Evaluation of the influence of the reaction rate of the thermodynamic subsystem on the dynamics of the cutting process in metalworking

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 TECHNOLOGY Fig. 3. Graphs of tool deformation coordinates during embedding ( T Q = 0.7) Fig. 4. Phase trajectories of strain coordinates at T Q = 0.7 an increase in temperature, for an adequate consideration of this issue; graphs of changes in the cutting force, temperature, and  ( Q ) are provided (see Figure 5). As it can be seen from Figure 5, in fact, the cutting force, depending on  ( Q ), falls in about 1.05 seconds from almost 80 N to a value of less than 60 N, that is, by a quarter, which affects the coordinates of the tool deformation (see Figures 3 and 4). However, of interest is the relationship between the reaction time of the thermodynamic subsystem and the vibrations of the instrument, which can be conveniently, measured using the following integral indicator: 2 0 1 v T v dy VA dt T dt           ( 6 ) where VA – shows the vibration energy of the instrument for the period of observation (experiment) – T v . For the case shown in fi gure 4, the value VA = 2 mm/s, for example, for the variant TQ = 1.0009 mm/s. The graph of changes in the state coordinates for this case is shown in fi gure 6. As can be seen from the comparison of Figures 6 and 3, the difference in the oscillations is not visually observed, but as it was indicated earlier, it is convenient to consider for such an analysis the graphs of the phase trajectories, which are shown in fi gure 7. As can be seen from the comparison of fi gures 7 and 4, the graphs of the phase trajectories actually became smaller in amplitude, almost without changing in the direction of the coordinates of the deformations. The series of experiments made it possible to obtain a curve that characterizes the changes in the calculated value of the vibration signal energy when the reaction time of the thermodynamic subsystem of the cutting system changes, this curve and the curve approximating the obtained studies. The calculated curve is based on the synthesis of a second-order polynomial by the least squares method. As can be seen from Figure 8, the calculated curve differs signi fi cantly from the curve obtained on the basis of a series of numerical experiments. The deviations are maximum at the left and right ends of the graph, in the center of the graph, these deviations are minimal, we did this on purpose in order to obtain maximum convergence in the center of the graph, where the minimum point of the characteristic is. The enlarged area of the chart with the minimum point is shown in Figure 9.