High-precision method for determining the optimal trajectory of movement of a conical grinding wheel relative to the helical groove of solid ceramic mills

摘要

The helical groove, which has a complex shape in the radial section, strongly affects the performance of solid ceramic mills. The accuracy of shaping is strongly affected by the size of the grinding wheel and the kinematic parameters of its movement and rotation relative to the workpiece. Although it is possible to obtain the aforementioned properties using the existing methods, there does not exist a general approach the determination the acceptable ranges of the diameter of the grinding wheel and radius of curvature of its profiling section. In this paper we have analyzed the main features of the design of the profiling sections of grinding wheels, have formed a set of initial parameters that most efficiently implement the trajectory of the shaping movement, which in turn constitutes a new general method of shaping for the helical surfaces of ceramic cutters, have analyzed the character of rolling of a set of profiling sections on a helical surface, have derived new analytical relationships determining impacts of the grinding wheel design and parameters controlling the trajectory of the grinding wheel movement on the shape of the cutter profile in the axial section, and have demonstrated advantages of the developed general approach in designing a new ceramic mill. The new method of shaping allows to unambiguously realize movements of the grinding wheel on various machine layouts and to exclude the displacement of the shaping point by replacing rotation with displacement. Further development of this method will make it possible to replace five- coordinate machines with four-coordinate ones when manufacturing milling cutters with a helical surface that can significantly reduce the production costs.