Checking the adequacy of the method for generating a random process of disturbance of oscillations of rail carriages according to the impulse response of the forming filter

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.

1. Akishin A.A. Horizontal vibrations and motion in curves of a motor car of an electric train on four uniaxial bogies with pneumatic suspension. Cand. tech. sci. diss. Moscow, 2015, 355 p.

2. Savos'kin A.N., Romen Yu.S., Akishin A.A. Characteristics of disturbances causing oscillations of rail carriages. Vestnik of the Railway Research Institute, 2013, no. 6, pp. 21–30.

3. Biryukov I.V., Savos'kin A.N., Burchak G.P. et al. Mechanical part of traction rolling stock. Textbook for universities of railway transport. Reprintnoe vosproizvedenie izdaniya 1992 g. Moscow, Al'yans Publ., 2013, 440 p.

4. Savos'kin A.N., Akishin A.A. Generation of multidimensional stochastic process of perturbation in the problems of railways rolling stock dynamics. Computer Modeling and Simulation: proc. of the International Scientific and Technical Conference (St. Petersburg, July 2–4, 2014). St. Peterburg, Publishing house of the Polytechnic University, 2014, pp. 135–141.

5. Savos'kin A., Akishin A., Yurchеnko D. Design of a New TwoAxle Bogie for a High Speed Train Design of a New Two-Axle Bogie for a High Speed Train. Proceedings of the Third International Conference on Railway Technology: Research, Development and Maintenance. Stirlingshire (UK), Civil-Comp Press, 2016, p. 85. DOI:10.4203/ccp.110.85.

6. Matyash I., Shilkhanek Ya. Generator of random processes with a given matrix of spectral densities. Avtomatika i telemekhanika, 1960, Vol. 21, no. 1, pp. 29–35.

7. Savos'kin A.N., Polyakov A.I. Modeling equivalent irregularities of the track for the study of vibrations of rolling stock. Soiskatel', 2005, no. 1, pp. 106–118.

8. Vershinskiy S.V., Danilov V.N., Chelnokov I.I. Dynamics of the car. Textbook for universities of railway transport. Moscow, Transport Publ., 1978, 352 p.

9. Savos'kin A.N., Burchak G.P., Vasil'ev A.P. Lecture notes for the discipline “Dynamics of EMP”. Chapter 3. Random fluctuations. Moscow, MIIT Publ., 2002, 74 p.

10. Potemkin V.G. Calculations in the MATLAB environment. Moscow, Dialog-MIFI Publ., 2004, 714 p.

11. Akishin A.A. Application of the Matlab—Simulink package for modeling mechanical vibrations in the real-time hardware and software complex. Scientific and technical statements of the St. Petersburg State Polytechnic University. Computer science. Telecommunications. Management, 2013, no. 4, pp. 145–149.

12. Savos'kin A.N., Romen Yu.S., Akishin A.A. Random processes of disturbance in the dynamics of rail carriages. World of Transport and Transportation, 2015, no. 1, pp. 6–15.

13. Bendat Dzh., Pirsol A. Measurement and analysis of stochastic processes. Moscow, Mir Publ., 1974, 463 p.

14. Venttsel' E. S. Probability theory. Moscow, Vysshaya shkola Publ., 1999, 576 p.

15. Savos'kin A.N., Burchak G.P., Nasyrov R.K., Akishin A.A. Features of the probabilistic characteristics of random oscillations of rail carriages. Increasing the energy efficiency of ground transport systems: materials of the International Scientific and Practical Conference (Omsk, December 11–12, 2014). Omsk State University of Railway Transport. Omsk, OmGUPS Publ., 2014, pp. 314–339.