A method of circle center fitting for water wall cladding

Abstract

In the process of automatic laser cladding of the water wall, the determination of the cladding path is a vital step. As the cladding progresses, the central angle of the measurable pipe gradually decreases, and the pipe will be slightly deformed due to thermal stress. A method for obtaining the center of the pipe is proposed to guarantee a high fitting accuracy under the condition of small arc. The principle of the method is to introduce Lagrangian constraint parameters λx, λy to the circle center obtained by a fitting curve. Then the gradient descent method is performed on the parameters to find the optimal solution for the center of the section circle. For the problem of poor fitting accuracy for small arc, the simulation and experimental results show that when the central angle is 10 degrees, the center of the fitting circle's error is 0.2326 mm. It possesses a higher fitting circle center accuracy for water wall cladding.