# Cutting Formulas

This page introduces formulas for calculating basic parameters necessary for machine cutting. The figures obtained from the calculations are for reference only. The conditions for machining depend on the machine tool you are using. Use the optimal conditions according to your actual machining circumstances.

## Cutting Speed (vc)

• π (3.14): Circular constant
• Dm (mm): Diameter of workpiece
• n (min-1): Spindle speed
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This formula is used to calculate the cutting speed from the spindle speed and the diameter of the workpiece.
Example:
Diameter (Dm) = 60 mm
Spindle speed (n) = 500 min-1
In this case, the cutting speed (vc) is approximately 94 m/min.

## Feed (f)

• l (mm/min): Machined length per minute
• n (min-1): Spindle speed
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This formula is used to calculate the feed rate per revolution from the spindle speed and the length cut per minute.
Example:
Machined length per minute (l) = 150 mm/min
Spindle speed (n) = 600 min-1
In this case, the feed rate per revolution (f) is 0.25 mm/rev.

## Machining Time (Tc)

• lm (mm): Length of workpiece
• l (mm/min): Machined length per minute
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This formula is used to calculate the machining time from the length of the workpiece and the spindle speed.
Example:
Feed (f) = 0.2 mm/rev
Spindle speed (n) = 1100 min-1
Length of workpiece (lm) = 120 mm
First, the machined length per minute is calculated, in this case from the rotational speed and the feed amount.
Machined length per minute (l) = n × f
= 0.2 × 1100 = 220 mm/min
Substitute this into the formula:
Tc = lm ÷ l
= 120 ÷ 220
= 0.55 (min) × 60
= 33 (sec)
The machining time (Tc) is approximately 33 seconds.

## Theoretical Finished Surface Roughness (h)

• f (mm/rev): Feed per revolution
• Re (mm): Insert’s corner radius
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This formula is used to calculate the theoretical finished surface roughness from the blade corner radius of the insert and the feed per revolution.
Example:
Feed per revolution (f) = 0.1 mm/rev
In this case, the theoretical finished surface roughness (h) is 2.5 µm.

## Net Power (Pc)

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This formula is used to calculate the net power from the depth of cut, the feed per revolution, the cutting speed, the specific cutting force, and the machine efficiency.
Example:
Depth of cut (mild steel: ap) = 5 mm
Feed per revolution (f) = 0.1 mm/rev
Cutting speed (vc) = 140 m/min
Machine efficiency (η) = 80% (0.8)
Given:
Specific cutting force (Kc) = 3610 MPa
In this case, the net power for machining (Pc) is 5.26 kW.

## Kc Values (Cutting)

Workpiece material Tensile strength (MPa) and stiffness Specific cutting force Kc (MPa) for each feed
0.1 (mm/rev) 0.2 (mm/rev) 0.3 (mm/rev) 0.4 (mm/rev) 0.6 (mm/rev)
Mild steel (SS400, S10C, etc.) 520 3610 3100 2720 2500 2280
Medium steel (S45C, S50C, etc.) 620 3080 2700 2570 2450 2300
Hard steel (S55C, S58C, etc.) 720 4050 3600 3250 2950 2640
Tool steel (Carbon tool steel (SK), etc.) 670 3040 2800 2630 2500 2400
Tool steel (Alloy tool steel (SKS), etc.) 770 3150 2850 2620 2450 2340
Chrome-manganese steel (Manganese carbide (MnC), etc.) 770 3830 3250 2900 2650 2400
Chrome-manganese steel (Manganese carbide (MnC), etc.) 630 4510 3900 3240 2900 2630
Chrome molybdenum steel (SCM grades, etc.) 730 4500 3900 3400 3150 2850
Chrome molybdenum steel (SCM grades, etc.) 600 3610 3200 2880 2700 2500
Nickel chrome molybdenum steel (SNCM415, etc.) 900 3070 2650 2350 2200 1980
Nickel chrome molybdenum steel (SNCM439, etc.) 352HB 3310 2900 2580 2400 2200
Hard cast iron 46HRC 3190 2800 2600 2450 2270
Meehanite cast iron (FC350, etc.) 360 2300 1930 1730 1600 1450
Gray cast iron (FC250, etc.) 200HB 2110 1800 1600 1400 1330

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