Euler angles and numerical representation of the railroad track geometry

As railroad infrastructure becomes older and older and rail transportation is developing towards higher speed and heavier axle, the risk to safe rail transport and the expenses for railroad maintenance are increasing. The railroad infrastructure deterioration (prediction) model is vital to reducing the risk and the expenses. A short-range track condition prediction method was developed in our previous research on railroad track deterioration analysis. It is intended to provide track maintenance managers with two or three months of track condition in advance to schedule track maintenance activities more smartly. Recent comparison analyses on track geometrical exceptions calculated from track condition measured with track geometry cars and those predicted by the method showed that the method fails to provide reliable condition for some analysis sections. This paper presented the enhancement to the method. One year of track geometry data for the Jiulong-Beijing railroad from track geometry cars was used to conduct error analyses and comparison analyses. Analysis results imply that the enhanced model is robust to make reliable predictions. Our in-process work on applying those predicted conditions for optimal track maintenance scheduling is discussed in brief as well.

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Optimization of Process Field Measurement GNSS-RTK for Railway Infrastructure

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.258.481 ◽

2016 ◽

Vol 258 ◽

pp. 481-484

Author(s):

Dalibor Bartonek ◽

Jiří Bures ◽

Otakar Svabensky

Keyword(s):

Field Measurement ◽

Optimization Method ◽

Heuristic Methods ◽

Railroad Track ◽

Time Intervals ◽

Track Geometry ◽

Railway Infrastructure ◽

The Status ◽

Dynamic Data Structure ◽

Material Wear

The paper describes optimized measurements in field on points of railway control by the GNSS-RTK method. The purpose of measurement is to monitor the status of railroad track geometry. Good geometry extends the life of superstructure, reduces tracks and sleepers material wear during passing of the trains, and thus lowers the overall maintenance demands. In the model each of these points can be represented by node in graph and evaluation of graph edges corresponds to the distance between individual nodes. The task is to measure on every node even one times and to absolve the total route with minimal sum of distance. In fact it is searching of the Hamilton's path in a graph. The situation is complicated because the conditions for GNSS surveying in nodes are suitable only at certain time intervals during the day. Generally the above mentioned is difficult task, which is solved in the practice in many cases by heuristic methods. The authors proposed the optimization method based on Floyd algorithm and dynamic data structure - events list. The optimization of field measurement solves the time demands and brings economic effectiveness.

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Analytical Elastic Modeling of Rail and Fastener Longitudinal Response

Transportation Research Record Journal of the Transportation Research Board ◽

10.1177/0361198120985848 ◽

2021 ◽

pp. 036119812098584

Author(s):

Matheus Trizotto ◽

Marcus S. Dersch ◽

J. Riley Edwards ◽

Arthur Lima

Keyword(s):

Analytical Model ◽

Critical Role ◽

Valuable Insight ◽

Railroad Track ◽

Track Geometry ◽

Longitudinal Response ◽

Ballasted Track ◽

Track Stiffness ◽

Component Failures ◽

Insight Into

The rail fastening system plays a critical role in maintaining proper railroad track geometry by transferring vertical, lateral, and longitudinal forces from the rails to crossties. Broken spikes in elastic fastening systems have been linked to inadequate transfer of longitudinal loads, posing a safety risk for timber crosstie ballasted track. Longitudinal track demand caused by passing trains has been investigated in previous research, but the magnitude and distribution of longitudinal fastener loads is not well understood or documented. To address these track component failures and improve fastener design, this paper presents a validated analytical model that estimates longitudinal rail seat loads, advancing current formulations to focus specifically on the rail seat. The validated method was used to quantify the distribution and magnitude of longitudinal loads in both the rail and fastening system caused by passing trains. Further, this paper quantifies the effect of track stiffness, number of powered locomotives, and wheel spacing on these distributions and magnitudes. This information provides valuable insight into the specific type of spike failures that have led to at least ten derailments and the requirement of manual walking inspections on multiple North American heavy axle load railroads as detailed in this paper. Further, this method can be used to quantify the longitudinal fastener loads for different track conditions to advance the mechanistic-empirical track design philosophy for elastic fastening systems.

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Rail Geometry and Euler Angles

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.2198878 ◽

2006 ◽

Vol 1 (3) ◽

pp. 264-268 ◽

Cited By ~ 9

Author(s):

Cheta Rathod ◽

Ahmed A. Shabana

Keyword(s):

Vehicle Dynamics ◽

Euler Angles ◽

Frenet Frame ◽

Geometric Properties ◽

Track Geometry ◽

Railroad Vehicle Dynamics ◽

Space Curves ◽

Curvature And Torsion ◽

The Relationship ◽

Railroad Vehicle

In railroad vehicle dynamics, Euler angles are often used to describe the track geometry (track centerline and rail space curves). The tangent and curvature vectors as well as local geometric properties such as the curvature and torsion can be expressed in terms of Euler angles. Some of the local geometric properties and Euler angles can be related to measured parameters that are often used to define the track geometry. The Euler angles employed, however, define a coordinate system that may differ from the Frenet frame used in the classical differential geometry. The relationship between the track frame used in railroad vehicle dynamics and the Frenet frame used in the theory of curves is developed in this paper and is used to shed light on some of the formulas and identities used in the geometric description in railroad vehicle dynamics. The conditions under which the two frames (track and Frenet) become equivalent are presented and used to obtain expressions for the curvature and torsion in terms of Euler angles and their derivatives with respect to the arc length.

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Modeling of track geometry degradation and decisions on safety and maintenance: A literature review and possible future research directions

Proceedings of the Institution of Mechanical Engineers Part F Journal of Rail and Rapid Transit ◽

10.1177/0954409717721870 ◽

2017 ◽

Vol 232 (5) ◽

pp. 1385-1397 ◽

Cited By ~ 13

Author(s):

Christian Higgins ◽

Xiang Liu

Keyword(s):

Data Analysis ◽

Literature Review ◽

Future Research ◽

Statistical Techniques ◽

Railroad Track ◽

Knowledge Gaps ◽

Research Directions ◽

Track Geometry ◽

Maintenance Decisions ◽

Future Research Directions

In a railroad track, the inherent and small geometrical deviations in the position of rails from their ideal design states constitute imperfections that can have a significant impact on the safety and the rate of degradation of the rail system. These deviations are measured by various technologies and further assessed using various algorithms and statistical techniques to quantify the condition of the system. This paper reviews the existing research regarding the collection of track geometry data, analysis of degradation, and the associated safety and maintenance decisions. The knowledge gaps in the existing literature are identified and possible future research directions are suggested. The review can be used as a reference by practitioners and researchers to determine optimal practices for assuring the safety of tracks.

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Rail Geometry and Euler Angles

Rail Transportation ◽

10.1115/imece2006-13965 ◽

2006 ◽

Cited By ~ 1

Author(s):

Cheta M. Rathod ◽

Ahmed A. Shabana

Keyword(s):

Vehicle Dynamics ◽

Euler Angles ◽

Frenet Frame ◽

Geometric Properties ◽

Track Geometry ◽

Railroad Vehicle Dynamics ◽

Space Curves ◽

Curvature And Torsion ◽

The Relationship ◽

Railroad Vehicle

In railroad vehicle dynamics, Euler angles are often used to describe the track geometry (track centerline and rail space curves). The tangent and curvature vectors as well as local geometric properties such as the curvature and torsion can be expressed in terms of Euler angles. Some of the local geometric properties and Euler angles can be related to measured parameters that are often used to define the track geometry. The Euler angles employed, however, define a coordinate system that may differ from the Frenet frame used in the classical differential geometry. The relationship between the track frame used in railroad vehicle dynamics and the Frenet frame used in the theory of curves is developed in this paper and used to shed light on some of the formulas and identities used in the geometric description in railroad vehicle dynamics. The conditions under which the two frames (track and Frenet) become equivalent are presented and used to obtain expressions for the curvature and torsion in terms of Euler angles and their derivatives with respect to the arc length.

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