To pursue high performance 5-axis CNC milling in industry, it is crucial to simulate each specific mill process in high fidelity beforehand, which should model the machined surfaces and predict the cutting forces in the process planning. However, the kernel technique, representation of the un-deformed chip geometry removed by cutter in 5-axis milling, is far from mature. Aiming to solve the problem, this paper presents a generic approach to representing un-deformed chip geometry mathematically in 5-axis CNC milling. The unique features of this research are: (1) the machine tool kinematics chain is investigated and a 5-axis CNC interpolation algorithm is adopted to establish the tool kinematics model, and (2) the closed-form equation of the un-deformed chip geometry representation is derived based on the machined shape being the envelope of a group of ellipses. This approach can model a machined surface with high accuracy and efficiently, and can be used to evaluate the machine surface quality and machining parameters. It can greatly promote the technique of high performance 5-axis CNC milling.

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