Fundamental analysis of the dynamics of discrete-continuous rotary systems of tracked machines with mechatronic control systems
DOI:
https://doi.org/10.32347/2410-2547.2026.116.344-359Keywords:
fundamental analysis, dynamics, oscillations, discrete-continuous rotary systems, tracked vehiclesAbstract
When constructing a model of tracked machines, it is not possible to limit oneself to discrete parameters – masses and rigidities – if the shafts of the rotary system have significant masses and lengths. In long shaft lines, wave processes may occur under the action of external disturbances applied to the discrete masses of the system. The complexity of analyzing wave processes in discrete-continuous systems that arise in them when operating modes change forces us to look for simpler solution methods that still give satisfactory results in terms of accuracy. One such method is to replace the discrete-continuous model with a discrete one, which differs slightly in its dynamic properties from the original. In this case, the finite element method is used, into which each section of the shaft with discrete masses concentrated on it can be divided, and the shaft itself is a distributed mass. In this regard, there is a need to formulate a criterion that allows establishing an equivalent system of discrete masses that replace the discrete-continuous system. A similar task is the analysis of dynamic processes occurring in hydromechanical systems, which include long pipelines and large masses of hydraulic mechanism links.
The paper presents equations of motion for a tracked vehicle shaft with distributed mass, analyzes a weighted shaft with masses at its ends, and determines the natural frequencies of a multi-mass rotary system of a tracked vehicle, taking into account the shaft mass. The Prager method was used to find the natural numbers of the system. The results of calculating the amplitudes of shaft vibrations can be used to find the maximum values of the moments of elastic forces of the shaft sections. The change in the moment of elastic forces has a beating character. Each of the natural frequencies of a system with several degrees of freedom corresponds to a certain form of vibration, therefore, at close values of natural frequencies, there is a continuous transition from one form of vibration to another and, accordingly, a periodic exchange of energy between individual sections of the system while maintaining their energy constant. Control over the movement of the system in transient processes (start-up) can be carried out by mechatronic control systems.
References
Kozhevnykov S.N. Dynamyka nestatsyonarnykh protsessov v mashynakh (Dynamics of non-stationary processes in machines). – K.: Naukova dumka, 1986. – 228 s.
Kozhevnykov S.N. Dynamyka mashyn s upruhymy zveniamy (Dynamics of machines with elastic links). – K.: Yzd-vo AN USSR, 1961. – 160 s.
Korotkyi A.Y. Obratnye zadachy dynamyky upravliaemykh system s raspredelennymy parametramy (Inverse problems of dynamics of control systems with distributed parameters). Yzvestyia vuzov. Matematyka. 1995. №11. – S. 101-124.
Dehtiarёv H.L., Syrazetdynov T.K. Syntez optymalnoho upravlenyia v systemakh s raspredelennymy parametramy pry nepolnom yzmerenyy sostoianyia (obzor) (Synthesis of optimal control in systems with distributed parameters with incomplete state measurement (review)). Yzvestyia AN SSSR. Kybernetyka. 1983. №2. – S.123-136.
Butkovskyi A.H. Metody upravlenyia systemamy s raspredelennymy parametramy (Methods for controlling systems with distributed parameters). – M.: Nauka, 1975. – 568 s.
Znamenskaia L.N. Upravlenye upruhymy kolebanyiamy (Elastic vibration control). – M.: Fyzmatlyt, 2004. – 176 s.
Habryelian M.S., Movsysian L.A. K optymalnomu upravlenyiu dvyzhenyem upruhykh system (Towards optimal control of the motion of elastic systems). Mekhanyka tverdoho tela. 1991. №6. – S. 146-153.
Ylyn V.A., Moyseev E.Y. Optymyzatsyia hranychnykh upravlenyi kolebanyiamy struny. Uspekhy matematycheskykh nauk (Optimization of boundary controls for string vibrations). 2005. Vyp. 6 (366). – S.89-114.
Barsehian V.R., Movsysian L.A. K optymalnomu upravlenyiu kolebanyem upruhykh system (Towards optimal control of oscillations of elastic systems). Prykladnaia mekhanyka. 2012. T. 48. №2. – S. 137-142.
Vybratsyy v tekhnyke: spravochnyk (Vibrations in technology: a guide). V 6-ty T.; red. sovet: Chelomei V.N. – M.: Mashynostroenye, 1981. T. 1. – 356 s.
Dolhov N.M. Elementy dynamyky system na podvyzhnykh deformyruemykh osnovanyiakh (Elements of dynamics of systems on moving deformable foundations). – K.: Tekhnika, 1996. – 92 s.
Dolhov N.M. Vysshaia matematyka (Higher mathematics). – K.: Vyshcha shkola, 1988. – 416 s.
Obod I.I., Zavolodko H.E., Svyd I.V. Matematychne modeliuvannia system (Mathematical modeling of systems). – Kharkiv: Drukarnia Madryd, 2019. – 268 s.
Sprazetdynov T.K. Optymyzatsyia system s raspredelennymy parametramy (Optimization of systems with distributed parameters). – M.: Nauka, 1977. – 480 s.
Zubov V.Y. Lektsyy po teoryy upravlenyia(Lectures on control theory). – M.: Nauka, 1975. – 496 s.
Kharkevych A.A. Neustanovyvshyesia volnovye yavlenyia (Transient wave phenomena). – M. – L.: HYTTL, 1950. – 202 s.
Kharkevych A.A. Spektry y analyz (Spectra and analysis). – M.: Hos. yzd-vofyz.-mat. l-rы, 1962. – 236 s.
Skuchyk E. Prostye y slozhnye kolebatelnye systemy (Simple and complex oscillatory systems). – M.: Myr, 1971. – 558 s.
Bolotyn V.V. O parametrycheskom vozbuzhdenyy poperechnykh kolebanyi (On parametric excitation of transverse vibrations). – M.: Yzd-vo AN SSSR, 1953. Sb. «Poperechnye kolebanyia y krytycheskye skorosty». Vyp. 2.
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