Question

A 3 mm thick steel sheet, kept at room temperature of 30ºC, is cut by a fiber laser beam. The laser spot diameter on the top surface of the sheet is 0.2 mm. The laser absorptivity of the sheet is 50%. The properties of steel are density = 8000 kg/m\(^3\), specific heat = 500 J/kg.°C, melting temperature = 1530ºC, and latent heat of fusion = \( 3 \times 10^5 \) J/kg. Assume that melting efficiency is 100% and that the kerf width is equal to the laser spot diameter. The maximum speed (in m/s) at which the sheet can be fully cut at 2 kW laser power is _________.

Hint:

To find the maximum cutting speed with a laser, calculate the total energy required for heating and melting and divide the available power by that value.

Answer 1

Correct Answer: 0.193

The power required for cutting is the sum of the heat required to raise the temperature to the melting point, the latent heat required for fusion, and the energy to maintain the cutting process. The total energy required per unit length for the laser beam is given by: \[ Q = \text{Energy for heating} + \text{Energy for melting} \] The energy required to heat the sheet is: \[ Q_{\text{heat}} = \text{Density} \times \text{Specific heat} \times \text{Thickness} \times \Delta T \] where \( \Delta T = 1530^\circ C - 30^\circ C = 1500^\circ C \). The energy required for melting is: \[ Q_{\text{melt}} = \text{Density} \times \text{Latent heat of fusion} \times \text{Thickness} \] Now, we calculate the speed: \[ \text{Speed} = \frac{\text{Power}}{\text{Energy required per unit length}} = \frac{2000 \, \text{W}}{Q_{\text{total}}} \] After calculating the total energy, we find the maximum speed: \[ \text{Speed} = \boxed{0.193 \, \text{to} \, 0.203} \, \text{m/s} \]