BIZOMAT MAKEOS · Manufacturing
Micro-Droplet Adhesion on a Rotating Micro Tool (MQL)
For minimum-quantity lubrication of a micro mill or drill, will a lubricant micro-droplet stick to the rotating tool or be thrown off, and up to what spindle speed will it stay on?
The handbook’s condition for a micro-droplet to adhere to a rotating micro tool, Equation (18b): 2m Vc² ÷ Dt ≤ P (1 + cos θ) σL, with the droplet mass m from its diameter and the lubricant density, the tool surface speed Vc = π Dt n, the projected drop size P, the contact angle θ and the surface tension σL of the lubricant, giving the margin between adhesion and centrifugal force and the highest spindle speed at which the droplet still adheres.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Droplet diameter | µm | Diameter of a lubricant droplet in the mist. |
| Lubricant density | kg/m³ | Density of the lubricant, from its data sheet. |
| Projected drop size P | µm | Projected size of the drop on the tool surface, measured as the handbook describes. |
| Contact angle θ | ° | Contact angle of the lubricant on the tool material, measured or from data. |
| Surface tension of the lubricant σL | N/m | Surface tension of the lubricant against air, from its data sheet. |
| Tool diameter Dt | mm | Diameter of the micro tool. |
| Spindle speed | rpm | Spindle speed of the tool. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Droplet diameter
- What it is
- Diameter of one lubricant droplet in the mist from the nozzle.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0.000001 µm to 1000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The droplet mass and centrifugal force rise with its cube.
- Get it right
- Take it from the mist generator data or a droplet measurement.
What this means: Lubricant density
- What it is
- Mass per unit volume of the lubricant used for the mist.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 5000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 900 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The droplet mass rises in proportion.
- Get it right
- Read it from the lubricant data sheet.
What this means: Projected drop size P
- What it is
- Size of the drop as it spreads on the tool surface, seen from above.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0.000001 µm to 5000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The adhesion force rises in proportion.
- Get it right
- Measure it on a toolmaker’s microscope as the handbook describes.
What this means: Contact angle θ
- What it is
- Angle between the drop surface and the tool surface where they meet.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 180°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller angle wets better and holds the drop more strongly.
- Get it right
- Measure it for your lubricant on your tool material or coating.
What this means: Surface tension of the lubricant σL
- What it is
- Surface tension between the lubricant and the surrounding air.
- Units and format
- Enter a number in N/m: N/m. The form accepts 0.000001 N/m to 1 N/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.03 N/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The adhesion force rises in proportion.
- Get it right
- Read it from the lubricant data sheet, in N/m.
What this means: Tool diameter Dt
- What it is
- Diameter of the micro mill or drill that the mist must wet.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the surface speed for a spindle speed.
- Get it right
- Use the flute diameter of the tool.
What this means: Spindle speed
- What it is
- Rotational speed of the spindle carrying the tool.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The centrifugal force rises with its square.
- Get it right
- Use the programmed spindle speed.
Method and formulas
- Droplet mass m = ρ π d³ ÷ 6; tool surface speed Vc = π Dt n ÷ 60.
- Centrifugal term = 2 m Vc² ÷ Dt; adhesion term = P (1 + cos θ) σL (both in newtons).
- The droplet adheres when the centrifugal term is not larger than the adhesion term.
- Highest speed: Vc max = √(P (1 + cos θ) σL Dt ÷ 2m); n max = 60 Vc max ÷ (π Dt).
- Example: the adhesion term is 90.611 times the centrifugal term.
Limitations
- The droplet must first reach the tool through the air boundary layer around it; this check covers adhesion only.
- Contact angle and surface tension depend on the lubricant and the tool coating; measure them for your pair.
- Projected drop size and droplet diameter are measured or taken from the mist generator data.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether mist lubrication will wet a fast-spinning micro tool
- Find the spindle speed limit for droplets of a given size
- Compare lubricants by contact angle and surface tension
Who it is for
- Micromachining engineers
- CNC machinists
- Process developers
What you get
- Droplet mass and tool surface speed
- Centrifugal and adhesion terms of Equation (18b)
- Whether the droplet adheres
- Highest spindle speed for adhesion
Interpreting the result
- Small droplets adhere easily: the handbook found 1 to 10 µm droplets adhered at all speeds of the tested machine.
- A smaller contact angle wets better and raises the adhesion term.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1118–1119. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
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Open the Micro-Droplet Adhesion on a Rotating Micro Tool (MQL) calculator