In the article for practical application within the framework of creating a matrix theory of accuracy of multi-tool machining for a range of multi-tool adjustments (tool setups) of previously developed models of machining error, the necessity of dependence of the coordinate components of cutting forces on technological factors is shown. (parameters of cutting conditions, strength properties of the material being machined, deformation properties of the technological system, etc.). For this purpose, the tasks of cutting force models are established, a systematics of machining schemes used on modern lathes is carried out, highlighting two schemes for the formation of a machined surface (trajectory and profile), and the principles for developing cutting force models are given. Thus, the development of an algorithmic unified complex of mathematical models of cutting forces is substantiated, taking into account the introduced systematics of machining schemes according to the mechanism of formation of the machined surface.