Synergetic approach to improve the efficiency of machining process control on metal-cutting machines

OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. No. 3 2021 Introduction Currently, the system-synergetic paradigm of analysis and synthesis of complex systems has been formed [1–4]. It is used in controlling technical systems [5–8], including machining processes on machine tools [9–13], and in studying the dynamics of systems interacting with different environments [14–16]. When determining CNC programs that specify trajectories of executive elements (TEE), the knowledge base, based on various ideas about the influence of technological parameters on machining, is used [16–24]. It is shown that the wear intensity is influenced by the power released in the cutting zone. It is estimated, as a rule, by temperature [25–32]. Various techniques have been developed for correcting control programs that depend on information exchanges in subsystems [33–38]. One effective method for ensuring part qual- ity is to control the elastic deformations of the tool relative to the workpiece [39]. This method has gained recognition especially in cases where the workpiece stiffness varies along the machine’s TEE [40–44]. It has also been shown that the machining output characteristics depend on the state of the dynamic system (DS) [45–54]. Machining modes, as a rule, remain unchanged. Changes in DS properties, such as power path-dependent irreversible energy transformations by performed work, are not taken into account [55–58]. The next step, aimed at increasing the machining efficiency, is the synergistic coordination of the CNC program with the cutting DS. Firstly, it is necessary to coordinate the technological modes and the cor- responding CNC programs with the cutting system. Secondly, it is necessary to ensure this coordination with the changing properties of the system in the course of evolution. The aim of the research is to develop algorithms, mathematical tools and methods of matching the CNC program with the changing properties of the cutting DS along the tool trajectory. Research methodology State space Let’s consider the space in which we will place the workpiece and consider the tool tip movement tra- jectories consisting of the machine tool tip (3) 1 2 3 { , , } = ∈ℜ T L L L L and deformation displacement trajecto- ries (4) 1 2 3 { , , , } = ∈ℜ T X X X X Y X , in which we will distinguish the deformation displacements of the tool tip (3) 1 2 3 { ( ), ( ), ( )} = ∈ℜ T X X t X t X t X(t) relative to the machine carrier system and the deformation displacements of the workpiece ( ) Y t in the direction normal to its axis. The origin of the space coordinates is placed in the right rotation center of the workpiece (Fig. 1). In addition, we will set the trajectory of its rotation ( 4 / , W = α α = d dt L ). Space (3) ℜ X is movable. Its motion is constrained to trajectories L . The orientation of space coordinates (3) ℜ X is shown in Fig. 1. Vectors L and X correspond to its velocities (4) 1 2 3 4 { , , , } = ∈ℜ T V V V V V(t) and (4) ,1 ,2 ,3 ,4 { , , , } = ∈ℜ T X X X X v v v v X v . At that, 4 = π W V D . The set of L(t) and V(t) is defined by the CNC program. Let us also consider the trajectories of the form-forming motions 1 2 3 4 { , , , } = T l l l l l(t) , = − l(t) L(t) X(t) (1) as well as its velocities (4) 1 2 3 4 { ( ), ( ), ( ), ( )} = ∈ℜ T v t v t v t v t v(t) , that is = ∫ l(t) v( d t 0 ) ξ ξ . If l(t) is set, then the skeletal geometrical topology ⊂ (l) (0) Ψ Ψ of the surface formed by cutting [10–12] is also defined, from which it is possible to determine the geometry estimates used in engineering practice without taking into account the influence of independent physical processes accompanying processing on the surface. Condi- tion