Cutting force modeling for non-uniform helix tools based on compensated chip thickness in five-axis flank milling process

Cutters with non-uniform helix and pitch angles are increasingly used in modern industries. However, few works have studied the cutting forces of this type of tool. Therefore, this study presents a compensated-chip thickness-based cutting force model for non-uniform helix tools in the five-axis milling process. First, the geometry of this special cutter is mathematically expressed. Based on this, the instantaneous uncut chip thickness (IUCT) model is established using error compensation theory combined with real trajectories of cutter edges. This model can overcome the disadvantages of numerical methods Subsequently, the cutting force coefficients are computed using the average IUCT. The engagement between the cutter and the workpiece is discussed. Finally, for verifying the validity and accuracy of the force model, the proposed IUCT, classical, vector-form and true models are compared for a traditional cutter and a cutter with variable helix and pitch angle. Two toolpaths including a line and a circle are selected to predict the IUCT values. The results show that the presented IUCT model exhibits the highest accuracy among the first three models. Additionally, some experiments are conducted. For the three-axis machining process, the toolpaths including a line and a circle are selected. The results show that the cutter with the variable helix angles can predict cutting forces with variable toolpaths. Using the same tool and for the five-axis machining process, a conical surface is selected as toolpath surface. The results show the validity of the cutting force model.