The unprecedented scope of the physical sub-processes included in CALCut enables the three-dimensional stationary cutting front geometry and the resulting cut kerf geometry to be calculated.

The parameterization of the cutting front is based on vertically stacked, semicircular cutting front segments of defined height being horizontally resolved by discrete facets. The shape and position of every single segment is parameterized by its height, curvature radius, melt film thickness, vertex and flank inclinations and its horizontal distance from the laser beam axis in cutting direction.

In a closed formulation, the three-dimensional, steady-state model links the sub-processes of beam focusing, beam propagation, Fresnel absorption and reflection, compressible cutting gas flow, exothermic reaction (when indicated), heat conduction, phase transformation into the molten and vaporous states and mass transport due to melt and vapor flows taking into account the shear-stress induced by the cutting gas flow, capillary forces due to surface tension and driving forces due to vapor pressure gradients. The viscous melt is treated as a Newtonian fluid. 

The cutting gas flow is modelled as a function of the cutting gas type and the cutting gas pressure and depends on the geometry and temperature of cutting front and kerf. Below the nozzle exit, the gas jet is assumed to initially expand isentropicly and subsequently, via a normal compression shock above the workpiece, experiences an increase in entropy. This is taken into account as a loss in static pressure before the second isentropic expansion in the kerf. The resulting flow rate in the kerf is calculated. The locally induced shear stress is estimated according to the laws of turbulent channel flow. The maximum penetration depth of the supersonic flow field – here called “maximum jet penetration” – is determined by calculating the flow distance where the highest physically allowable pressure increase due to the friction losses occurs. This part of the model makes use of the conservation equations for compressible tubular flow in isothermal approximation.

In the steady-state equilibrium, the cutting front arises in such a way that the locally absorbed power density corresponds to the local heat-flow requirement. Beside the power balance, mass and force balance have to be fulfilled simultaneously.