THE USAGE THE LYAPUNOV INDICATOR FOR DETERMINATION OF DROPS

Abstract

At this time, there is a widespread use of numerical control lathes, which aims to develop technical solutions for automatic control of the state of the technological system, in particular the tool. In the process of cutting, the cutter fails as a result of a dull (end of durability period), breaks (complete destruction of the cutting edge or crumbles into particles of cutting material), softens (loss of hardness in steel and welding are almost unobservable in hard alloy) and, in the end, the result is increased wear.At the same time, the main requirement is a higher reliability of the results obtained, this is largely determined by the chosen methods of information analysis, which characterizes the state of the technological system. Durability of the tool should provide high performance and the lowest material costs associated with the manufacture of the product. This resistance is called economic. Its approximate values for different cutting tools, adopted in the standards for cutting conditions, are given in the relevant directories.The most promising methods are synergistic. One of the most important results of synergetics was the conclusion that the length of the time horizon of the prediction of circulation was limited even for relatively simple systems. This applies to systems that are sensitive to initial conditions. The main task is to choose a characteristic or group of characteristics by which it is supposed to evaluate the state of the processing system and establish the dependence of the selected characteristic on time. As the initial data it is supposed to use a vibrosignal which is generated by the process of turning, as the initial data – wear of the cutter.Calculations of cross-correlation showed that its value reaches 0.72 Ra/μm, which indicates the presence of a relationship between the values. Three characteristic areas can be identified. In the first region there is an intensive increase in the values of the Lyapunov index. In the second area, there are slight fluctuations in the indicator values, and when a certain wear chamfer threshold is reached - changes in the Lyapunov indicator values are extremely small (about 10-5 ... 10-6) – this area corresponds to a period of catastrophic wear.As established during the study was observed in all the experiments carried out at the finishing turning. Analyzing the obtained results, we can conclude that the use of the Lyapunov indicator is justified for tracking the pathological changes in the mill of the technological processing system – that is, by the value of the Lyapunov indicator, one can judge the occurrence or non-occurrence of catastrophic tool wear.