Speed Planning and Interpolation Algorithm of Archimedes Spiral Based on Tangential Vector

Abstract

The primary challenge in CNC machining is optimizing arc interpolation for better smoothness and precision, as traditional methods often fail to maintain a consistent curvature, resulting in inefficiencies and inaccuracies. This study utilizes the Archimedes spiral, comprising a series of seamlessly connected circular arcs, as an innovative interpolation curve to improve arc interpolation efficiency and accuracy. The proposed methodology addressed the issue of constant arc interpolation curvature and facilitated the implementation of the spiral’s interpolation algorithm. It employs the parametric equation of the Archimedes spiral to define tangent vectors, which is pivotal for the execution of the algorithm. In the context of speed planning, the curve was segmented into different sections, allowing the calculation of maximum acceleration based on the interval segmentation angle of the tangent vector. This segmentation facilitates the analysis of speed variations, which are consequently integrated to determine the speed distribution across different curve sections. Through this integration, the motion process is categorized, thereby achieving a refined speed distribution curve. This study introduces a realtime interpolation algorithm capable of calculating the largest axis of the tangent vector, thereby enabling precise pulse coordinates. This coordinate information are then effortlessly derived from the simple geometric relationships inherent in the spiral's structure. The effectiveness of the proposed method is demonstrated through simulation and practical machining on two distinct graphical representations. Compared with the traditional linear interpolation algorithm, the proposed method improves the machining efficiency of heart-shaped curves by 6.85% while ensuring the machining accuracy. Comprehensive evaluation, encompassing track error, and surface roughness assessments, validates the enhanced performance of this interpolation technique.