Theory
Formula for Laser Cutting Speed
Is there a simple formula to calculate the cutting speed of a laser? Unfortunately, the answer is not straightforward. It depends on a massive variety of factors, from material properties and laser power to focus quality. In real life, it even depends on unknown variables like the type and thickness of the glue used in your specific batch of plywood.
This means you will always need to run a test cut on your material. Nevertheless, understanding the theory behind it allows you to make informed decisions and optimize your cutting process.
Laser Cutting Speed Model
The cutting speed is determined by a simple energy balance: the energy delivered by the laser must equal the energy required to destroy and remove a 1 mm slice of material along the kerf.
Energy required to remove 1 mm of kerf $E_{\text{req}}$
To remove material, the laser must supply enough energy to heat it to its pyrolysis (decomposition) or melting point, and then vaporize it.
\[ E_{\text{req}} = \rho \cdot k \cdot t \cdot \bigl(c \Delta T + L_v\bigr) \]
Where:
- $\rho$ — material density (kg/m³)
- $k$ — kerf width (mm)
- $t$ — material thickness (mm)
- $c$ — specific heat capacity (J/kg·K)
- $\Delta T$ — temperature rise to pyrolysis/melting (K)
- $L_v$ — latent heat of vaporization/pyrolysis (J/kg)
Energy delivered by the laser per mm of travel
\[ E_{\text{laser/mm}} = \frac{P \cdot A \cdot F}{v} \]
Where:
- $P$ — optical laser power at the workpiece (W)
- $A$ — absorption coefficient of material (0–1)
- $F$ — focus quality factor (0–1)
- $v$ — cutting speed (mm/s)
Cutting speed formula
By equating the delivered energy and required energy:
\[ v = \frac{P \cdot A \cdot F} {\rho \cdot k \cdot t \cdot \bigl(c \Delta T + L_v\bigr)} \]
This formula perfectly predicts how cutting speed scales. It makes intuitive sense: more power ($P$) or better focus ($\eta$) increases speed. Conversely, thicker ($d$) or denser ($\rho$) materials will slow you down.
Simplified engineering model
Because measuring variables like latent heat ($L_v$) or absorption ($A$) in a dusty workshop is impossible, we can group all those material and optical constants into a single empirical coefficient ($K$) This gives us a highly practical engineering model:
\[ v = K \cdot \frac{P}{t^{\alpha}} \]
Where:
- $K$ — material constant (empirically measured)
- $P$ — optical power (W)
- $t$ — thickness (mm)
- $\alpha$ — thickness exponent (typically $1.0$ to $1.3$ for wood, accounting for gas dynamics and heat loss in deeper cuts)