轮轨匹配优化及其可视化的研究与应用

针对目前工程上采用经验和试验方法确定轮轨外形匹配的问题,提出了轮轨接触的几何外形匹配优化及其可视化算法。算法用三次样条曲线拟合轮轨外形,差分法确定插值边界条件;采用二分法迭代求解轮对侧滚角解算出轮轨接触点位置,进而得到轮轨接触几何参数;利用MATLAB及Visual C++动态地将计算结果可视化。该算法实现了轮对等效锥度与横移量的定量分析,为轮轨匹配优化提供了新的方法,仿真结果表明,该算法具有较强的鲁棒性和通用性。     

A numerical method for prediction of curved rail wear

Important published papers on rail wear in the past were reviewed. A numerical method was put forward to predict curved rail wear during a railway vehicle curving. The numerical method was discussed in detail. It considered a combination of Kalker’s non-Hertzian rolling contact theory, rail material wear model, the coupling dynamics of the vehicle and track, and the three-dimensional contact geometry analysis of wheel-rail. In its numerical implementation, the dynamical parameters of all the parts of the vehicle and track, such as normal loads and creepages of the wheels and rails, were firstly obtained through the curving dynamics analysis. The wheel-rail contact geometry calculation gave the wheel-rail contact geometry parameters, which were used in the wheel-rail rolling contact calculation with Kalker’s non-Hertzian rolling contact theory modified. The friction work densities on the contact areas of the wheels and rails were obtained in the rolling contact calculation, and were used to predict the rail running surface wears caused by the multiple wheels of the vehicle simultaneously with the rail material wear model. In the rail material wear model, it was assumed that the mass loss of each unit area was proportional to the frictional work density in the contact area. A numerical example was present to verify the present method. The numerical results of the example are reasonable, and indicate that the high rail wear of the curved track caused by the leading wheelset is much more serious than those caused by the other three wheels of the same bogie.     

基于柔性轮对的轨道车辆动力学仿真分析

为研究柔性轮对对轨道车辆动力学性能的影响,应用ANSYS创建轮对实体有限元分析模型,并选用Guyan缩减法和Lanczos分块法对其进行子结构模态分析.联合SIMPACK创建柔性轮对车辆仿真模型,此模型的构架、车体等部件仍视作刚性体.与刚体车辆仿真模型对比分析出在中国高铁谱和美国六级谱激励作用下两模型的动力学性能的差异.分析结果表明:轮对采用柔性体的车辆非线性临界速度较全刚体车辆的非线性临界速度稍稍降低.在两激励线路下,轮对采用柔性体对车辆的平稳性和曲线通过性能也有一定程度的影响.     

柔性轮对结构振动对车辆动力学性能的影响

为研究轮对柔性对车辆动力学的影响,建立高速列车轮对的有限元模型,对轮对进行自由模态分析.通过模态综合法获取柔性轮对模态信息,应用多体系统动力学理论建立柔性轮对-刚性轨道接触力学模型;建立包含高速旋转柔性轮对的车辆-轨道耦合动力学模型,研究高速列车在直线和曲线通过时轮对结构振动对车辆动力学性能的影响.结果表明:轮对的结构振动对轮轨接触点位置、蠕滑率、蠕滑力和脱轨因数等均产生较明显的影响,但是对轮重减载率影响较小,因此应采用更加精确的柔性轮轨耦合模型研究轮轨相互作用、轮轨滚动接触疲劳和轮轨噪声等.     

A method to predict the derailment of rolling stock due to collision using a theoretical wheelset derailment model

A wheelset derailment model on rolling stock was developed to predict train collision-induced derailment. This model is based on the theoretical derailment behaviors of a wheelset under suspension loads. This theoretical derailment model was numerically simulated using commercial dynamics software, wherein it is demonstrated that this model is useful for predicting train collision-induced derailment. Furthermore, this theoretical derailment model was incorporated into a virtual testing model that did not consider wheel–rail contact conditions in order to evaluate useful applications to the derailment prediction of a train collision. The derailment behaviors of this virtual testing model, which were predicted by applying the theoretical derailment model under the condition of no wheel–rail contact, were closely correlated to those derived from simulations that considered surface-to-surface contact conditions.     

二维动边界发汗控制数学仿真研究

本文给出二维加热且具有表面烧蚀的发汗控制数学模型。采用时间跨半步的交替方法,将二维活动边界分布参数控制方程差分化,得到三对角方程组。对电磁炮弹飞行进行数学仿真后表明:控制参数对温度场和活动边界的控制是有效的;该数学模型符合实际物理过程。从数值角度提供了数学理论问题解析性质的依据,给出了二维温度场特点并讨论了同步烧蚀问题。     

车轮滑行轮轨热接触耦合有限元分析

为研究轮轨接触温升和热应力规律,用有限元法分别建立锥型踏面车轮和磨耗型踏面车轮在60kg／m钢轨上滑行的三维热接触耦合模型．考虑温度场与结构场相互影响、相关材料参数随温度变化以及轮轨接触问题,对在一定速度下抱死滑行时轮轨温度场和应力场的热一结构直接耦合进行分析．结果表明磨耗型踏面车轮的接触斑面积大于锥型踏面车轮的接触斑面积,且前者接触斑趋近于圆形,后者接触斑为细长椭圆形;材料参数随温度的变化对轮轨温度场和应力场影响很大,不可忽略;温度场对应力场的影响很大,温度升高的趋势与应力升高的趋势相同;磨耗型踏面对轮轨的热损伤比锥型踏面小很多．     

Modeling and controlling a robotic convoy using guidance laws strategies.

This paper deals with the problem of modeling and controlling a robotic convoy. Guidance laws techniques are used to provide a mathematical formulation of the problem. The guidance laws used for this purpose are the velocity pursuit, the deviated pursuit, and the proportional navigation. The velocity pursuit equations model the robot's path under various sensors based control laws. A systematic study of the tracking problem based on this technique is undertaken. These guidance laws are applied to derive decentralized control laws for the angular and linear velocities. For the angular velocity, the control law is directly derived from the guidance laws after considering the relative kinematics equations between successive robots. The second control law maintains the distance between successive robots constant by controlling the linear velocity. This control law is derived by considering the kinematics equations between successive robots under the considered guidance law. Properties of the method are discussed and proven. Simulation results confirm the validity of our approach, as well as the validity of the properties of the method. Index Terms-Guidance laws, relative kinematics equations, robotic convoy, tracking.     

长春轻轨3号线钢轨轨底坡对列车车轮磨耗的影响

摘要： 为探究小半径曲线钢轨轨底坡对车轮磨耗的影响规律,建立长春市轻轨3号线70%低地板轻轨列车车轮磨耗预测分析模型,包括独立旋转轮对的车辆 轨道耦合动力学计算模型、轮轨接触模型和Archard材料磨耗模型,并采用这些模型分析轻轨列车通过小半径曲线轨道时轨底坡对车轮磨耗的影响。分析结果表明：轻轨列车通过小半径曲线轨道时,动车轮对的磨耗程度比拖车轮对更严重,动车轮对总磨耗量为拖车轮对总磨耗量的159%;从轮对自身来看,内侧车轮的磨耗均比外侧车轮的磨耗严重,内侧车轮总磨耗量为外侧车轮总磨耗量的165%;钢轨轨底坡对车轮磨耗的影响显著,车轮踏面最大磨耗量出现位置随轨底坡变化的规律较为复杂,车轮轮缘磨耗量在轨底坡为1/20时最小。     

适定性分析在醇酮氧化动力学中的应用

在化工系统DCS先进控制领域和基于机理模型的化工类商品化软件中,大型装置的过程数学模型通常处于核心地位,同时这些场合也对模型的稳定性和动态特性有较高要求。而适定性分析有利于从物理意义和数学的角度分析模型的合理性,并指导正确的数值求解方法,从而产生高质量数学模型。本文结合醇酮氧化过程模拟的实践应用了Lipschitz条件、解的存在唯一性定理、解的延拓、解对初值的连续性和可微性定理和相关常微方程稳定性理论等数学工具,发现了文献中动力学方程组存在的问题,并对其进行了改进与提高；在实际应用中也取得了更好的效果；同时,对于其它类似的数学建模与求解问题也具有理论和实践的参考意义。     

On one-dimensional fox-rabies dynamics of advection type

A one-dimensional model of fox-rabies of two nonlinear partial differential equations of hyperbolic type is studied. Finite difference techniques are applied to compute the numerical solutions of the initial/boundary value problem. The convergence of the resulting schemes, which have a second order accuracy in space and time, is investigated. The method is tested for different values of advection rate; numerical and graphical results showed that the method is consistent with the dynamic behaviour of fox-rabies.     

汽轮机转子碰摩热弯曲动力特性研究

本文简化了汽轮机转子模型,并根据转子碰摩理论建立了一种简单的求解碰摩截面热分布的计算模型,使得碰摩截面热分布的计算大大简化.依据转子动力学理论推导了本模型的运动方程,并作无量纲化以便于MATLAB数值求解收敛,最终建立了转子系统由摩擦引起的弹性热弯曲——碰摩耦合故障动力模型.利用四阶Runge-Kutta方法求解微分方程组得到了在不平衡力、碰摩力和碰摩热弯矩耦合作用下转子系统的响应,并对低于、接近和高于临界转速下碰摩热弯曲转子的动力学特性进行了数值仿真研究,包括时域、频谱、轴心轨迹以及碰摩力的变化.结果表明,转子在低于和接近临界转速运行发生碰摩,转子的振动由平稳状态逐渐发散,而在高于临界转速发生碰摩时转子的振动会逐渐减小.     

Balancing and Trajectory Tracking of Two-Wheeled Mobile Robot Using Backstepping Sliding Mode Control: Design and Experiments

The key attributes of Two Wheeled Balancing Mobile Robots (TWBMRs) are nonholonomic constraints and inherent instability. This paper deals with the problem of balancing and trajectory tracking of TWBMR using backstepping Sliding Mode Controller (SMC). First, the mathematical representation of TWBMR is derived using Lagrangian method by incorporating the dynamics of DC motors. Then, a decoupling approach is applied for simplifying the dynamic equations. The backstepping SMC technique is finally adopted to achieve the balancing and trajectory tracking of the TWBMR, whereas both model uncertainties and exogenous disturbance are taken into account in the controller design methodology. In order to determine the velocity, the trajectory tracking is achieved by the kinematic control, which is a common backstepping controller. For the velocity convergence of TWBMR to the generated desired value, two SMCs are designed, in which the motors voltage are directly controlled as the control laws. Simplicity in practical implementation and control law, ability to overcome uncertainties and appropriate performance are the main advantages of the proposed controller. The effectiveness of the proposed controller is verified through simulation and experimental results.     

Solving the Dynamic Optimal Set Partitioning Problem with Arrangement of Centers of Subsets

A mathematical model is presented for the dynamic problem of optimal partitioning of a set from a space Rⁿ with arrangement of centers of subsets under joint constraints on the partition and phase variable. A method is described that solves this problem and synthesizes the essentials of the theory of continuous partitioning problems and optimal control theory for dynamic systems. A numerical algorithm for solving the problem and an analysis of the results of computational experiments are presented.     

CATEGORY-FUNCTOR MODELLING OF NATURAL SYSTEMS

An approach to the derivation of dynamic equations for natural systems modelled by mathematical structures is suggested. The approach rests on an extremum principle which postulates that among all possible states of a system those are actually realized that correspond to an extremal in a rigorous mathematical sense structure. The suggested method of ordering the structured sets with the aid of category and functor theory generalizes the cardinality ordering of structureless sets. The method makes it possible to determine the functionals for the variational problem which describes a system under study. The approach is illustrated by a model of an ecological community.     

Dynamic Analysis Tool for Legged Robots

The paper introduces a systematic approach for dealing with legged robot mechanism analysis. First, we briefly summarize basic mathematical tools for studying the dynamics of these multi-loop and parallel mechanisms using a unified spatial formulation which is useful for computer algorithms. The dynamic behavior analysis is based on two stages. The first one deals with establishing the equations of motion of the whole mechanism including legs tip impact effects and allowing us to solve the direct and inverse dynamic problems. The second concerns the feet–ground interaction aspect which is one of the major problem in the context of dynamic simulation for walking devices. We focus on the phenomenon of contact by introducing a general model for dynamic simulation of contacts between a walking robot and ground. This model considers a force distribution and uses an analytical form for each force depending only on the known state of the robot system. Finally, some simulation results of biped robot are given. The simulation includes all phenomena that may occur during the locomotion cycle: impact, transition from impact to contact, contact during support with static friction, transition from static to sliding friction and sliding friction.     

Well-posedness and exponential stability of two-dimensional vibration model of a boundary-controlled curved beam with tip mass

This paper studies the well-posedness and exponential stability of two-dimensional vibration model of a curved beam with tip mass under linear boundary control. The control task is to stabilise the tangential and radial vibrations, which are coupled due to the beam curvature. To reach the main results of the paper, mathematical analyses based on the semigroup theory and Lyapunov approach are conducted, and it is shown that the proposed closed-loop model holds a unique solution that converges to zero exponentially fast. These analyses are based on a hybrid dynamic model that incorporates two coupled partial differential equations and six boundary conditions, including two ordinary differential equations. Simulation results are used to illustrate the efficacy of the suggested method.     

Second International Conference on Production Research

A mathematical model that predicts the dynamic flows in cellular mobile networks with handoff procedures is described in this paper. Two types of handoff procedures considered in the model are the non-prioritized and the prioritized or reserved channel schemes. The dynamic behaviour of this model makes it suitable to analyse dynamic channel allocation methods as well as to analyse the robustness of the system under perturbation. The basic concept of our model is based on the fluid flow theory and the queueing theory. Discrete event simulations were performed and the results were found to be comparable to the results obtained using the mathematical model.     

Synergetic control of asynchronous electric traction drives of locomotives

The problem of synthesis of the control system of locomotive asynchronous electric traction drives with regard to processes in the wheel-rail contact. In this system, the wheels can slip relative to the rail, and the excessive slippage has a negative effect on the locomotive traction properties and increases the wear of the wheel pair and rail surface. Modern techniques of solving this problem are based on the forced increase of the coefficient of traction in the wheel-rail contact and on tracking the acceleration of the wage wheels rotation rate as the wheel slip development is evaluated. A new approach to the synthesis of locomotive traction controllers is proposed that is based on the theory of synergetic control. The proposed traction controller ensures a prescribed slip rate of the wage wheels relative to the rail thus ensuring the maximum traction; furthermore, this controller minimizes the loss of energy in the power unit of the electric traction drive.