APPLICATION OF BLOW-UP THEORY TO DETERMINE THE SERVICE LIFE OF SMALL-SERIES AND SINGLE ITEMS

Abstract

Context. The actual task of developing a method for determining the service life of small-series and single items based on the blow-up modes theory has been solved. Objective. Application of the blow-up theory in conditions where there are no statistical data on the dynamics of behaviour during the operation of small-series and single items. Method. To determine the service life of a particular product manufactured in large series, information obtained for a set of similar products of the same type is used. This information is based on numerous experiments, mathematical statistics and probability theory. When operating small-series and single items, such information is not available. In this case, it is necessary to determine the individual resource of an individual product based on the results of an analysis of its behaviour in the past. The method presented in the article is based on the application for such an analysis of the method used when considering systems operating in blow-up mode. The essence of the technique is to extract the periodic component from the temporal realization of the control parameter. This component is modelled by a Fourier series consisting of log-periodic functions. The main coefficients of these functions are the time equal to the operating time of the product until the end of its service life. Results. The method under consideration has been successfully tested in determining the service life of the transport-dumping bridge, related to products that are actually single items. Conclusions. An analysis of the experimental data on the behaviour of the load-bearing elements of a transport-dump bridge confirms the assumption about the behaviour of the bridge structure as a system operating in a blow-up mode. This made it possible to determine in advance the service life of the power units of the bridge and obtain the result directly in units of time, without requiring information about the maximum permissible value of the controlled parameter to obtain this information. For the first time, the possibility is shown to consider the behaviour of small-series and single items as dynamic systems operating in a blow-up mode. Practical significance. A solution to the topical problem of determining the service life of small-series and single items is proposed.