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EN
The work presents research of defective railway wheel and rail dynamics and mathematical model of system “Railway vehicle wheel – track”. An assumption was made that the Rail R–65 and railway wheel with flats are with unevenness. The aim of this investigation is to identify the contact forces resulting from the wheel/rail contact at the various defects. Rail track dynamics is described by finite element method, while soil and wagon dynamics is described by the discrete elements. The mathematical model is to assess physical and mechanical properties, roughness of wheel and rail surface, and their geometry. In the mathematical model of the rail is evaluated: the impact of axial force, the initial deformation of rail, the foundation of soil, the gap between sleeper and rail. Profile of railway wheel is defined as a function of radius variable depending on the polar angle and described by Fourier series. In this mathematical model of railway wheel and rail contact area is divided into small sections, where the force is set in contact using the Hertz theory. Total system of non-linear equations of motion is solved by applying the Newton-Raphson method. The speed of the train is 100 km/h and static load on the rail is 100 kN. The flat of the wagon wheel is L=100 mm. Numerical results of contact problem are obtained. Duration of contact is nearly equal to period during which the wheel set passes a half of the flat length. The contact force operating the wheelset is equal to approximately 1.0 MN. Maximum value of the sleeper acceleration is equal 410 g.
EN
Modelling the process of traffic flow was previously studied from different points of view and different mathematical methods where used to describe the same process. All authors have an agreement on basic traffic flow parameters like, traffic flow density, traffic flow rate or the average speed of traffic flow. Besides, a lot of different investigations into the use of traffic flow models to deal with various problems of engineering are carried out. A comparison of different continuum models has drawn that a number of scientific works were based on fluid dynamic theory and gas - kinetic traffic flow theory. The kinetic traffic flow theory is used in ‘microscopic’ or “macroscopic”, traffic flow models. The kinetic traffic flow theory is used in Flötteröd G., Nagel K., Ging A., Li L., Li-qun X., Prigogine I., Herman R. works where various approaches to the similar method are discussed. The ‘macroscopic’ theory of traffic flows also can be developed as the hydrodynamic theory of fluids that was first introduced by Lighthill-Whitham and Richards’s model. Plenty of traffic flow models are based on car–following theories supported by the analogues to Newton’s equation for each individual vehicle interacting in a system of vehicles on the road. Different forms of the equation of motion give different versions of car–following models. This work presents research of traffic flow dynamic processes, as nonlinear dynamic system, by using a discrete model of traffic flow (DMTF). The main variables in DMTF are traffic flow density and speed. DMTF can be used to describe various traffic flow situations in the roads. The mathematical simulation of traffic flow is made when constant value of traffic flow speed and traffic flow rate is entered. Numerical results of traffic flow dynamics are obtained.
3
Content available Dynamics of the air blower with gyroscopic couple
EN
To avoid damaging of tilting pad journal bearings, the problem of safety shut down of high speed air blower cantilever rotor becoming important in modern industry. The experimental testing, modeling and simulation of dynamic behavior of rotating system was run to directly evaluate gyroscopic negative effect damaging journal bearings. A dynamic model of air blower rotating system was designed and simulated. A simulation and experimental measurement results of rotating system were used to optimize the shut down regime of machine. Gyroscopic effect influences of rotor bearing stability are confirmed. Results of numerical simulation confirm results of experimental vibration measuring. The theoretical research results are given and conclusions are made. Experimental testing and simulations results was applied to typical air blower rotating systems for elimination of huge negative forces acting on new bearings during shut down of the machine.
EN
The general mathematical model of the system “ road - vehicle - obstacle ”, which consists of the models of road pavement surface, vehicle, rigid and deforming obstacles, and the interaction between the vehicle and the obstacle has been constructed. The variation of interaction force and contact position are estimated at the moment of the vehicle collision with the obstacle. The model evaluates interaction of the vehicle wheels with the road pavement surface; blocking of wheels; change of forces (air resistance, cohesion and centrifugal), which influence the vehicle. According to the generał mathematical model of the system “ road - vehicle - obstacle ”, different traffic situations can be investigated on certain road sections with known physical and mechanical properties of the road surface.
PL
Został utworzony model matematyczny systemu “droga -samochód (inny środek transportu) - przeszkoda“, składający się z modeli: odcinka drogi; samochodu; deformującej i nie deformującej się przeszkody; wzajemnego oddziaływania samochodu i przeszkody. Podczas wzajemnego oddziaływania samochodu i przeszkody (np. ogrodzenia drogi) bierze się pod uwagę: zmianę sił oddziaływania; zmianę miejsca kontaktu samochodu z przeszkodą; fizyko-matematyczne parametry powierzchni drogi; istnienie kontaktu między kołami samochodu a powierzchnią drogi; blokowanie kół samochodu; zmianę sił (siły oporu powietrza; siły kontaktu kół samochodu z powierzchnią drogi; siły odśrodkowej), działających na samochód. Za pomocą ogólnego matematycznego modelu systemu “droga - samochód (inny środek transportu) - przeszkoda“ można modelować i badać różne sytuacje ruchu transportowego na konkretnym odcinku drogi.
EN
The introduced mathematical simulation of motion of rigid bodies, component's bulk material’s, takes into account their interaction among themselves and with wali limiting the volume. The values and received precondition’s, taken into account, are indicated.
PL
Przedstawiony jest model środowiska sypkiego, składającego się z ciał twardych. Bada się ruch ciał twardych w ograniczonym pojemniku, biorąc pod uwagę wzajemne oddziaływanie ciał ze ścianami zamkniętego pojemnika (np., bunkra) oraz oddziaływanie wzajemne ciał twardych między sobą. Przedstawiony jest przykład ruchu środowiska sypkiego w ograniczonym pojemniku (bunkrze).
PL
W artykule rozważano ruch wagonu motorowego na nierównych torach Republiki Litewskiej. Przedstawiono przestrzenny model dynamiczny wagonu motorowego. Model ten składa się z elementów dyskretnych o nieliniowych charakterystykach. Dynamiczne obciążenia łożysk uzyskano w funkcji rozstawu szyn oraz prędkości jazdy wagonu motorowego.
EN
In the article the motion of the motorailer on uneven railways path of the Lithuanian Republic is considered. The three dimensional dynamie model of the motorailer is shown. The dynamic model is composed of discrete elements part of which have nonlinear characteristics. The dynamic loads of bearings are obtained depending on the gap between rails and the running speed of the motorailer.
EN
In the article the dynamic processes in an axial-reciprocating hydraulic motor and mechanical drive are considered. The mathematical model of an axial-reciprocating hydraulic motor is presented, where the flow of fluid in each cylinder of the motor and the interaction of liquid with the piston are taken into account. The flow in a hydraulic system is described by acharacteristics method. An instance of the mathematical simulation of the activity of an axial-reciprocating motor in a hydraulic system together with the mechanical drive is shown.
PL
W artykule rozpatrzono dynamiczne procesy występujące w hydraulicznym silniku tłokowym osiowym połączonym z częściom mechaniczną układu napędowego zaprezentowano matematyczny model tego silnika, w którym uwzględniono przepływ płynu z tłokami. Przepływ płynu w układzie hydraulocznym opisano układem równań hiperbolicznych, które można rozwiązać za pomocą standardowych metod. Przedstawiono istotne wyniki symulacji numerycznych pracy rozpatrywanego układu napędowego.
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