Research on multivariate nonlinear regression model of specific energy of rock with laser drilling based on response surface methodology

Abstract

Based on Box–Behnken Design of response surface methodology, multiple experiments of laser drilling (four centimeters thickness of sandstone) were performed by continuous fiber laser (Model MFSC) with a maximum laser power 1 kW to obtain the specific energy of rock with three experimental parameters of laser power (400∼800 W), irradiation time (6∼10 s) and spot diameter (0.01∼0.03 m). According to experimental results, a multivariate nonlinear mathematical regression model correlating the experimental parameters with the specific energy of rock was established and the accuracy of the model was found to be good by variance analysis. Univariate analysis of the model revealed that laser power had the greatest influence on the specific energy of rock, while irradiation time affected the least. Considering the interaction effect among three experimental parameters, calculation results of the model exhibited that the combination of laser power and irradiation time, as well as that of laser power and spot diameter, had obvious influence on the specific energy of rock, while the combination of irradiation time and spot diameter showed little effect. After that, the optimal parameter combination (P=768.9 W, t=8.3 s, d=0.01 m) was obtained. Five repeated experiments under the optimal parameter combination clearly illustrated good agreement between predicted values and measured values. This paper proposed a multivariate nonlinear model based on the response surface method with high precision in predicting the specific energy of rock, which could help reduce the specific energy of rock and improve the efficiency of rock breaking.