A general method for instantaneous undeformed chip thickness calculation in five-axis milling based on Boolean operations

Instantaneous undeformed chip thickness (IUCT) plays a critical role in optimizing and monitoring of five-axis milling processes, as it determines machining precision and tool life by affecting cutting forces. Analytical and numerical methods have been widely used for IUCT calculation. However, these methods have some deficiencies, such as solving the unsolvable transcendental equations, modeling the complex cutting edge trajectory, and poor adaptability for five-axis milling. Therefore, a Boolean method which consists of subtraction and intersection operations is developed. First, the blank for the current cutting edge is obtained by the Boolean subtraction operation between the workpiece and the swept volume that produced by the front cutting edges. Second, the Boolean intersection operation is executed between the blank and the auxiliary edge entity (AEE) that corresponding to the tool edge. Then, the IUCT of each cutting edge or each cutting point can be deduced based on the Boolean result with the known blank geometry, tool geometry, tool path, and machining parameters. The method is verified by milling force experiments. It is an efficient, accurate, and general method because it does not need to establish complex mathematical or numerical models. The calculated IUCT will promote the optimizing and monitoring of five-axis milling processes.