Modified cutting force prediction model considering the true trajectory of cutting edge and in-process workpiece geometry in ball-end milling operation

Cutting force prediction is very important for optimizing machining parameters ahead of the costly physical test. Ball-end milling operation is widely used for machining sculptured surface. Mechanistic approach can precisely predict elemental cutting force at each cutting element and integrate them into the cutter tooth with high fidelity to predict the cutting force for ball-end milling operation. However, the intersection between the cutting tool and workpiece could be complicated due to the trochoid motion trajectory of cutting edge and constantly changing workpiece geometry, making it difficult to determine the cutter-workpiece engagement (CWE) and undeformed chip thickness (UCT). In this present research, a modified cutting force prediction model was developed with considering the true trajectory of cutting edge and in-process workpiece geometry in ball-end milling operation. First, a triangular mesh model of the in-process workpiece surface was developed, and its mesh points were continuously updated by the intersection between the vertical reference line of the selected mesh point and the motion trajectory of cutting edge. Secondly, the UCT was calculated directly using the linear distance between a selected point on the cutting edge and the intersection between the radial reference line of the selected point and the triangular mesh of the in-process workpiece surface. Meanwhile, the CWE was expressed as a step function of UCT. Thirdly, a modified mechanistic approach was established by incorporation into the developed UCT and CWE models. The cutting force of ball-end milling operation was predicted with mechanistic approaches. Finally, ball-end milling experiments of AISI P20 steel were carried out for calibrating cutting force coefficients and validating cutting force model. The relative error between the predicted and measured cutting force is less than 15%, which indicates the predicted cutting force is in good agreement with measured cutting force. The works presented in this paper are one important step for optimizing machining parameters and compensating cutting force induced form error, which could improve the surface accuracy and machining efficiency.