Deep Hole Drilling Power, Torque, and Thrust Force Calculation

Deep Hole Drilling Power, Torque, and Thrust Force Calculation

Selecting the correct machine for a deep hole drilling application requires accurate estimation of cutting forces, torque, and power requirements. Undersized machines experience chatter, stalled spindles, and poor hole quality. Oversized machines waste capital and energy.

This guide provides the calculation methods for estimating the mechanical loads in deep hole drilling, with worked examples for common scenarios.

Cutting Force Model

Specific Cutting Force (Kc)

The fundamental parameter for cutting force calculation is the specific cutting force:

Kc = kc1.1 × (h × sin(κ))^(-mc)

Where:
Kc = specific cutting force (N/mm²)
kc1.1 = specific cutting force for 1 mm² chip cross-section
h = chip thickness (mm) = feed (mm/rev) for single-edge
mc = material factor (typically 0.25–0.35)
κ = cutting edge angle (°)

Simplified: Kc = kc1.1 × feed^(-mc)

Typical Kc Values

Gun Drilling: Single-Lip Force Calculation

Cutting Force

Fc = Kc × h × ap

Where:
Fc = cutting force (N)
Kc = specific cutting force (N/mm²)
h = chip thickness = feed per revolution (mm/rev)
ap = depth of cut = drill diameter (mm) for gun drilling

Torque

Torque (N·m) = Fc × (D/2) × kt

Where:
D = drill diameter (mm)
kt = torque coefficient (typically 0.4–0.6 for gun drilling)

Simplified: Torque (N·m) = Kc × f × D² / 4 × kt

Power

P (kW) = (Fc × Vc) / (60,000 × η)

Where:
Vc = cutting speed (m/min)
η = machine efficiency (typically 0.80–0.90)

Or directly from torque:
P (kW) = (Torque (N·m) × RPM) / (9,550 × η)

Thrust Force

Thrust (N) = Kc × f × D × kt2

Where:
kt2 = thrust coefficient (typically 0.6–0.9 for gun drilling)

Note: Gun drilling thrust is moderated by the pilot hole guide bushing
— actual machine thrust requirement is 50–70% of calculated value.

Example 1: Gun Drilling Ø10 mm × 500 mm deep, 4140 Steel

Step 1: Specific cutting force

Kc = 1,960 × (0.020)^(-0.27)
Kc = 1,960 × 2.86 = 5,606 N/mm²

Step 2: Cutting force

Fc = 5,606 × 0.020 × 10 = 1,121 N

Step 3: Torque

Torque = 1,121 × (10/2) × 0.5 / 1,000 = 2.80 N·m

Step 4: Power

P = (2.80 × 2,546) / (9,550 × 0.85) = 0.88 kW

Step 5: Thrust

Thrust = 5,606 × 0.020 × 10 × 0.75 = 841 N
Actual (with bushing guide) ≈ 841 × 0.6 = 505 N

Result: A 1.5–2.0 kW spindle is adequate for this operation.

BTA Drilling: Multi-Edge Force Calculation

Key Differences from Gun Drilling

Force Calculation for BTA

Total cutting force:
Fc_total = Kc × f × (D/2) × N   (approximate, for N edges)

Total torque:
Torque_total = Kc × f × (D/2) × N × (D/4) × kt
             = Kc × f × D² × N × kt / 8

Where kt for BTA = 0.5–0.7

Example 2: BTA Drilling Ø50 mm × 600 mm deep, 4140 Steel

Step 1: Specific cutting force

Kc = 1,960 × (0.25/3)^(-0.27)
Kc = 1,960 × 1.70 = 3,332 N/mm²

Step 2: Total torque

Torque_total = 3,332 × 0.25 × 50² × 3 × 0.6 / 8
             = 3,332 × 0.25 × 2,500 × 3 × 0.6 / 8
             = 468,562 / 8 = 468.6 N·m

Step 3: Power

P = (468.6 × 446) / (9,550 × 0.85) = 25.8 kW

Step 4: Thrust (approximately)

Thrust ≈ Kc × f × D × 0.3
       = 3,332 × 0.25 × 50 × 0.3
       = 12,495 N

Result: Requires approximately 26 kW spindle power. A 30–40 kW machine is appropriate.

Coolant Pump Power Calculation

Formula

Pump power (kW) = (Pressure (bar) × Flow (L/min)) / (600 × η_pump)

Where:
η_pump = pump efficiency (typically 0.75–0.85)

Example 3: Coolant Pump for Gun Drilling, Ø10 mm

P_pump = (100 × 30) / (600 × 0.80) = 6.25 kW

Example 4: Coolant Pump for BTA Drilling, Ø50 mm

P_pump = (40 × 350) / (600 × 0.80) = 29.2 kW

Total Machine Power

Total installed power = Spindle power + Coolant pump power + Auxiliaries

Auxiliaries (chip conveyor, hydraulics, controls): typically 5–15% of spindle + pump

Example: Complete Machine Sizing

Quick Reference: Power by Diameter

Gun Drilling — Approximate Spindle Power (kW)

BTA Drilling — Approximate Spindle Power (kW)

Summary

Accurate power, torque, and thrust calculation for deep hole drilling requires the specific cutting force model (Kc) appropriate to the material, the number of cutting edges (1 for gun drilling, 2–4 for BTA/ejector), and proper torque coefficients. For gun drilling, power requirements are moderate (0.3–5.5 kW for 5–40 mm diameter in steel). For BTA drilling, power increases significantly with diameter (8–80 kW for 25–100 mm in steel). Coolant pump power often exceeds spindle power, especially for high-pressure gun drilling. For parameter selection, see the parameters quick reference guide. For multi-spindle setups, see multi-spindle parameter coordination.