Commonly used CNC calculation formulas, worth collecting!

　　Common CNC Calculation Formulas

　　1. Cutting Speed

　　V=πDN/1000 N=rpm (Spindle Speed) D=Φmm (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/sq.mm q=f×d [Cutting Area (sq.mm)]

　　4. Cutting Torque

　　T=P×(D/2) T=kg-m D=Φmm (Cutting Diameter)

　　5. Feed Rate and Feed per Revolution Vf=N×f Vf=Feed Rate (mm/min) N=rpm (Spindle Speed) f=Feed per Revolution (mm/rev)

　　6. Drilling Time T=L/Nf=πDL/1000Vf T=Drilling Time (min) D=Φmm (Drill Diameter) L=Drilling Depth (mm) V=M/min f=Feed per Revolution (mm/rev)

　　7. Tool Nose Radius Compensation

　　Z=r(1-tanθ/2) X=Ztanθ Z=Z-axis Compensation X=X-axis Compensation r=Tool Nose Radius θ=Angle

　　8. Worktable Feed Rate Vf=fz×Z×n Vf=Worktable Feed Rate (mm/min) fz=Feed per Tooth (mm/t) Z=Number of Cutter Teeth n=Cutter Speed

　　Top Ten Commonly Used Calculation Formulas in CNC Machining

　　International Standard

　　1. Internal Diameter Calculation Formula for Tapping a Thread:

　　Formula: Outer Diameter of Thread - 1/2 × Thread 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-System Taps:

　　1 inch = 25.4mm (code)

　　Example 1: (1/4-30)

　　1/4×25.4=6.35 (Thread Diameter)

　　25.4÷30=0.846 (Thread Pitch)

　　Therefore, 1/4-30 converted to metric thread should be: M6.35×0.846

　　Example 2: (3/16-32)

　　3/16×25.4=4.76 (Thread Diameter)

　　25.4÷32=0.79 (Thread Pitch)

　　Therefore, 3/16-32 converted to metric thread should be: M4.76×0.79

　　3. Formula for Converting General Inch Threads to Metric Threads:

　　Numerator ÷ Denominator × 25.4 = Outer Diameter of Thread (same as above)

　　Example 1: (3/8-24)

　　3÷8×25.4=9.525 (Outer Diameter of Thread)

　　25.4÷24=1.058 (Metric Thread Pitch)

　　Therefore, 3/8-24 converted to metric thread should be: M9.525×1.058

　　4. Formula for Converting US Threads to Metric Threads:

　　Example: 6-32

　　6-32 (0.06+0.013)/code × 6 = 0.138

　　0.138×25.4=3.505 (Outer Diameter of Thread)

　　25.4÷32=0.635 (Thread Pitch)

　　Therefore, 6-32 converted to metric thread should be: M3.505×0.635

　　1. Hole Diameter Calculation Formula:

　　Outer Diameter of Thread - 1/2 × Thread Pitch should be:

　　M3.505-1/2×0.635=3.19

　　Therefore, the internal diameter of 6-32 should be 3.19

　　2. Tapping Hole Calculation Method:

　　Simplified Calculation Formula 1 for Tap Drill Size:

　　Outer Diameter of Thread - (Thread Pitch × 0.4250.475)/code = Tap Drill Size

　　Example 1: M6×1.0

　　M6-(1.0×0.425)=5.575 (Maximum Tap Drill Size)

　　M6-(1.0×0.475)=5.525 (Minimum)

　　Example 2: Simplified Calculation Formula for Cutting Tap Drill Size:

　　M6-(1.0×0.85)=5.15 (Maximum)

　　M6-(1.0×0.95)=5.05 (Minimum)

　　M6-(Thread Pitch × 0.860.96)/code = Tap Drill Size

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

　　5. Simplified Calculation Formula for Thread Outer Diameter:

　　1. Diameter - 0.01 × 0.645 × Pitch (GO/NO-GO gauge required)

　　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)

　　VI. Metric thread rolling diameter calculation formula: (full thread calculation)

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

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

　　VII. Embossing outer diameter depth (outer diameter)

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

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

　　VIII. Conversion formula for polygonal materials:

　　1. Quadrilateral: Side length × 1.414 = Diagonal length

　　2. Pentagon: Side length × 1.2361 = Diagonal length

　　3. Hexagon: Side diameter × 1.1547 = Diagonal diameter

　　Formula 2: 1. Quadrilateral: Side length ÷ 0.71 = Diagonal length

　　2. Hexagon: Side length ÷ 0.866 = Diagonal length

　　IX. Tool thickness (cutting tool): Material outer diameter ÷ 10 + 0.7 reference value

　　X. Taper calculation formula:

　　Formula 1: (Large diameter - Small diameter) ÷ (2 × Total length of taper) = Angle

　　Equals to checking trigonometric function values

　　Formula 2: Simplified

　　(Large diameter - Small diameter) ÷ 28.7 ÷ Total length = Angle

　　Common calculation formulas for CNC machining centers

　　I. Trigonometric function calculation 1. tgθ = b/a ctgθ = a/b 2. Sinθ = b/c Cos = a/c II. Cutting speed calculation Vc = (π * D * S) / 1000 Vc: Linear velocity (m/min) π: Pi (3.14159) D: Tool diameter (mm) S: Speed (rpm) Example. Using Φ25 milling cutter Vc is (m/min) 25 Find S =? rpm Vc = πds/1000 25 = π * 25 * S/1000 S = 1000 * 25/ π * 25 S = 320 rpm III. Feed rate (F value) calculation F = S * Z * Fz F: Feed rate (mm/min) S: Speed (rpm) Z: Number of blades Fz: (Actual feed per blade) Example. A standard 2-blade end mill cuts the workpiece at a speed of 2000 rpm), find the feed rate (F value)? (Fz = 0.25 mm) F = S * Z * Fz F = 2000 * 2 * 0.25 F = 1000 (mm/min) IV. Calculation of residual material height Scallop = (ae * ae) / 8R Scallop: Residual material height (mm) ae: XY pitch (mm) R Tool radius (mm) Example. Φ20R10 fine-tuning 2 blades, pre-residual material height 0.002 mm, find Pitch? mm Scallop = ae2/8R 0.002 = ae2/8 * 10 ae = 0.4 mm

　　V. Calculation of escape holes 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 mold cavity needs to be processed with an escape angle (as shown in the figure), and the milling cutter used is ψ10; what is the minimum escape angle hole? What are the coordinates of the center? Φ = √2R2 Φ = √2 * 52 Φ = 7.1 (mm) X, Y = D/4 X, Y = 10/4 X, Y = 2.5 mm The coordinates of the center are (2.5, -2.5)

　　VI. Calculation of material removal rate Q = (ae * ap * F) / 1000 Q: Material removal rate (cm3/min) ae: XY pitch (mm) ap: Z pitch (mm) Example. It is known that a mold core needs to be processed with equal height cavity, the XY pitch of Φ35R5 cutter is 60% of the tool, each layer cuts 1.5 mm, and the feed rate is 2000 mm/min. What is the material removal rate of this tool? Q = (ae * ap * F) / 1000 Q = 35 * 0.6 * 1.5 * 2000/1000 Q = 63 cm3/min VII. Calculation of feed per tooth Fz = hm * √(D/ap) Fz: Actual feed per tooth hm: Theoretical feed per tooth ap: Z pitch (mm) D: Blade diameter (mm) Example (Premise: depo XY pitch is 60% of the tool) depo Φ35R5 cutter, cutting NAK80 material hm is 0.15 mm, Z-axis cutting depth is 1.5 mm, what is the feed per tooth? Fz = hm * √(D/ap) Fz = 0.2 * √10/1.5 Fz = 0.5 mm VIII. Die cutting edge processing method Cutting edge processing depth = Plate thickness - Cutting edge height + Drill tip (0.3D) D represents the drill diameter IX. Drill hole time formula T (min) = L (min) / N (rpm) * f (mm/rev) = πDL/1000vf L: Full length of drill hole N: Rotation speed f: Feed rate coefficient D: Drill diameter v: Cutting speed As shown in the figure, hole depth l, drill hole full length L, then L = l + D/3 T = L/Nf = πDL/1000vf

　　Drill coefficient table fz

　　X. Pipe thread calculation formula 1 inch = 25.4 mm = 8 points For example, 25.4/number of teeth = pitch 25.4/18 = 1.414 The pitch is 5/16 tap XI. Horsepower (gun drill) W = Md * N/97.410 W: Required power (KW) Md: Torque (kg-cm) N: Rotation speed (r.p.m) XII. Torque calculation formula is as follows: Md = 1/20 * f * ps * r2 f is the feed rate mm/rev coefficient r is the drill radius (mm) α: Cutting resistance ratio ps. When the feed is small, generally steel is 500 kg/m㎡; generally cast iron is 300 kg/m㎡;