•  
  •  
 

Abstract

The article proposes a new analytical method for investigating nonlinear magnetic circuits with a special structure of parameter distribution. The method is based on introducing into the system of nonlinear differential equations of such circuits the condition that the second derivative of the magnetic flux along the length of the circuit is equal to zero, as well as on the assumption that one of the geometric parameters of the studied magnetic circuit – the size of the air gap between the ferromagnetic rods, their thickness, width, or the linear value of the number of turns of the distributed excitation winding is a function of the coordinate along the length of the circuit. The combination of these conditions makes it possible to significantly simplify the initial system of equations and obtain exact analytical expressions for the distribution of magnetic fluxes and magnetic tensions along the investigated magnetic circuit. The application of this method to the study of nonlinear magnetic circuits with a special structure of parameter distribution has made it possible to obtain analytical dependencies of the air gap between long ferromagnetic rods, their width, and the linear value of the number of turns of the distributed excitation winding on the coordinate of the circuit length. The obtained dependencies ensure an increase in the linearity of the magnetic flux distribution in long ferromagnetic rods and, in a few cases, also maintain constant magnetic tension between them, which is a necessary condition for ensuring the linearity of the static characteristics of many electromagnetic measuring transducers of electrical and non-electrical quantities.

First Page

22

Last Page

36

References

  1. Kabanov, V.N. (2010). Elementy avtomatiki: uchebnoe posobie [Elements of automation: A textbook]. Yekaterinburg: Ural State University of Railway Transport. (in Russian).
  2. Yusupbekov, N.R., Igamberdiev, Kh.Z., Malikov, A.V. (2007). Osnovy avtomatizatsii tekhnologicheskikh protsessov: uchebnoe posobie dlya vysshego i srednego spetsial’nogo obrazovaniya [Fundamentals of automation of technological processes: A textbook for higher and secondary specialized education]. Tashkent: Tashkent State Technical University. (in Russian).
  3. Polishchuk, E.S. (2008). Sredstva i metody izmereniya neelektricheskikh velichin [Methods and instruments for measuring non-electrical quantities]. Moscow: Beskid-BT. (in Russian).
  4. Zaripov, M.F., Urakseyev, M.A. (1976). Raschet elektromekhanicheskikh schetno-reshayushchikh preobrazovateley [Calculation of electromechanical counting and solving converters]. Moscow: Nauka. (in Russian).
  5. Sharapov, V.M., Polishchuk, E.S. (2012). Datchiki: spravochnoe posobie [Sensors: A reference guide]. Moscow: Tekhnosfera. (in Russian).
  6. Zudin, V.L., Zhukov, Yu.P., Malanov, A.G. (2024). Datchiki: izmerenie peremeshcheniy, deformatsiy i usiliy [Sensors: Measurement of displacements, deformations, and forces]. Moscow: Yurayt Publishing. (in Russian).
  7. Rannev, G.G. (2007). Informatsionno-izmeritel’naya tekhnika i elektronika [Information-measuring technology and electronics]. Moscow: Akademiya. (in Russian).
  8. Zaripov, M.F. (1969). Preobrazovateli s raspredelennymi parametrami dlya avtomatiki i informatsionno-izmeritel’noy tekhniki [Converters with distributed parameters for automation and information-measuring technology]. Moscow: Energiya. (in Russian).
  9. Konyukhov, N.E., Mednikov, F.M., Nechaevskiy, M.L. (1987). Elektromagnitnye datchiki mekhanicheskikh velichin [Electromagnetic sensors of mechanical quantities]. Moscow: Mashinostroenie. (in Russian)
  10. Fedotov, A.V. (2011). Teoriya i raschet induktivnykh datchikov peremeshcheniy dlya sistem avtomaticheskogo kontrolya [Theory and calculation of inductive displacement sensors for automatic control systems]. Omsk: Omsk State Technical University Press. (in Russian).
  11. Plakhtiev, A.M. (2009). Bes kontaktnye ferromagnitnye preobrazovateli s raspredelennymi magnitnymi parametrami dlya sistem kontrolya i upravleniya [Contactless ferromagnetic transducers with distributed magnetic parameters for control systems]. Tashkent: Tashkent State Technical University. (in Russian).
  12. Bedritsky, I.M., Jurayeva, K.K., Bazarov, L.Kh., Nazirova, Z.G. (2023). Using incomplete polynomials to approximate magnetization curves of electrical steels. AIP Conference Proceedings, 2612, 1-6. https://doi.org/10.1063/5.0132400.
  13. Belkina, E.N., Zhukov, S.A. (2015). Analiz sposobov approksimatsii krivoy namagnichivaniya elektrotekhnicheskoy stali [Analysis of methods for approximating the magnetization curve of electrical steel]. Innovatsionnaya Nauka, 5, 22-27. (in Russian).
  14. Zubkov, Yu.V. (2007). Approksimatsiya krivykh namagnichivaniya elektrotekhnicheskoy stali pri proyektirovanii sovmeshchennykh elektromekhanicheskikh preobrazovateley [Approximation of magnetization curves of electrical steel in designing combined electromechanical converters]. Izvestiya VUZov. Elektromekhanika, 6, 19-22. (in Russian).
  15. Zubritskiy, S.M. (2002). Approksimatsiya osnovnoy krivoy namagnichivaniya magnitomyagkikh materialov [Approximation of the main magnetization curve of soft magnetic materials]. Vestnik Irkutskogo Universiteta, Special issue: Annual Theoretical Conference of Young Scientists, 28-29. (in Russian)
  16. Fayzullayev, J.S. (2025). Approksimiruyushchiye funktsii i ikh effektivnost’ pri issledovanii nelineynykh magnitnykh tsepey s raspredelennymi parametrami [Approximating functions and their efficiency in the study of nonlinear magnetic circuits with distributed parameters]. Zheleznodorozhnyy transport: aktual’nye zadachi i innovatsii, 2, 218-229. (in Russian).
  17. Jurayeva, K.K., Fayzullayev, J.S., Mukhtorov, U.B. (2024). Flow distribution in magnetic circuits of measuring transducers with distributed parameters and a concentrated longitudinal excitation winding. Chemical Technology, Control and Management, 5–6(109), 9-17.
  18. Fayzullayev, J.S., Jurayeva, K.K., Mukhtorov, U.B. (2024). Investigation of magnetic circuits of measuring transducers with a distributed longitudinal excitation winding. Chemical Technology, Control and Management, 5–6(109), 68-78.
  19. Bronshteyn, I.N., Semendyaev, K.A. (2010). Spravochnik po matematike dlya inzhenerov i uchashchikhsya vtuzov [Handbook of mathematics for engineers and technical students]. St. Petersburg: Lan’ Publishing. (in Russian).
  20. Amirov, S.F., Sulliyev, A.Kh., Fayzullayev, J.S., Sharapov, Sh.A., Mamadaliev, U.Sh., Sattorov, T.A. (2023). Transformatornyy datchik bol’shikh lineynykh peremeshcheniy [Transformer-type sensor for large linear displacements]. IAP 07521, Republic of Uzbekistan, 11. (in Russian).
  21. Herman, R.L. (2025). A second course in ordinary differential equations: Dynamical systems and boundary value problems. 321 p.
  22. Piskunov, N.S. (1985). Differentsial’noe i integral’noe ischislenie dlya vtuzov [Differential and integral calculus for technical universities]. Moscow: Nauka. (in Russian).
  23. Amirov, S.F., Sulliyev, A.Kh., Fayzullayev, J.S., Sharapov, Sh.A., Mamadaliev, U.Sh., Sattorov, T.A. (2023). Preobrazovatel’ uglovykh peremeshcheniy [Angular displacement converter]. IAP 07519, Republic of Uzbekistan, 11. (in Russian).
  24. Amirov, S.F., Sulliyev, A.Kh., Fayzullayev, J.S., Sharapov, Sh.A., Mamadaliev, U.Sh., Yuldashev, N.R. (2025). Preobrazovatel’ uglovykh peremeshcheniy [Angular displacement converter]. IAP 8010, Republic of Uzbekistan, 5. (in Russian).

Download

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.