Essential CNC Calculation Formulas You Should Know

I. The calculation of trigonometric

1.tgθ=b/a      ctgθ=a/b

2.Sinθ=b/c      Cos=a/c

II. Calculation of cutting speed

Vc＝(πDS)/1000

• Vc: linear velocity (m/min)
• π: Circumference (3.14159)
• D: Tool diameter (mm)
• S: Rotational speed (rpm)

III. Calculation of the feed (F-value)

F＝SZFz

• F: Feed rate (mm/min)
• S: Rotational speed (rpm)
• Z: Number of blades
• Fz: (actual feed per blade)

IV. Calculation of residue height

Scallop＝(ae*ae)/8R

• Scallop: Residue height(mm)
• ae: XY  pitch(mm)
• R: Tool radius(mm)

V. Calculation of slug holes

Φ＝√2R2

X. Y＝D/4

• Φ: Diameter of slug holes(mm)
• R: Tool radius (mm)
• D: Tool diameter (mm)

VI. Calculation of material intake

Q＝(aeapF)/1000

• Q: The quantity of material taken(cm3/min)
• ae: XY  pitch(mm)
• ap: Z  pitch(mm)

VII. Calculation of the feed rate per blade

Fz＝hm * √(D/ap )

• Fz: Actual feed per blade
• hm: theoretical feed per blade
• ap：Z  pitch(mm)
• D: Blade diameter (mm)

VIII. Die cutting edge processing method

Tooling depth = plate thickness – tool height + drill tip (0.3D)

• D : Knife diameter

IX. Drill drilling time formula

T(min)=L(min)/N(rpm)*f(mm/rev)＝πDL/1000vf

• L: Full length of the drilling
• N: Number of turns
• f: feed volume factor
• D: Bit diameter
• v: Cutting speed

Drill factor table fz 

X. Formulas for calculating pipe teeth

1 inch = 25.4 mm.

XI. Horsepower (gun drill)

• W = Md*N/97.410.
• W: Power required (KW)
• Md: torque (kg-cm)
• N: Number of rotations (r.p.m.)

XII. The formula for calculating torque is as follows.

• Md=1/20*f*ps*r2
• f is the coefficient of feed mm/rev.
• r is the drill radius (mm)
• α: cutting resistance ratio ps. at small feed, general steel 500kg/m²; general cast iron 300kg/m²