An analytical model to estimate angle formed by laser

In this paper, an analytical model to estimate the angle formed by a laser is established. In the proposed model, the angle induced by the laser is considered to be the sum of the angle bent during the heating process and that bent during the cooling process. The angle bent during the heating process is assumed to be a function of the temperature distribution at the moment that the highest temperature is achieved, whilst the angle bent during the cooling process is assumed to be a function of the surrounding temperature. By using the proposed model with known temperature distributions, the bending angle induced by the laser can be calculated. In order to verify the proposed model, bending angles estimated by the proposed model are compared with those measured experimentally and those estimated using other analytical models. The results show that the proposed model is more accurate than the analytical models proposed by other researchers in predicting the angle formed by a laser.