Calculations of chip thickness and cutting forces in flexible end milling

In the end milling process of a flexible workpiece, it is well recognized that the precise determination of the instantaneous uncut chip thickness (IUCT) is essential for the cutting force calculation. This paper will present a general method that incorporates simultaneously the cutter/workpiece deflections and the immersion angle variation into the calculation of the IUCT and cutting forces. Contributions are twofold. Firstly, considering the regeneration model, a new scheme for the IUCT calculation is determined based on the relative positions between two adjacent tooth path centers. Secondly, a general approach is established to perform numerical validations. On one hand, the engagement/separation of the cutter from the workpiece is instantaneously identified. On the other hand, the calculation of the IUCT is iteratively performed. To demonstrate the validity of the method, several examples are used to show the convergence history of the cutting force and the IUCT during the flexible end milling process. Both theoretical analyses and numerical results show that the regeneration mechanism is short lived and will disappear after several tooth periods in flexible static end milling process.