# CNC Commonly Used Calculation Formula ## 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)
• Fz: (actual feed per blade)

## IV. Calculation of residue height

Scallop＝(ae*ae)/8R

• Scallop: Residue height(mm)
• ae: XY  pitch(mm)

## V. Calculation of slug holes

Φ＝√2R2

X. Y＝D/4

• Φ: Diameter of slug holes(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)

## 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

 Dia. mm Feed knife mm/rev 1.6~3.2 0.025~0.075 3.2~6.4 0.05~0.15 6.4~12.8 0.10~0.25 12.8~25 0.175~0.375 >25 0.376~0.625

## 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

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### 1 thought on “CNC Commonly Used Calculation Formula”

1. Question: I have a screen shot of a tooling estimate spreadsheet that was included in a tooling estimating seminar I attended. I have tried to fill in the formulas to utilize it for myself to quote tools but the one thing I cant figure out is the CNC portion of the sheet.
The formula calls for ‘cut volume’, ‘# of details’, Machine run rate (3″/hr.) [with a given number of 10] & a formula for machine time (cut volume x # of details / machine run rate)
Once you get the machine time you can calculate the cost by multiplying it by the amount per hour charged. for example it the volume was 25 & there were 2 details then it would be ((25 x 2)/10) x \$95.00/hr. = \$474.00 The only thing I cant figure out is how to get the cut volume. Any ideas?

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