Virtual simulation of high-resolution multi-axis machining processes nowadays plays an important role in the production of complex parts in various industries. In order to improve the surface quality and productivity, process parameters, such as spindle speed, feedrate, and depth of cut, need to be optimized by using an accurate process model of milling, which requires both the fast virtual prototyping of machined part geometry for tool path verification and accurate determination of cutter–workpiece engagement for cutting force predictions. Under these circumstances, this paper presents an effective volumetric method that can accurately provide the required geometric information with high and stable computational efficiency under the condition of high grid resolution. The proposed method is built on a tri-level grid, which applies two levels of adaptive refinement in space decomposition to abolish the adverse effect of a large fine-level branching factor on its efficiency. Since hierarchical space decomposition is used, this multi-level representation enables the batch processing of affected voxels and minimal intersection calculations, achieving fast and accurate modeling results. To calculate the instantaneous engagement region, the immersion angles are obtained by fusing the intersection points between the bottom-level voxel edges and the cutter surface, which are then trimmed by feasible contact arcs determined using envelope theory. In a series of test cases, the proposed method shows higher efficiency than the tri-dexel model and stronger applicability in high-precision machining than the two-level grid.

This paper presents an efficient method for computing machined part geometry and cutter-workpiece engagement in general multi-axis milling. The milling process in this work is simulated by multi-level voxel update and edge intersection point update in sub-voxel level. The computed intersection points are used not only for building the machined part mesh model via dynamic marching cubes algorithm, but also for determining the instantaneous cutter-workpiece engagement region. The multi-level representation of the workpiece enables batch processing of affected voxels and minimal intersection calculations for more rapid and accurate modeling results. Virtual prototyping of the milled part geometry is critical for tool path planning, while cutter-workpiece engagement is one of the most important inputs for cutting force prediction. In a series of test cases, the proposed method has shown satisfactory modeling accuracy and higher efficiency compared to the tri-dexel model. More importantly, this volumetric method is implemented on six different data structures which are obtained by combining the fundamental spatial decomposition strategies. The efficiency characteristics of the resulting data structures are studied quantitatively which will help select the most appropriate scheme according to the performance requirements and realize its full potential for improved efficiency by choosing the optimal branching factors.