scholarly journals Dynamic Investigation of the Hunting Motion of a Railway Bogie in a Curved Track via Bifurcation Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Caglar Uyulan ◽  
Metin Gokasan ◽  
Seta Bogosyan
Keyword(s):  
Lateral Displacement ◽  
Dead Zone ◽  
Power Spectra ◽  
Creep Model ◽  
Stable Model ◽  
Curved Track ◽  
Railway Bogie ◽  
Hunting Frequency ◽  
Type Oscillation ◽  
Dynamic Investigation

The main purpose of this paper is to analyze and compare the Hopf bifurcation behavior of a two-axle railway bogie and a dual wheelset in the presence of nonlinearities, which are yaw damping forces in the longitudinal suspension system and heuristic creep model of the wheel-rail contact including dead-zone clearance, while running on a curved track. Two-axle railway bogie and dual wheelset were modeled using 12-DOF and 8-DOF system with considering lateral, vertical, roll, and yaw motions. By utilizing Lyapunov’s indirect method, the critical hunting speeds related to these models are evaluated as track radius changes. Hunting defined as the lateral vibration of the wheelset with a large domain was characterized by a limit cycle-type oscillation behavior. Influence of the curved track radius on the lateral displacement of the leading wheelset was also investigated through 2D bifurcation diagram, which is employed in the design of a stable model. Frequency power spectra at critical speeds, which are related to the subcritical and supercritical bifurcations, were represented by comparing the two-axle bogie and dual wheelset model. The evaluated accuracy to predict the critical hunting speed is higher and the hunting frequency in unstable region is lower compared to the dual wheelset model.

Stability and bifurcation analysis of the non-linear railway bogie dynamics

2017 ◽  
Vol 232 (16) ◽  
pp. 2787-2802
Author(s):  
Çağlar Uyulan ◽  
Metin Gokasan ◽  
Seta Bogosyan
Keyword(s):  
Hopf Bifurcation ◽  
Critical Speed ◽  
Lateral Displacement ◽  
Creep Model ◽  
Phase Portraits ◽  
Subcritical State ◽  
Critical Speeds ◽  
Railway Vehicles ◽  
Non Linear ◽  
Railway Bogie

It is a critical issue to maintain stability in high-speed railway vehicles and to ensure comfortable and safe driving. Multi-body models of railway vehicles have non-linear properties originated from the wheel–rail contact and characteristics of the suspension systems. The critical speed values at which the unstable oscillations and the amplitudes of the limit cycle-type vibrations take place vary by adjusting the design parameters; therefore, these effects on non-linear railway dynamics must be evaluated with a higher precision by using numerical and/or analytical methods to determine the bifurcation behavior. The main objective of this paper is to examine the non-linear phenomena in a railway bogie from a broad perspective, concentrating on non-linear analysis methods. Thus, non-linear equations of motion of a 12-degrees of freedom railway bogie involving dual wheelsets, non-linear wheel flange contact, heuristic non-linear creep model, and suspension system are solved in the time domain with small time steps by using ode23s (stiff/Mod.Rosenbrock) method. The critical speeds were calculated with respect to the effects of various lateral stiffness and damping coefficients. The bifurcation diagrams of the maximum lateral displacement of the leading wheelset were depicted within a wide speed range. In the case of the suspension parameter set where the subcritical/supercritical Hopf bifurcation takes place, the phase portraits and the symmetric/asymmetric oscillations of the leading wheelset at the critical speed were represented. The type of the Hopf bifurcation can be transformed from the subcritical state to the supercritical state by increasing the given suspension ratio. The Lyapunov exponents of the lateral displacement, lateral velocity, yaw angular displacement, and yaw angular velocity of the leading wheelset were evaluated above the critical speeds to examine chaotic motion. The effect of the suspension parameters on the non-linear dynamical behavior of the railway bogie at the stability limit and on the bifurcation type has been proved.

Hunting Stability Analysis of a New High-Speed Railway Vehicle Model Moving on Curved Tracks

2007 ◽  
Author(s):  
Yung-Chang Cheng ◽  
Sen-Yung Lee
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Nonlinear Creep ◽  
Car Body ◽  
Suspension Parameters ◽  
Virtual Boundary ◽  
Hunting Stability

A new dynamic model of railway vehicle moving on curved tracks is proposed. In this new model, the motion of the car body is considered and the motion of the tuck frame is not restricted by a virtual boundary. Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of a fourteen degrees of freedom car system, considering the lateral displacement and the yaw angle of the each wheelset, the truck frame and the car body, moving on curved tracks are derived in completeness. To illustrate the accuracy of the analysis, the limiting cases are examined. In addition, the influences of the suspension parameters on the critical hunting speeds evaluated via the linear and the nonlinear creep models respectively are studied. Furthermore, the influences of the suspension parameters on the critical hunting speeds evaluated via the fourteen degrees of freedom car system and the six degrees of freedom truck system, which the motion of the tuck frame is restricted by a virtual boundary, are compared.

Spectral Distribution of Derailment Coefficient in Non-Linear Model of Railway Vehicle–Track System With Random Track Irregularities

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Ewa Kardas-Cinal
Keyword(s):  
Spatial Frequency ◽  
Second Harmonic ◽  
Lateral Displacement ◽  
Strong Dependence ◽  
Contact Forces ◽  
Railway Vehicle ◽  
Characteristic Structure ◽  
Window Width ◽  
Derailment Coefficient ◽  
Hunting Frequency

Improving the running safety and reducing the risk of derailments are the key objectives in the assessment of the running characteristics of railway vehicles. The present study of the safety against derailment is focused on the effect of wheelset hunting on the derailment coefficient Y/Q and, especially, how it is reflected in the power spectral density (PSD) of Y/Q. The lateral Y and vertical Q forces at the wheel/rail contact are obtained in numerical simulations for a four-axle railway vehicle moving at a constant velocity along a tangent track with random geometrical irregularities. The PSD of Y/Q, calculated as a function of spatial frequency, is found to have a characteristic structure with three peaks for the leading wheelsets and one peak for the trailing wheelsets of the front and rear bogies. The positions of the PSD maxima remain unchanged with increasing ride velocity, while their magnitudes and shapes evolve. One of the PSD peaks occurs for all wheelsets at the same spatial frequency corresponding to the wheelset hunting, while an additional peak at the double hunting frequency is found for the leading wheelsets. Such a peak structure is also found in the PSD of Y/Q determined in simulations with modified parameters of the vehicle primary suspension and for different track sections. The peak at the double hunting frequency is shown, by a detailed analysis of the contact forces, the flange angles and their PSDs, to result from the nonlinear geometry of the wheel/rail contact leading to the second-harmonic term in Y/Q. The emergence of this peak is also closely related to the phase difference between the hunting oscillations of the wheelset lateral displacement and the oscillations of its yaw angle, for which the difference is significantly smaller for the leading wheelset than for the trailing one. Finally, the effect of wheelset hunting is also shown to manifest itself in the strong dependence of the running average of Y/Q, which is used in the railway technical safety standards for the assessment of the safety against derailment (with the Nadal criterion), on the applied window width.

Hunting stability analysis of a railway vehicle system using a novel non-linear creep model

2012 ◽  
Vol 226 (6) ◽  
pp. 612-629 ◽  
Author(s):  
Yung-Chang Cheng
Keyword(s):  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
System Parameters ◽  
Proposed Model ◽  
Linear Creep ◽  
Non Linear ◽  
Six Dof

A non-linear creep model that considers non-constant creep coefficients that vary as a function of vehicle speed is derived using Hertz contact theory, Kalker’s linear theory and a heuristic non-linear creep model. The proposed model is created by modifying the heuristic non-linear creep model by adding a linear creep moment and the semi-axis lengths in the non-linearity of the saturation constant. In this paper, the vehicle is modeled by a system with 28 degrees of freedom, taking into consideration the lateral displacement, vertical displacement, roll angle and yaw angle of each wheelset, the truck frames and car body. To analyze the respective effects of the major system parameters on the vehicle dynamics, the 28 degree-of-freedom (DOF) system is reduced to a 25-DOF model, by excluding designated subsets of the system parameters. The accuracy of the present analysis is verified by comparing a six-DOF system and the current numerical results with results in the literature. The effects of suspension parameters of a vehicle on the critical hunting speeds evaluated by the currently proposed model, the traditional non-linear creep model and the linear creep model are illustrated. In most cases, the obtained results show that the critical hunting speed evaluated using the new non-linear creep model is greater than that derived using the traditional non-linear creep model. Additionally, the critical hunting speed evaluated using the linear creep model is higher than that evaluated using the currently proposed non-linear creep model.

Derailment Analysis of High-Speed Railway Vehicle Bogies

2011 ◽  
Vol 110-116 ◽  
pp. 186-195 ◽  
Author(s):  
Yung Chang Cheng ◽  
Chern Hwa Chen ◽  
Che Jung Yang
Keyword(s):  
High Speed ◽  
Lateral Displacement ◽  
Vertical Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Nonlinear Creep ◽  
Bogie Frame ◽  
Suspension Parameters ◽  
Yaw Angle

Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of a 12 degree-of-freedom (12-DOF) bogie system which takes account of the lateral displacement, vertical displacement, the roll angle and the yaw angle of the each wheelset and the bogie frame, moving on curved tracks are derived. The nonlinear creep forces and moments are constructed via the saturation constant of the nonlinear creep model in completeness. The effect of the suspension parameters of a bogie system on the derailment quotient is investigated. Results obtained in this study show that the derailment quotient of a bogie system increases as the vehicle speed increases. In addition, the derailment quotient of a bogie system is generally decreased with the increasing values of suspension parameters.

Running Safety and Comfort Analysis of Railway Vehicles Moving on Curved Tracks

2014 ◽  
Vol 14 (04) ◽  
pp. 1450004 ◽  
Author(s):  
Yung-Chang Cheng ◽  
Chin-Te Hsu
Keyword(s):  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Creep Model ◽  
Railway Vehicle ◽  
Nonlinear Creep ◽  
Running Safety ◽  
Comfort Index ◽  
Vertical Displacements ◽  
Index Formulas

Using a heuristic linear creep model, this study derives the governing differential equations of motion for the railway vehicle traveling on curved tracks. The railway vehicle is modeled as a car system with 27 degrees-of-freedom (DOFs), taking into account the lateral and vertical displacements, roll and yaw angles of the wheelsets and truck frames, as well as the lateral displacement, roll and yaw angles of the car body. The effects of railway vehicle speeds on the derailment quotients and offload factors related to running safety are evaluated by both the linear and nonlinear creep models for various radii of curved tracks. Using the Sperling and modified Sperling index formulas, the effects of railway vehicle speeds on lateral riding quality and comfort are illustrated for the two models with various radii of curved tracks. Furthermore, the effects of railway vehicle speeds on the lateral Sperling comfort index of the 27-DOF car model are presented and compared for various suspension parameters. Finally, the acceptable region for riding quality and comfort are drawn.

Dynamic Analysis for Derailment Safety of High-Speed Railway Vehicle Bogies

2011 ◽  
Vol 199-200 ◽  
pp. 239-242
Author(s):  
Chern Hwa Chen ◽  
Yung Chang Cheng ◽  
Shun Chin Yang ◽  
Yuh Yi Lin ◽  
Cheng Hsin Chang ◽  
...  
Keyword(s):  
High Speed ◽  
Lateral Displacement ◽  
Vertical Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Nonlinear Creep ◽  
Suspension Parameters ◽  
Derailment Safety ◽  
Yaw Angle

Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of a 12 degree-of-freedom (12-DOF) bogie system which takes account of the lateral displacement, vertical displacement, the roll angle and the yaw angle of the each wheelset and the bogie frame, moving on curved tracks are derived. The nonlinear creep forces and moments are constructed via the saturation constant of the nonlinear creep model in completeness. The effect of the suspension parameters of a bogie system on the derailment quotient is investigated. Results obtained in this study show that the derailment quotient of a bogie system increases as the vehicle speed increases. In addition, the derailment quotient of a bogie system is generally decreased with the increasing values of suspension parameters.

Parametric Analysis of Ride Comfort for Tilting Railway Vehicles Running on Irregular Curved Tracks

2016 ◽  
Vol 16 (09) ◽  
pp. 1550056 ◽  
Author(s):  
Yung-Chang Cheng ◽  
Chin-Te Hsu
Keyword(s):  
Ride Comfort ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Roll Angle ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Nonlinear Creep ◽  
Rail Irregularities ◽  
Yaw Angle

The ride comfort of a tilting railway vehicle moving on curved tracks with rail irregularities is studied. Using the nonlinear creep model and Kalker's linear theory, the governing differential equations of motion for a tilting railway vehicle running on irregular tracks are first derived. The tilting railway vehicle is modeled by a 27 degree-of-freedom (DOF) car system, considering the lateral displacement, vertical displacement, roll angle and yaw angle of both the wheelsets and bogie frames, as well as the lateral displacement, roll angle and yaw angle of the car body. Based on the international standard ISO 2631-1, the effect of vehicle speed on the ride comfort index of the tilting vehicle is investigated for various tilting angles, using both linear and nonlinear creep models, and various radii of curved tracks, as well as for various suspension parameters. Finally, the ride comfort indices computed with rail irregularities are found to be higher than those with no rail irregularities, indicating that the effect of rail irregularities on the ride comfort of a tilting vehicle cannot be disregarded in practice.

Hunting stability and derailment analysis of a car model of a railway vehicle system

2011 ◽  
Vol 226 (2) ◽  
pp. 187-202 ◽  
Author(s):  
Y-C Cheng ◽  
C-T Hsu
Keyword(s):  
Lateral Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
System Parameters ◽  
Suspension Parameters ◽  
Linear Creep ◽  
Non Linear ◽  
Creep Models ◽  
Yaw Angle

Using a heuristic linear creep model, this article derives the governing differential equations of motion for a vehicle travelling on curved tracks. The vehicle is modelled by a 27-degrees-of-freedom (27-DOF) car system, with lateral and vertical displacement, roll and yaw angle of each wheelset and the bogie frames, as well as lateral displacement, and roll and yaw angle of the car body taken into consideration. To analyse the respective effects of major system parameters on vehicle dynamics, the 27-DOF system is reduced to a 14-DOF system by excluding designated subsets of the system parameters. The effects of suspension parameters of a vehicle on the critical hunting speeds were evaluated by the 14- and 27-DOF systems. The results obtained in this study, show that the critical hunting speeds derived using the 14-DOF system are generally higher than those obtained using the 27-DOF system. Additionally, the critical hunting speeds derived using the heuristic non-linear creep model are lower than those achieved using the linear creep model. The effects on derailment quotients of vehicle speeds are evaluated using both linear and non-linear creep models with various suspension parameters. Finally, the effects of vehicle speed on the derailment quotient for sharp curves and low vehicle speed are investigated and compared with both linear and non-linear creep models.

scholarly journals INFLUENCE OF LATERAL DISPLACEMENT OF BOGIES ON THE FREIGHT CAR DYNAMICS

2021 ◽  
pp. 66-81
Author(s):  
A. O Shvets
Keyword(s):  
Mathematical Model ◽  
Lateral Displacement ◽  
Operating Conditions ◽  
Movement Speed ◽  
Rolling Stock ◽  
Transverse Displacement ◽  
Resource Saving ◽  
Freight Car ◽  
Curved Track ◽  
Dynamic Indicators

Purpose. The work is aimed at determining the influence of the lateral displacement of a freight car bogie, taking into account the value of the movement speed on its main dynamic indicators and interaction indicators of the rolling stock and the track. Methodology. The quantitative assessment of dynamic indicators was obtained by the method of mathematical and computer modeling. The design scheme of the car takes into account the interaction peculiarities of cars as part of the train: the possibility of all modes of body vibration in space, the transmission of longitudinal force from neighboring cars in vertical and horizontal directions, taking into account the technical condition of individual parts of the car and their design features, as well as various operating conditions. Findings. During the research, a mathematical model of a coupling of five freight cars was applied to study the dynamic loading of a gondola car and a track. Main dynamic and interaction indicators of the rolling stock and the track in case of transverse bogie displacement when moving along curved track sections assessment were assessed. The maximum possible values of the lateral displacement of the freight car bogie were substantiated. Originality. The mathematical model of the coupling of freight cars in the train has been improved. In the calculation schemes describing the vibrations of the cars, the peculiarities of the freight car bogies, lozenging of the bogie side frames are taken into account. The model makes it possible to study the effect of changing rotation angle of the central axis of the car body, which in turn leads to the lateral displacement of bogies relative to each other, on the main dynamic and interaction indicators of the rolling stock and the track. For the first time, the influence of transverse displacement of the bogie was investigated, taking into account the wear of its parts and assemblies when moving on track sections with unevenness. Practical value. The calculation results can be used to assess the influence of the bogie transverse displacement on the dynamic qualities of the rolling stock and interaction indicators of the rolling stock and the track, taking into account the wear of parts and units of the bogie when moving in straight and curved track sections with irregularities. The application of the results obtained will contribute to an increase in the stability of freight rolling stock in the conditions of increasing travel speeds, which in turn will allow developing technical conditions for the implementation of resource-saving technologies for transporting goods that meet the safety requirements of train traffic.

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