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Milling machines - Cutting Speed calculations
 
Cutting speed
 
Cutting speed is defined as the speed (usually in meter per minute or feet per minute) of a tool when it is cutting the work.

The formula is

V = ∏ x D x N

Were

  • V is velocity or speed in metre (m) per Minute

  • ∏ is pie 22/7 or 3,142

  • D is cutter, drill or in case of a lathe the diameter of the work in millimetre (mm)

  • N is the revolutions per minute of the machine spindle (RPM)

Many people do not understand the difference between speed (velocity) and rotational frequency (RPM).  Let take the tractor above.  Is the speed of the front wheel and the rear wheel the same?  The answer is yes it is the same.  What is difference is the rotational frequency, the smaller front wheel is rotating faster than the larger rear wheel.  Let proof this:

Let say the tractor travel at a speed of 25 kilometre per hour (km/h), what will the rotational frequency be of the front and rear wheel?

Front wheel

Given information:

  • V = 25 km/h

  • ∏ = 3.142

  • D = 900 mm

  • N = ? RPM

V = ∏ x D x N

N = (∏ x D)/V

But N must be in RPM and V is in km/h, thus must be change to m/s by dividing by 3.6. 

Thus V = 25/3.6 = 6.94 m/s

Diameter is in mm and must be changed to m by dividing by 1000, thus 900/1000 = 0,9 m

N    = V/(∏ x D)
      = 6.94/(3,142 x 0.9)
      = 2.45 r/s

r/s to RPM 2.45 x 60 = 147.36 RPM

Front wheel

Given information:

  • V = 25 km/h

  • ∏ = 3.142

  • D = 1500 mm

  • N = ? RPM

V = ∏ x D x N

N = (∏ x D)/V

But N must be in RPM and V is in km/h, thus must be change to m/s by dividing by 3.6. 

Thus V = 25/3.6 = 6.94 m/s

Diameter is in mm and must be changed to m by dividing by 1000, thus 1500/1000 = 1.5 m

N    = V/(∏ x D)
      = 6.94/(3,142 x 1.5)
      = 1.47 r/s

r/s to RPM 1.47 x 60 = 88.41 RPM

It can be seen that although both wheels are moving at the same speed their rotational frequency's are different.  Small wheel rotate faster than large wheel foe same speed (velocity)
 
The table below indicate cutting speeds of different materials:

Cutting speed and feed calculator 1

Cutting speed and feed calculator 2

Cutting speed and feed calculator 3

Cutting speed and feed calculator 4

Calculation examples

Example 1

An aluminium workpiece has to be drilled with a 30 mm drill bit. The cutting speed for aluminium is 50 m/min. Calculate the spindle speed (N) in revolutions per minute

D = 30 mm S = 50 m/min N = ?
S = π ?D ?N
N = 50/π ?30
    = 0,5307 r/min

 

 Example 2

Calculate the cutting speed in metres per minute if the rotational speed is 159,15 rpm and a rose cutter of 60 mm diameter is used on a milling machine.

S = ?
N = 159,15 RPM
D = 60 mm divided 1 000 = 0,06 m
S = π ?D ?N
    = π ?0,06 ?159,15
    = 30,003 m/min.
    = 30 m/min

 Example 3

Calculate the spindle speed in revolutions per minute for drilling an 8mm diameter hole on an Aluminium plate. The cutting speed for Aluminium is 50m/min

D = 8mm=0,008m
S = 50m/min
N = ?
S = π x D x N
N = S/π x D
   = 50/πX0,008
   = 1989,44r/m