Mathematical model and sensitivity analysis for helical groove machining

In any drill design, the helical groove shape plays a key role in ensuring an adequate flute space and an efficient chip removal capability. Moreover, the shape of the helical groove determines the principal drill angles. This study establishes a mathematical model of the helical groove and conducts a sensitivity analysis for helical groove machining performed on a 6-axis tool-grinding machine. Combining homogenous coordinate transformation and conjugate surface theory, a kinematic model is developed to facilitate the design of the helical groove shape (a direct problem). In determining the tool profile required to generate a desired helical groove (an inverse problem), this study exploits the condition that the common normal at the contact point between the tool and the helical groove surface must intersect the axis of the tool. The sensitivity of the helical groove profile with respect to the machining parameters is investigated. Finally, numerical examples are provided to demonstrate the validity of the developed models and algorithms. The numerical results reveal that the current design and sensitivity analysis methodology is comprehensive, simple and applicable to a wide range of helical groove machining applications.