material Length
ｌ(mm/min):Cutting Length per Min.

(Problem)
What is the cutting time when 100mm work material is machined at 1000min^-1 with feed = 0.2mm/rev ?
(Answer)
First, calculate the cutting length per min. from the feed and spindle speed.
l=f×n=0.2×1000=200(mm/min)
Substitute the answer above into the formula.
Tc=lm÷l=100÷200=0.5(min)×60=30(sec)
The answer is 30 sec.

Theoretical finished surface roughness (h)

h (µm):Finished Surface Roughness
f (mm/rev):Feed per Revolution
RE (mm):Insert Corner Radius

(Problem)
What is the theoretical finished surface roughness when the insert corner radius is 0.8mm and feed is 0.2mm/rev ?
(Answer)
Substitute f=0.2mm/rev, RE=0.8 into the formula.
h=f²÷(8×RE)×1000=0.2²÷(8×0.8)×1000=6.25µm
The theoretical finished surface roughness is 6µm.