Method for determining the cut quality of a laser cutting process using a simulation program

A method for determining a cut quality of a laser cutting process, said quality being assessed on a basis of a formation of solidification ridges along a cut face of a sheet metal workpiece and/or a burr formation on a lower edge of the cut face, whereby in a simulation program a virtual laser cutting machine is provided that can be operated virtually with a set of values P0 from a parameter space P,

• wherein the parameter space P is defined by
• P=(λLaser,l0(t),f(x,z,t),s(x,z,t),p(x,z,t),Pg(x,z,t),τg(x,z,t),v0(t),d,PMaterial), where
• PMaterial=(ρs,cps,λs,ρl,cpl,λl,Hm,Hv,Tm,Tv,η,σ,ncs,ncl,
• where
• λLaser represents a wavelength of the laser radiation,
• l0(t) the maximum value of the laser radiation intensity over time,
• f(x,z,t) represents a spatial distribution of the laser radiation intensity over time,
• s(x,z,t) represents a spatial distribution of the direction of the laser radiation over time,
• p(x,z,t) represents a spatial distribution of the polarization state of the laser radiation over time,
• Pg(x,z,t) represents a cutting gas pressure over time,
• τg(x,z,t) represents a shear stress of the cutting gas over time,
• v0(t) represents a feed rate, defined as the relative velocity between the laser beam axis and the workpiece over time,
• d represents a thickness of the sheet metal to be cut,
• ρs represents a density of a workpiece material to be cut in the solid state,
• cps the specific heat capacity of the material in the solid state,
• λs represents a thermal conductivity of the material in the solid state,
• ρl represents a density of a laser cut melt of the workpiece,
• cpl represents a specific heat capacity of the melt,
• λi represents a thermal conductivity of the melt,
• Hm represents a melting enthalpy of the material to be cut,
• Hv represents a evaporation enthalpy of the material to be cut,
• Tm represents a melting temperature of the material to be cut,
• Tv represents a evaporation temperature of the material to be cut,
• η represents a dynamic viscosity of the melt,
• σ represents a surface tension of the melt,
• ncs represents a complex refractive index of the material in the solid state,
• ncl represents a complex refractive index of the melt,
• and where
• x represents a coordinate in the direction of the relative movement between the material and the laser beam axis and
• z represents a coordinate perpendicular to the top of the material, and
• t represents a time,
• said method comprising the following steps in order to start the virtual cutting machine:
• (a) specifying a starting point P0 by acquiring the machine parameters of a current, real cutting machine, wherein the set of values P0 is selected from a parameter space P, as defined above, and the parameter set P0 is entered into the virtual cutting machine for the sequence of the simulation program,
• and thereafter starting the simulation program by
• (b) making a virtual cut with the virtual cutting machine that may be based on real values, wherein the progression of melt film thickness over time h=h(z,t) and the position M=M(z,t) of the melt front at the apex of the cutting front is calculated according to the depth of the cut z (0<z<d, d sheet metal thickness) and the time t from partial differential equations PDE normalized to v0
• ∂
• h
• ∂
• t
• +
• G
• ⁡
• (
• z
• ,
• t
• ;
• h
• ,
• P
• 0
• )
• ⁢
• ∂
• h
• ∂
• z
• +
• D
• ⁡
• (
• z
• ,
• t
• ;
• h
• ,
• P
• 0
• )
• =
• v
• p
• ,
• ∂
• M
• ∂
• t
• =
• v
• p
• -
• 1
• with initial and boundary values
• h(z,t=0)=h0(z), M(z,t=0)=M0(z)
• h(z=0,t)=0, M(z=0,t)=m0(t;P0)
• where h0(z) and M0(z) represent any initial distributions, m0(t;P0) the position of the upper edge of the cutting front, vp=vp(z,t) the velocity of the melt front, vs=G(z,t;
• h, P0) the flow velocity at the surface of the melt and D(z,t;h,P0) a damping of the melt film dynamics, for a given parameter set P0 is calculated from P,
• and thereafter
• (c) by a projection of the time course of the absorption front, defined as the position M(z,t)−h(z,t), onto the cut face with a transfer function determined by the feed rate v0 that depicts t on x, specifying the spatial distribution of the ridge amplitude R(x,z) on the cut face and calculating a spatial distribution of the burr B(x) at the lower edge of the cut face from the time course of the melt film thickness h(z=d,t) and the outflow velocity G(zd,t;
• h(z=d,t), P0) at the lower edge of the cut face, and
• (d) providing a virtual cutting result comprising at least one of R(x,z) and B(x), for further assessment,
• whereby in an additional step values of the parameters from the parameter space P of the laser cutting process are determined for the purpose of achieving defined cut faces and/or for determining the cut faces that can be achieved with a specified laser cutting machine and/or for configuring components of an optimised laser cutting machine that meets or at least approximates the specifications regarding stated requirements on the cut face, by repeating steps a) to d) each time with changed parameters from the parameter space P,
• and wherein rules are derived for the continued and/or new development of components of a real laser cutting machine from the values of the parameters from the parameter space P of the laser cutting process for obtaining defined cut faces that meet or at least approximate the specifications regarding requirements on the cut faces, if the determined values cannot be transferred to a real laser cutting machine with machine-specific parameters, known as machine-specific design space DM, where DM is the subset of P that can be achieved without structural changes to the real laser cutting machine.