1. Cutting Speed (Vc)
Metric: [ Vc = \frac{\pi \times D \times n}{1{,}000} ]
Imperial (SFM): [ Vc = \frac{\pi \times D \times n}{12} \quad \text{or} \quad SFM = 0.2618 \times D \times RPM ]
Where:
- Vc = cutting speed (m/min or SFM)
- D = drill diameter (mm or in)
- n = spindle speed (RPM)
Sources: Guhring Drilling Formulas; Sandvik Coromant drilling formulas.
2. Spindle Speed (n)
From cutting speed: [ n = \frac{Vc \times 1{,}000}{\pi \times D} \quad (\text{metric}) ] [ RPM = \frac{Vc \times 12}{\pi \times D} \quad \text{or} \quad RPM = \frac{3.8197 \times SFM}{D} \quad (\text{imperial}) ]
Example — 10 mm drill at 70 m/min: [ n = \frac{70 \times 1{,}000}{\pi \times 10} = 2{,}228 \text{ RPM} ]
3. Feed Rate
Feed per minute (penetration rate): [ Vf = f \times n ]
Where:
- Vf = feed rate (mm/min or in/min)
- f = feed per revolution (mm/rev or in/rev)
- n = spindle speed (RPM)
Example — 0.05 mm/rev at 2,228 RPM: [ Vf = 0.05 \times 2{,}228 = 111 \text{ mm/min} ]
Sources: Guhring; Sandvik Coromant.
4. Material Removal Rate (MRR)
General formula: [ MRR = \frac{\pi}{4} \times D^2 \times f \times n ]
Simplified using feed rate: [ MRR = \frac{\pi \times D^2}{4} \times Vf ]
Cross-section method: [ MRR = Vf \times A \quad \text{where} \quad A = \frac{\pi \times D^2}{4} ]
Example — 10 mm drill, 0.05 mm/rev, 2,228 RPM: [ MRR = \frac{\pi}{4} \times 10^2 \times 0.05 \times 2{,}228 = 8{,}745 \text{ mm}^3/\text{min} \approx 8.7 \text{ cm}^3/\text{min} ]
Sources: Engineers Edge; ISCAR Drilling Handbook (p. 312); Guhring.
5. Machining Time
[ Tc = \frac{L}{Vf} = \frac{L}{f \times n} ]
Where:
- Tc = machining time (min)
- L = total axial travel including drill point length + overtravel (mm)
- Vf = feed rate (mm/min)
Drill point length addition: For a standard 118° point drill, add approximately (0.3 \times D) to the hole depth.
Example — 100 mm deep hole, 10 mm drill, 0.05 mm/rev, 2,228 RPM: [ L = 100 + (0.3 \times 10) = 103 \text{ mm} ] [ Tc = 103 \div (0.05 \times 2{,}228) = 103 \div 111 = 0.93 \text{ min} ]
Source: Guhring Drilling Formulas; Sandvik Coromant.
6. Net Cutting Power (Pc)
From cutting force and speed: [ Pc = \frac{Fc \times Vc}{60{,}000} \quad (\text{kW}) ]
Where Fc = cutting force (N), Vc = cutting speed (m/min).
From specific cutting force (imperial): [ Pc = \frac{D \times f \times Vc \times kc}{4 \times 33{,}000 \times \eta} ]
Quick estimate for BTA drilling: [ \text{Power} \approx 11 \text{ hp per inch of hole diameter} ]
Example — 3 in (76 mm) BTA drill: approximately 33 hp (25 kW) at the spindle.
Sources: ISCAR Drilling Handbook; Guhring; ScienceDirect (Cutting Power).
7. Torque (Mc)
Metric: [ Mc = \frac{Fc \times D}{2{,}000} \quad (\text{Nm}) ]
Imperial (from horsepower): [ Mc = \frac{Hp \times 5{,}252}{RPM} \quad (\text{ft-lbs}) ]
Sources: ISCAR Drilling Handbook (p. 312); Guhring.
8. Coolant Pressure Drop Model (Blasius Equation)
For turbulent flow in the coolant channel of a gun drill or BTA tube:
[ \Delta p \approx 0.241 \times L \times \rho^{3/4} \times \mu^{1/4} \times d^{-4.75} \times Q^{1.75} ]
Where:
- Δp = pressure drop (Pa)
- L = coolant channel length (m)
- ρ = fluid density (kg/m³)
- μ = dynamic viscosity (kg/(m·s))
- d = coolant channel hydraulic diameter (m)
- Q = volume flow rate (m³/s)
Practical implication: Reducing the coolant hole diameter by 10% increases pressure drop by approximately 60%, due to the (d^{-4.75}) exponent.
Source: Jung & Ni, “Prediction of Coolant Pressure and Volume Flow Rate in Gundrilling,” ASME, 2003. See Coolant Pressure Guide for practical tables.
9. Nozzle Flow Formula (Gun Drilling Coolant Hole)
[ Q = 30 \times d^2 \times \sqrt{P} ]
Where:
- Q = flow rate (GPM)
- d = coolant hole diameter (inches)
- P = pressure (psi)
Example — 0.060 in coolant hole at 1,000 psi: [ Q = 30 \times (0.060)^2 \times \sqrt{1{,}000} = 3.4 \text{ GPM (12.9 L/min)} ]
Source: Master Chemical / Rotem gun drilling guide.
10. Coolant Flow — Volume-Per-Revolution Rule (Gun Drilling)
For estimating required flow rate:
[ Q = \frac{\pi \times D^2}{4} \times f \times n ]
Where Q = flow rate (mm³/min). Convert to L/min by dividing by 1,000,000.
Practical rule: For every revolution of the drill, deliver enough coolant to fill the volume of the hole being drilled.
See the Speeds and Feeds Reference for diameter-specific coolant pressure and flow recommendations.
11. Tooling Cost per Edge
Reground tool (gun drill): [ C_E = \frac{C_T + (R \times C_R)}{1 + R} ]
Where:
- C_E = cost per edge
- C_T = initial tool cost
- R = number of regrinds
- C_R = cost per regrind
Indexable insert tool (BTA): [ C_E = \left(\frac{C_I}{E}\right) \times \frac{4}{3} + \frac{C_B}{B_L} ]
Where:
- C_I = insert cost
- E = edges per insert
- 4/3 = safety factor for insert breakage
- C_B = cutter body cost
- B_L = cutter body life in number of edges
Example — Gun drill, $120 tool, 10 regrinds at $15 each: [ C_E = (120 + 10 \times 15) \div (1 + 10) = $24.55 \text{ per edge} ]
Source: Machinery’s Handbook econometric formulas.
12. L/D Ratio and Hole Classification
[ L/D = \frac{\text{Hole depth}}{\text{Hole diameter}} ]
| L/D Range | Classification | Practical Method |
|---|---|---|
| < 3:1 | Shallow | Conventional twist drill |
| 3:1–5:1 | Semi-deep | Twist drill with pecking |
| 5:1–10:1 | Transition | Through-coolant twist drill |
| 10:1–30:1 | Deep | Gun drilling |
| 30:1–100:1 | Very deep | Gun drilling (dedicated machine) |
| > 100:1 | Ultra-deep | Specialized gun drilling |
Source: VDI 3210; UNISIG. See Depth-to-Diameter Ratio Guide.
13. Surface Finish Conversion (Approximate)
| Ra (µm) | Ra (µ-in) | Rz (µm) | RMS (µ-in) | ISO N Grade |
|---|---|---|---|---|
| 0.05 | 2 | 0.4 | 2.2 | N1 |
| 0.1 | 4 | 0.8 | 4.4 | N2 |
| 0.2 | 8 | 1.6 | 8.8 | N3 |
| 0.4 | 16 | 3.2 | 17.6 | N4 |
| 0.8 | 32 | 6.3 | 35.2 | N5 |
| 1.6 | 63 | 12.5 | 69.3 | N6 |
| 3.2 | 125 | 25 | 138 | N7 |
| 6.3 | 250 | 50 | 276 | N8 |
Approximate conversion: Rz ≈ 7.6 × Ra (varies by material and process). RMS ≈ 1.11 × Ra.
Sources: ISO 1302; Widma surface finish reference; multiple chart sources.
14. Unit Conversions (Common)
| Convert | Multiply By |
|---|---|
| mm → in | 0.03937 |
| in → mm | 25.4 |
| m/min → SFM | 3.281 |
| SFM → m/min | 0.3048 |
| bar → psi | 14.504 |
| psi → bar | 0.06895 |
| L/min → GPM | 0.2642 |
| GPM → L/min | 3.785 |
| kW → hp | 1.341 |
| hp → kW | 0.7457 |
| N·m → ft·lb | 0.7376 |
| ft·lb → N·m | 1.356 |
| mm/rev → in/rev | 0.03937 |
| in/rev → mm/rev | 25.4 |
Key Sources
- Guhring, “Drilling Formulas Technical Document” — RPM, speed, feed, MRR, power, torque formulas
- Sandvik Coromant, “Drilling Formulas and Definitions” — cutting speed, penetration rate, MRR, net power
- ISCAR Drilling Handbook (pages 312, 287–288) — MRR, torque, net power, BTA coolant and power charts
- Engineers Edge, “Machining and Material Removal Rate Calculator” — MRR formula
- Jung & Ni, “Prediction of Coolant Pressure and Volume Flow Rate in Gundrilling,” ASME, 2003 — Blasius model
- Master Chemical / Rotem — nozzle flow formula and volume-per-revolution rule
- Machinery’s Handbook (29th ed.) — tooling cost econometric formulas
- VDI 3210 — L/D ratio classification
- ISO 1302 — surface finish parameters and conversion
- Widma Engineering Calculators — surface finish and unit conversion reference