# Physics of Laser Cutting

## Laser Machining Processes

Several major laser machining processes are illustrated below. (The notable omission is welding, beyond the scope of this document.) (Chryssolouris, 1991)

This diagram illustrates the cutting process in cross section. Note that a gas assist can be used to speed cutting of metals. (Chryssolouris, 1991)

## Drilling Rates

A simple method of analysis is proposed in (Wilson, 1987).

The energy to vaporize a mass m of solid material at intial temperature T is

 Ev = m(CS(Tm-T)+CL(Tv-Tm)+Lf+Lv) CS = solid specific heat capacity CL = liquid specific heat capacity Tm = melting point Tv = boiling point Lf = latent heat of fusion Lv = latent heat of vaporization

Usually, Lf << Lv and T << Tv , and Cs » CL = C. We then have the simple form Ev = m(CTv+Lv). Now, consider a circular laser beam of area A boring into the surface of such a material with a velocity vs directed into the material. It must remove a section of mass vsr A per unit time. Ignoring reflectance from the material surface, the heat flow is equal to the beam power P. Assuming a beam with diameter d and equal power over A, we have P = vs (p d2/4)(CTv+Lv).

If vs exceeds the normal rate of heat diffusion into the material, this equation is fairly accurate for estimating drilling rates or hole depths. To find hole depths, solve for the quantity vst, where t is the duration of the beam pulse. For example, consider a 100-msec pulse from a 10W laser with a beam diameter of 1mm. If this were to strike a Perspex (methyl methacrylate) sheet, the resultant hole would have a depth of 1.6mm.

Note the inverse-square dependence of hole depth on beam diameter. Halving the beam diameter results in a hole four times deeper. This highlights the importance of beam focusing in laser machine design.

## Cutting Rates

This model can be used to estimate cutting rates as well. Consider the laser scanning over the surface of the material with velocity vb. As it scans, it cuts through the material to a depth z = vsd/vb. We now have

P = (p /4)zvbr d(CTv+Lv)

The following table can then be used to approximate the laser power necessary to cut a given material. (Wilson, 1987)

(Chryssolouris, 1991) describes a model that accounts for the material absorptivity as well. s = cutting depth a = material absorptivity P = laser beam power = material density v = scanning velocity d = beam spot diameter cp = specific heat Tv = temperature at surface (melting temp.) T = temperature of ambient L = latent heat of fusion

Note the following:

• The cutting depth is proportional to P/vd, which is the energy input per area of workpiece.
• Cutting depth is small for materials with a high melting point and a high latent heat of evaporization.