Automatic Spraying Painting Trajectory Optimization Based On Bezier Curves And Surfaces

Automatic spraying painting equipment is widely used in automotive manufacturing. And spray painting is an important process in the manufacturing of many products, such as automobiles, airplanes,etc. Now the automated trajectory planning of automatic spraying painting equipment is still a challenging problem, especially for complex curved surfaces. Hence, the research of new mathematical methods for automated trajectory planning is very important.This work is supported by the national natural science foundation program.The main work and innovation points of this dissertation consist of four parts as follows:Firstly, surface modeling is the first step of automatic spraying painting equipment trajectory planning.A new surface modeling scheme based on Bezier method is developed.And two methods of surface modeling are introduced. The Bezier tensor product method of a surface is introduced first. This method is mainly used for the small and simple workpiece surface modeling.Then another method of Bezier triangular surface modeling is discussed. The Bezier triangular surface is constructed by Bernstein polynomial.And each triangle in Bezier triangular mesh is called the B-B(Bezier-Bernstein) triangle. Then the construction of the flat patch adjacency graph is discussed. Based on the flat patch adjacency graph, a merging algorithm is proposed to form big patches. The experimental results illustrate the feasibility and availability of the method of surface modeling.Secondly, a new trajectory optimization scheme for Bezier surface is developed. The method of optimal initial trajectory planning for Bezier surface is introduced first.Then a spray painting model of Bezier surface is established,and the paint deposition rate function for Bezier surface is given. The discrete points arrayed on equidistant surface of Bezier surface are found. And the path planning is completed for Cardinal curve and Hermite curve. A multi-objective constraint optimization problem is formulated. An optimal tool trajectory with an optimal time and film quantity deviation is generated. And ideal point method is adopted here to calculate the values by iteration. The experimental results illustrate the feasibility and availability of the method.Thirdly, a new trajectory optimization scheme for complex curved surfaces is developed. After Bezier triangular surface modeling for complex curved surface is completed, the discrete points arrayed on equidistant surface of Bezier surface are found. A new path planning scheme based on the Bezier curve of the logarthmic mean is developed.And a new trajectory optimization method is introduced. The experimental results illustrate that Bezier curve of the logarthmic mean enhanced flexibility of the path planning. With this method,it is better to keep uniform speed of spray painting for complex curved surfaces.Finally,air field turbulence model,electrostatic field model and electrostatic spraying droplet trajectory model are studied by fluid mechanics. A T-Bezier basis is presented and a T-Bezier curve is developed. After the discrete points array on equidistant surface are found,the electrostatic spray painting trajectory is formed. Simulations are made by ANSYS for major design schemes. The results of simulations have shown that the three models are feasible. The experiment by the four ABB electrostatic spray painting robots on automobile demonstrates the feasibility and availability of these methods.