Master's Dissertation
DOI
https://doi.org/10.11606/D.3.2021.tde-25102021-145823
Document
Author
Full name
Lucas da Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2021
Supervisor
Committee
Gay Neto, Alfredo (President)
Santos, Guilherme Fabiano Mendonça dos
Silva, Emilio Carlos Nelli
Title in Portuguese
Modelagem geométrica do par roda-trilho com descrição por meio de NURBS.
Keywords in Portuguese
Algoritmos geométricos
Curvas de superfícies (Geometria e modelagem computacional
Geometria e modelagem computacional
Otimização não linear
Reconstrução (Geometria e modelagem computacional)
Abstract in Portuguese
Title in English
Geometric modelling of the wheel-rail pair with NURBS description.
Keywords in English
Arc-splines
Curve approximation
Geometric reconstruction
NURBS
Wheel-rail contact
Abstract in English
The mathematical description of the touching bodies surfaces is a fundamental part of computational contact modelling. This work proposal is to systematize the reconstruction of wheel and rail surfaces in computational environment, given a set of discrete samples measured from existing railway elements. The aim is to employ these representations in finite elements simulations of various interesting situations to the railway context. The fitting procedure developed is based on arc-splines, a family of curves composed of circular arcs smoothly joined (the tangent vector is continuous across segments). Given a sequence of points sampled from a planar curve, we estimate geometric properties such as arc-length and curvature. An initial approximation is obtained from the estimated curvature. Then, a better fitting is found deforming the arc-spline by a least-squares method. Arc-splines are rational curves and can be parametrized as NURBS (Non-Uniform Rational B-splines). The second half of this work concerns the parametrization of arc-splines using rational functions. As well as the parametrization of NURBS surfaces generated by extrusion and revolution of the approximate curves for modelling the surfaces of rails and wheels.

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Publishing Date
2021-10-26

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