Capability evaluation of self-location machining algorithm for ultra-precision workpiece based on SVD

Abstract

In order to further improve the final precision, efficiency and cost-effectiveness of ultra-precision surface modification, and optimize the process direction and process decision-making of ultra-precision self-positioning processing, this paper studies the point cloud fusion process of self-positioning processing algorithm for ultra-precision workpieces. Based on the evaluation, it proposes a self-positioning processing algorithm capability evaluation method based on SVD. Firstly, based on the kinematics method, the matrix representation of point cloud fusion is established. The transformation matrix representation of self-positioning results is established for the translation, rotation and compound motion, respectively. Then the self-positioning point cloud fusion transformation matrix is obtained. A singular value decomposition is performed to obtain a singular value list of the transformation matrix. finally, the largest singular value in the list is used to characterize the self-positioning processing algorithm. By analyzing the free-precision states of a certain type of ultra-precision blade (a total of 1078 sets of free-standing state) it is found that the proposed evaluation index can correctly characterize self-positioning under the condition of independent translation and independent rotation. For the independent translation, the self-positioning processing algorithm can be positioned normally, and the maximum singular deviation value is also less than the pre-set value. For the independent rotation, when the angle is less than 45°, the self-positioning machining can be correctly performed. The singular value difference also approaches zero. Above 45°, the algorithm's self-positioning machining capability deteriorates, and this feature can be correctly captured by the proposed indicators. For the composite motion consisting of translation and rotation, the proposed index shows that about 35% of the cases can be correctly self-positioned, and the rest can not be correctly self-homing. It indicates that the indicators established by the proposed method can correctly characterize the self-positioning machining algorithm.