有限元轮轨滚动接触理论及其应用研究
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摘要
当前世界铁路正朝着高速和重载方向发展,随之而来的列车牵引和制动对轮轨的黏着的控制与利用的要求也越来越高,而且轮轨磨耗、滚动接触疲劳、脱轨和噪声等问题越来越严重,其解决与否直接影响铁路的快速发展。这些问题的研究涉及到许多学科,但都必须以轮轨滚动接触理论研究为基础。
轮轨滚动接触理论是研究列车运动时,轮轨相对运动状态和接触斑上作用力的关系。本文第2章详细讨论了目前常用于车辆动力学研究中的几个经典基于Hertz理论的轮轨滚动接触模型,以及Kalker于20世纪90年代初完成的三维弹性体非Hertz滚动接触理论。Kalker的三维弹性体非Hertz滚动接触理论至今未突破弹性半空间假设限制,无法对复杂的轮轨作用问题作进一步的研究。大量的工程应用已经充分证明有限元法是解决轮轨滚动接触问题的先进的、行之有效的方法。
本文应用基于Lagrangian网格的有限元接触理论和基于ALE的稳态滚动接触有限元理论分别建立了三维轮轨瞬态滚动接触有限元模型和三维接触稳态滚动接触有限元模型。在基于ALE三维接触稳态滚动接触有限元模型中,通过Lagrange乘子法处理切向接触约束,可以精确地计算接触斑的黏着特性。在三维瞬态轮轨滚动接触分析中,首次联合使用有限元隐式和显式求解方法模拟轮轨瞬态滚动接触过程,使轮轨滚动瞬态计算在很短的时间内就能得到稳定解。这些模型不但可以考虑材料、几何和接触非线性问题,还可以考虑车轮滚动速度、轮轨的实际几何形态,以及惯性力的影响。这些模型突破了经典轮轨滚动接触理论Hertz接触条件和弹性半空间假设的局限性,使轮轨滚动接触问题真正的变成一个动力问题。
本文用基于ALE的稳态轮轨滚动接触的三维有限元模型对单轮对在轨道上稳态滚动时的接触状态进行了分析;应用Kalker三维弹性体非Hertz滚动接触理论也对单轮对在轨道上滚动接触蠕滑力进行了分析;并对两种轮轨滚动接触模型的计算结果进行对比分析。
本文在基于ALE的稳态轮轨滚动接触有限元模型中,分别采用Lagrange乘子法和罚函数法处理切向接触约束,通过这些模型分析轮轨接触表面在干燥条件下的轮轨黏滑特性曲线。在基于罚函数法处理切向接触约束的ALE的稳态轮轨滚动接触有限元模型中通过引入粗糙度平顺摩擦响应,讨论不同的滑动容差对轮轨黏滑特性曲线的影响。
本文提出基于三维瞬态有限元模型的轮轨形面磨耗的数值预测方法,在轮轨磨耗数值模拟得以实现的重要技术环节上,推导了适用于有限元模型的基于微面积的Archard磨损模型的积分形式,实现了用Laplace网格光滑技术对车轮踏面和轨头内部网格的光滑化处理技术,用该方法数值模拟日本铁道综合技术研究所(RTRI)的双轮盘式轮轨磨耗试验台的轮轨磨耗试验过程,对预测结果和试验结果进行了对比分析。提出基于ALE稳态轮轨滚动接触的三维有限元模型建立轮轨形面磨耗的数值预测方法,在该方法中应用车辆系统动力学与有限元的联合求解,可以得到相对准确的载荷工况,应用该方法对重载车辆通过小曲线时的车轮磨损进行预测。
The development tendency of the railway construction in the world today is serving high speed trains and carrying heavy load. With the development some problems of the wheel/rail performance arises, and the requirement of the train traction for the adhesion of wheel/rail will become more and more strict, and wheel/rail wear, rolling contact fatigue, derailment and noise will become more and more serious. The solution to the problems will have direct effects on the railway development. Although the investigations in the problem are concerned with many disciplines, they are based on the theory of wheel/rail rolling contact.
The theory of wheel/rail rolling contact is used to study the statement of wheel/rail relative motion and contact force on contact patch as a train running. Chapter 2 gives detailed derivation of a few typical theoretical models of rolling contact with Hertzian form, which are widely used in the dynamical analysis of railway vehicle at present. And the chapter gives Kalker’s theory of three-dimensional elastic bodies in rolling contact with non-Hertzian form, which was completed by the 1990s. But Kalker’s theory has not broken the limit of elastic half space assumption, which can not be used to make further investigation in the problem of complicated wheel/rail reaction.
Lots of engineering applications demonstrate that the finite element method (FEM) is an advanced and efficient method in solving wheel/rail rolling contact problems. In this paper, a wheel/rail rolling contact finite element model based on Arbitrary Lagrangian Eulerian(ALE) is established and applied to the wheel/rail steady state rolling contact analysis. The adhesion condition of no shear slip velocity is applied by Lagrange multiplier method in the ALE contact weak form, by which method the adhesive character on contact patch is accurately calculated. A three-dimensional wheel/rail transient rolling contact FEM model based on Lagrangian FEM is established and used in the simulation of wheel/rail dynamic rolling contact process. The implicit and explicit FEM have been coupled to simulate wheel/rail rolling contact process. By these methods, stabile results are obtained in short time for the wheel/rail rolling contact. The nonlinear material constitutive model, nonlinear contact shape, rolling velocity of the wheel and inertia force are considered in the models. These methods have broken the limit of Hertz contact conditions and elastic half space assumption, and the methods make the wheel/rail rolling contact problems really become into a dynamic problem.
In this paper, the wheel/rail rolling contact FEM model based on ALE FEM is applied to analyse a wheelset steady state rolling contact on a rail. The contact stress、friction shear stress and relate slip velocity in the contact patch are analyzed by the method. Kalker’s theory of three-dimensional elastic bodies in rolling contact with non-Hertzian form is applied to analyse a wheelset rolling contact on a rail. The numerical results of the two methods are compared.
In this paper, the adhesion condition of no shear slip velocity is applied by Lagrange multiplier method in the ALE steady state rolling contact FEM model. The model is used to analyse the creep force characteristic curve in dry friction condition. The adhesion condition of no shear slip velocity is applied by penalty method in the ALE steady state rolling contact FEM model. In this model, penalty method may be thought of as a regularization of the contact interface condition, and the regularization can smooth Coulomb fiction by importing coarseness. Effect of slip tolerate on the creep force characteristic curve is discussed.
A wheel/rail profile wear prediction methodology based on three-dimensional transient wheel/rail rolling contact is presented. The wear model and adaptive mesh adjustment technique are important techniques for numerical method of wheel/rail wear. The integral form of Archard wear model is obtained, which is based on tiny area and is suited to FEM. Laplacian smoothing with area weights is used to smooth the meshes of wheel and rail. The wear method is applied to the wheel/rail disc test about the wear of flange and gauge. The simulation results are compared with measurements of Laboratory wear test and verify the effectiveness of wear prediction methodology. Based on the wheel/rail steady state rolling contact analysis, a wheel profile wear prediction methodology is developed and applied to the wheel wear when the heavy haul train passes in curved track with the small radius. In the loop of the prediction methodology, the vehicle dynamics model is built by the ADAMS software and the forces of the bearing boxes from the vehicle system dynamics model are loaded on the model of three-dimensional nonlinear finite element steady state analysis for wheelset rolling contact process.
轮轨滚动接触理论是研究列车运动时,轮轨相对运动状态和接触斑上作用力的关系。本文第2章详细讨论了目前常用于车辆动力学研究中的几个经典基于Hertz理论的轮轨滚动接触模型,以及Kalker于20世纪90年代初完成的三维弹性体非Hertz滚动接触理论。Kalker的三维弹性体非Hertz滚动接触理论至今未突破弹性半空间假设限制,无法对复杂的轮轨作用问题作进一步的研究。大量的工程应用已经充分证明有限元法是解决轮轨滚动接触问题的先进的、行之有效的方法。
本文应用基于Lagrangian网格的有限元接触理论和基于ALE的稳态滚动接触有限元理论分别建立了三维轮轨瞬态滚动接触有限元模型和三维接触稳态滚动接触有限元模型。在基于ALE三维接触稳态滚动接触有限元模型中,通过Lagrange乘子法处理切向接触约束,可以精确地计算接触斑的黏着特性。在三维瞬态轮轨滚动接触分析中,首次联合使用有限元隐式和显式求解方法模拟轮轨瞬态滚动接触过程,使轮轨滚动瞬态计算在很短的时间内就能得到稳定解。这些模型不但可以考虑材料、几何和接触非线性问题,还可以考虑车轮滚动速度、轮轨的实际几何形态,以及惯性力的影响。这些模型突破了经典轮轨滚动接触理论Hertz接触条件和弹性半空间假设的局限性,使轮轨滚动接触问题真正的变成一个动力问题。
本文用基于ALE的稳态轮轨滚动接触的三维有限元模型对单轮对在轨道上稳态滚动时的接触状态进行了分析;应用Kalker三维弹性体非Hertz滚动接触理论也对单轮对在轨道上滚动接触蠕滑力进行了分析;并对两种轮轨滚动接触模型的计算结果进行对比分析。
本文在基于ALE的稳态轮轨滚动接触有限元模型中,分别采用Lagrange乘子法和罚函数法处理切向接触约束,通过这些模型分析轮轨接触表面在干燥条件下的轮轨黏滑特性曲线。在基于罚函数法处理切向接触约束的ALE的稳态轮轨滚动接触有限元模型中通过引入粗糙度平顺摩擦响应,讨论不同的滑动容差对轮轨黏滑特性曲线的影响。
本文提出基于三维瞬态有限元模型的轮轨形面磨耗的数值预测方法,在轮轨磨耗数值模拟得以实现的重要技术环节上,推导了适用于有限元模型的基于微面积的Archard磨损模型的积分形式,实现了用Laplace网格光滑技术对车轮踏面和轨头内部网格的光滑化处理技术,用该方法数值模拟日本铁道综合技术研究所(RTRI)的双轮盘式轮轨磨耗试验台的轮轨磨耗试验过程,对预测结果和试验结果进行了对比分析。提出基于ALE稳态轮轨滚动接触的三维有限元模型建立轮轨形面磨耗的数值预测方法,在该方法中应用车辆系统动力学与有限元的联合求解,可以得到相对准确的载荷工况,应用该方法对重载车辆通过小曲线时的车轮磨损进行预测。
The development tendency of the railway construction in the world today is serving high speed trains and carrying heavy load. With the development some problems of the wheel/rail performance arises, and the requirement of the train traction for the adhesion of wheel/rail will become more and more strict, and wheel/rail wear, rolling contact fatigue, derailment and noise will become more and more serious. The solution to the problems will have direct effects on the railway development. Although the investigations in the problem are concerned with many disciplines, they are based on the theory of wheel/rail rolling contact.
The theory of wheel/rail rolling contact is used to study the statement of wheel/rail relative motion and contact force on contact patch as a train running. Chapter 2 gives detailed derivation of a few typical theoretical models of rolling contact with Hertzian form, which are widely used in the dynamical analysis of railway vehicle at present. And the chapter gives Kalker’s theory of three-dimensional elastic bodies in rolling contact with non-Hertzian form, which was completed by the 1990s. But Kalker’s theory has not broken the limit of elastic half space assumption, which can not be used to make further investigation in the problem of complicated wheel/rail reaction.
Lots of engineering applications demonstrate that the finite element method (FEM) is an advanced and efficient method in solving wheel/rail rolling contact problems. In this paper, a wheel/rail rolling contact finite element model based on Arbitrary Lagrangian Eulerian(ALE) is established and applied to the wheel/rail steady state rolling contact analysis. The adhesion condition of no shear slip velocity is applied by Lagrange multiplier method in the ALE contact weak form, by which method the adhesive character on contact patch is accurately calculated. A three-dimensional wheel/rail transient rolling contact FEM model based on Lagrangian FEM is established and used in the simulation of wheel/rail dynamic rolling contact process. The implicit and explicit FEM have been coupled to simulate wheel/rail rolling contact process. By these methods, stabile results are obtained in short time for the wheel/rail rolling contact. The nonlinear material constitutive model, nonlinear contact shape, rolling velocity of the wheel and inertia force are considered in the models. These methods have broken the limit of Hertz contact conditions and elastic half space assumption, and the methods make the wheel/rail rolling contact problems really become into a dynamic problem.
In this paper, the wheel/rail rolling contact FEM model based on ALE FEM is applied to analyse a wheelset steady state rolling contact on a rail. The contact stress、friction shear stress and relate slip velocity in the contact patch are analyzed by the method. Kalker’s theory of three-dimensional elastic bodies in rolling contact with non-Hertzian form is applied to analyse a wheelset rolling contact on a rail. The numerical results of the two methods are compared.
In this paper, the adhesion condition of no shear slip velocity is applied by Lagrange multiplier method in the ALE steady state rolling contact FEM model. The model is used to analyse the creep force characteristic curve in dry friction condition. The adhesion condition of no shear slip velocity is applied by penalty method in the ALE steady state rolling contact FEM model. In this model, penalty method may be thought of as a regularization of the contact interface condition, and the regularization can smooth Coulomb fiction by importing coarseness. Effect of slip tolerate on the creep force characteristic curve is discussed.
A wheel/rail profile wear prediction methodology based on three-dimensional transient wheel/rail rolling contact is presented. The wear model and adaptive mesh adjustment technique are important techniques for numerical method of wheel/rail wear. The integral form of Archard wear model is obtained, which is based on tiny area and is suited to FEM. Laplacian smoothing with area weights is used to smooth the meshes of wheel and rail. The wear method is applied to the wheel/rail disc test about the wear of flange and gauge. The simulation results are compared with measurements of Laboratory wear test and verify the effectiveness of wear prediction methodology. Based on the wheel/rail steady state rolling contact analysis, a wheel profile wear prediction methodology is developed and applied to the wheel wear when the heavy haul train passes in curved track with the small radius. In the loop of the prediction methodology, the vehicle dynamics model is built by the ADAMS software and the forces of the bearing boxes from the vehicle system dynamics model are loaded on the model of three-dimensional nonlinear finite element steady state analysis for wheelset rolling contact process.
引文
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