Rail Vehicle Modelling and Simulation using Lagrangian Method

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Rakesh Chandmal Sharma ◽  
Sunil Kumar Sharma ◽  
Srihari Palli
Keyword(s):  
Vehicle Dynamics ◽  
Lagrangian Function ◽  
Railway Vehicle ◽  
Analytical Dynamics ◽  
Rail Vehicle ◽  
Vehicle System ◽  
Complete Set ◽  
Generalised Coordinates ◽  
Broad Understanding ◽  
Lagrange’S Method

Formulation of vehicle dynamics problem is dealt either with Newton’s method or Lagrange’s method. This paper provides a broad understanding of Lagrange’s method applied to railway vehicle system. The Lagrange’s method of analytical dynamics provides a complete set of equations through differentiations of a function called Lagrangian function which includes kinetic and potential energy with respect to independent generalised coordinates assigned to the system. This paper also discusses rigid body rotational dynamics along with the concept of generalised coordinates (constrained and un-constrained) and generalised forces in detail.

Development of a reduced dynamic model for comfort evaluation of rail vehicle systems

2016 ◽  
Vol 230 (4) ◽  
pp. 489-504 ◽  
Author(s):  
Mortadha Graa ◽  
Mohamed Nejlaoui ◽  
Ajmi Houidi ◽  
Zouhaier Affi ◽  
Lotfi Romdhane
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Railway Vehicle ◽  
Passenger Comfort ◽  
Rail Vehicle ◽  
Vehicle System ◽  
Comfort Evaluation ◽  
Complex Models ◽  
Reduced Dynamic

In this paper, an analytical reduced dynamic model of a rail vehicle system is developed. This model considers only 38 degrees of freedom of the rail vehicle system. This reduced model can predict the dynamic behaviour of the rail vehicle while being simpler than existing dynamic models. The developed model is validated using experimental results found in the bibliography and its results are compared with existing more complex models from the literature. The developed model is used for the passenger comfort evaluation, which is based on the value of the weighted root mean square acceleration according to the ISO 2631 standard. Several parameters of the system, i.e., passenger position, loading of the railway vehicle and its speed, and their effect on the passenger comfort are investigated. It was shown that the level of comfort is mostly affected by the speed of the railway vehicle and the position of the seat. The load, however, did not have a significant effect on the level of comfort of the passenger.

Analysis of generalized force and its influence on ride and stability of railway vehicle

2020 ◽  
Vol 51 (6) ◽  
pp. 95-109
Author(s):  
Rakesh Chandmal Sharma ◽  
Sakshi Sharma ◽  
Sunil Kumar Sharma ◽  
Neeraj Sharma
Keyword(s):  
Potential Energy ◽  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Contact Point ◽  
Railway Vehicle ◽  
Energy Potential ◽  
Dissipation Energy ◽  
Rail Vehicle ◽  
Random Track Irregularities ◽  
Lagrange’S Method

Formulation of a rail vehicle model using Lagrange’s method requires the system’s kinetic energy, potential energy, spring potential energy, Rayleigh’s dissipation energy and generalized forces to be determined. This article presents a detailed analysis of generalized forces developed at wheel–rail contact point for 27 degrees of freedom–coupled vertical–lateral model of a rail vehicle formulated using Lagrange’s method and subjected to random track irregularities. The vertical–lateral ride comfort of the vehicle and the ride index of the vehicle are evaluated based on ISO 2631-1 comfort specifications and stability is determined using eigenvalue analysis. The parameters that constitute the generalized forces and critically influence ride and stability have been identified and their influences on the same have been analysed in this work.

Mechatronic suspension design for full rail vehicle system

2016 ◽  
Vol 231 (4) ◽  
pp. 571-590 ◽  
Author(s):  
Mortadha Graa ◽  
Mohamed Nejlaoui ◽  
Ajmi Houidi ◽  
Zouhaier Affi ◽  
Lotfi Romdhane
Keyword(s):  
Tracking Error ◽  
Linear Quadratic Regulator ◽  
Experimental Result ◽  
Railway Vehicle ◽  
Linear Quadratic ◽  
Rail Vehicle ◽  
Vehicle System ◽  
Frequency Domains ◽  
Rail Irregularities ◽  
Vehicle Motion

In this paper, an analytical mechatronic dynamic design model of a full rail vehicle system is developed. Based on the rail vehicle motion, its degree of freedom can be reduced to only 38. This reduction is necessary for the model simplicity. The developed model is validated with experimental result and compared with other one from literature. The real characteristics of the actuators are discussed, and its controller is designed. A mechatronic model that expresses the controlled tracking error as function of the vehicle dynamics and the actuator characteristics is developed. This model is used by the linear quadratic regulator approach to identify the mechatronic rail vehicle proportional–integral–derivative controller’s gains. The mechatronic rail vehicle comfort is evaluated in terms of the passenger displacement, acceleration and frequency as a response of a rail irregularities caused by a lateral and two vertical track irregularities. The simulations of vibration analysis are obtained in time and frequency domains and compared with railway vehicle status. The robustness of the designed mechatronic rail vehicle is verified by simulations, carried out for the cases of car body mass variations. The results show the effectiveness of the proposed mechatronic rail vehicle design which improves significantly the transportation of passengers.

Flexible Wheel/Rail Contact Model for Railway Vehicle Dynamics Without Pre-Calculation

2007 ◽  
Author(s):  
Mohammad Durali ◽  
S. Hassan Salehi ◽  
Mohammad Mehdi Jalili
Keyword(s):  
Vehicle Dynamics ◽  
Contact Forces ◽  
Contact Model ◽  
Railway Vehicle ◽  
Dynamic Problems ◽  
Vehicle Dynamic ◽  
Rail Vehicle ◽  
Rigid Contact ◽  
Contact Situation ◽  
Contact Mechanism

An advanced method using progressive concept of geometrical correspondence is applied to create a new wheel/rail contact model based on virtual penetration theory. The geometry and contact mechanism are solved simultaneously because of the independency in a defined correspondence. The model takes the penetrated profiles of wheel and rail and also associated creeps as inputs, and produces driving contact forces as output. The advantage of this model is that it doesn’t require pretabulation of rigid contact situation. The method allows calculating flexible, non-elliptical, multiple contact patches during integration of the model. Consequently the rails with substructures can vibrate separately from the vehicle in a flexible wheel/rail contact model. The simulation results indicate that this method can be used in various rail vehicle dynamic problems.

On the Singularity Theory Applied in Rail Vehicle Bifurcation Problem

2018 ◽  
Vol 13 (4) ◽  
Author(s):  
Hao Dong ◽  
Bin Zhao ◽  
Jianhua Xie
Keyword(s):  
Vehicle Dynamics ◽  
Degrees Of Freedom ◽  
Singularity Theory ◽  
Universal Unfolding ◽  
Rail Vehicle ◽  
Vehicle System ◽  
Spring System ◽  
Rail Vehicle Dynamics ◽  
Perturbation Parameters ◽  
The Relationship

The application of Hopf bifurcation is essential to rail vehicle dynamics because it corresponds to the linear critical speed. In engineering, researchers always wonder which vehicle parameters are sensitive to it. With the nonlinear singularity theory's development, it has been widely applied in many other engineering areas. This paper mainly studies the singularity theory applied in nonlinear rail vehicle dynamics. First, the bifurcation norm forms of wheelset and bogie system are, respectively, deduced. Then the universal unfolding is obtained and the influences of perturbation on bifurcation are investigated. By the analysis of a simple bar-spring system, the relationship between the unfolding and original perturbation parameters can be found. But this may be difficult to calculate for the case in vehicle system because of higher degrees-of-freedom (DOFs) and indicate that can explain the influence of all possible parameters perturbations on vehicle bifurcation.

Control and monitoring for railway vehicle dynamics

2007 ◽  
Vol 45 (7-8) ◽  
pp. 743-779 ◽  
Author(s):  
Stefano Bruni ◽  
Roger Goodall ◽  
T. X. Mei ◽  
Hitoshi Tsunashima
Keyword(s):  
Vehicle Dynamics ◽  
Railway Vehicle

Vehicle coupled bifurcation analysis of steering angle and driving torque

2021 ◽  
pp. 095440702098540
Author(s):  
Xianbin Wang ◽  
Shuming Shi
Keyword(s):  
Bifurcation Analysis ◽  
Hybrid Method ◽  
Vehicle Dynamics ◽  
Front Wheel ◽  
Steering Angle ◽  
Driving Mode ◽  
Vehicle System ◽  
Autonomous Equation ◽  
Real Coded Genetic Algorithm ◽  
Driving Torque

The mechanism of vehicle dynamics steering bifurcation has almost been confirmed. But the present steering bifurcation mechanism cannot explain the bifurcation phenomena caused by the driving torque. As a result, the vehicle coupled bifurcation analysis of the steering angle and driving torque has not been studied. Based on the five degrees of freedom (5DOF) vehicle system dynamics model with driving torque involved, the vehicle dynamics equilibriums under different driving torque and driving mode were searched by a hybrid method in this paper. The hybrid method combined the real-coded Genetic Algorithm with Quasi-Newton gradient method. According to the definition of static bifurcation of nonlinear systems, the equilibrium bifurcation of 5DOF vehicle system was confirmed. Then, the 5DOF vehicle system model was transformed into autonomous equation with the front wheel steering angle as intermediate variable. From the two aspects of constant steering angle amplitude and constant driving torque, the bifurcation diagrams of different driving mode were calculated. The vehicle coupled bifurcation characteristics of steering angle and driving torque were analyzed. The results show that the values of the driving torque will directly affect the bifurcation characteristics of vehicle dynamics system. The coupled feature of the front wheel steering angle and driving torque effect on vehicle bifurcation is obvious.

Railway vehicle dynamics

1986 ◽  
Vol 17 (4) ◽  
pp. 181-186 ◽  
Author(s):  
B V Brickle
Keyword(s):  
Vehicle Dynamics ◽  
Railway Vehicle

scholarly journals Effect of Rail Vehicle–Track Coupled Dynamics on Fatigue Failure of Coil Spring in a Suspension System

2021 ◽  
Vol 11 (6) ◽  
pp. 2650
Author(s):  
Sunil Kumar Sharma ◽  
Rakesh Chandmal Sharma ◽  
Jaesun Lee
Keyword(s):  
Mathematical Model ◽  
Fatigue Fracture ◽  
Suspension System ◽  
Railway Vehicle ◽  
Coil Spring ◽  
Internal Resonances ◽  
Rail Vehicle ◽  
Rail Vehicles ◽  
Stress Result ◽  
Wheel Track

In a rail vehicle, fatigue fracture causes a significant number of failures in the coil spring of the suspension system. In this work, the origin of these failures is examined by studying the rail wheel–track interaction, the modal analysis of the coil springs and the stresses induced during operation. The spring is tested experimentally, and a mathematical model is developed to show its force vs. displacement characteristics. A vertical 10-degree-of-freedom (DOF) mathematical model of a full-scale railway vehicle is developed, showing the motions of the car body, bogies and wheelsets, which are then combined with a track. The springs show internal resonances at nearly 50–60 Hz, where significant stresses are induced in them. From the stress result, the weakest position in the innerspring is identified and a few guidelines are proposed for the reduction of vibration and stress in rail vehicles.

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