Generalized model for dynamics and stability of multi-axis milling with complex tool geometries

Multi-axis milling offers increased accessibility in milling of parts having geometrical constraints or free form surfaces, where variety of cutting tools and edge geometries are utilized to improve stability and productivity of the processes. In order to machine the desired geometries effectively, in conjunction with multi-axis orientations, special tools ranging from taper end mills to process specific form tools are utilized. For such cases, the cutter workpiece engagement boundaries (CWEB) and directional force vector definitions are very complex and cannot be defined analytically. Furthermore, irregular cutting edge geometries, such as variable helix, pitch and serrations introduce multiple time delays between successive cuts where the conventional analytical frequency domain stability solution cannot be used. Prediction of stability diagrams for such variety of tool forms and edge geometries requires both the process and the tool to be defined in a generalized manner. In this paper, a numerical frequency domain milling stability solution method is proposed. The CWEB for complex multi-axis cases are calculated by the general projective geometry approach, where the cutting tool envelope and the cutting edges are represented as organized point clouds. Zeroth-Order approximation (ZOA) frequency domain method is adapted by introducing a speed average time delay term to encompass regular and irregular tool geometries. The stability limits are predicted by iterative solution of the eigenvalue problem using the ZOA frequency domain with the proposed revision. The effect of the process damping is also introduced into the generalized stability solution in order to predict the increase in the stability limits at low cutting speeds. A previously proposed approach is used to calculate the average process damping coefficients, which are introduced as modifiers to the modal parameters. The proposed generalized methodology is applied on several cases and it is shown that stability limits can be predicted within a reasonable accuracy for wide variety of cutting tools and milling operations.