Some Basic Properties of Bogies, an Analytical Approach

An important function of a bogie of a railway vehicle (or of the running gear of guided vehicles in general) is to guide or steer the vehicle along the course of the track while isolating the vehicle and its payload as well as possible from unintended but inevitable imperfections in the position of the track. Against this background, an analytical expression is derived for the low speed transfer function of a bogie, from which conclusions can be drawn regarding the effect of the elastic connections between wheelsets on dynamic behaviour. At higher speeds inertia effects of the unsprung masses have a negative effect on dynamic behaviour, the magnitude of this effect being different for different types of elastic connections. This is also reflected in the critical speed and the interaction between body and bogie. With respect to the wear of wheels and rails on curved track, the range of radii of curves which can be traversed without flange contact and, for smaller radii, the rate of increase of flange force and angle of attack of the leading wheelset are important factors. Some expressions are derived for the effect of the elastic connections between wheelsets on these factors.     

Parametric Excitation of a Single Railway Wheelset

This paper presents the results of analytical, numerical and experimental investigations of a single railway wheelset. Periodic parametric excitation is added to one of the simplest linear mechanical models. This extended model describes, for example, the geometric deviations often experienced on roller rigs. Above a certain critical speed, the stationary running of the wheelset loses its stability. To verify the analytical and numerical results for the critical speed, experiments were carried out on a simple roller rig having a large ratio of the radii of the roller and the railway wheel.     

Parametric Excitation of a Single Railway Wheelset

This paper presents the results of analytical, numerical and experimental investigations of a single railway wheelset. Periodic parametric excitation is added to one of the simplest linear mechanical models. This extended model describes, for example, the geometric deviations often experienced on roller rigs. Above a certain critical speed, the stationary running of the wheelset loses its stability. To verify the analytical and numerical results for the critical speed, experiments were carried out on a simple roller rig having a large ratio of the radii of the roller and the railway wheel.     

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.     

Study on the derailment behaviour of a railway wheelset with solid axles in a railway turnout

ABSTRACT

Dynamic wheel–rail interaction in railway turnouts is more complicated than on ordinary track. In order to evaluate the derailment behaviour of railway wheelsets in railway turnouts, this paper presents a study of dynamic wheel–rail interaction during a wheel flange climbs on the turnout rails, by applying the elasticity positioning wheelset model. A numerical model is established based on a coupled finite element method and multi-body dynamics, and applied to study the derailment behaviour of a railway wheelset in both the facing and trailing directions in a railway turnout, as well as dynamic wheel–turnout rail interaction during the wheel flange climbing on the turnout rails. The influence of the wheel–rail attack angle and the friction coefficient on the dynamic derailment behaviour is investigated through the proposed model. The results show that the derailment safety for a wheelset passing the railway turnout in facing direction is significantly lower than that for the trailing direction and the ordinary track. The possibility of derailment for the wheelset passing the railway turnout in facing and trailing directions at positive wheel–rail attack angles will increase with an increase in the attack angles, and the possibility of derailment can be reduced by decreasing the friction coefficient.     

大攻角下超大跨度斜拉桥颤振性能节段模型风洞试验

为了研究一座1 400 m跨径流线型闭口箱梁断面斜拉桥的颤振性能,根据其风致静力失稳或颤振前主梁最大有效风攻角已接近±10°的特点,通过弹簧悬挂节段模型试验,开展了大攻角下桥梁颤振性能研究。试验发现,在4°~10°风攻角下,高风速时模型均出现了弯扭耦合程度较弱的自限幅非线性颤振现象;而在其他攻角下,高风速时模型则表现为常规的发散型弯扭耦合颤振。研究发现,经典的线性颤振理论无法适用于研究试验中大攻角下出现的非线性颤振现象。因此,采用了一种简化的非线性半经验数学模型来表示非线性颤振中的自激扭矩,并从试验模型颤振位移时程中识别得到了模型参数。基于这一非线性自激力模型,通过试验测得的位移信号来构造自激扭矩时程,再利用自激扭矩的做功时程来识别各个气动参数。之后,利用其中的部分气动参数构造气动阻尼,并基于结构阻尼系数与气动线性阻尼系数之和为零的判断条件,提出了一种针对非线性颤振现象的临界风速确定方法,同时将线性和非线性颤振的起振判断条件进行了很好的统一。研究结果表明,利用这一方法求得的颤振临界风速与风洞试验中出现的现象基本吻合。     

Dynamics of an isolated railway wheelset with conformal wheel–rail interactions

ABSTRACT

In multi-body dynamics, we model a non-conformal wheel/rail contact at one centre point since this contact is flat and Hertzian. However, the quasi-conformal contact requires more points since the contact is curved and non-Hertzian. The methodology in solving these points during dynamic simulations is the basis of this development. In this online effort, first, we present a general contact joint and the gutter search method of Pascal and Jourdan [The rigid-multi-Hertzian method as applied to conformal contacts. USA: ASME; 2007] in the context of a multi-body approach. Next, by adopting the non-iterative approach, a subset of these points with positive profile interpenetrations is selected to idealise one curved contact by a set of multi-Hertzian patches for which the Hertz normal contact solution is available. Finally, the feasibility of this multibody approach together with its implementation in two different codes is evaluated by simulating the motion of an isolated wheelset with realistic inertia. On tangent tracks, the wheelset with non-conformal pairing displays self-excited unstable oscillations while it displays a stable behaviour below a critical speed with conformal profiles. A further study reveals the net friction losses at multiple patches within the curved contact being the reason for the stable behavior.     

Locomotive dynamic performance under traction/braking conditions considering effect of gear transmissions

Traction or braking operations are usually applied to trains or locomotives for acceleration, speed adjustment, and stopping. During these operations, gear transmission equipment plays a very significant role in the delivery of traction or electrical braking power. Failures of the gear transmissions are likely to cause power loses and even threaten the operation safety of the train. Its dynamic performance is closely related to the normal operation and service safety of the entire train, especially under some emergency braking conditions. In this paper, a locomotive–track coupled vertical–longitudinal dynamics model is employed with considering the dynamic action from the gear transmissions. This dynamics model enables the detailed analysis and more practical simulation on the characteristics of power transmission path, namely motor–gear transmission–wheelset–longitudinal motion of locomotive, especially for traction or braking conditions. Multi-excitation sources, such as time-varying mesh stiffness and nonlinear wheel–rail contact excitations, are considered in this study. This dynamics model is then validated by comparing the simulated results with the experimental test results under braking conditions. The calculated results indicate that involvement of gear transmission could reveal the load reduction of the wheelset due to transmitted forces. Vibrations of the wheelset and the motor are dominated by variation of the gear dynamic mesh forces in the low speed range and by rail geometric irregularity in the higher speed range. Rail vertical geometric irregularity could also cause wheelset longitudinal vibrations, and do modulations to the gear dynamic mesh forces. Besides, the hauling weight has little effect on the locomotive vibrations and the dynamic mesh forces of the gear transmissions for both traction and braking conditions under the same running speed.     

A Model Reduction Procedure for the Dynamic Analysis of Rail Vehicles Subjected to Linear Creep Forces

The set of differential equations governing the motion of an unrestrained coned wheelset travelling on a tangent section of track and acted upon by creep forces arising from the contact between wheel and rail are, in the terminology of numerical analysis, extremely "stiff". This stiffness can be attributed to the existence of two negative real eigenvalues in the solution of the eigenproblem associated with the linearized equations of motion. Compared with the two complex conjugate eigenvalues that complete this solution, the real eigenvalues have large magnitudes and necessitate that relatively. small timesteps be used in order to obtain an accurate numerical integration of the full set of equations of motion. However, by truncating the set of left and right eigenvectors to eliminate these real eigenvalues in a modal analysis of the wheelset, it was found that their contribution to the overall dynamic response is negligible. This same modal truncation approach was then applied to the sub-structured equations of motion for a simple rail vehicle system consisting of two wheelsets connected to a main body by linear springs and dampers. Essentially, the physical degrees of freedom for each wheelset substructure were replaced by a single complex coordinate obtained from the previous normal modes analysis. Using this model reduction procedure, accurate numerical results for the motion of the rail vehicle were generated several times faster than the results obtained by numerically integrating the full set of differential equations directly.     

Wheel/Rail Contact: Geometrical Study*

Before trying to ascertain the precise nature of the Wheel-Rail contact (internal stresses and strains, wear and friction, security against a derailment, dynamic behaviour of the vehicle, etc.) the geometrical problem must necessarily be solved. That is, for each position of the wheelset (this is defined by 6 parameters, of which only 4 are independent) the two dependent parameters and the coordinates of the points of contact of each wheel, and rail must be obtained. A new method is proposed of obtaining the spatial position of a wheelset with reference to the rails, from the most general point of view.     

城门洞形断面输水隧洞临界水深的计算方法

在城门洞形断面输水隧洞的水力计算中,其临界水深的求解方程无显函数形式的表达公式。为尝试避免传统低效的经验试算法、图解法等,通过对城门洞形断面输水隧洞临界流基本方程进行数学变换,其临界水深计算问题可归结为一非线性优化问题,再运用实数编码加速遗传算法(RAGA)求解。基于Borland JBuilder9 Enterprise环境编写了算法实现程序,对不同断面尺寸的城门洞形输水隧洞临界流进行了计算和分析。结果表明,RAGA方法具有计算速度快、精度和自动化程度高、通用性强等优点,比常用方法简便。     

Design of an Active Wheelset on a Scaled Roller Rig

The article describes the application of a 1:5-scaled roller rig with a two-axled experimental vehicle to the design of a torque-controlled railway wheelset. Particular attention is drawn to the scaling problem and the dynamic similarity laws behind it and in addition to the chosen scaling strategy. For the controller design of the active wheelset the experiments with the scaled vehicle were combined with multibody computer simulations. The complete mechatronic system has therefore been modelled using the SIMPACK-MATLAB/Simulink interface. The steering behaviour, typical for this particular active wheelset, is demonstrated by results from roller rig experiments.     

千米级斜拉桥空间非线性两阶段索力优化

针对斜拉桥的施工控制技术问题,提出了斜拉桥两阶段索力优化的方法,采用一阶最优化计算方法来确定某千米级斜拉桥在施工状态和成桥状态下的合理索力。首先将斜拉桥成桥后的线形和梁塔的最小弯曲应变能设为目标函数,通过对目标函数的最优化处理,求出各施工阶段的斜拉索索力和主梁的预转折角,用空间非线性有限元法模拟钢箱梁的悬臂拼装过程;成桥后,将斜拉桥梁塔的最大和最小弯矩设为目标函数,求出斜拉索索力的合理调整值。计算结果表明:该方法是可行的,结果也是合理的。     

Robust state feedback stabilization of articulated steer vehicles

In this work, a full-state feedback controller is designed to prevent the oscillatory instability or snaking behaviour of an articulated steer vehicle. To design the controller, first, a linearized model of the vehicle is developed and analyzed to identify the most important uncertain tire parameters with regard to the snaking mode. By using this linearized model, the equations of motion are represented in the form of a polytopic system, which depends affinely on the most important uncertain tire parameters. Then, by solving some linear matrix inequalities, both the Lyapunov and state feedback matrices for the robust stabilization of the vehicle are found. The performance of the resulting controller is evaluated by conducting several simulations based on the linearized model. To verify the results from the linearized model analysis, some simulations are also done by a virtual prototype of the vehicle in ADAMS. The results based on the linearized model are reasonably consistent with those from the simulations in ADAMS. They show that the controller can effectively stabilize the vehicle during the snaking mode in different driving conditions.     

Research into the problem of wheel tread spalling caused by wheelset longitudinal vibration

This study mainly focuses on the mechanism of wheel tread spalling through wheelset longitudinal vibration that has been often neglected. Analysis of two actual cases of the wheel tread spalling problem leads to the conclusion that the wheel tread spalling is closely related to the wheelset longitudinal vibration in some locomotives, and many of these problems can be reasonably explained if the wheelset longitudinal vibration is considered. For better understanding of some abnormal wheel spalling problems, the formations of the wheelset longitudinal vibration and the wheel/rail contact parameters were analysed in the initial wheel tread spalling. With the preliminary analytical results, the wheelset longitudinal dynamic behaviour, the characteristics of wheel/rail contact and the mechanics in the condition of the wheelset longitudinal vibration were further studied quantitatively. The results showed that the wheelset longitudinal vibration changed not only the limit of these parameters and the position of principal stress, but also the direction of the principal stress on the surface of wheel/rail contact patch. It is likely that the significant stress changes provoke too much stress on the surface of wheel/rail contact patch, cause fatigue in wheel/rail contact patch and eventually lead to wheel tread spalling. The results of these studies suggest that the suppression of the wheelset longitudinal vibration extends wheel/rail life and the addition of a vertical damper with an ahead angle provides a possible solution to the wheel spalling problem.     

High-speed wheel/rail contact determining method with rotating flexible wheelset and validation under wheel polygon excitation

A rotating flexible wheelset model is developed and integrated into a vehicle/track dynamic model. Flexible wheelset modes with natural frequencies less than 1000?Hz are considered in the wheelset modelling. An innovation of the paper is that wheel/rail rolling contact calculation considers the effect of the wheelset flexibility and the rotating effect. By introducing two half dummy rigid wheelsets the rolling contact between the flexible wheelset and the two rails can be transformed to that between a rigid wheelset and the rails. As an extension application, the wheel OOR (Out-Of-Round) wears with the 11th, 15th, and 17th orders are used to the vehicle system dynamic model with rigid, flexible and rotating-flexible wheelset model. The results of the three models are compared to study the influence of wheelset flexibility and rotation. The ‘online searching contact method’ developed in this paper is compared with the traditional contact method with considering the rotating flexible wheelset. And then a measured OOR is used to excite the rotating flexible wheelset, the response of which is analysed and verified.     

Robust state feedback stabilization of articulated steer vehicles

In this work, a full-state feedback controller is designed to prevent the oscillatory instability or snaking behaviour of an articulated steer vehicle. To design the controller, first, a linearized model of the vehicle is developed and analyzed to identify the most important uncertain tire parameters with regard to the snaking mode. By using this linearized model, the equations of motion are represented in the form of a polytopic system, which depends affinely on the most important uncertain tire parameters. Then, by solving some linear matrix inequalities, both the Lyapunov and state feedback matrices for the robust stabilization of the vehicle are found. The performance of the resulting controller is evaluated by conducting several simulations based on the linearized model. To verify the results from the linearized model analysis, some simulations are also done by a virtual prototype of the vehicle in ADAMS. The results based on the linearized model are reasonably consistent with those from the simulations in ADAMS. They show that the controller can effectively stabilize the vehicle during the snaking mode in different driving conditions.     

The Geometrical Contact between Track and Wheelset

In previous publications the author has described a so-called first-order theory for the motion of a railway vehicle wheelset on a tangent track. In the present report the geometrical aspect of this theory is further evaluated and a method for solving the constraint equations between the coordinates of the wheelset is indicated.     

Experimental investigation into the mechanism of the polygonal wear of electric locomotive wheels

Experiments were conducted at field sites to investigate the mechanism of the polygonal wear of electric locomotive wheels. The polygonal wear rule of electric locomotive wheels was obtained. Moreover, two on-track tests have been carried out to investigate the vibration characteristics of the electric locomotive's key components. The measurement results of wheels out-of-round show that most electric locomotive wheels exhibit polygonal wear. The main centre wavelength in the 1/3 octave bands is 200?mm and/or 160?mm. The test results of vibration characteristics indicate that the dominating frequency of the vertical acceleration measured on the axle box is approximately equal to the passing frequency of a polygonal wheel, and does not vary with the locomotive speed during the acceleration course. The wheelset modal analysis using the finite element method (FEM) indicates that the first bending resonant frequency of the wheelset is quite close to the main vibration frequency of the axle box. The FEM results are verified by the experimental modal analysis of the wheelset. Moreover, different plans were designed to verify whether the braking system and the locomotive's adhesion control have significant influence on the wheel polygon or not. The test results indicate that they are not responsible for the initiation of the wheel polygon. The first bending resonance of the wheelset is easy to be excited in the locomotive operation and it is the root cause of wheel polygon with centre wavelength of 200?mm in the 1/3 octave bands.     

斜风下扁平箱形截面桥梁颤振性能风洞试验研究

扁平箱形截面桥梁的颤振临界风速与风偏角的关系明显地受到风攻角的影响。在0°风攻角情况下,扁平箱形截面流线性好,其颤振性能与平板接近,颤振临界风速随风偏角的增加而增加,用传统的平均风分解方法可以获得较好的结果;而对于非0°风攻角的情况,扁平箱形截面的流线性变差,随着风偏角的增加其颤振临界风速呈起伏变化,最低值一般在斜风的情况下出现,此时,传统的平均风分解方法不再适用。