Commenced in January 2007
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Analytical Track Surface Modelling for Multi-Body Analyses of Rail Vehicles in MATLAB SIMULINK

Authors: Stefan Heinrich, Tom Morris


Wheel-rail contact simulation behavior is generally determined using external Multi-Physics libraries, such as Vtech CMCC CONTACT or perhaps self-developed solutions, when establishing and modeling rail track networks for vehicle dynamic and safety analysis. Commercial software such as SIMPACK or VAMPIRE Pro rely upon such external libraries for example. To date however there is no integration of a CONTACT library into MATLAB SIMULINK that would serve to accurately perform Multi-Body analysis of rail vehicles within this particular software environment. Since MATLAB SIMULINK holds an advantage over the aforementioned commercial software regarding topics such as hardware in the loop (HIL), control design and multi-physical system analysis, this study focuses on the analytical description of the track profile. By meshing this profile as a surface for use in the SIMULINK SIMSCAPE Multi-Body environment, it supports the simulation of a hydraulic-mechatronic active steering system with individually suspended single-driven wheels, integrated into a modified tram designed for the Zurich network. Starting with a 60R2 profile, an analytical description of the profile is created using trigonometric functions and tangential radius transitions as boundary conditions. The description provides a one-dimensional, closed-curve which can be evaluated in the Cartesian y-z coordinate system by specifying a point density. The exact analytical description in combination with a line-point density allows the geometry of the profile to be easily varied. In the next step, the considered track section is modeled using the shape-preserving piecewise cubic spline interpolation. The support points for the spline are also calculated analytically combining straight lines, circular arcs and clothoids. The spline and its normal and binormal vectors enable the first step of the track profile generation before being extruded along the given track points. A three-dimensional point cloud of the track is then transformed into a surface model according to the surface meshing available in MATLAB. A current limitation here is that the orthogonal mesh generation leads to a certain number of unused points depending on the chosen combinations of curves in the track model. Therefore, a segmentation of the track is performed before the actual meshing. This optimization approach fits these segments into rectangles of the smallest possible area. Created in this way, the mesh segments are then passed to SIMULINK SIMSCAPE and used for the rail-wheel contact description in the Multi-Body Simulation. In addition, information such as spatial features and positioning can be stored using this analytical approach. This allows for incorporating any track profile changes, such as in switches, crossings or shallow parts, and to use linear or non-linear profile transitions as a function of the position on the track. This analytical, twice differentiable mesh description is shown to result in significantly lower computation times (factor 5 to 10) compared to earlier contact modeling options associated with multiple contact bodies. The improved contact approach and the integration of external libraries now allow for an increased complexity of modeling towards the HIL and Co-Simulation architecture, and thus support the design of bogie concepts with more detailed statements of the tram system behavior.

Keywords: analytical track description, wheel-rail contact, SIMULINK SIMSCAPE, track modelling

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