The energy efficiency of the process of metal cutting at the expense of the sustainability of the evolutionary trajectory of the cutting

The problem of ensuring the sustainability of the processing process is directly related to the energy efficiency of the entire processing process. Virtually any machine the control of motion of which is considered interacts with the environment (technological, aerodynamic, trybologic, etc.). If one sticks to the synergetic analytical concept, the influence of the environment is described by a model of forces in state coordinates. The interaction is also characterized by the irreversible transformation capacity trajectory on the work. As a result, the system parameters are change causing additional strain displacements changing the trajectory. This transformation characterizes internal control and they are defined not by external action but by internal self-organization and defines the evolutionary trajectory. The properties of the system along the evolutionary trajectory change and the trajectory can lose its stability. The article considers the process of mathematical simulation of the evolutionary trajectory forming by the example of metalwork by cutting at turning machines and analyzes its stability. The evolution is presented as the parameters of the system depending on the capacity and work trajectory and presented by the Volterra integral equation of the second kind. When the trajectory loses its stability, irreversible changes can be formed in the system which may cause a complete system breakdown. In addition, the loss of stability leads to an increase in the oscillation amplitude of the tool and, as a consequence, an increase in energy costs for processing