Calculation of envelope area between grinding tool and curved surface

Abstract

Typical aerospace curved surface parts have high contour accuracy, which directly affects the working performance and service life of the equipment. To improve the contour accuracy of these parts, the freestyle abrasive belt grinding technology can be employed, where the size of the envelope area determines the material removal volume. However, due to the complex contour of the curved surface and large contact deformation of the belt, the envelope area between the flexible belt and curved surface parts is complex and time-varying. The accurate calculation of the envelope area is still an open problem. To this end, a novel locally approximate distance fields-mass spring systems (LADF-MSS) method is proposed. Firstly, the improved distance field is established accurately: the octree is applied to search for the reference point where the curved surface is a local quadric approximation, and then the projection point is calculated based on the reference point. Secondly, the locally approximate distance field is combined with efficient mass-spring systems to extract the envelope area. The experimental results of grinding the curved surface show that the average area error and average centroid error of the envelope area are 0.7 mm2 and 1.08 mm respectively, and the average computing time is 7.5 min. Compared with the finite element method (FEM), the average calculation errors through utilizing the LADF-MSS method are reduced by 40.3% and 76.4% respectively, and calculation efficiency is increased by 166%. These results demonstrate that the proposed method offers both higher calculation accuracy and efficiency.