Boundary Conditions for Modeling the Impact of Wheels on Railway Track
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ry Conditions for Modeling the Impact of Wheels on Railway Track A. A. Kozhemyachenkoa,*, I. B. Petrova,b, A. V. Favorskayaa,b,c, and N. I. Khokhlova,b a
Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, 141701 Russia b Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, 117218 Russia c National Research Center “Kurchatov Institute”, Moscow, 123182 Russia *е-mail: [email protected] Received October 4, 2019; revised December 12, 2019; accepted April 9, 2020
Abstract—The distribution of the dynamic load on railroad track caused by a moving heavy train is numerically simulated. The track is represented as a multilayered linear elastic medium. A complete system of equations describing the state of a linear elastic body and a system of continuum mechanics equations are solved. The grid-characteristic method is used, which ensures the formulation of correct contact and boundary conditions. Analytical expressions taking into account the impact of damaged wheels on rails are derived, and corresponding boundary conditions are developed and numerically implemented. Keywords: grid-characteristic method, numerical simulation, wheel–rail system DOI: 10.1134/S0965542520090110
1. INTRODUCTION Problems related to detecting defects in elements of a rail–wheel system, including with the application of computer simulation, have been addressed by numerous research teams all over the world. There are different approaches to the simulation of the effect exerted by flat spots on railroad tracks. The scientific research in this direction over recent years can be briefly outlined as follows. Flat spots are created by wheel slide in braking under the decreased traction in the wheel–rail area. During an emergency stop, the wheel is locked, propelling along the rail, and this can generate a flat spot on the rolling surface. In [1] spatiotemporal models of the wheel–rail interaction were used to predict the impact force caused by a flat spot, experimental results obtained for an irregularity in the railhead were described, and an inverse proportion between the flat size and the given diameter of the wheel was shown. A similar modeling approach was used in [2]. In [3] measurement data were compared with finite-element numerical results obtained for the wheel–rail system; they were found to agree rather well for speeds up to 120 km/h. Numerical methods for problems in contact mechanics, such as matrix transposition and variational methods, can be used for non-Hertzian problems [4]. In [5] these methods were adapted for the application to actual rail– wheel systems. However, all of them are based on the assumption that the elastic behavior of contacting bodies can be approximated by an elastic half-space [4]. The method proposed in this paper deals with a heterogeneous linear elastic medium consisting of rails, ties, tie airspace, embankment, and the underlying rock and relies on full-wave simulation. The effect of out-of-roundness, including f
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