Simulation and Visualisation of the Dynamic Behaviour of an Overhead Power System with Contact Breaking

For high speed rail traffic it is necessary to design overhead power systems which minimize the contact loss between pantograph head and contact wire. To predict how different design solutions will behave it is favourable to model and simulate the dynamic behaviour. In this paper a model of an overhead power system is specified and used in simulation. The model is suitable for simulation with contact loss since it includes specifications of impact conditions between pantograph head and contact wire. Two sets of equations of motion are specified, one for the contact case and one for the non-contact case. The model also includes lateral movement of the wire due to the zigzag span and friction between the pantograph head and the contact wire. It is shown how to make animations of the system behaviour using a MCAE-system. The animations are made using a geometrical model of the system together with results from numerical simulations.

Through the examples provided, use of the mathematical model and the geometrical model is presented. The response is visualised as time histories and phase plane diagrams of different coordinates and as animations of the total system response. The different types of visualisations make an excellent combination when studying the system behaviour of different design solutions.

In one example, simulation using the linearised set of equations gives the same results as simulation using the set of fully nonlinear equations, due to periodic response and the simple alternation of contact conditions. It is shown that the situation when any of the parameters vary suddenly is possible to simulate using the fully nonlinear equations of motion.     

SPOPS statement of methods

The Simulation Programme for Overhead contact lines – Pantograph System (SPOPS) is based on a two-dimensional finite element model of an overhead contact line and a lumped mass model for a pantograph. The SPOPS allows for a lateral change of contact points between the pantograph and the contact wire and for the rolling motions of contact strips in the pantograph model. Thus, the programme can consider the stagger of a contact wire in a dynamic simulation. Either a penalty method or a Lagrange multiplier method can be chosen to model the contact phenomenon between a pantograph and a contact wire. According to pantograph–catenary benchmark results, the simulation results obtained from the SPOPS are very close to the average values of the simulation results obtained from programmes implemented in the benchmark work in all cases, including a three-dimensional (3-D) case. These benchmark results demonstrate that the SPOPS is as accurate as other fully 3-D simulation programmes while utilising minimal computational efforts.     

Analysis of dynamic interaction between catenary and pantograph with experimental verification and performance evaluation in new high-speed line

Understanding the dynamic interaction between the catenary and pantograph of a high-speed train is the one of the most important technical issues in the railway industry. This is because the catenary–pantograph system plays a crucial role in providing electric power to the railway vehicle for stable operation. The aim of the present paper is to estimate the current-collection performance of this system by using numerical analysis, in particular, the flexible multibody dynamic analysis technique. To implement large deformable catenary wires, an absolute nodal coordinate formulation is used for the cable element. Additionally, an efficient contact element and an interactive model for the catenary–pantograph system are introduced. Each developed model is then used for analytical and experimental verification. Actual on-line test results of existing high-speed railway vehicles are presented and used to verify the analysis model. Finally, the performance characteristics of a new 400 km/h-class high-speed line are estimated and evaluated on the basis of international standards.     

Roadway Elevation Profile Generation for Vehicle Simulation

With a simplified approach for creating road surface elevation information for simulation of vehicle vertical response to roadway unevenness, roadways for single and parallel track simulations and averaged roads for variable velocity simulation are developed. Sets of correctly chosen random roadway slopes are averaged appropriately for the variable velocity simulation. The procedure generates approximately “white” slope spectral density roadways in the frequency ranges of interest, and the elevation profiles are representative of average road profiles. The method is simple in practice yet suffices for many parameter studies of suspensions and vehicle dynamics.     

Design of an Active Unilateral Brake Control System for Five-Axle Tractor-Semitrailer Based on Sensitivity Analysis

This paper presents the results of a parametric sensitivity analysis of a five-axle tractor-semitrailer vehicle combination using 3-DOF linear yaw/plane model. The first order logarithmic sensitivity functions are derived with respect to several vehicle design parameters. For stabilization of the vehicle's directional behaviour a fairly new control concept called “Active Unilateral Braking Control (AUBC)” acting on the tractor rear wheel's in order to produce a stabilizing yaw torque is investigated. The AUBC system improves not only the directional stability, but also affects the roll dynamics of the vehicle. The sensitivity of the controlled vehicle system with linear quadratic controller (LQR) is also examined, a robust controller design procedure is proposed as a result of the sensitivity analysis. The robustness of this controller in the presence of both internal (including parametric uncertainties, non-linear dynamics) and external disturbances (such as road irregularities and side wind) allows its implementation with confidence with a non-linear vehicle model. The applicability of this control system to a non-linear vehicle model is tested using a 34 DOF, non-linear vehicle model of the tractor-semitrailer combination.     

利用计算机仿真技术预测车身零件疲劳寿命

为缩短新车开发周期、节约样本制造费用，本文提出了一种在计算机仿真环境中预测车身零件疲劳寿命的新方法。以某轻型客车为例，首先建立了该车的整体有限元模型。然后将采自试车场的典型路面谱作用于轮胎与路面 的接触点进行随机激励。不仅首次在计算机上模拟了汽车随机振动过程，而且得到了关键部位的加速度和动态应力响应及其相应的功率谱密度。最后，应用随机振动和疲劳累积损伤理论对仿真结果进行后处理，估算出该车在一定速度下连续行驶的疲劳寿命。其分析结果显示的危险部位与道路试验基本一致。     

<TPL-PCRUN> Statement of methods

TPL-PCRUN is a software program for the dynamic interaction simulation of pantograph–catenary systems. In the benchmark, based on the finite element method, the catenary model was built and the pantograph was considered as a three-level spring–damper–mass system. Then, through the contact definition between pantograph and catenary, the coupled model of the pantograph and catenary system was established. The respective dynamic equations of motions were solved by the time integration method. Thus, the simulation results were obtained and submitted for the comparison with the other software. On the other hand, a standard model from EN50318 was established and analysed by TPL-PCRUN. The simulation results by TPL-PCRUN were remarkably consistent with the reference values given by EN50318. It was proved that the results by TPL-PCRUN can be reliable. Recently, the software has been updated and improved. Some new models and algorithms are proposed, including the rigid–flexible hybrid pantograph model, contact definition considering appearance characteristics of the contact surfaces, a fluid–solid coupling algorithm of the pantograph and catenary system, etc.     

Total dynamic response of a PSS vehicle negotiating asymmetric road excitations

A planar suspension system (PSS) is a novel automobile suspension system in which an individual spring–damper strut is implemented in both the vertical and longitudinal directions, respectively. The wheels in a vehicle with such a suspension system can move back and forth relative to the chassis. When a PSS vehicle experiences asymmetric road excitations, the relative longitudinal motion of wheels with respect to the chassis in two sides of the same axle are not identical, and thus the two wheels at one axle will not be aligned in the same axis. The total dynamic responses, including those of the bounce, pitch and the roll of the PSS vehicle, to the asymmetric road excitation may exhibit different characteristics from those of a conventional vehicle. This paper presents an investigation into the comprehensive dynamic behaviour of a vehicle with the PSS, in such a road condition, on both the straight and curved roads. The study was carried out using an 18 DOF full-car model incorporating a radial-spring tyre–ground contact model and a 2D tyre–ground dynamic friction model. Results demonstrate that the total dynamic behaviour of a PSS vehicle is generally comparable with that of the conventional vehicle, while PSS exhibits significant improvement in absorbing the impact forces along the longitudinal direction when compared to the conventional suspension system. The PSS vehicle is found to be more stable than the conventional vehicle in terms of the directional performance against the disturbance of the road potholes on a straight line manoeuvre, while exhibiting a very similar handling performance on a curved line.     

Real-time catenary models for the hardware-in-the-loop simulation of the pantograph–catenary interaction

Hardware-in-the-loop (HIL) simulation is a promising technique to study the pantograph–catenary interaction problems by realising the interaction of a physical pantograph with a mathematical model of the overhead equipment (catenary). However, the computing power presently available on real-time CPUs only allows to run simplified models of the overhead equipment. Therefore, it is important to define catenary models that are suitable for real-time simulation and at the same time capable of accurately representing the dynamic behaviour of the catenary. In this paper, the use of a catenary model based on modal superposition is considered, and the effect of changing the number of modelled spans and the number of modal components allocated to the contact and messenger wires is investigated in view of finding the best model compatible with real-time simulation. Comparisons between HIL simulation results and line measurements are presented, to quantify the accuracy of the hybrid simulation method developed.     

重型车辆与路面耦合作用的仿真分析研究

针对车-路系统以及车-路耦合作用的特点,运用ADAMS动力学仿真软件,建立了某重型车的多自由度仿真模型,并利用ADAMS对模型进行了仿真计算,分析了车辆以不同载重量、不同速度行驶于不同等级路面时,车辆对路面的动载荷作用。结果表明：车-路耦合产生的动载作用受路面工况的影响较大,随着路面等级的降低,车辆对路面的动载荷有着显著的增大;在车辆正常行驶速度范围内,车辆对路面的动载荷也随着车速的增加而增大;而在相同条件下。满载车辆较空载车辆对路面的动载荷要大很多,即满载对路面的破坏作用更为显著。     

A 3D Brush-type Dynamic Tire Friction Model

The use of advanced dynamic friction models can improve the brush-type tire friction models. This paper presents a 3D dynamic brush model based on the LuGre friction model. The model describes the dynamics of longitudinal and lateral tire friction forces, as well as the self aligning torque dynamics. It has been originally derived in a distributed-parameter form, and then transformed to a simpler lumped-parameter form with only three internal states. Both uniform and non-uniform normal pressure distributions are considered. The model has analytical solution for steady-state conditions. The steady-state behavior is validated with respect to “magic” formula static model, which served as an “ideal” benchmark. The lumped model dynamic behavior is validated by comparing its time-responses with original distributed model responses. The model parameterization with respect to normal force and other tire/road parameters is considered as well.     

PantoCat statement of method

The pantograph–catenary dynamic interaction analysis program (PantoCat) addresses the need for a dynamic analysis code able to analyse models of the complete overhead energy collecting systems that include all mechanical details of the pantographs and the complete topology and structural details of the catenary. PantoCat is a code based on the finite element method, for the catenary, and multibody dynamics methods, for the pantograph, integrated via a co-simulation procedure. A contact model based on a penalty formulation is selected to represent the pantograph–catenary interaction. PantoCat enables models of catenaries with multiple sections, including their overlap, the operation of multiple pantographs and the use of any complex loading of the catenary or pantograph mechanical elements including aerodynamic effects. The models of the pantograph and catenary are fully spatial being simulated in tangential or curved tracks, with or without irregularities and perturbations. User-friendly interfaces facilitate the construction of the models while the post-processing facilities provide all quantities of interest of the system response according to the norms and industrial requirements.     

Performance of Low-bandwidth, Semi-active Damping Concepts for Suspension Control

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

Influence of tyre–road contact model on vehicle vibration response

The influence of the tyre–road contact model on the simulated vertical vibration response was analysed. Three contact models were compared: tyre–road point contact model, moving averaged profile and tyre-enveloping model. In total, 1600 real asphalt concrete and Portland cement concrete longitudinal road profiles were processed. The linear planar model of automobile with 12 degrees of freedom (DOF) was used. Five vibration responses as the measures of ride comfort, ride safety and dynamic load of cargo were investigated. The results were calculated as a function of vibration response, vehicle velocity, road quality and road surface type. The marked differences in the dynamic tyre forces and the negligible differences in the ride comfort quantities were observed among the tyre–road contact models. The seat acceleration response for three contact models and 331 DOF multibody model of the truck semi-trailer was compared with the measured response for a known profile of test section.     

Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

用于公路车-桥系统振动分析的精细化轮胎模型

为了解决当前公路车桥耦合振动模型中轮胎模型过于简化、车轮-路面接触力与桥梁响应计算结果不够精确的问题,提出了一种精细化轮胎模型.首先基于车辆橡胶轮胎的几何、力学特征,建立了径向弹簧力学模型并进行了理论推导;然后考虑轮胎与路面接触面的刚度分布特征和高速状况下轮胎的惯性力,提出了轮胎接触面分布刚度的计算方法,保证了轮胎接触...     

Roll and pitch independently tuned interconnected suspension: modelling and dynamic analysis

In this paper, a roll and pitch independently tuned hydraulically interconnected passive suspension is presented. Due to decoupling of vibration modes and the improved lateral and longitudinal stability, the stiffness of individual suspension spring can be reduced for improving ride comfort and road grip. A generalised 14 degree-of-freedom nonlinear vehicle model with anti-roll bars is established to investigate the vehicle ride and handling dynamic responses. The nonlinear fluidic model of the hydraulically interconnected suspension is developed and integrated with the full vehicle model to investigate the anti-roll and anti-pitch characteristics. Time domain analysis of the vehicle model with the proposed suspension is conducted under different road excitations and steering/braking manoeuvres. The dynamic responses are compared with conventional suspensions to demonstrate the potential of enhanced ride and handling performance. The results illustrate the model-decoupling property of the hydraulically interconnected system. The anti-roll and anti-pitch performance could be tuned independently by the interconnected systems. With the improved anti-roll and anti-pitch characteristics, the bounce stiffness and ride damping can be optimised for better ride comfort and tyre grip.     

The Calculation of the Vibrations of a Four-wheeled Vehicle, Induced by Random Road Roughness of the Left and Right Track

When applying the known power spectra of the random road roughness to the suspension behaviour of a four-wheeled vehicle, each of the four vertical input signals together with their related interdependence are to be considered, if exact results are to be obtained. The correlations are determined by way of calculation. The resulting roughness spectra of bounce, pitch, roll and torsional excitations will be applied to various vehicles, characterized by different design parameters. By means of a three-dimensional simulation model the virtual values of the random vehicle vibrations are calculated, while determining at the same time the influence of vehicle speed, waviness exponent, track width, wheel base, and axle design feature as well as the relationship between the vertical vibrations and the reference point in the vehicle body.     

Dynamic Behaviour of a Mobile Robot Vehicle with a Two Caster and Two Driving Wheel Configuration

The actual trajectory covered by a mobile robot in motion differs from the trajectory planned on the basis of the kinematic characteristics of its directional control system. This difference is essentially related to the behaviour of wheel-road contact, the influence of dynamic loads and the presence of caster wheels.

This paper presents a mathematical model (“ DDPP) which simulates the motion of a generic mobile robot vehicle with a propulsion and directional control system based on two independent driving wheels and two caster wheels.

The differential equations of motion have been obtained by applying modified equations of Lagrange.

The role played by the dynamic loads, the wheel-road contact features and the caster wheels is discussed hereof.     

Random Response of Tractor-Semitrailer System

This work describes an analytical study of the dynamic behaviour of a tractor-semitrailer vehicle. A digital computer simulation was used to describe the longitudinal, vertical, and pitching motions of the vehicle travelling over a stationary random road surface. A man-seat model was also incorporated into the simulation. Vehicle response to road irregularities has been studied by assuming two different roads for loaded and unloaded cases.

Numerical results are presented for vehicle, showing system eigenvalues, power spectral densities and root mean square values of the linear and angular accelerations and displacements. Vehicle acceleration response is compared with the ISO riding comfort standard. All results for the loaded and unloaded cases and for smooth and rough roads indicated that an uncomfortable ride would result from vehicle response.