A two-level grid framework for efficient multi-axis milling simulation

Multi-axis milling simulation plays a critical role in tool path verification and material removal analysis for complex part manufacturing. This paper presents a two-level voxel grid framework that enables efficient workpiece update and cutter-workpiece engagement determination under high-resolution conditions. The direct voxel tracing algorithm, designed for efficient localized updates on the uniform grid, is extended to two-level uniform/adaptive grids to balance efficiency and memory usage, but suffers degradation when applied naively due to hierarchical access overhead and redundant computation. To address this, a dynamic computation localization strategy is proposed, comprising three predictive mechanisms: an oriented bounding cylinder for direction-aware spatial filtering, a predictive engagement region strategy to reduce unnecessary computation, and a dual-stage Boolean reduction process to compress the voxel update domain. These mechanisms collectively confine computation to regions with actual cutter-workpiece interaction, systematically reducing computational cost. Comparative studies demonstrate the superior performance of the proposed method over uniform grid and tri-dexel representations under high-resolution conditions.