Question

A CO₂ laser in continuous mode is used for drilling a plate. The process parameters and their values are

Laser power intensity	1 × 108 W/mm2
Vaporization energy	5 × 106 J/mm3
Efficiency of the process	15%
Laser spot diameter	200 micrometer

The drilled depth (in mm) after 2 seconds is ______

Answer 1

Concept:

\(Volume \ of \ metal \ vaporized = \frac{Net \ energy \ provided \ for \ laser \ operation}{Vaporization\ energy}\)

Calculation:

Given:

Laser power intensity = 1 × 108 W/mm2, Vaporization energy = 5 × 106 J/mm3, Efficiency of the process = 15%, Laser spot diameter = 200 μm = 0.2 mm,

Power consumption for laser operation,

P = Laser power intensity × Area of hole

P = 1 × 108 × \(\frac{\pi d^2 }{4}\)

P = 1 × 108 × \(\frac{\pi \ \times\ 0.2 ^2 }{4}\)

P = 3.14 MW

Net energy provided for laser operation for 2 seconds = P × η_process × 2 = 3.14 × 10⁶ × 0.15 × 2 = 942.477 kJ

Vaporization energy = 5 × 106 J/mm3 = 5000 kJ/mm³

\(Volume \ of \ metal \ vaporized = \frac{Net \ energy \ provided \ for \ laser \ operation}{Vaporization\ energy}\)

\(Volume \ of \ metal \ vaporized = \frac{942.477}{5000}\)

The volume of the metal vaporized = 0.188 mm³

∴ \(\frac{\pi}{4}\times d^2\times H =0.188\)

\(\frac{\pi}{4}\times 0.2^2\times H =0.188\)

H = 6 mm