Abstract
This paper represents new results obtained by its authors while searching for the proper shape of polynomial railway transition curves (TCs). The search for the proper shape means the evaluation of the curve properties based on chosen dynamical quantities and generation of such shape with use of mathematically understood optimisation methods. The studies presented now and in the past always had got a character of the numerical tests. For needs of this work advanced vehicle model, dynamical track-vehicle and vehicle-passenger interactions, and optimisation methods were exploited. In this software complete rail vehicle model of 2-axle freight car, the track discrete model, and non-linear description od wheel-rail contact are used. That part of the software, being vehicle simulation software, is combined with library optimisation procedures into the final computer programme. The main difference between this and previous papers by the authors are the degrees of examinated polynomials. Previously they tested polynomial curves of odd degrees, now they focus on TCs of 6th, 8th and 10th degrees with and without curvature and superelevation ramp tangence in the TC’s terminal points. Possibility to take account of fundamental demands (corresponding values of curvature in terminal points) concerning TC should be preserved. Results of optimisation are compared both among themselves and with 3rd degree parabola. The aim of present article is to find the polynomial TCs’ optimum shapes which are determined by the possible polynomial configurations. Only one dynamical quantities being the results of simulation of railway vehicle advanced model is exploited in the determination of quality function (QF1). This is: minimum of integral of vehicle body lateral acceleration.
Highlights
In recent works (Woźnica, 2012; Zboiński, 2012), authors of this article showed, that for the polynomial transition curves of odd degrees (5th, 7th, 9th and 11th) the best dynamical properties have curves with the biggest possible number of their terms
In Woźnica (2012) and Zboiński (2012) it was shown univocally that the polynomial transition curves (TCs) of odd degrees with the biggest possible number of their terms have the smallest values of QF
For conventional rail, the authors conclude on the basis of vehicle dynamics simulation, that polynomial and trigonometric TCs do not show the superiority over 3rd degree parabola
Summary
In recent works (Woźnica, 2012; Zboiński, 2012), authors of this article showed, that for the polynomial transition curves of odd degrees (5th, 7th, 9th and 11th) the best dynamical properties (the smallest values of QF1) have curves with the biggest possible number of their terms. For curves of 5th degree the number of terms was 3, for curves of 7th degree – 5, for curves of 9th degree – 7, and corresponding for curves of 11th degree – 9. It was shown that use of polynomial TCs in railway conditions could be an advantage. This can only be achieved, as mentioned, for the curves of high degree and preferably with the maximum number of the terms
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
