# Common Calculation Formulas for CNC Machining

The precision of CNC machining center affects the machining quality. Therefore, the industry has been studying the method to reduce or even eliminate the error on the precision of CNC machining center. How to judge the common formula of a CNC machining?

As we all know, when we do CNC machining, we often encounter some places that need formulas to calculate, but many people forget them completely. Today, I will share with you eight common calculation formulas of CNC machining centers for free, hoping to help you.

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Eight common calculation formulas of CNC machining centers

**1. Cutting linear speed**

V=πDN/1000

- N=rpm (spindle speed)
- D=￠ mm (cutting diameter)
- V=M/min
- π=3.14

**2. Cutting power**

KW=(Ks × V × d × f)÷(6000 ×λ)

- W=Kw (cutting power)
- F=feed rate (mm/rev)
- D=cutting depth (mm)
- λ= 0.7-0.85 (mechanical efficiency)

**3. Cutting resistance**

P=Ks × q

- P=KG
- Ks=kg/mm2
- q=f × D [Cutting area [mm2]

**4. Cutting torque**

T=P × (D/2)

- T=kg-m
- D=￠ mm (cutting diameter)

**5. Feed speed and feed quantity**

Vf=N × f

- Vf=feed speed (mm/min)
- N=rpm (spindle speed)
- F=feed rate (mm/rev)

**6. Drilling time**

T=L/Nf=πDL/1000Vf

- T=drilling time (min)
- D=￠ mm (drill diameter)
- L=drilling depth (mm)
- V=M/min
- F=feed rate (mm/rev)

**7. Tool tip arc radius compensation**

Z=r(1-tan θ/ 2)

- X=Ztan θ
- Z=Z direction correction value
- X=correction value in X direction
- R=radius of tool tip arc
- θ= Inclined angle of diagonal line

**8. Table feed**

Vf=fz × Z × n

- Vf=worktable feed rate (mm/min)
- Fz=feed per tooth (mm/t)
- Z=number of milling cutter teeth
- N=number of milling cutter revolutions

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International standard for aperture accounting

**1. The calculation formula of the inner diameter of the thread extrusion tapping**

Formula: tooth outer diameter – 1/2 × Tooth pitch

Example 1: Formula: M3 × 0.5=3-(1/2 × 0.5)=2.75mm

M6 × 1.0=6-(1/2 × 1.0)=5.5mm

Example 2: Formula: M3 × 0.5=3-(0.5÷2)=2.75mm

M6 × 1.0=6-(1.0÷2)=5.5mm

**2. Conversion formula for general inch tapping**

1 inch=25.4mm (code)

Example 1: (1/4-30)

1/4 × 25.4=6.35 (tooth diameter)

25.4 ÷ 30=0.846 (pitch)

Then 1/4-30 converted to metric tooth shall be M6.35 × 0.846

Example 2: (3/16-32)

3/16 × 25.4=4.76 (tooth diameter)

25.4 ÷ 32=0.79 (pitch)

Then 3/16-32 converted to metric tooth shall be M4.76 × 0.79

**3. The formula for converting English system teeth into metric system teeth**

Numerator ÷ denominator × 25.4=tooth outer diameter (as above)

Example 1: (3/8-24)

3÷8 × 25.4=9.525 (tooth diameter)

25.4 ÷ 24=1.058 (metric pitch)

The conversion from 3/8-24 to metric tooth shall be M9.525 ×0.058

**4. Formula for converting American dental system to metric dental system**

Example: 6-32-

6-32 (0.06+0.013)/code × 6=0.138

0.138 × 25.4=3.505 (tooth diameter)

25.4 ÷ 32=0.635 (pitch)

Then conversion from 6-32 to metric tooth shall be: M3.505 × 0.635

**Hole inner diameter calculation formula:**

Tooth OD – 1/2 × The tooth pitch shall be:

M3.505-1/2 × 0.635=3.19

Then the internal diameter of 6-32 should be 3.19

**Algorithm for kneading and tapping inner holes:**

Simple calculation formula 1 for lower hole diameter:

Tooth OD – (Pitch × 0.4250.475)/code=lower hole diameter

Example 1: M6 × 1

M6-(1.0 × 0.425)=5.575 (maximum lower hole diameter)

M6-(1.0 × 0.475)=5.525 (min)

Example 2: Simple calculation formula for the inner diameter of the hole tapped by the cutting thread:

M6-(1.0 × 0.85)=5.15 (maximum)

M6-(1.0 × 0.95)=5.05 min

M6 – (Pitch × 0.860.96)/code=lower hole diameter

Example 3: M6 × 1.0=6-1.0=5.0+0.05=5.05

**5. Simple formula for calculating the external diameter of pressing teeth**

1. Diameter -0.01 × zero point six four five × Tooth pitch (go no go gauge is required)

Example 1: M3 × 0.5=3-0.01 × zero point six four five × 0.5=2.58 (outer diameter)

Example 2: M6 × 1.0=6-0.1 × zero point six four five × 1.0=5.25 (outer diameter)

**6. Calculation formula for metric roll diameter: (full tooth calculation)**

Example 1: M3 × 0.5=3-0.6495 × 0.5=2.68 (outer diameter before turning)

Example 2: M6 × 1.0=6-0.6495 × 1.0=5.35 (outer diameter before turning)

**7. Depth of embossed outer diameter (outer diameter)**

Outer diameter ÷ 25.4 × Tooth pitch=outer diameter before embossing

Example: 4.1 ÷ 25.4 × 0.8 (distance between flowers)=0.13 The embossing depth should be 0.13

**8. Diagonal conversion formula for polygonal materials:**

- 1. Quadrangle: opposite diameter × 1.414=diagonal diameter
- 2. Pentagon: opposite diameter × 1.2361=diagonal diameter
- 3. Hexagon: diameter of opposite side × 1.1547=diagonal diameter

Formula 2:

- 1. Four corners: opposite diameter ÷ 0.71=diagonal diameter
- 2. Hexagon: opposite diameter ÷ 0.866=diagonal diameter

**9. Tool thickness (cutter):**

Cutting knife width

Approximately equal to (05. – 0.6) √ D

**10. Calculation formula of taper:**

Formula 1: (big end diameter – small end diameter) ÷ (2 × Total length of taper)=bevel value

Look up trigonometric function value-

Formula 2: Approximate accounting formula (degree ≤ 6 °)

- (big end diameter small end diameter) ÷ total length × 28.7=degrees

**11. Thread turning speed selection:**

- Speed=1200/pitch – safety value (claimed value 80)

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Calculation Formula and Usage of Roughness of CNC Lathe

- Feed – the greater the feed, the greater the roughness, the higher the feed, the higher the machining efficiency, and the smaller the tool wear, so the feed is generally final, and the feed is finally determined according to the required roughness
- Tool tip R – The larger the tool tip R is, the lower the roughness is, but the cutting force will continue to increase, requiring higher rigidity of the machine tool and the material itself. It is recommended that generally lathes that cut steel parts under 6150 should not use tool tips above R0.8, while those for duralumin alloys should not use tool tips above R0.4, otherwise the true roundness, straightness and other form and location tolerances of the lathes can not be guaranteed, even if the roughness can be reduced, it is useless!
- The equipment power shall be calculated during cutting. As for how to calculate the power required during cutting (80% of the motor KW is taken as the limit), we will talk about it in the next post. It should be noted that most CNC lathes now use variable frequency motors. The characteristics of variable frequency motors are that the higher the speed, the greater the torque, and the lower the speed, the smaller the torque. Therefore, it is safer to divide the KW of variable frequency motors by two when calculating power. While the speed is closely related to the linear speed during cutting, the traditional ordinary car uses a constant speed/torque motor to change the speed by relying on mechanical speed change, so it is always “100% maximum torque output”, which is better than the variable frequency motor. But of course, if your spindle is driven by an expensive constant torque servo motor, it is the perfect choice.

The minimum roughness that the lathe can reach is primarily due to the spindle accuracy. According to the calculation method of maximum roughness, if the runout accuracy of the lathe spindle is 0.002mm, that is, 2 μ m runout, it is theoretically impossible to process workpieces with a roughness lower than 0.002mm (RY2.0), but this is the maximum possible value. Generally, 50% is good on average, and workpieces with a roughness of 1.0 can be processed! Combined with RA algorithm, it will not get more than 50% of the RY value, which will become RA0.5, and then calculate that the effect of the polishing blade will be reduced by 50%, so that the lathe limit of the final spindle runout of 0.002 can process workpieces with RA0.2!