Common calculation formulas for CNC machining

  1. Trigonometric function measurement

1.tanθ=b/a θ=tan-1b/a

2.Sinθ=b/c Cos=a/c
Common calculation methods for production and cnc machining

  1. Measurement of cutting parameters


Vc: angular velocity (m/min) π: circumference ratio (3.14159) D: CNC blade straight length (mm)

S: Speed ​​ratio (rpm)

Exercises. Applying Φ25 turning tool Vc to (m/min)25 to find S=?rpm



S=100025/ π25


  1. Measurement of cutting speed (F value)


F: Cutting speed (mm/min) S: Speed ​​ratio (rpm) Z: Number of blades

Fz: (Actually each blade moves the knife)

Exercises. A standard 2-flute end mill is used to drill steel parts at a rate of 2000rpm, and find the cutting speed (F

What is    value)? (Fz=0.25mm)




Fourth, the calculation of the residual material height


Scallop: Residual material height (mm) ae: XYpitch (mm) R CNC blade semi-warp (mm)

Exercises. Φ20R10 product refined 2 blades, pre-residual height 0.002mm, ask for more pitch

Less? mm




  1. Calculation of escape hole


Φ: Straight length of escape hole (mm) R CNC blade half length (mm) D: NC blade straight length (mm)

Exercises. As shown in the picture, a mold cavity must escape the corner production and processing (the picture is known),

The commonly used turning tool is ψ10; I want to ask about the least escape angle hole

How much is   ? What are the center coordinates?




X, Y = D/4

X, Y = 10/4

X、Y=2.5 mm

The coordinates of the center of the circle are (2.5, -2.5)

VI. Measurement of reclaiming amount


Q: Reclaiming amount (cm3/min) ae: XYpitch(mm)ap: Zpitch(mm)

Exercises. As shown in the picture, a mold with a cavity contour line is produced and processed. The XYpitch of the Φ35R5 knife is 60% of the CNC blade, the six-layer cutting is 1.5mm, and the cutting speed is 2000mm/min. Find the material withdrawal of this CNC blade For what?



Q=63 cm3/min

Seven. Measurement of cutting speed per blade

Fz=hm * √(D/ap)

Fz: Implement cutting speed per blade hm: Basic theory cutting speed per blade ap: Zpitch(mm)

D: Saw blade straight length (mm)

Practice questions (prerequisite depo XYpitch is 60% of CNC blade)

depoΦ35R5 cutter, drilling NAK80 raw material hm is 0.15mm, Z-axis cutting depth is 1.5mm, what is the cutting speed per blade?

Fz=hm * √(D/ap)


Fz = 0.5mm

Stamping die wound production and processing methods

Wound production and cnc machining depth = plate thickness-wound height + drill point (0.3D)

D expression knife path

Twist drill turning time relation



L: Total length of the rotating hole N: Number of revolutions f: Index of the amount of cutting

D: Twist drill straight warp v: Cutting amount

The hole depth is known as shown in the figure. The total length of the twist drill hole L is then L=l+D/3


Index table f Straight through mm/cut 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

Around 25 0.376~0.625

Tube tooth calculation method

1 foot = 25.4mm = 8 points

25.4/tooth number = tooth pitch

For example, 25.4/18=1.414 tooth pitch is 5/16 tap

high horsepower (gun drill)


W: Required driving force (KW)

Md: Torque (kg-cm)

N: Number of rotations (r.p. m)

The torque calculation formula gives:


F is the cutting speed mm/rev index

R is the twist drill half-time race (mm)

Α: Drilling resistance ratio ps. In the small pass, the steel is usually 500kg/mm2; the pig iron is usually 300kg/mm2

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