Voxel-based analysis and modeling of MRR computational accuracy in milling process

Abstract

Material removal rate (MRR) is a commonly used metric for determining the efficiency of a toolpath design, as it is usually used to determine the amount of machining time spent doing useful work. Voxel-based computer-aided manufacturing (CAM) software enables simple computation of MRR by counting the number of voxels removed (N) in one feed step. However, depending on the geometry of the cutting tool and the voxel size used in the CAM software, there can be disagreement between theoretical and simulated MRR values. The cause of oscillation in voxel-based simulated MRR is the misjudgment of voxel removal due to the discrete nature of the voxel model. MRR has a linear relationship with N, so the analysis of MRR can be equivalent to the analysis of N as other conditions keep invariable. A series of simulation experiments were conducted on GPGPU by using computer programs that were developed to simulate the milling process. Discrepancies between voxel-based simulated MRR and the theoretical MRR were investigated. The dependence with respect to the ratio (M) between the radius of the tool and voxels size, the use of single or double precision floating-point computations, and the end shape of the cutting tool was studied. Results indicate that double precision improves the ability of judgment on voxel removal, thereby decreases the standard deviation of the N curve. Besides, ball-end milling has good computational accuracy with a lower standard deviation than flat-end milling. The relative range, mean absolute error, and standard deviation analysis were used to describe the oscillation regularity of N curves. The probability distribution of normal distance from the voxel center to tool boundary was studied. The result indicates that the distance obeys a uniform distribution when M is large enough. Modeling of MRR computation with computational error domain was proposed to represent the oscillation behavior of MRR, and the result shows that the model can well predict the magnitude and period of N curves during the milling process.