Theoretical modeling and error analysis for CNC whirling of the helical surfaces of custom screws using common inserts

With the wide use of complex helical surfaces in screw components, it becomes more and more urgent to investigate efficient ways for the design and manufacture of components of this kind. This study establishes the mathematical model of helical surface based on discrete points on its axial section profile using cubic spline curve fitting method, and presents a theoretical approach to calculate the tool path for the whirling process which aims to produce the helical surface through enwrapping movements of standard cutters inserted in the tool ring. The approach is implemented in MATLAB environment focusing on the calculation of the cutter location points. After that, the theoretical machining error is analyzed focusing on the scallop height, which can be divided into axial and cross-sectional errors. Finally, a case study is provided, together with numerical simulation demonstrating the validity of the proposed approach.