# FORMULAS FOR CUTTING

Inch
CUTTING SPEED (vc)

vc (SFM)
:Cutting Speed
Dm (inch)
:Workpiece Diameter
π (3.14)
:Pi
n (min-1)
:Main Axis Spindle Speed
Check the item you want to calculate, input values in the two boxes, and then press the Calculate button.
n (min-1)
Dm (inch)
vc (SFM)

(Problem) :
What is the cutting speed when main axis spindle speed is 700 min-1and external diameter is Ø2" ?

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 (inch/min)
:Cutting Length per Min.
n (min-1)
:Main Axis Spindle Speed
Check the item you want to calculate, input values in the two boxes, and then press the Calculate button.
I (inch/min)
n (min-1)
f (IPR)

(Problem):
What is the feed per revolution when main axis spindle speed is 500min-1 and cutting length per minute is 120 mm/min?

Substitute n=500, I=4.72 into the formulae.
f=I÷n=4.72÷500=.009IPR

CUTTING TIME (Tc)
Tc (min)
:Cutting Time
Im (inch)
:Workpiece Length
I (inch/min)
:Cutting Length per Min.
Input the values
lm(inch)
l (inch/min)

Tc (min)
second (s)
(Problem):
What is the cutting time when 4inch workpiece is machined at 1000min-1 with feed= .008IPR ?

First, calculate the cutting length per min. from the feed and spindle speed.
I=f×n=.008×1000=8inch/min
Substitute the answer above into the formulae.
Tc=Im÷I=4÷8=0.5min

THEORETICAL FINISHED SURFACE ROUGHNESS (h)
h (μinch)
:Finished Surface Roughness
f (IPR)
:Feed per Revolution
Re (inch)
Input the values
f (IPR)
Re (inch)

h(μinch)
(Problem):
What is the theoretical finished surface roughness when the insert corner radius is .031inch and feed is .008 IPR ?

Substitute f=.008IPR,Re=.031 into the formulae.
h =(.008)2÷(8×.031)×10002=258μinch

The theoretical finished surface roughness is 258μinch.

Metric
CUTTING SPEED (Pc)

*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

Check the item you want to calculate, input values in the two boxes, and then press the Calculate button.
n (min-1)
Dm (mm)
vc (m/min)

(Problem)
What is the cutting speed when main axis spindle speed is 700min-1 and external diameter is Ø50? Substitute π=3.14, Dm=50, n=700 into the formula.
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 110 m/min.

FEED (f)
f (mm/rev.)
Feed per revolution
l (mm/min)
Cutting length per Min
n (min-1)
Main Axis Spindle Speed
Check the item you want to calculate, input values in the two boxes, and then press the Calculate button.
l (mm/min)
n (min-1)
f (mm/rev)

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

CUTTING TIME (Tc)
Tc (min.)
Cutting Time
lm (mm)
Workpiece Length
l (mm/min)
Cutting Length per Min.
Input the values
lm (mm)
l (mm/min)

Tc (min)
second (s)

(Problem)
What is the cutting time when 100mm workpiece is machined at 1,000min-1, with feed=0.2mm/rev?
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 formulae.

Tc=lm÷l=100÷200=0.5(min)
0.5×60=30(sec.) The answer is 30 seconds.

THEORETICAL FINISHED SURFACE ROUGHNESS (h)
h (µm)
Finished Surface Roughness
f (mm/rev.)
Feed per Revolution
Re (mm)