Appearance
A deep hole drilling operation producing 25 mm × 2,000 mm bores in alloy steel experiences erratic chip evacuation and intermittent coolant pressure spikes. Analysis reveals that the coolant pump is undersized — delivering 80 L/min at 2.0 MPa against a system requirement of 120 L/min at 3.0 MPa for stable chip transport in the annular gap. The annular gap velocity is calculated at 4.2 m/s, below the minimum 6.0 m/s required for reliable chip conveyance in steel. Replacing the pump with a 150 L/min unit at 4.0 MPa restores annular velocity to 7.8 m/s, resolving chip packing.
Fundamental Fluid Dynamics for Deep Hole Drilling
Coolant flow in deep hole drilling serves three simultaneous functions: cooling the cutting zone to prevent thermal damage, lubricating the tool-chip interface to reduce friction, and transporting chips out of the bore through the annular gap or flute. The coolant system must deliver sufficient flow and pressure to maintain all three functions across the full hole depth.
The two fundamental equations governing coolant flow in deep hole drilling are the continuity equation (mass conservation) and the Bernoulli equation (energy conservation):
Continuity equation: Q = A₁ · v₁ = A₂ · v₂
Where:
- Q = volumetric flow rate (m³/s)
- A = cross-sectional area (m²)
- v = flow velocity (m/s)
Bernoulli equation with head loss: P₁ / (ρ·g) + v₁² / (2g) + z₁ = P₂ / (ρ·g) + v₂² / (2g) + z₂ + h_f
Where:
- P = pressure (Pa)
- ρ = coolant density (kg/m³)
- g = gravitational acceleration (m/s²)
- v = velocity (m/s)
- z = elevation head (m)
- h_f = head loss due to friction (m)
In deep hole drilling, the elevation term is typically negligible, and the dominant losses are frictional pressure drops through the coolant circuit.
Hydraulic Diameter and Annular Gap Geometry
The coolant in BTA drilling flows through two distinct passages: the annular gap between the drill tube outer wall and the bore surface (coolant delivery in BTA), and the interior of the drill tube (chip-laden coolant return). In gun drilling, coolant is delivered through an internal passage in the gun drill and returns through the V-shaped flute.
For BTA drilling, the annular gap between the drill tube and the bore wall is the critical flow passage. The hydraulic diameter of this annulus is:
Dh = Do − Di
Where:
- Dh = hydraulic diameter (mm)
- Do = bore diameter (mm)
- Di = drill tube outer diameter (mm)
The annular gap cross-sectional area is:
A = (π / 4) × (Do² − Di²)
For a typical BTA system, the drill tube outer diameter is approximately 0.7–0.85 × bore diameter. This means the annular gap area is approximately 28–50% of the bore cross-sectional area.
| Bore Dia (mm) | Tube OD (mm) | Gap (mm) | Annular Area (mm²) | Hydraulic Diameter (mm) |
|---|---|---|---|---|
| 10 | 8 | 1.0 | 28.3 | 2.0 |
| 20 | 16 | 2.0 | 113.1 | 4.0 |
| 30 | 24 | 3.0 | 254.5 | 6.0 |
| 40 | 32 | 4.0 | 452.4 | 8.0 |
| 50 | 40 | 5.0 | 706.9 | 10.0 |
| 80 | 64 | 8.0 | 1,809.6 | 16.0 |
| 100 | 80 | 10.0 | 2,827.4 | 20.0 |
Coolant Flow Velocity Calculation
The mean coolant velocity in the annular gap is the primary parameter controlling chip transport capability. From the continuity equation:
v = Q / A = 4Q / (π × (Do² − Di²))
Where:
- v = mean annular velocity (m/s)
- Q = volumetric flow rate (m³/s)
- Do = bore diameter (m)
- Di = tube outer diameter (m)
For reliable chip transport in deep hole drilling, the minimum annular velocity must exceed the settling velocity of the largest chip particle. Industry practice recommends:
- Minimum annular velocity for steel chips: 5–8 m/s
- Minimum annular velocity for cast iron chips: 3–5 m/s
- Minimum annular velocity for aluminium chips: 4–6 m/s
- Minimum annular velocity for titanium chips: 6–10 m/s
TIP
The annular velocity is the single most important coolant parameter for chip evacuation. If the annular velocity is too low, chips settle in the annular gap and pack, causing coolant pressure to spike and cutting torque to increase. A simple check: at the target flow rate, coolant should stream from the drill tube exit at a velocity that carries chips at least 500 mm horizontally before settling. Sandvik Coromant recommends that in horizontal drilling, the coolant stream should project at least 300 mm without visible drop. For a given bore diameter, increasing flow rate by 40% approximately doubles the annular velocity (since v ∝ Q), making flow rate the most effective adjustment for improving chip evacuation.
Reynolds Number and Flow Regime
The Reynolds number determines whether the coolant flow is laminar or turbulent, which directly affects both heat transfer and chip transport capability:
Re = ρ × v × Dh / μ = v × Dh / ν
Where:
- Re = Reynolds number (dimensionless)
- ρ = coolant density (kg/m³)
- v = mean annular velocity (m/s)
- Dh = hydraulic diameter (m)
- μ = dynamic viscosity (Pa·s)
- ν = kinematic viscosity (m²/s)
Substituting the expressions for annular velocity and hydraulic diameter:
Re = 4Q / (π × ν × (Do + Di))
| Flow Regime | Reynolds Number | Heat Transfer | Chip Transport | Occurrence in Deep Hole Drilling |
|---|---|---|---|---|
| Laminar | Re < 2,000 | Poor | Poor — chips settle | Low-flow or high-viscosity coolant |
| Transitional | 2,000 < Re < 4,000 | Moderate | Unstable | Intermittent flow conditions |
| Turbulent | Re > 4,000 | Excellent | Good — chips suspended | Preferred regime for BTA drilling |
| Fully turbulent | Re > 10,000 | Maximum | Best — high shear lifts chips | High-flow BTA and gun drilling |
For water-soluble emulsion at 8–12% concentration (ν ≈ 1.0–1.5 × 10⁻⁶ m²/s at 30°C), most BTA drilling operations operate in the turbulent regime. For neat oils (ν ≈ 10–40 × 10⁻⁶ m²/s), the same flow rate produces lower Reynolds numbers, and larger bores may operate in the transitional regime.
Example calculation: For a 25 mm bore with a 20 mm tube, coolant flow of 120 L/min, and emulsion coolant at ν = 1.2 × 10⁻⁶ m²/s:
Re = 4 × (0.120/60) / (π × 1.2 × 10⁻⁶ × (0.025 + 0.020)) Re = 4 × 0.002 / (π × 1.2 × 10⁻⁶ × 0.045) Re = 0.008 / (1.696 × 10⁻⁷) Re = 47,170 → Fully turbulent
Pressure Drop Calculation — Darcy-Weisbach Equation
The total coolant pressure required at the pump must overcome frictional losses through the entire coolant circuit: supply lines, annular gap, drill head passages, return tube, and chip collection system. The dominant loss is typically the annular gap.
The Darcy-Weisbach equation gives the pressure drop for flow through a straight passage:
ΔP = f × (L / Dh) × (ρ × v² / 2)
Where:
- ΔP = pressure drop (Pa)
- f = Darcy friction factor (dimensionless)
- L = passage length (m)
- Dh = hydraulic diameter (m)
- ρ = coolant density (kg/m³)
- v = mean velocity (m/s)
Friction Factor Determination
For turbulent flow (Re > 4,000), the Colebrook equation gives the friction factor:
1 / √f = −2 × log₁₀[(ε / Dh) / 3.7 + 2.51 / (Re × √f)]
Where ε is the surface roughness of the passage wall (m). For smooth drill tubes and bore surfaces, ε ≈ 0.001–0.005 mm.
For practical deep hole drilling calculations, the Blasius correlation provides a good approximation for smooth pipes in the range 4,000 < Re < 10⁵:
f = 0.079 × Re⁻⁰·²⁵
For laminar flow (Re < 2,000):
f = 64 / Re
Total System Pressure Requirement
The total pump pressure requirement is the sum of all losses in the coolant circuit:
P_total = ΔP_annular + ΔP_return_tube + ΔP_drill_head + ΔP_supply_line + ΔP_filters + P_backpressure
| Circuit Component | Typical Pressure Drop | Notes |
|---|---|---|
| Supply lines and swivel | 0.1–0.5 MPa | Depends on line diameter and length |
| Annular gap (BTA) | 0.5–3.0 MPa | Dominant loss; increases with depth |
| Drill head passages | 0.2–0.8 MPa | Includes nozzle and chip throat |
| Return tube (internal) | 0.3–1.5 MPa | Chip-laden flow increases loss |
| Filters | 0.1–0.5 MPa | Clean filters; increases as filter loads |
| Chip collection system | 0.1–0.3 MPa | Settlement tank and baffles |
A safety factor of 20–30% should be added to the calculated total to account for wear, filter loading, and coolant property variations.
Coolant Pressure Requirements by Bore Diameter
The following table summarises practical coolant pressure and flow requirements for BTA drilling based on industry data and the VDI 3209 standard:
| Bore Dia (mm) | Flow Rate (L/min) | Pressure (MPa) | Annular Velocity (m/s) | Typical Application |
|---|---|---|---|---|
| 6–10 | 20–50 | 3.0–8.0 | 6–12 | Gun drilling, micro BTA |
| 10–20 | 50–100 | 2.5–5.0 | 6–10 | Small BTA, gun drilling |
| 20–30 | 80–150 | 2.0–4.0 | 5–9 | Standard BTA |
| 30–50 | 120–250 | 1.5–3.5 | 5–8 | Medium BTA |
| 50–80 | 200–400 | 1.0–3.0 | 4–7 | Large BTA |
| 80–120 | 300–600 | 0.8–2.5 | 4–6 | Extra-large BTA |
For gun drilling, the coolant pressure requirements are significantly higher because the coolant must pass through the internal drill passage and return through the V-shaped flute with its small cross-sectional area:
| Bore Dia (mm) | Flow Rate (L/min) | Pressure (MPa) | L/D Ratio |
|---|---|---|---|
| 1–3 | 2–10 | 10–20 | < 100 |
| 1–3 | 3–12 | 15–30 | > 100 |
| 3–6 | 5–20 | 8–17 | < 100 |
| 3–6 | 8–30 | 12–25 | > 100 |
| 6–10 | 10–40 | 6–12 | < 100 |
| 6–10 | 15–50 | 10–20 | > 100 |
| 10–20 | 20–80 | 4–10 | < 100 |
| 10–20 | 30–100 | 8–15 | > 100 |
Chip Transport Mechanics
Settling Velocity
The settling velocity of a chip particle in the coolant determines the minimum flow velocity required for transport. For a spherical particle in the Stokes regime, the terminal settling velocity is:
v_t = (ρ_c − ρ_f) × g × d_p² / (18 × μ)
Where:
- v_t = terminal settling velocity (m/s)
- ρ_c = chip density (kg/m³) — 7,800 for steel
- ρ_f = coolant density (kg/m³) — 980–1,050 for emulsion
- g = gravitational acceleration (9.81 m/s²)
- d_p = equivalent particle diameter (m)
- μ = dynamic viscosity (Pa·s)
For non-spherical chips typical of deep hole drilling, the drag coefficient correction must be applied. A C-shaped chip 5 mm long has an effective settling velocity approximately 2–3× higher than a sphere of equivalent mass due to its flat shape presenting a larger area perpendicular to flow.
Chip Transport Ratio
The chip transport ratio is defined as:
CTR = v_annular / v_t
| CTR Value | Chip Transport Condition | Risk |
|---|---|---|
| < 1.0 | Chips settle | Immediate packing risk |
| 1.0–2.0 | Marginal transport | Intermittent evacuation |
| 2.0–5.0 | Good transport | Reliable operation |
| > 5.0 | Excellent transport | Best chip evacuation |
For reliable deep hole drilling, a CTR of at least 3.0 is recommended. For steel chips in water-soluble emulsion, this typically requires annular velocities of 5–8 m/s depending on chip size and shape.
Chip-Laden Flow Pressure Drop
The presence of chips in the coolant increases the effective viscosity and pressure drop. The modified pressure drop for chip-laden flow is:
ΔP_slurry = ΔP_clean × (1 + K × C_v)
Where:
- K = empirical constant (2.5–5.0 for metal chips)
- C_v = volumetric concentration of chips in coolant (typically 0.1–1.0%)
In practice, the chip concentration in the return flow varies with drilling parameters. At a penetration rate of 100 mm/min in a 25 mm bore, the chip generation rate is approximately 0.4 kg/min. At 120 L/min coolant flow, this gives a chip concentration of approximately 0.04% by volume — negligible for pressure drop but significant for chip settling behaviour.
Pump Sizing and Coolant System Design
Pump Selection Criteria
| Pump Type | Pressure Range | Flow Range | Efficiency | Application |
|---|---|---|---|---|
| Centrifugal (multistage) | 0.5–5.0 MPa | 50–1,000 L/min | 70–85% | BTA drilling, moderate pressure |
| Piston / plunger | 5.0–30 MPa | 10–200 L/min | 80–90% | Gun drilling, high pressure |
| Gear pump | 0.5–3.0 MPa | 20–300 L/min | 60–75% | Low-pressure BTA, chip transfer |
| Screw pump | 0.5–4.0 MPa | 50–800 L/min | 65–80% | High-viscosity coolant |
System Design Rules
- Coolant reservoir capacity: 5–10× the pump flow rate per minute (per Sandvik Coromant)
- Filtration: 30–50 µm for BTA (paper band or cartridge); 5–20 µm for gun drilling
- Coolant temperature: 20–35°C, controlled by heat exchanger for high-pressure systems
- Pressure regulation: Bypass valve with accumulator to dampen pressure spikes from chip blockages
- Flow measurement: Magnetic flow meter or turbine meter with digital readout
- Pressure monitoring: Transducer at pump outlet and at drill head inlet
WARNING
Pressure spikes from chip blockages are a common cause of drill tube failure and coolant system damage. A sudden pressure increase of 50% or more above normal operating pressure indicates chip packing in the annular gap or drill tube. The coolant system must include a pressure relief valve set at 120% of maximum normal operating pressure, and the machine control should trigger a feed hold if pressure exceeds a programmable threshold. In BTA drilling, a pressure spike followed by a sudden drop typically indicates that a packed chip column has been expelled — the drill should be retracted and inspected after such an event. For automated operation, pressure trend monitoring is more informative than instantaneous pressure: a gradual pressure increase over several seconds indicates progressive chip packing, while instantaneous spikes indicate a blockage event.
Coolant Selection and Viscosity Effects
| Coolant Type | Viscosity at 30°C (mm²/s) | Density (kg/m³) | Application | Chip Transport |
|---|---|---|---|---|
| Water-soluble emulsion 5–8% | 0.8–1.2 | 990–1,010 | General steel BTA drilling | Good — low viscosity = high Re |
| Water-soluble emulsion 8–12% | 1.0–1.5 | 995–1,020 | Stainless, alloy steel BTA | Good |
| Synthetic solution | 1.0–2.0 | 990–1,010 | High-pressure gun drilling | Good |
| Neat oil (low viscosity) | 10–15 | 850–880 | Gun drilling, small bores | Moderate — higher Re needed |
| Neat oil (medium viscosity) | 15–30 | 860–900 | Gun drilling, deep holes | Fair — compensate with higher pressure |
| Neat oil (high viscosity) | 30–50 | 870–920 | Specialised deep hole drilling | Poor — laminar flow risk |
The viscosity of the coolant directly affects the Reynolds number and therefore the flow regime. At the same flow rate, switching from emulsion to neat oil reduces the Reynolds number by a factor of 10–20, potentially dropping from turbulent to laminar flow.
Troubleshooting Coolant-Related Problems
| Problem | Likely Cause | Corrective Action |
|---|---|---|
| Annular velocity too low | Insufficient flow for bore diameter | Increase pump flow; reduce tube OD if possible |
| Pressure spikes during drilling | Chip packing in annular gap | Increase flow; check chip breaker geometry |
| Gradual pressure increase over hole depth | Chip accumulation in return tube | Increase flow; check chip size and shape |
| Sudden pressure drop | Chip blockage cleared or tube rupture | Retract and inspect; pressure test system |
| Low pressure at drill head | Supply line leak or worn pump seal | Inspect supply lines; service pump |
| Coolant temperature rising | Insufficient heat exchanger capacity | Add cooler; increase reservoir size |
| Chips not reaching filter | Settling in tank or lines | Increase flow velocity in return lines |
| Foaming at coolant return | Excessive aeration or wrong coolant | Add defoamer; check return line immersion |
| Filter loading too fast | Chip breaker producing fines | Optimise chip breaker; check filtration |
| Erosion at drill head passages | Abrasive chip-laden flow at high velocity | Check for chip recirculation; harden passages |
FAQ
What is the minimum coolant flow rate for BTA drilling?
The minimum flow rate for BTA drilling is determined by the annular gap velocity requirement. For reliable chip transport in steel, a minimum annular velocity of 5–8 m/s is required. The flow rate is calculated from Q = v × A, where A is the annular cross-sectional area. For a 25 mm bore with a 20 mm drill tube (annular area = 177 mm²), achieving 6 m/s requires Q = 6 × 177 × 10⁻⁶ × 60 × 1000 = 63.7 L/min, rounded to 65 L/min minimum. For conservative design, use 100–120 L/min. The rule of thumb is 3–5 L/min per mm of bore diameter.
How is coolant pressure calculated for deep hole drilling?
Coolant pressure is calculated by summing all frictional losses in the coolant circuit, using the Darcy-Weisbach equation for each segment. The dominant loss is typically the annular gap between the drill tube and bore wall. The total pressure requirement is the sum of annular gap loss, return tube loss, drill head loss, supply line loss, filter loss, and a 20–30% safety factor. For a 25 mm × 2,000 mm BTA bore at 120 L/min, the total pressure requirement is typically 2.0–4.0 MPa depending on tube geometry and coolant properties.
What is the difference between BTA and gun drilling coolant requirements?
BTA drilling uses external coolant delivery through the annular gap between the drill tube and bore wall, operating at moderate pressure (1.5–5.0 MPa) and high flow (50–600 L/min). Gun drilling uses internal coolant delivery through the drill's internal passage, operating at high pressure (5–30 MPa) and low flow (2–100 L/min). The fundamental difference is that BTA coolant must fill a large annular area requiring high flow, while gun drilling coolant must pass through a small internal drill passage requiring high pressure to overcome the restrictive flow path.
What is the annular gap and why is it important for coolant flow?
The annular gap in BTA drilling is the space between the drill tube outer diameter and the bore surface. It serves as the coolant delivery passage from the pump to the cutting zone. The gap width (typically 1–10 mm depending on bore diameter) determines the annular area, which together with flow rate determines the coolant velocity. The hydraulic diameter of the annular gap (equal to the gap width for concentric annuli) is the characteristic length for Reynolds number calculation. A larger gap reduces velocity at the same flow rate, while a smaller gap increases velocity but also increases pressure drop.
What flow regime should coolant operate in for deep hole drilling?
Coolant should operate in the turbulent regime (Re > 4,000) for reliable chip transport and heat transfer. Turbulent flow creates eddies that keep chips suspended in the coolant stream, prevents chip settling in the annular gap, and maximises heat transfer from the cutting zone. Most BTA operations with water-soluble emulsion operate well into the turbulent regime (Re = 10,000–100,000). Gun drilling with neat oil may operate in the transitional regime (Re = 2,000–4,000) due to higher viscosity, requiring higher pressure to compensate.
How does coolant viscosity affect chip transport?
Coolant viscosity affects both the Reynolds number (flow regime) and the chip settling velocity. Higher viscosity increases drag force on chips (improving suspension) but reduces the Reynolds number (potentially causing laminar flow). In the laminar regime, chip transport relies entirely on viscous drag rather than turbulent eddies, which is less effective for large or dense chips. For water-soluble emulsions (ν ≈ 1.0–1.5 mm²/s), turbulent flow is easily achieved. For neat oils (ν ≈ 10–40 mm²/s), higher flow rates are needed to reach turbulent conditions. The optimal viscosity for chip transport is the lowest viscosity that still provides adequate lubricity and corrosion protection.
What is the settling velocity of steel chips in coolant?
The settling velocity depends on chip size, shape, and coolant properties. For a 3 mm equivalent spherical steel chip in emulsion coolant, the Stokes settling velocity is approximately 0.8 m/s. However, actual C-shaped chips settle at 1.5–3.0 m/s due to their non-spherical shape and larger projected area. For reliable chip transport, the annular velocity must exceed the settling velocity by a factor of at least 3 (CTR ≥ 3). For steel chips in emulsion, this means annular velocity ≥ 5–8 m/s depending on chip size.
How is the pump sized for a BTA drilling system?
Pump sizing begins with the bore diameter and depth requirements. The flow rate is selected to achieve an annular velocity of 5–8 m/s for the given annular gap geometry. The pressure is calculated from the Darcy-Weisbach equation for the full coolant circuit. A pump curve with the required flow at the required pressure is selected, with a 20–30% safety margin. The reservoir is sized at 5–10× the pump flow per minute. The filtration system is sized to handle the full flow rate at 30–50 µm for BTA or 5–20 µm for gun drilling. The heat exchanger capacity is sized to maintain coolant temperature at 20–35°C.
What causes coolant pressure spikes in deep hole drilling?
Coolant pressure spikes are most commonly caused by chip packing in the annular gap or drill tube. When a large chip or cluster of chips blocks the coolant passage, pressure rises rapidly until either the blockage is cleared (pressure drops suddenly) or the relief valve opens. Other causes include: collapsed chip tube, blocked filter, drill head chip throat obstruction, or pump cavitation. Pressure spikes are dangerous because they can rupture the drill tube, damage the coolant seals, or cause the drill head to seize in the bore.
What is the most common coolant system design error?
The most common error is undersizing the coolant pump. Operators often select a pump based on the machine manufacturer's minimum specification without accounting for the specific bore diameter, depth, and material being drilled. The second most common error is inadequate filtration — especially in gun drilling where coolant passages as small as 0.3 mm diameter are easily blocked by particles larger than 5 µm. The third most common error is neglecting coolant temperature control — temperature changes alter coolant viscosity, which affects both Reynolds number and chip transport capability.
Summary
Coolant flow and pressure calculation for deep hole drilling is governed by the continuity equation, Darcy-Weisbach pressure drop, and chip transport mechanics. The annular gap velocity is the primary parameter for chip evacuation — 5–8 m/s minimum for steel, achieved by matching flow rate to bore diameter and tube geometry. The Reynolds number determines flow regime, with turbulent flow (Re > 4,000) essential for reliable chip transport and heat transfer. Total system pressure is calculated by summing frictional losses through the complete coolant circuit, with a 20–30% safety factor. Pump sizing requires matching flow and pressure to the specific bore geometry, depth, and material — the rule of thumb is 3–5 L/min per mm of bore diameter at 1.5–5.0 MPa for BTA, and 5–20 MPa for gun drilling depending on bore size and L/D ratio. Coolant viscosity, filtration level, and temperature control are supporting parameters that significantly affect system performance.