OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 2 4 convert vibration velocities to displacements, with the removal of the trend caused by the uncertainty of the initial conditions. All instruments provide direct access to the computer memory for further automatic processing of information. Let us first consider the change of 1 2 , ( ) X R K ω . When machining a shaft, the profile function ( ) R t is represented as the deviation of the radius from the coordinate of the tool tip without taking into account elastic deformations 2(0) / 2 L d = . Rotational speed of the workpiece is const Ω = . Therefore, the functions R(t) and R(L3) differ by a constant coefficient, since d t = π Ω 3 L (here πdΩ is constant). As before, the conditions, under which the process is asymptotically stable and the strain variations are small, are considered. In this case, the coupling of X1(t) and R(t) can be evaluated using the coherence function 1 2 , ( ) X R K ω . Fig. 6 shows 1 2 , ( ) X R K ω for the modes, at which the adequacy of the mathematical modeling of the system was analyzed (fig. 4). In fig. 6 the red dotted curves show the coherence functions averaged by moving average algorithms. The regions in which 1 2 , ( ) 0, 7 X R K ω 〉 are highlighted. The frequency region 0,0 (0, ) ω∈ ω is estimated as the range in which the formed relief is explained by L (Φ)(t) trajectories. Here the frequency ω0,0 depends on the modes. It increases with increasing cutting speed and decreases with the development of tool wear, as well as with changes in all conditions under which the volume of a b c Fig. 7. Variation of micro surface morphology as a function of cutting speed: a – dispersion normalized spectra of relief reduced to time sequence; b, c – surface morphologies
RkJQdWJsaXNoZXIy MTk0ODM1