Abstract
Usually, to study the vibrations of rail carriages, the equivalent geometric unevenness of the track obtained as a result of processing the records of the track measuring car is taken as a disturbance. Such a record contains a certain set of irregularity wavelengths, for example, 50, 25 and 12.5 m. However, when it is used to simulate disturbances at different operation speeds, these wavelengths will correspond to frequencies depending on the given speed of motion, which is not permissible, since a stable frequency range from 0.2 to 10 Hz is required to excite the vibrations of all the bodies included in the carriage. To eliminate this drawback, in the previously performed works it was proposed to generate a random process of geometric irregularities for a given operation speed by changing the set of wavelengths included in the irregularities. In this paper, based on the study of random oscillations of a simplified model of a rail carriage, as a system with one degree of freedom, the adequacy of the method for generating a random disturbance process is verified in two ways. In the first method, it was found that the characteristics of random oscillations of such a model, obtained in the time domain on the basis of numerical integration of the equation of motion when specifying the generated disturbance, have satisfactory convergence with similar characteristics found by the frequency method using Shannon's formula. In the second verification method, the cross-correlation function and the mutual spectral density between the disturbance and the bouncing oscillations were determined from the generated disturbance realization and obtained by numerical integration of the vibration process realization. Then, using the method of identifying the dynamic system, experimental amplitude and phase frequency characteristics were found, which showed satisfactory convergence with the corresponding calculated characteristics obtained by numerically solving the equation of oscillations of the model under study. On the basis of the results obtained, it was concluded that the considered method of generating a random process of disturbance is sufficiently adequate and that it can be applied to solve problems of the dynamics of rail carriages.
Highlights
In the previously performed works it was proposed to generate a random process of geometric irregularities for a given operation speed by changing the set of wavelengths included in the irregularities
It was found that the characteristics of random oscillations of such a model, obtained in the time domain on the basis of numerical integration of the equation of motion when specifying the generated disturbance, have satisfactory convergence with similar characteristics found by the frequency method using Shannon's formula
In the second verification method, the cross-correlation function and the mutual spectral density between the disturbance and the bouncing oscillations were determined from the generated disturbance realization and obtained by numerical integration of the vibration pro cess realization
Summary
Нормиро- Нормиванный ко- рованная эффициент частота затухания βi , м−1/Li, м затухания αi, м−1 v αi, Гц v βi , Гц/ Li, м. Во временной области выполнялось численное решение дифференциального уравнения колебаний упрощенной модели рельсового экипажа как системы с одной степенью свободы. При этом кинематическое возмущение η(t = x / v) задавалось в виде одномерного стационарного случайного процесса, сгенерированного с помощью формирующего механизма Полученная реализация была использована в качестве возмущения для исследования вертикальных колебаний упрощенной модели экипажа, описываемых уравнением (4), при его движении по рельсовому пути со скоростью v = 50 м/с. 2. Структурная схема формирующего механизма для генерации одномерного стационарного случайного процесса во временной области: ГШ — генератор белого шума; y(lT ) — последовательность дискретных случайных чисел; kф (τ) — импульсная характеристика формирующего фильтра; u(lT ) — произведение последовательности дискретных случайных чисел и импульсной характеристики ò формирующего фильтра; u(τ)dτ — интеграл свертки; η(lT ) — случайный процесс возмущения. 4. Сгенерированная реализация вертикальных неровностей η(t) для системы с одной степенью свободы при скорости движения 50 м/с. В нуле автокорреляционная функция (рис. 3, кривая 2) равна дисперсии случайного процесса и квадрату значения импульсной характеристики в нуле z1
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