Theoretical Study On Quantification Of Bonnet Polishing Residue Height Adapted To Free Surface Curvature

Free-form surface parts are widely used in many fields,and there are various methods for processing free-form surfaces.In order to obtain high-precision free-form surfaces,polishing is usually performed.Residual height quantification is the basis for the study of roughness.In order to improve the surface quality,in recent years,there has been a defect in the conventional polishing processing method for the processing of free-form surfaces due to low processing efficiency and poor matching of polishing tools with free-form surfaces.The new method,airbag polishing,has emerged as a new way of thinking about the study of free-form surface polishing.The main research in this paper is related to the basic research on the quantitative quantification of free-formed airbag polishing residue.The specific research contents are as follows:(1)The NURBS method is used to establish a free-form surface model,and the surface feature analysis based on the principal curvature and Gaussian curvature of the free-form surface will be free.The surface shape is segmented,and the segmentation result is divided according to the surface shape,and is divided into a convex surface,a concave surface,and a transition surface.And through the zebra stripe function of Solidworks software to find the free-form surface transition zone,to determine whether the transition zone is intersecting,tangent or continuous curvature.(2)The mathematical formula solution is the most intuitive expression of quantitative research.In the establishment of the material removal function,the classical Preston equation is used as the basis for the removal of the free-form surface material.The elastic mechanics Boussinesq solution formula and the calculus knowledge are used to obtain the factors affecting the elastic coefficient of the bonnet polishing head,and the related mathematics is given.According to the equivalent spherical surface treatment in the processing of the free-form surface transition region,the problem of how the convex surface,the concave surface and especially the transition region in the free-form surface are treated equivalently is solved,and the equivalent curvature radius formula is given mathematically.It is proved that the equivalent radius of curvature formula is applicable in both the transition zone and the non-transition zone,and it is found by MATLAB that the equivalent curvature radius is changed when the angle between the average curvatures of the two different directions in the transition zone is between 0-180°.(3)Using MATLAB software to solve some unknown parameters in the material removal model through simulation,and compare the material removal function simulation results with the actual experimental conditions to judge the material removal model and the application of equivalent radius of curvature.(4)In the study of the quantification of free-form surfaces,the main research is on the residual height.The spatial coordinate system transformation principle is used to deal with the contours of the material removal functions of different points in the free-form surface.The residual height at the polishing point is solved and analyzed process and calculation formula.