Modelling,simulation and applications of longitudinal train dynamics

ABSTRACT

Significant developments in longitudinal train simulation and an overview of the approaches to train models and modelling vehicle force inputs are firstly presented. The most important modelling task, that of the wagon connection, consisting of energy absorption devices such as draft gears and buffers, draw gear stiffness, coupler slack and structural stiffness is then presented. Detailed attention is given to the modelling approaches for friction wedge damped and polymer draft gears. A significant issue in longitudinal train dynamics is the modelling and calculation of the input forces – the co-dimensional problem. The need to push traction performances higher has led to research and improvement in the accuracy of traction modelling which is discussed. A co-simulation method that combines longitudinal train simulation, locomotive traction control and locomotive vehicle dynamics is presented. The modelling of other forces, braking propulsion resistance, curve drag and grade forces are also discussed. As extensions to conventional longitudinal train dynamics, lateral forces and coupler impacts are examined in regards to interaction with wagon lateral and vertical dynamics. Various applications of longitudinal train dynamics are then presented. As an alternative to the tradition single wagon mass approach to longitudinal train dynamics, an example incorporating fully detailed wagon dynamics is presented for a crash analysis problem. Further applications of starting traction, air braking, distributed power, energy analysis and tippler operation are also presented.     

Direct yaw moment control and power consumption of in-wheel motor vehicle in steady-state turning

Driving force distribution control is one of the characteristic performance aspects of in-wheel motor vehicles and various methods have been developed to control direct yaw moment while turning. However, while these controls significantly enhance vehicle dynamic performance, the additional power required to control vehicle motion still remains to be clarified. This paper constructed new formulae of the mechanism by which direct yaw moment alters the cornering resistance and mechanical power of all wheels based on a simple bicycle model, including the electric loss of the motors and the inverters. These formulation results were validated by an actual test vehicle equipped with in-wheel motors in steady-state turning. The validated theory was also applied to a comparison of several different driving force distribution mechanisms from the standpoint of innate mechanical power.     

Insights into vehicle trajectories at the handling limits: analysing open data from race car drivers

Race car drivers can offer insights into vehicle control during extreme manoeuvres; however, little data from race teams is publicly available for analysis. The Revs Program at Stanford has built a collection of vehicle dynamics data acquired from vintage race cars during live racing events with the intent of making this database publicly available for future analysis. This paper discusses the data acquisition, post-processing, and storage methods used to generate the database. An analysis of available data quantifies the repeatability of professional race car driver performance by examining the statistical dispersion of their driven paths. Certain map features, such as sections with high path curvature, consistently corresponded to local minima in path dispersion, quantifying the qualitative concept that drivers anchor their racing lines at specific locations around the track. A case study explores how two professional drivers employ distinct driving styles to achieve similar lap times, supporting the idea that driving at the limits allows a family of solutions in terms of paths and speed that can be adapted based on specific spatial, temporal, or other constraints and objectives.     

Design of tyre force excitation for tyre–road friction estimation

Knowledge of the current tyre–road friction coefficient is essential for future autonomous vehicles. The environmental conditions, and the tyre–road friction in particular, determine both the braking distance and the maximum cornering velocity and thus set the boundaries for the vehicle. Tyre–road friction is difficult to estimate during normal driving due to low levels of tyre force excitation. This problem can be solved by using active tyre force excitation. A torque is added to one or several wheels in the purpose of estimating the tyre–road friction coefficient. Active tyre force excitation provides the opportunity to design the tyre force excitation freely. This study investigates how the tyre force should be applied to minimise the error of the tyre–road friction estimate. The performance of different excitation strategies was found to be dependent on both tyre model choice and noise level. Furthermore, the advantage with using tyre models with more parameters decreased when noise was added to the force and slip ratio.     

State estimation in roll dynamics for commercial vehicles

Accurate lateral load transfer estimation plays an important role in improving the performance of the active rollover prevention system equipped in commercial vehicles. This estimation depends on the accurate prediction of roll angles for both the sprung and the unsprung subsystems. This paper proposes a novel computational method for roll-angle estimation in commercial vehicles employing sensors which are already used in a vehicle dynamic control system without additional expensive measurement units. The estimation strategy integrates two blocks. The first block contains a sliding-mode observer which is responsible for calculating the lateral tyre forces, while in the second block, the Kalman filter estimates the roll angles of the sprung mass and those of axles in the truck. The validation is conducted through MATLAB/TruckSim co-simulation. Based on the comparison between the estimated results and the simulation results from TruckSim, it can be concluded that the proposed estimation method has a promising tracking performance with low computational cost and high convergence speed. This approach enables a low-cost solution for the rollover prevention in commercial vehicles.     

The Kalker book of tables for non-Hertzian contact of wheel and rail

A new regularisation of non-elliptical contact patches has been introduced, which enables building the look-up table called by us the Kalker book of tables for non-Hertzian contact (KBTNH), which is a fast creep force generator that can be used by multibody dynamics system simulation programs. The non-elliptical contact patch is regularised by a simple double-elliptical contact region (SDEC). The SDEC region is especially suitable for regularisation of contact patches obtained with approximate non-Hertzian methods for solving the normal contact problem of wheel and rail. The new regularisation is suitable for wheels and rails with any profiles, including worn profiles.

The paper describes the new procedure of regularisation of the non-elliptical contact patch, the structure of the Kalker book of tables, and parameterisation of the independent variables of the tables and creep forces.

A moderate volume Kalker book of tables for SDEC region suitable for simulation of modern running gears has been computed in co-simulation of Matlab and program CONTACT.

To access the creep forces of the Kalker book of tables, the linear interpolation has been applied.

The creep forces obtained from KBTNH have been compared to those obtained by program CONTACT and FASTSIM algorithm. FASTSIM has been applied on both the contact ellipse and the SDEC contact patch. The comparison shows that KBTNH is in good agreement with CONTACT for a wide range of creepage condition and shapes of the contact patch, whereas the use of FASTSIM on the elliptical patch and SDEC may lead to significant deviations from the reference CONTACT solutions.

The computational cost of calling creep forces from KBTNH has been estimated by comparing CPU time of FASTSIM and KBTNH. The KBTNH is 7.8–51 times faster than FASTSIM working on 36–256 discretisation elements, respectively.

In the example of application, the KBTNH has been applied for curving simulations and results compared with those obtained with the creep force generator employing the elliptical regularisation. The results significantly differ, especially in predicted creepages, because the elliptical regularisation neglects generation of the longitudinal creep force by spin creepage.     

具有模块化结构的汽车动力学仿真模型的初步研究

初步探讨了面向开发型驾驶模拟器的具有模块化结构的汽车动力学仿真模型建立方法，从而可以在此基础上进一步建立一套通用的面向结构的汽车动力学仿真程序，便捷地在开发型驾驶模拟器上实现对不同类型或同类型不同结构车辆性能的仿真。     

缓和竖曲线的反演设计研究

应用已有的车辆简化模型,借助反演设计理论,研究了缓和竖曲线的反演设计方法;探讨了依据车辆—路面耦合动力学模型的安全性和舒适性动力学评价指标,给出了缓和竖曲线反演设计的一般流程。该方法为开发宜人化路面CAD系统提供了理论依据。     

Vehicle response-based track geometry assessment using multi-body simulation

The assessment of the geometry of railway tracks is an indispensable requirement for safe rail traffic. Defects which represent a risk for the safety of the train have to be identified and the necessary measures taken. According to current standards, amplitude thresholds are applied to the track geometry parameters measured by recording cars. This geometry-based assessment has proved its value but suffers from the low correlation between the geometry parameters and the vehicle reactions. Experience shows that some defects leading to critical vehicle reactions are underestimated by this approach. The use of vehicle responses in the track geometry assessment process allows identifying critical defects and improving the maintenance operations. This work presents a vehicle response-based assessment method using multi-body simulation. The choice of the relevant operation conditions and the estimation of the simulation uncertainty are outlined. The defects are identified from exceedances of track geometry and vehicle response parameters. They are then classified using clustering methods and the correlation with vehicle response is analysed. The use of vehicle responses allows the detection of critical defects which are not identified from geometry parameters.     

Method for obtaining the wheel–rail contact location and its application to the normal problem calculation through ‘CONTACT’

This work presents a robust methodology for calculating inter-penetration areas between railway wheel and rail surfaces, the profiles of which are defined by a series of points. The method allows general three-dimensional displacements of the wheelset to be considered, and its characteristics make it especially suitable for dynamic simulations where the wheel–rail contact is assumed to be flexible. The technique is based on the discretisation of the geometries of the surfaces in contact, considering the wheel as a set of truncated cones and the rail as points. By means of this approach, it is possible to reduce the problem to the calculation of the intersections between cones and lines, the solution for which has a closed-form expression. The method has been used in conjunction with the CONTACT algorithm in order to solve the static normal contact problem when the lateral displacement of the wheelset, its yaw angle and the vertical force applied in the wheelset centroid are prescribed. The results consist of smooth functions when the dependent coordinates are represented as a function of the independent ones, lacking the jump discontinuities that are present when a rigid contact model is adopted. Example results are shown and assessed for the normal contact problem for different lateral and yaw positions of the wheelset on the track.