Formula for Cutting Speed in Milling

π (3.14): Circular constant
DC (mm): Cutter diameter
n (min^-1): Spindle speed

This formula is used to calculate the cutting speed from the spindle speed and the outer diameter of the cutter.
Example:
Cutter diameter (DC) = 100 mm
Spindle speed (n) = 400 min^-1
In this case, the cutting speed (vc) is approximately 125.6 m/min.

Increasing the spindle speed (n) or using a larger tool (DC) raises the resulting cutting speed (VC). A larger cutter travels a greater distance per rotation, which raises surface speed even if the rotations per minute (RPM) stay the same. Because of this, cutting speed must always be calculated using the actual tool size in use.

Cutting speeds for milling are not selected in isolation. These speeds are tied to the material being cut and the overall condition of the tool. Softer materials can typically support higher cutting speeds, while harder materials require a lower speed to reduce heat and wear down the tooling edge.

This equation shows that spindle speed (n) depends on both cutting speed (VC) and tool diameter (D or DC). Smaller tools require higher RPMs to reach the same cutting speed because each rotation covers less distance. Larger tools require lower RPM for the same reason.

This relationship becomes important when the tool size changes during an operation. If the diameter is reduced and the spindle speed remains unchanged, then the cutting speed will also decrease.

This change in cutting speed can lead to inconsistent cutting behavior, especially in operations where surface finish is a priority. Because of this, spindle speed should always be recalculated when the tool diameter changes rather than being reused from previous setups.

vf (mm/min): Table feed per minute
z: Number of teeth
n (min^-1): Spindle speed (Feed rate fr = zxfz)

This formula is used to calculate the feed per tooth from the table feed per minute (feed rate), the number of teeth, and the spindle speed.
Example:
Table feed per minute (vf) = 450 mm/min
Number of teeth (z) = 10
Spindle speed (n) = 600 min^-1
In this case, the feed per tooth (f) is 0.075 mm/t.

fz (mm/tooth): Feed per tooth
z: Number of teeth
n (min^-1): Spindle speed (Feed rate fr = zxfz)

This formula is used to calculate the table feed per minute (feed rate) from the feed per tooth, the number of teeth, and the spindle speed.
Example:
Feed per tooth (fz) = 0.2 mm/tooth
Number of teeth (z) = 8
Spindle speed (n) = 600 min^-1
In this case, the table feed rate is 960 mm/min.

Feed per tooth determines how much material each tool insertion removes during a single pass. When the spindle speed increases, each cutting edge engages the material more frequently, which raises the overall feed rate. Increasing the number of cutting tools also has a similar effect.

The feed rate has to stay in line with the spindle speed in order to maintain a consistent chip load or material removal. If the feed is too low relative to the RPM, the cutting edge may not interact with the material properly. This can lead to excess heat at the tool's surface. However, with the right balance, each interaction removes material evenly.

L (mm): Total table feed length (Length of material (l) + Face mill diameter (DC))
vf (mm/min): Table feed per minute

This formula is used to calculate the machining time from the total table feed length and the table feed per minute (feed rate).
Example of finishing a block of FC200 cast iron to have a flat surface of:
Width = 150 m
Length = 250 mm
Face milling conditions used:
Feed per tooth (fz) = 0.35 mm
Number of teeth (z) = 12
Spindle speed (n) = 200 min^-1
Cutting speed (vc) = 120 m/min
Face mill diameter (D1) = 220 mm
In this case,
the table feed per minute (vf) and the total table feed length (L) are:
vf = 0.35 × 12 × 200 = 840 mm/min
L = 350 + 220 = 570 mm
Substitute these values into the formula:
Tc = L ÷ vf
= 570 ÷ 1120
= 0.679 (min) × 60
= 40.74 (sec)
The machining time (Tc) is approximately 40.74 seconds.

ap (mm): Depth of cut
ae (mm): Width of cut
vf (mm/min): Table feed per minute
Kc (MPa): Specific cutting force
η: Machine efficiency

This formula is used to calculate the net power required for face milling based on the depth and width of cut, the table feed per minute, the specific cutting force, and the machine efficiency. Example of calculating the net power required to cut tool steel with:
Depth of cut (ap) = 5 mm
Width of cut (ae) = 70 mm
Table feed per minute (vf) = 300 mm/min
Other conditions:
Specific cutting force (Kc) = 1800 MPa
Machine efficiency (η) = 80% (0.8)
Cutting speed (vc) = 80 m/min
Cutter diameter (DC) = 250 mm
Number of teeth (z) = 16
In this case, first you calculate the spindle speed (n) and then the feed per tooth of the cutter (fz).
Spindle speed (n) = 1000・vc ÷ π・D
= (1000 × 80) ÷ (3.14 × 250)
= 101.91 min^-1
Feed per tooth (fz) = vf ÷ (Z × n)
= 300 ÷ (16 × 101.91)
= 0.184 mm/tooth
Substitute the above into the formula:
Pc = (5 × 70 × 300 × 1800) ÷ (60 × 10⁶× 0.8)
= 3.937 kw
The net power required for face milling (Pc) is approximately 3.94 kW.

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