The article solves the problem of assessing the preference and sequence of stages of application of priority methods for improving grinding and cutting equipment depending on the quantitative dynamics for the appearance of theoretical works characterized by analytical mechanisms of description, on the one hand, and interspersed with publications of heuristic works using the theory of solving inventive tasks, on the other. We statistically studied the change in publication activity in terms of publishing scientific papers on improving the grinding and cutting technology and the intensity of heuristic inventive activity in this information field. As a result, the provisions are substantiated and stated, from which it logically follows the need for timely activation of the processes of improving screw grinding equipment by analytical or heuristic methods, with a focus on the cyclicity and phasing of the productivity of these methods. For this purpose, a generalized structural design and technological scheme of the grinding-cutting system has been developed. The main features, geometric parameters and physical and mechanical characteristics of the components are determined. It is shown that the task of identifying priority analytical or heuristic step-by-step methods of assessing directions for improving the parameters of grinding and cutting equipment is one of the most important and logically complete system elements in the theory and practice of optimal synthesis of screw grinders. It seems that the proposed concept is applicable to any branch of technology. For auger grinding and cutting equipment, on the basis of the above methodology, another priority task was formulated, which consists in an analytical description of the distribution law of the blade sharpening angle along the length of the cutting edge, taking into account the phenomenon of its kinematic transformation.