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EN
This work is focused on the possible ways of improving the running safety of a railway vehicle, which uses IRWs (independently rotating wheels) in a bogie. It discusses the main positive and negative properties of an application of IRWs for a railway vehicle while it is running in a curve. There are evaluated running properties of a railway vehicle in terms of safety for IRWs and a standard wheelset (SW). It is assumed that a wheelset design with IRWs will reduce the risk of derailment of a railway vehicle in a curve with a smaller radius because it will be reached a more favourable distribution of decisive forces in the wheel/rail contact. A designed wheelset with IRWs differs from other IRWs designs; in this case, only a flange can rotate independently from a wheel treat surface about the axis of rotation. Further, this research presents an analysis of a friction forces distribution of the friction forces in a contact of a flange and a rail head and a comparison with an SW. The obtained results allow concluding that it is advisable to use the wheels with the perspective wheel design (including independently rotating) to reduce the resistance to movement and improve the running properties of a railway vehicle for safety.
2
Content available remote Mathematical task statement
EN
The text describes a task which must be solved on the analyze of propounded problem. Pupils and students solving these types of tasks are taught to think about the mathematical problem and to develop mathematical consideration. The following task also shows what way the mathematical problem statement can affect the difficulty of task solving.
3
EN
The purpose of this paper is to present the solutions of a time-optimal control problem of a position mechanism, in a case when the motion resistance function depends on a position of this mechanism. The dynamics of the controlled object is described by a planar, non-linear and discontinuous differential equation: x=f(x)+u, where |u| is less than or equal to 1, motion resistance function f(x) = 0 if x is less than or equal to 0, f(x) = -A if x is greater than 0 and 0 is less than or equal to A is less than 1. In a case of such defined motion resistance function the two following singular phenomena appears: 1) if the target z[1] = (0,0) and A is greater than A[b], A[b] = 2-2^(1/2) then the switching curve is composed of two branches, but only one of them is formed by the solution of the time-optimal problem. Thus, the closed-loop system executes none, one or two switching operations and any small change in the value of the resistance function requires to change the closed-loop system structure. 2) if the target z[1] = (x[1], 0), x[1] is greater than 0 then there exists the set of states from which two different trajectories reaching the target in the same minimum time start. The switching curve is composed of three branches. One of the branches is induced by a singular set of states and is formed by none of the solutions of time-optimal problem. The paper presents the sets of non-unique states for different values of the motion resistance function and the target z[1] = (1,0) in the graphical form. Finally, some suggestions as to practical application are given.
4
PL
Model maszyny został zapisany na podstawie przytoczonych wcześniejszych prac. Jego równania podano w wirującym układzie współrzędnych zespolonych 0,f,b. Parametry modelu są wyrażone przez pochodne cząstkowe funkcji koenergii względem prądu magnesującego dla pierwszej i trzeciej harmonicznej przepływu wypadkowego. Funkcja koenergii została wyznaczona metodą modelowania pola magnetycznego dla wybranego silnika o wirniku pierścieniowym. Przy realnej zawartości trzeciej harmonicznej przepływu koenergia praktycznie nie zależy od chwilowej pozycji harmonicznych a wpływ trzeciej harmonicznej na parametry równania dla skladowej zgodnej jest niewielki. Natomiast bardzo silne jest oddziaływanie skladowej zgodnej prądów na indukcyjność dla składowej zerowej.
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