Receipt date: 
Bibliographic description of the article: 

Cherepanov A. P., Lyapustin P. K. Zakonomernosti snizheniya resursa unikal'nykh mashin [The pattern of decrease of a resource of unique machines]. Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie [Modern Technologies. System Analysis. Modeling], 2019. Vol. 63, No. 3, pp. 37–45. DOI: 10.26731/1813-9108.2019.3(63).37–45

Journal number: 
620.171: 621.039.548.58


Article File: 

The article provides theoretical substantiation of the regularity of reducing the life of machines in the process of their operation. The mathematical description of the resource reduction regularity is shown on the basis of a graphical interpretation of the forecast and correction. This makes it possible to present the relationship between the original (at the initial moment, in the manufacture), the actual (at the present time) and the predicted (for the subsequent period of operation) technical indicators characterizing the damage and wear of components and machine parts during a certain time interval. However, with the help of the predictor-corrector function, the exact definition of the resource was possible only with a uniform grid step, but, as is known from practice, the resource of machines is predicted mainly with an uneven grid step, as it is difficult to carry out technical diagnosis regularly, at fixed intervals during operation. It is also established that the graphical interpretation shows only the regularity of the transition of the initial state to the limit state, but for the applied researcher it would be more important to build a curve that would reflect the true decrease in the resource of the machine with a decrease in the strength reserves of its components and parts. Research and practice show that one of the measures to reduce the risks of machine operation is to create a model of resource forecasting, which takes into account the largest number of factors affecting the resource, as well as the most complete use of technical diagnostics data, the results of the assessment of the technical condition and the residual strength of the machine elements. To solve this problem, an exponential dependence is presented, which shows the reduction of the resource from the degree of wear, defects, the effectiveness of technical diagnosis and the degree of danger when reaching the limit state at different stages of the life cycle of the machine. Mathematic description of this pattern can be used to predict the initial, current and residual life of single, unique machines and technical devices.

List of references: 
  1. RD 50-423-83. Metodicheskie ukazaniya. Nadezhnost' v tekhnike. Metodika prognozirovaniya ostatochnogo resursa mashin i detalei, podverzhennykh iznashivaniyu [Methodical instructions. Reliability in technology. The methodology for predicting the residual life of machines and parts subject to wear].
  2. GOST 21571-76. Sistema tekhnicheskogo obsluzhivaniya i remonta tekhniki. Metody opredeleniya dopuskaemogo otkloneniya parametra tekhnicheskogo sostoyaniya i prognozirovaniya ostatochnogo resursa sostavnykh chastei agregatov mashin [System maintenance and repair of equipment. Methods for determining the permissible deviation of the technical condition parameter and predicting the residual life of component parts of machine assemblies.].
  3. Bolotin V.V. Prognozirovanie resursa mashin i konstruktsii [Prediction of the resource of machines and structures]. Moscow: Mashinostroenie Publ., 1984. 312 p.
  4. ANSI SQL Standard. The 1992 ISO–ANSI SQL standard is available through ANSI as document X3.135–1992 and through ISO as document ISO/EC 9075:1992.
  5. Trishin V. N., Shatrov M.V. Osnovnye zadachi i tekhnicheskie resheniya, realizovannye v komp'yuternoi sisteme pomoshchi otsenshchiku i auditoru ASIS [The main tasks and technical solutions implemented in the computer system help the ASIS evaluator and auditor]. Imushchestvennye otnosheniya v Rossiiskoi Federatsii [Property relations in the Russian Federation], 2004. No.11. URL: http//www.okp– (access date: Oct 28, 2010).
  6. Leifer L.A., Kashnikova P.M., Opredelenie ostatochnogo sroka sluzhby mashin i oborudovaniya na osnove veroyatnostnykh modelei [An electronic medium]: (access date: Oct 05, 2007).
  7. Mitrofanov A.V., Kichenko S.B. Raschet gamma protsentnogo resursa sosudov i rezervuarov [Calculation of the gamma of the percentage resource of vessels and reservoirs]. Bezopasnost' truda v promyshlennosti [Occupational safety in industry], 2000. No. 9. Pp. 28–33.
  8. Makhutov N.A., Pimshtein P.G. Problemy bezopasnosti pri chrezvychainykh situatsiyakh [Safety issues in emergency situations]. Issue 5. Moscow, 1995. 16 p.
  9. RD 03–421–01. Metodicheskie ukazaniya po provedeniyu tekhnicheskogo diagnostirovaniya tekhnicheskogo sostoyaniya i opredeleniyu ostatochnogo sroka sluzhby sosudov i apparatov [RD 03–421–01. Guidelines for the technical diagnosis of the technical condition and the determination of the residual life of vessels and apparatuses]. Moscow: SUE SRC Promyshlennaya bezopasnost' Publ., 2002.  136 p.
  10. Krasnykh B.A., Mokrousov S.N., Makhutov N.A., Mitrofanov A.V., Baryshov S.N. Ogranichenie prognoziruemogo resursa i naznachaemogo sroka bezopasnoi ekspluatatsii oborudovaniya neftegazovogo kompleksa [Limitation of the predicted resource and the appointed term for the safe operation of the equipment of the oil and gas complex]. Bezopasnost' truda v promyshlennosti [Occupational safety in industry], 2008. No. 6. Pp. 30–33.
  11. Makhutov N.A. Konstruktsionnaya prochnost', resurs i tekhnogennaya bezopasnost': V 2 ch. [Structural strength, resource and technological safety:  In 2 parts].  Novosibirsk: Nauka Publ., 2005. Part 2: Obosnovanie resursa i bezopasnosti [Part 2: Justification of the resource and security]. 610 p.
  12. Bezopasnost' Rossii. Pravovye, sotsial'no-ekonomicheskie i nauchno-tekhnicheskie aspekty. Upravlenie resursom ekspluatatsii vysokoriskovykh ob"ektov [Security of Russia. Legal, socio-economic and scientific-technical aspects. Resource management of high-risk facilities]. In Makhutov N.A. (gen. ed.). Moscow: IHPF Znanie, 2015, 600 p.
  13. Numerical Recipes: The Art of Scientific Computing, page 942 «…multistep… Predictor–corrector is a particular subcategory of these methods – in fact, the most widely used» [An electronic medium]. URL:–ode/1–3.html (access date:  Jul 15, 2012).
  14. Hoyne's scheme, or a predictor-corrector [An electronic medium].  URL: (access date: Jul 19, 2012).
  15. Wikipedia. The free encyclopedia [An electronic medium]. URL: (access date: Jul 19, 2012).
  16. Chen W., Kee D. Advanced Mathematics for Engineering and Science, MA, USA: World Scientific, 2003, ISBN981–238–292–5 [An electronic medium]. URL: (access date: Jul 16, 2012).
  17. SFU (RSU) Department of Physical Chemistry. Numerical methods and programming. Materials for the lecture course. [An electronic medium]. URL: (access date: Sept 07, 2011).
  18. Cherepanov A., Lyapustin P. Forecasting Resource as a Method of Increasing the Security. IOP Conference Series: Materials Science and Engineering. 253 012004. 2017.