A method of circle center fitting for water wall cladding. (October 2022) - Wang, Mingtian
Highlights: The Lagrangian constraint parameters λx and λy to constrain the fitting center coordinates are introduced into the objective function based on the least square method for the circle center fitting. The gradient descent method is performed on the parameters λx and λy, to find the optimal solution for the center of a short arc. The algorithm is proposed to calculate the center of a short arc with the center angle between 10 degreesand 60 degrees in high accuracy. The experimental result has an error of 0.2326 mm when fitting a 10 degrees arc using a laser sensor with error of 0.3 mm, which can improve the measurement accuracy for the pipe 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.