Analysis of Steady Motions on Curved Tracks Using Multibody Models

2007 ◽  
Author(s):  
Jose´ L. Escalona ◽  
Rosario Chamorro
Keyword(s):  
Periodic Orbit ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Contact Method ◽  
Elastic Contact ◽  
Coordinate Transformations ◽  
Railroad Vehicles ◽  
Curving Performance ◽  
The Stability ◽  
Steady Motions

In this paper a systematic procedure for evaluating the steady curving of railroad vehicles is developed. The equations of motion obtained using multibody dynamics and the elastic contact method are used to this end. The method proposed can deal with flange contact of the wheels. Two coordinate transformations are needed to evaluate the steady curving as an equilibrium position of the system instead of a periodic orbit. The stability of the motions is also evaluated by using a special eigenvalue analysis of the equations of motion. The procedure developed simplifies significantly the analysis of the curving performance of railroad vehicles without loosing accuracy or generality. The paper includes as a numerical example the steady motion of an unsuspended wheelset. The comparison of the numerical results with classical theories shows the accuracy of the method proposed.

Eigenvalue Analysis of Multibody Models of Railroad Vehicles Including Track Flexibility

2011 ◽  
Author(s):  
Jose´ L. Escalona ◽  
Rosario Chamorro ◽  
Antonio M. Recuero
Keyword(s):  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Differential Algebraic Equations ◽  
Eigenvalue Analysis ◽  
Ride Quality ◽  
Algebraic Equations ◽  
Essential Information ◽  
Railroad Vehicles ◽  
The Stability

The stability analysis of railroad vehicles using eigenvalue analysis can provide essential information about the stability of the motion, ride quality or passengers comfort. The system eigenvalues are not in general a vehicle property but a property of a vehicle travelling steadily on a periodic track. Therefore the eigenvalue analysis follows three steps: calculation of steady motion, linearization of the equations of motion and eigenvalue calculation. This paper deals with different numerical methods that can be used for the eigenvalue analysis of multibody models of railroad vehicles that can include deformable tracks. Depending on the degree of nonlinearity of the model, coordinate selection or the coordinate system used for the description of the motion, different methodologies are used in the eigenvalue analysis. A direct eigenvalue analysis is used to analyse the vehicle dynamics from the differential-algebraic equations of motion written in terms of a set of constrained coordinates. In this case not all the obtained eigenvalues are related to the dynamics of the system. As an alternative the equations of motion can be obtained in terms of independent coordinates taking the form of ordinary differential equations. This procedure requires more computations but the interpretation of the results is straightforward.

Description of Methods for the Eigenvalue Analysis of Railroad Vehicles Including Track Flexibility

2012 ◽  
Vol 7 (4) ◽  
Author(s):  
José L. Escalona ◽  
Rosario Chamorro ◽  
Antonio M. Recuero
Keyword(s):  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Differential Algebraic Equations ◽  
Eigenvalue Analysis ◽  
Ride Quality ◽  
Algebraic Equations ◽  
Essential Information ◽  
Railroad Vehicles ◽  
The Stability

The stability analysis of railroad vehicles using eigenvalue analysis can provide essential information about the stability of the motion, ride quality, or passengers’ comfort. The eigenvalue analysis follows three steps: calculation of steady motion, linearization of the equations of motion, and eigenvalue calculation. This paper deals with different numerical methods that can be used for the eigenvalue analysis of multibody models of railroad vehicles that can include deformable tracks. Depending on the degree of nonlinearity of the model and coordinate selection, different methodologies can be used. A direct eigenvalue analysis is used to analyze the vehicle dynamics from the differential-algebraic equations of motion written in terms of a set of constrained coordinates. As an alternative, the equations of motion can be obtained in terms of independent coordinates taking the form of ordinary differential equations. This procedure requires more computations, but the interpretation of the results is straightforward.

scholarly journals Experiments on the motion of solid bodies in rotating fluids

1923 ◽  
Vol 104 (725) ◽  
pp. 213-218 ◽  
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Steady Motion ◽  
The Body ◽  
Two Dimensional ◽  
Experimental Conditions ◽  
Axis Of Rotation ◽  
Rotating Liquid ◽  
Steady Motions ◽  
Solid Bodies

Some years ago it was pointed out by Prof. Proudman that all slow steady motions of a rotating liquid must be two-dimensional. If the motion is produced by moving a cylindrical object slowly through the liquid in such a way that its axis remains parallel to the axis of rotation, or if a two-dimensional motion is conceived as already existing, it seems clear that it will remain two-dimensional. If a slow three-dimensional motion is produced, then it cannot be a steady one. On the other hand, if an attempt is made to produce a slow steady motion by moving a three-dimensional body with a small uniform velocity (relative to axes which rotate with the fluid) three possibilities present themselves:— ( a ) The motion in the liquid may never become steady, however long the body goes on moving. ( b ) The motion may be steady but it may not be small in the neighbourhood of the body. ( c ) The motion may be steady and two-dimensional. In considering these three possibilities it seems very unlikely that ( a ) will be the true one. In an infinite rotating fluid the disturbance produced by starting the motion of the body might go on spreading out for ever and steady motion might never be attained, but if the body were moved steadily in a direction at right angles to the axis of rotation, and if the fluid were contained between parallel planes also perpendicular to the axis of rotation, it seems very improbable that no steady motion satisfying the equations of motion could be attained. There is more chance that ( b ) may be true. A class of mathematical expressions representing the steady motion of a sphere along the axis of a rotating liquid has been obtained. This solution of the problem breaks down when the velocity of the sphere becomes indefinitely small, in the sense that it represents a motion which does not decrease as the velocity of the sphere decreases. It seems unlikely that such a motion would be produced under experimental conditions.

scholarly journals The formation of vortices from a surface of discontinuity

1931 ◽  
Vol 134 (823) ◽  
pp. 170-192 ◽  
Keyword(s):  
Steady State ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Small Oscillations ◽  
Approximate Form ◽  
History Of ◽  
State Increase ◽  
Liquid Surfaces

Helmholtz was the first to remark on the instability of those “liquid surfaces” which separate portions of fluid moving with different velocities, and Kelvin, in investigating the influence of wind on waves in water, supposed frictionless, has discussed the conditions under which a plane surface of water becomes unstable. Adopting Kelvin’s method, Rayleigh investigated the instability of a surface of discontinuity. A clear and easily accessible rendering of the discussion is given by Lamb. The above investigations are conducted upon the well-known principle of “small oscillations”—there is a basic steady motion, upon which is superposed a flow, the squares of whose components of velocity can be neglected. This method has the advantage of making the equations of motion linear. If by this method the flow is found to be stable, the equations of motion give the subsequent history of the system, for the small oscillations about the steady state always remain “small.” If, however, the method indicates that the system is unstable, that is, if the deviations from the steady state increase exponentially with the time, the assumption of small motions cannot, after an appropriate interval of time, be applied to the case under consideration, and the equations of motion, in their approximate form, no longer give a picture of the flow. For this reason, which is well known, the investigations of Rayleigh only prove the existence of instability during the initial stages of the motion. It is the object of this note to investigate the form assumed by the surface of discontinuity when the displacements and velocities are no longer small.

Wheel-Rail Multi-Point Contact Method for Railway Turnouts

2011 ◽  
Vol 97-98 ◽  
pp. 378-381
Author(s):  
Zhi Wei Chen ◽  
Linan Li ◽  
Shi Gang Sun ◽  
Jun Long Zhou
Keyword(s):  
Calculation Method ◽  
Normal Force ◽  
Contact Point ◽  
Point Contact ◽  
Contact Model ◽  
Contact Method ◽  
Elastic Contact ◽  
Simulation Calculation ◽  
Acute Change

A calculation method of wheel-rail multi-point contact based on the elastic contact model is introduced. Moreover, the simulation calculation of vehicles passing through branch lines of No.18 turnouts is carried out. The result showed that the acute change of wheel-rail normal force caused by the transfers of wheel-rail contact point between two rails can be avoid by wheel-rail multi-point contact method, and the transfers of wheel-rail normal force between two rails is smoother. The validity of wheel-rail multi-point contact method is verified.

A Study of the Lateral Stability of Railroad Vehicles Using a Nonlinear Constrained Multibody Formulation

2001 ◽  
Author(s):  
Davide Valtorta ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana ◽  
Jalil R. Sany
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Theory ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Operating Conditions ◽  
Lateral Stability ◽  
Railroad Vehicles ◽  
Contact Formulation ◽  
The Stability

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

Efficient Dynamic Computer Simulation of Simple-Closed Spatial Linkages

1990 ◽  
Author(s):  
L. T. Wang
Keyword(s):  
Computer Simulation ◽  
Computational Algorithm ◽  
Equations Of Motion ◽  
Joint Space ◽  
Kinematic Chains ◽  
Spatial Linkages ◽  
Dynamic Computer Simulation ◽  
The Stability ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Abstract A new method of formulating the generalized equations of motion for simple-closed (single loop) spatial linkages is presented in this paper. This method is based on the generalized principle of D’Alembert and the use of the transformation Jacobian matrices. The number of the differential equations of motion is minimized by performing the method of generalized coordinate partitioning in the joint space. Based on this formulation, a computational algorithm for computer simulation the dynamic motions of the linkage is developed, this algorithm is not only numerically stable but also fully exploits the efficient recursive computational schemes developed earlier for open kinematic chains. Two numerical examples are presented to demonstrate the stability and efficiency of the algorithm.

scholarly journals A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

1971 ◽  
Vol 13 (5) ◽  
pp. 330-343 ◽  
Author(s):  
D. F. Sheldon
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Recent Experience ◽  
Wind Tunnel Testing ◽  
Stability Derivatives ◽  
Direct Indication ◽  
Metric Dimensions ◽  
Set Up ◽  
The Stability ◽  
Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves

2003 ◽  
Vol 125 (2) ◽  
pp. 291-300 ◽  
Author(s):  
G. H. Jang ◽  
J. W. Yoon
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
High Rotational Speed ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Herringbone Grooves

This paper presents an analytical method to investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

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