In the monograph, the theoretical and logical bases of solving problems related to the
research of the cutting process of structural steels and alloys are considered. The approach
to the study of cutting tool geometry based on a logical analysis chain a research of cutting
wedge geometrical parameters from the cutting scheme construction through the coordinate
planes to the angles of a cutting tool is carried out. Problem solution on determining
kinematic angles of cutters when machining curvilinear contour on NC machine is
considered. Analysis of various physical phenomena occurring at metal excess layer
removal from the workpiece is performed. Study of physical phenomena is based on the
concept of the term "Cutting" as a set of simultaneously performed processes of elasticplastic
deformation of the cut layer, cutting tool wear and blunting as well as the formation
of the machined surface of the part. The peculiarity of the cutting tool wear process taking
into account the simultaneous effect of abrasive, adhesive, thermal and oxidative effects in
the process of cutting is noted. The analytical apparatus and algorithms of optimum cutting
modes search with the use of linear and geometrical programming methods and Lagrange
multipliers method are given. A software-methodological complex geometrical
programming for solving nonlinear problem with components in positive posinomials form
is implemented. A software-methodological complex on based Lagrange multipliers
method for determine a qualitative picture of cutting processes when the structure and
modes change is implemented.