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WELDING CALCULATIONS
Knowing the size of the focused spot is helpful in calculating energy density at the work surface.
For a fundamental mode (TEM00) beam:
where:
S = ( 4λ / ) × ( F / D)
In performing a laser weld, optics to focus the laser beam to the desired size are necessary.
For a multimode beam:
S = Focused Spot Diameter
λ = Laser Wavelength
F = Focal Length of Objective Lens
D = Diameter of Laser Beam
If one assumes the part to be welded as a semi-infinite solid, with a constant incident heat flux, then the temperature distribution as a function of depth into the material is given by:6
S = F · Φ ,where:
F = Focal Length of Objective Lens
Φ = Laser Beam Divergence
where:
T(x,t) = (2E/K) × [(kt/)½× exp(-x2/4kt) - (x/2)erfc(x/2(kt)½)]
T(x,t)=Temperature at a distance x below the work surface, at a time t after start of constant heat input E = constant heat flux input
and at the surface (x=0), the temperature rise will be: T(x,t)x=0 = (2E/K) × (kt/)½
K = thermal conductivity
k = thermal diffusivity
x = depth below surface
t = time after start of heat flux input
erfc = complimentary error function