Rail Geometry and Euler Angles

2006 ◽  
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.

Rail Geometry and Euler Angles

2006 ◽  
Vol 1 (3) ◽  
pp. 264-268 ◽  
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.

On the Contact Search Algorithms for Wheel/Rail Contact Problems

2009 ◽  
Vol 4 (4) ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Yoshihiro Suda
Keyword(s):  
Vehicle Dynamics ◽  
Line Search ◽  
Point Contact ◽  
Contact Problems ◽  
Search Algorithms ◽  
Railroad Vehicle Dynamics ◽  
Contact Points ◽  
Contact Search ◽  
On Line ◽  
Railroad Vehicle

In this investigation, contact search algorithms for the analysis of wheel/rail contact problems are discussed, and the on-line and off-line hybrid contact search method is developed for multibody railroad vehicle dynamics simulations using the elastic contact formulation. In the hybrid algorithm developed in this investigation, the off-line search that can be effectively used for the tread contact is switched to the on-line search when the contact point is jumped to the flange region. In the two-point contact scenarios encountered in curve negotiations, the on-line search is used for both tread and flange contacts to determine the two-point contact configuration. By so doing, contact points on the flange region given by the off-line tabular search are never used, but rather used as an initial estimate for the online iterative procedure for improving the numerical convergence. Furthermore, the continual on-line detection of the second point of contact is replaced with a simple table look-up. It is demonstrated by several numerical examples that include flange climb and curve negotiation scenarios that the proposed hybrid contact search algorithm can be effectively used for modeling wheel/rail contacts in the analysis of general multibody railroad vehicle dynamics.

Integration of geometry and analysis for the study of liquid sloshing in railroad vehicle dynamics

2017 ◽  
Vol 231 (4) ◽  
pp. 608-629 ◽  
Author(s):  
Huailong Shi ◽  
Liang Wang ◽  
Brynne Nicolsen ◽  
Ahmed A Shabana
Keyword(s):  
Rigid Body ◽  
Vehicle Dynamics ◽  
Three Dimensional ◽  
Liquid Sloshing ◽  
Inertia Force ◽  
Railroad Vehicle Dynamics ◽  
Body Model ◽  
Rigid Body Model ◽  
Railroad Vehicle ◽  
Curve Negotiation

A new continuum-based liquid sloshing approach that accounts for the effect of complex fluid and tank-car geometry on railroad vehicle dynamics is developed in this investigation. A unified geometry/analysis mesh is used from the outset to examine the effect of liquid sloshing on railroad vehicle dynamics during curve negotiation and during the application of electronically controlled pneumatic (ECP) brakes that produce braking forces uniformly and simultaneously across all cars. Using a non-modal approach, the geometry of the tank-car and fluid is accurately defined, a continuum-based fluid constitutive model is employed, and a fluid-tank contact algorithm is developed. The liquid sloshing model is integrated with a three-dimensional multibody system (MBS) railroad vehicle algorithm which accounts for the nonlinear wheel/rail contact. The three-dimensional wheel/rail contact force formulation used in this study accounts for the longitudinal, lateral, and spin creep forces that influence the vehicle stability. In order to examine the effect of the liquid sloshing on the railroad vehicle dynamics during curve negotiation, a general and precise definition of the outward inertia force is defined, and in order to correctly capture the fluid and tank-car geometry, the absolute nodal coordinate formulation (ANCF) is used. The balance speed and centrifugal effects in the case of tank-car partially filled with liquid are studied and compared with the equivalent rigid body model in curve negotiation and braking scenarios. In particular, the results obtained in the case of the ECP brake application of two freight car model are compared with the results obtained when using conventional braking. The traction analysis shows that liquid sloshing has a significant effect on the load distribution between the front and rear trucks. A larger coupler force develops when using conventional braking compared with ECP braking, and the liquid sloshing contributes to amplifying the coupler force in the ECP braking case compared to the equivalent rigid body model which does not capture the fluid nonlinear inertia effects. Furthermore, the results obtained in this study show that liquid sloshing can exacerbate the unbalance effects when the rail vehicle negotiates a curve at a velocity higher than the balance speed.

scholarly journals Geometric Characterizations of Canal Surfaces in Minkowski 3-Space II

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 703 ◽  
Author(s):  
Jinhua Qian ◽  
Mengfei Su ◽  
Xueshan Fu ◽  
Seoung Dal Jung
Keyword(s):  
Gaussian Curvature ◽  
Mean Curvature ◽  
Space Curve ◽  
Timelike Curve ◽  
Geometric Properties ◽  
Spacelike Curve ◽  
Space Curves ◽  
Canal Surfaces ◽  
The Mean ◽  
The Relationship

Canal surfaces are defined and divided into nine types in Minkowski 3-space E 1 3 , which are obtained as the envelope of a family of pseudospheres S 1 2 , pseudohyperbolic spheres H 0 2 , or lightlike cones Q 2 , whose centers lie on a space curve (resp. spacelike curve, timelike curve, or null curve). This paper focuses on canal surfaces foliated by pseudohyperbolic spheres H 0 2 along three kinds of space curves in E 1 3 . The geometric properties of such surfaces are presented by classifying the linear Weingarten canal surfaces, especially the relationship between the Gaussian curvature and the mean curvature of canal surfaces. Last but not least, two examples are shown to illustrate the construction of such surfaces.

Railroad Vehicle Dynamics

2007 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Khaled E. Zaazaa ◽  
Hiroyuki Sugiyama
Keyword(s):  
Vehicle Dynamics ◽  
Railroad Vehicle Dynamics ◽  
Railroad Vehicle

TORUS KNOTS EMBODYING CURVATURE AND TORSION IN AN OTHERWISE FEATURELESS CONTINUUM

2011 ◽  
Vol 20 (12) ◽  
pp. 1723-1739 ◽  
Author(s):  
J. S. AVRIN
Keyword(s):  
Elementary Particle ◽  
General Relativity ◽  
Geometric Model ◽  
The Other ◽  
Particle Model ◽  
Torus Knots ◽  
Torus Knot ◽  
The Subject ◽  
Curvature And Torsion ◽  
The Relationship

The subject is a localized disturbance in the form of a torus knot of an otherwise featureless continuum. The knot's topologically quantized, self-sustaining nature emerges in an elementary, straightforward way on the basis of a simple geometric model, one that constrains the differential geometric basis it otherwise shares with General Relativity (GR). Two approaches are employed to generate the knot's solitonic nature, one emphasizing basic differential geometry and the other based on a Lagrangian. The relationship to GR is also examined, especially in terms of the formulation of an energy density for the Lagrangian. The emergent knot formalism is used to derive estimates of some measurable quantities for a certain elementary particle model documented in previous publications. Also emerging is the compatibility of the torus knot formalism and, by extension, that of the cited particle model, with general relativity as well as with the Dirac theoretic notion of antiparticles.

Sign in / Sign up

Export Citation Format

Share Document