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## Calculation formulas commonly used by CNC are worth of collection!

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Calculation formulas commonly used by CNC are worth of collection!

- Categories:Industry News
- Time of issue:2021-08-30 14:29

#
Calculation formulas commonly used by CNC are worth of collection!

- Categories:Industry News
- Time of issue:2021-08-30 14:29

Calculation formulas commonly used by CNC

1. Cutting line speed

V=πDN/1000N=rpm (Rotation numbers of main shaft) D=￠mm (Cutting diameter) V=M/minπ=3.14

2. Cutting power

KW=(Ks×V×d×f)÷(6000×λ) W=Kw (Cutting power) f= Amount of feed (mm/rev) d=Cutting depth (mm) λ=0.7～0.85 (Mechanical efficiency)

3. Cutting impedance

P=Ks×q P=KG Ks=kg/ square mm q=f×d[Cutting area〔square mm〕]

4. Cutting torque

T=P×(D/2) T=kg-mD=￠mm (Cutting diameter)

5. Feed speed and feed amount Vf=N×fVf=Feed speed (mm/min) N=rpm (Rotation numbers of the main shaft) f=Feed amount (mm/rev)

6. Drilling time T=L/Nf=πDL/1000VfT= Drilling time(min) D=￠mm (Bit diameter) L= Drilling depth (mm) V=M/minf=Feed amount (mm/rev)

7. Arc radius compensation of cutter noise

Z=r(1-tanθ/2)X=ZtanθZ=Z compensation value X=X compensation value r= arc radius of cutter noise θ=angle between slashes

8. Workbench feed amount Vf=fz×Z×nVf= Workbench feed amount (mm/min) fz=Feed per tooth(mm/t) Z=Cutter teeth number n= Rotation numbers of milling cutters

Ten calculation formula commonly used by CNC machining

International Standard

1. Calculation formula of internal aperture of squeezing screw tap:

Formula: Outer diameter of tooth -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

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

M6×1.0=6-(1.0÷2)=5.5mm

2. Conversion formula of general inch screw tap:

1 inch =25.4mm (Code)

Example 1: (1/4-30)

1/4×25.4=6.35 (Tooth diameter)

25.4÷30=0.846 (Tooth pitch)

Then when 1/4-30 is converted into metric teeth, it should be: M6.35×0.846

Example 2:3/16-32)

3/16 * 25.4 = 4.76 (Tooth diameter)

25.4 ÷32 = 0.79 (Tooth pitch)

Then when 3/16-32 is converted into metric teeth, it should be: M4.76×0.79

3. The formula for converting ordinary British teeth into metric teeth is as follows:

Numerator ÷ Denominator ×25.4= Tooth outer diameter (Same as above)

Example 1:3/8-24)

3÷8×25.4=9.525 (Tooth outer diameter)

25.4÷24=1.058 (Metric tooth pitch)

Then 3/8-24 can be converted into metric teeth: M9.525×1.058

4. Formula for converting American teeth into metric teeth:

Example: 6-32

6-32 (0.06+0.013)/ Code ×6=0.138

0.138×25.4=3.505 (Tooth outer diameter)

25.4÷32=0.635 (Tooth pitch)

Then when 6-32 is converted into metric teeth, it should be: M3.505×0.635

1. Calculation formula of hole inside diameter:

Tooth outer diameter -1/2× Tooth pitch should be:

M3.505-1/2×0.635=3.19

So the hole inside diameter of 6-32 should be 3.19

2. Algorithm of squeezing screw tap:

Simple calculation formula of lower aperture 1:

Tooth outer diameter -(Pitch ×0.4250.475)/ Code = Lower aperture

Example 1: M6 x 1.0

M6-(1.0×0.425)=5.575(Maximum lower aperture)

M6 - (1.0 x 0.475) = 5.525 (Minimum)

Example 2: Simple calculation formula of cutting tapping screw hole inner diameter：

M6 - (1.0 x 0.85) = 5.15 (Maximum)

M6 - (1.0 x 0.95) = 5.05 (Minimum)

M6-(Tooth pitch ×0.860.96)/ Code = Lower aperture

Example 3: M6×1.0=6-1.0=5.0+0.05=5.05

5. A simple formula for calculating the outer diameter of pressing teeth:

1. Diameter -0.01×0.645× Tooth pitch (Go gauge, no-go gauge)

Example 1: M3×0.5=3-0.01×0.645×0.5=2.58 (Outer diameter)

Example 2: M6×1.0=6-0.1×0.645×1.0=5.25 (Outer diameter)

6. Formula for calculating metric tooth rolling diameter: (Full teeth 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. Embossed outer diameter depth (Outer diameter)

Outside diameter 25.4× Flower tooth distance = Outside diameter before embossing

Example: 4.1÷25.4×0.8(Flower tooth distance) =0.13, Embossing depth should be 0.13

8. Diagonal conversion formula for polygonal materials:

1. Quadrangle: Opposite diameter ×1.414= Diagonal diameter

2. Pentagonal: Opposite diameter ×1.2361= Diagonal diameter

3. Hexagonal: Opposite side diameter x 1.1547= Diagonal diameter

Formula 2:1. Four corners: Opposite side diameter ÷0.71= Diagonal diameter

2. Hexagonal: Opposite side diameter / 0.866= Diagonal diameter

9. Tool thickness (cutter): Material diameter ÷10+0.7 Reference value

10. The calculation formula of taper:：

Formula 1:(Big head diameter - Small head diameter)÷(2× Total length of the taper)= Degree

Equal to the trig value

Formula 2: Simple

(Big head diameter - Small head diameter)÷28.7÷ Total length = Degree

Calculation formulas commonly used by the CNC processing center

1. Calculation of Trigonometric function 1.Tgθ=b/a ctgθ=a/b 2.Sinθ=b/c Cos=a/c 2. Calculation of cutting speed Vc=(π*D*S)/1000 Vc: linear speed (m/min) π: PI (3.14159) D: tool diameter (mm) S: speed (RPM) Example: Use a milling cutter of Φ25, Vc is (m/min)25 and S=?rpm Vc=πds/1000 25=π*25*S/1000 S=1000*25/ π*25 S=320rpm 3. Calculation of feed (F value) F=S*Z*Fz F: feed rate (mm/min) S: speed (RPM) Z: blade number Fz: (Actual feed per blade) Example: A standard 2-edge end milling cutter cutting workpiece at 2,000rpm) speed, how much is the feed (F value)? (Fz=0.25mm) F=S*Z*Fz F=2000*2*0.25 F=1000(mm/min) 4. Calculation of residual material height, Scallop=(ae*ae)/8R Scallop: Residual material height (mm) ae: XY pitch(mm) R Tool radius (mm) Example: φ 20R10 fine repair 2 blades, pre-residual material height is 0.002mm, how much is the Pitch? mm Scallop=ae2/8R 0.002=ae2/8*10 ae=0.4mm

5. Calculation of slug hole Φ=√2R2 X, Y=D/4 φ: Escape hole diameter (mm) R tool radius (mm) D: tool diameter (mm) Example: It is known that a hole must be processed at slug incline angle (as shown in the figure). The milling cutter is ψ10; What is the minimum slug incline angle hole? What are the center coordinates? Φ= 2R2 Φ= 2*52 Φ=7.1(mm) X, Y=D/4 X, Y=10/4 X, Y=2.5 mm Center coordinate is (2.5,-2.5)

6. The calculation of the reclaiming amount Q=(ae*ap*F)/1000Q: reclaiming amount (cm3/min) ae: XY pitch(mm) ap: Z pitch(mm) Example: Given the high machining of a mold kernel and cavity, the XY pitch of φ 35R5 is 60% of the tool, each layer is cut 1.5mm, and the feed is 2,000mm/min. How much is the feed of this tool? Q=(ae*ap*F)/1000 Q=35*0.6*1.5*2000/1000 Q=63 cm3/min 7. Calculation of feed for each blade Fz=hm * √(D/ap ) Fz: Implement feeding per blade hm: theoretical feed per blade ap: Z pitch(mm) D: Blade diameter (mm) Example: (the premise of depo XY pitch is 60% of the tool) depo φ 35R5 knife, cutting NAK80 material hm is 0.15mm, Z axis cutting depth 1.5mm, how much is the feed of each edge? Fz=hm * √(D/ap) Fz=0.2*√10/1.5 Fz=0.5mm 8. Machining method of die edge Knife-edge processing depth = plate thickness - knife-edge height + drill point (0.3d) D represents knife diameter 9. Bit drilling time T(min)=L(min)/N(rpm)*f(mm/rev) =πDL/1000vfL: Total length of drilling N: number of turns f: feed coefficient D: bit diameter v: cutting speed as shown in the figure Hole depth l Drill hole length L L=l+D/3 T=L/Nf=πDL/1000vf

Bit coefficient table fz

10. Calculation formula of tube teeth 1 inch =25.4mm=8 minutes For example, 25.4/ number of teeth = 25.4/18=1.414. The tooth distance is 5/16 11. Horsepower (gun drill) W=Md*N/ 97.410W: Required power (KW) Md: Torque (Kg-cm) N: rotary number (R.P.M.) 12. The torque calculation formula is as follows: Md=1/20*f*ps*r2 f is the feed mm / Rev coefficient r is the bit radius match (mm) α: cutting resistance ratio ps. In the small feed, the general steel is 500kg/m㎡; General cast iron is 300kg/m㎡;

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