The article presents analysis of the stochastic technical stability of mathematical models (described by the second-order ordinary differential equations) of technical objects, on the example of a moving motor vehicle with the disturbed location of the center of mass, as a result of a non-uniform load. After conducting simulation of motion of a sport vehicle mathematical model, using the MSC Adams/Car software, executing a maneuver of double lane change without completely returning to the original road lane, interpretation of the results in accordance with the given definition has been attempted. Specifically, the aspect of determining the probability of the solution remaining in a certain area of feasible solutions has been highlighted, as well as determination of the magnitude of this probability for stable motion. In addition, attention has been paid to the selection of the upper limit of probability, for which, under certain conditions, stable motion can be determined.
The article presents mathematical considerations on the dynamics of the springing switch point being an element of the railway junction. Due to the structure of the switch point, mathematical analysis was divided into two stages: The first stage refers to the analysis of the dynamics of the switch point as a beam of variable rectilinear stiffness to which three forces (coming from three closures of switch drives) placed in the initial section of the switch point are applied. The next stage of the analysis concerns an identical beam, but curved, with a variable cross-section. In both cases, the beam is subjected to a vertical force resulting from forces from the rail vehicle. The calculations refer to a switch point of 23 m length and a curvature radius R = 1200 m. The first stage of the switch point analysis refers to the movement of a rail vehicle on a straight track, and the second stage concerns the rail vehicle movement on a reverse path. This article also provides an analysis of mode vibrations of a curved beam with a variable cross-section, and variable inertia and stiffness moments (further in the article the changes will be referred to as beam parameter changes). It is assumed that the beam is loaded with vertical forces (coming) from a rail vehicle. The solution was found by applying the Ritz method, which served to present the fourth-order partial equations as ordinary differential ones. The numerical research whose results are given aimed to define how the changes in beam parameters and vertical load affect mode vibrations of the beam.
The operation and maintenance of railroad turnouts for rail vehicle traffic moving at speeds from 200 km/h to 350 km/h significantly differ from the processes of track operation without turnouts, curves, and crossings. Intensive wear of the railroad turnout components (switch blade, retaining rods, rails, and cross-brace) occurs. The movement of a rail vehicle on a switch causes high-dynamic impact, including vertical, normal, and lateral forces. This causes intensive rail and wheel wear. This paper presents the wear of rails and of the needle in a railroad turnout on a straight track. Geometrical irregularities of the track and the generation of vertical and normal forces occurring at the point of contact of the wheel with turnout elements are additionally considered in this study. To analyse the causes of rail wear in turnouts, selected technical–operational parameters were assumed, such as the type of rail vehicle, the type of turnout, and the maximum allowable axle load. The wear process of turnout elements (along its length) and wheel wear is presented. An important element, considering the occurrence of large vertical and normal forces affecting wear and tear, was the adoption of variable track stiffness along the switch. This stiffness is assumed according to the results of measurements on the real track. The wear processes were determined by using the work of Kalker and Chudzikiewicz as a basis. This paper presents results from simulation studies of wear and wear coefficients for different speeds. Wear results were compared with nominal rail and wheel shapes. Finally, conclusions from the tests are formulated.
The paper will present a mathematical model for the guideway as a continuous system, followed by a moving force coming from the capsule and the capsule as a discrete system. The theoretical problem selected for analysis comes from a group of technical problems, which solve the dynamics of systems subjected to moving loads. Dynamic reactions in the system are described by a system of coupled partial and ordinary differential equations. Their solution was obtained using approximate numerical methods. The article concerns the analysis of Hyperloop vehicle guideway displacement in the occurrence of magnetic levitation phenomenon, which appears when starting, driving and braking the vehicle. The analysis was carried out using a numerical, three-dimensional model of the guideway. The results of the analysis are illustrated with calculation examples. The displacement of the guideway and magnet elements was determined by simulations. The simulations were conducted using MBS software. The presented results refer to the movements of the capsule of Hyperloop vehicles.
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