轮轨滚动接触弹塑性分析及疲劳损伤研究
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摘要
轮轨关系是轨道交通系统中的基础问题之一，其中轮轨接触问题一直以来都是国内外学者非常重视且从未停止研究的重要问题。近些年，随着数值方法和计算机的发展，有限元方法在轮轨滚动接触问题研究中得到广泛应用。为了高效、准确的研究轮轨滚动接触问题，本论文采用有限元方法在并行计算环境中完成了轮轨接触静态、稳态和瞬态分析，并在此基础之上结合轮轨间函数型摩擦系数模型完成了轮轨接触疲劳寿命预测和轮轨接触表面裂纹扩展分析。
具体开展的研究工作如下：
（1）针对轮轨接触区网格尺寸细化至1mm后，轮轨接触三维大规模有限元模型节点数在百万以上且在单机上难以完成计算的情况。采用非线性有限元软件ABAQUS的区域分解并行计算方式，在MPI通信模式的12节点并行计算环境中完成轮轨接触大规模有限元模型的并行计算。根据隐式计算和显式计算的特点，合理选择并行计算节点数以实现优质的并行计算效率，可以较好的解决有限元计算精度和计算效率的矛盾问题。
（2）以CRH2型动车组使用的LMA磨耗型车轮和我国标准CHN60钢轨为分析对象，按照Lagrangian方法建立轮轨滚动接触静态模型，重点研究轮对横移、冲角、轴重、转矩和摩擦系数对轮轨接触静态特性的影响。轮轨滚动接触稳态分析则采用mixed Lagrangian/Eulerian方法建立轮轨滚动接触有限元模型，其中车轮的滚动用Eulerian方法描述，而钢轨采用Lagrangian方法描述，轮轨网格无相对运动，采用隐式方法完成轮轨滚动接触稳态分析；以mixedLagrangian/Eulerian轮轨接触有限元模型的稳态计算结果为初始条件，按照Lagrangian方法建立轮轨滚动接触瞬态分析有限元模型并用显式方法完成计算。通过轮轨接触静态、稳态和瞬态分析结果发现摩擦系数对轮轨接触斑内纵向剪切应力和横向剪切应力影响较大，其值与摩擦系数取值成倍率变化，在轮轨滚动接触疲劳寿命分析和裂纹扩展分析中应予以重视。
（3）考虑到轮轨摩擦系数对轮轨滚动接触切向特性的影响，在有限元模型的接触定义中采用轮轨函数型摩擦系数替换传统的常数摩擦系数，并结合非线性有限元软件ABAQUS中集成的金属棘轮效应塑性本构模型进行轮轨滚动接触棘轮效应分析；在此基础上使用基于损伤因子的Jiang-Sehitoglu疲劳寿命预测模型进行轮轨滚动接触疲劳寿命分析；最后对滚动接触疲劳寿命分析结果与日本学者AKAMAM和瑞典学者Ringsberg的轮轨接触疲劳分析结果进行了对比，结果表明本文计算结果与日本学者计算结果更为接近，主要是因为轮轨材料参数以及计算工况等与日本学者AKAMAM所使用参数大致相同。
（4）扩展有限元方法是求解不连续力学问题的有效方法，在求解裂纹问题时不需要对裂尖进行高密度的网格细化，在模拟裂纹扩展时也不需要对裂纹进行网格重划。以轮轨滚动接触疲劳分析结果为基础，建立轮轨接触扩展有限元裂纹模型，重点分析了轮轨摩擦系数、裂纹位置和裂纹尺寸对轮轨接触表面裂纹扩展的影响。结果表明：轮轨表面裂纹尺寸在8mm左右时J积分值较大，超出钢轨材料在常温下的断裂韧度，裂纹易于扩展，可能导致钢轨横向断裂，该结果与现场观测结果较吻合。
已有的轮轨函数型摩擦系数虽然在一定程度上能反映轮轨间摩擦真实状态，但对于存在第三介质（如水、油、磁场）等多场耦合作用下的高速轮轨来说，还需要开展更深入的研究来揭示高速轮轨间的摩擦行为，建立更为准确的轮轨间函数型摩擦系数。另外，轮轨滚动接触疲劳寿命和表面裂纹扩展也与多因素相关，后续研究需要将试验手段和数值分析手段有效结合，系统开展轮轨滚动接触表面损伤的研究。
Wheel/rail relationship is one of basic issues in rail transportation system. In which,wheel/rail contact is an important problem continuous studied by domestic and foreign scholars.Recently, with the development of numerical method and computer, the finite element method(FEM) is widely applied in rolling contact problem. To efficiently andaccurately research wheel/rail rolling contact, the static, steady and transient analyses ofwheel/rail contact are finished by using FEM in parallel computing environment. Based onthose analysis results, the wheel/rail contact fatigue life prediction and wheel/rail contactsurface crack propagation are studied combined with wheel/rail functional friction coefficient.
Specific research work as follows:
(1) When the sizes of mesh in wheel/rail contact zone are refined to1mm, the number ofnodes of3D finite element model of wheel/rail contact is in a million. So this model is difficultto process in single computer. The large-scale wheel/rail contact finite element model isparallel computed in MPI parallel computing environment with12nodes. According to theimplicit and explicit calculation, reasonable parallel computing nodes are choosen to gain highquality efficiency of parallel computation. The contradiction with calculation precision andcalculation efficiency of finite element model is solved better.
(2)As analysis object of LMA worn profile wheel of CRH2EMU and Chinese standardrail CHN60, the wheel/rail rolling contact static model is established with Lagrangian methodand focuses on influence analysis of lateral displacements, attack angle, axle load, torque andfriction coefficient to wheel/rail contact static characteristic. The wheel/rail rolling contactfinite element model for steady analysis is constructed by using mixed Lagrangian/Eulerianmethod. The rolling of wheel is described with Eulerian, and Lagrangian method is used todescribe rail. There is no relative movement between wheel mesh and rail mesh. The steadyanalysis of wheel/rail rolling contact is computed by implicit method. The results of steadyanalysis as initial conditions, the finite element model for transient analysis of wheel/railrolling contact is established with Lagrangian method and computed with explicit method.Through static, steady and transient analysis results show that the friction coefficient influenceon the longitudinal shear stress and transverse shear stress of wheel/rail contact patch strongly.Their values change ratably with wheel/rail friction coefficient. So it should be attachedimportance to the wheel/rail rolling contact fatigue life analysis and simulation of crackpropagation.
(3) Considering the influence of friction coefficient to wheel/rail rolling contact tangentialcharacteristic, the ratcheting finite element model is established. In this model, the functionalfriction coefficient replace conventional constant friction coefficient. The ratcheting analysisfor wheel/rail rolling contact is done by using metal plasticity constitutive model integrated in the nonlinear finite element software-ABAQUS. Based on the ratcheting analysis results, thewheel/rail rolling contact fatigue life analysis is done by using fatigue life prediction model ofJiang-Sehitoglu. The fatigue life analysis results are compared with wheel/rail contact fatigueanalysis results of the Japanese scholar AKAMA M and Swedish scholar Ringsbergrespectively. It is found that the results in this paper are close to the results by Japanesescholars due to wheel/rail material parameters and conditions parameters roughly same tocalculation parameters of Japanese scholar AKAMA M.
(4) The extended finite element method is presented for solving discontinuous mechanicsproblem. It is no need high density mesh refinement to crack tip in solving crack problem andremeshing for crack in simulating crack growth. Based on wheel/rail rolling contact fatigueanalysis, the extended finite element crack model of wheel/rail contact is constructed. Theinfluence analysis of wheel/rail friction coefficient, crack location and size on the contactsurface crack growth are mainly done. The results show that J-integral value is large whenwheel/rail surface crack size of about8mm. It is beyond the fracture toughness of rail materialat room temperature. In this condition, crack propagation is so easy, may lead to lateral fractureof the rail. It is coincide with the results of the field observation.
The existing wheel/rail functional friction coefficient can reflect the real state of thefriction between wheel and rail to a certain extent. However, for high speed wheel/rail, thereare coupling third mediums, such as water, oil, magnetic field. So it is need to conduct morein-depth studies to reveal friction behavior of high-speed wheel/rail and construct moreaccurate functional friction coefficient between wheel and rail. In addition, the wheel/railrolling contact fatigue life and surface crack propagation is also associated with multiplefactors. It is need to systematic study wheel/rail rolling contact surface damage by effectivelycombining test method and the numerical method.
具体开展的研究工作如下：
（1）针对轮轨接触区网格尺寸细化至1mm后，轮轨接触三维大规模有限元模型节点数在百万以上且在单机上难以完成计算的情况。采用非线性有限元软件ABAQUS的区域分解并行计算方式，在MPI通信模式的12节点并行计算环境中完成轮轨接触大规模有限元模型的并行计算。根据隐式计算和显式计算的特点，合理选择并行计算节点数以实现优质的并行计算效率，可以较好的解决有限元计算精度和计算效率的矛盾问题。
（2）以CRH2型动车组使用的LMA磨耗型车轮和我国标准CHN60钢轨为分析对象，按照Lagrangian方法建立轮轨滚动接触静态模型，重点研究轮对横移、冲角、轴重、转矩和摩擦系数对轮轨接触静态特性的影响。轮轨滚动接触稳态分析则采用mixed Lagrangian/Eulerian方法建立轮轨滚动接触有限元模型，其中车轮的滚动用Eulerian方法描述，而钢轨采用Lagrangian方法描述，轮轨网格无相对运动，采用隐式方法完成轮轨滚动接触稳态分析；以mixedLagrangian/Eulerian轮轨接触有限元模型的稳态计算结果为初始条件，按照Lagrangian方法建立轮轨滚动接触瞬态分析有限元模型并用显式方法完成计算。通过轮轨接触静态、稳态和瞬态分析结果发现摩擦系数对轮轨接触斑内纵向剪切应力和横向剪切应力影响较大，其值与摩擦系数取值成倍率变化，在轮轨滚动接触疲劳寿命分析和裂纹扩展分析中应予以重视。
（3）考虑到轮轨摩擦系数对轮轨滚动接触切向特性的影响，在有限元模型的接触定义中采用轮轨函数型摩擦系数替换传统的常数摩擦系数，并结合非线性有限元软件ABAQUS中集成的金属棘轮效应塑性本构模型进行轮轨滚动接触棘轮效应分析；在此基础上使用基于损伤因子的Jiang-Sehitoglu疲劳寿命预测模型进行轮轨滚动接触疲劳寿命分析；最后对滚动接触疲劳寿命分析结果与日本学者AKAMAM和瑞典学者Ringsberg的轮轨接触疲劳分析结果进行了对比，结果表明本文计算结果与日本学者计算结果更为接近，主要是因为轮轨材料参数以及计算工况等与日本学者AKAMAM所使用参数大致相同。
（4）扩展有限元方法是求解不连续力学问题的有效方法，在求解裂纹问题时不需要对裂尖进行高密度的网格细化，在模拟裂纹扩展时也不需要对裂纹进行网格重划。以轮轨滚动接触疲劳分析结果为基础，建立轮轨接触扩展有限元裂纹模型，重点分析了轮轨摩擦系数、裂纹位置和裂纹尺寸对轮轨接触表面裂纹扩展的影响。结果表明：轮轨表面裂纹尺寸在8mm左右时J积分值较大，超出钢轨材料在常温下的断裂韧度，裂纹易于扩展，可能导致钢轨横向断裂，该结果与现场观测结果较吻合。
已有的轮轨函数型摩擦系数虽然在一定程度上能反映轮轨间摩擦真实状态，但对于存在第三介质（如水、油、磁场）等多场耦合作用下的高速轮轨来说，还需要开展更深入的研究来揭示高速轮轨间的摩擦行为，建立更为准确的轮轨间函数型摩擦系数。另外，轮轨滚动接触疲劳寿命和表面裂纹扩展也与多因素相关，后续研究需要将试验手段和数值分析手段有效结合，系统开展轮轨滚动接触表面损伤的研究。
Wheel/rail relationship is one of basic issues in rail transportation system. In which,wheel/rail contact is an important problem continuous studied by domestic and foreign scholars.Recently, with the development of numerical method and computer, the finite element method(FEM) is widely applied in rolling contact problem. To efficiently andaccurately research wheel/rail rolling contact, the static, steady and transient analyses ofwheel/rail contact are finished by using FEM in parallel computing environment. Based onthose analysis results, the wheel/rail contact fatigue life prediction and wheel/rail contactsurface crack propagation are studied combined with wheel/rail functional friction coefficient.
Specific research work as follows:
(1) When the sizes of mesh in wheel/rail contact zone are refined to1mm, the number ofnodes of3D finite element model of wheel/rail contact is in a million. So this model is difficultto process in single computer. The large-scale wheel/rail contact finite element model isparallel computed in MPI parallel computing environment with12nodes. According to theimplicit and explicit calculation, reasonable parallel computing nodes are choosen to gain highquality efficiency of parallel computation. The contradiction with calculation precision andcalculation efficiency of finite element model is solved better.
(2)As analysis object of LMA worn profile wheel of CRH2EMU and Chinese standardrail CHN60, the wheel/rail rolling contact static model is established with Lagrangian methodand focuses on influence analysis of lateral displacements, attack angle, axle load, torque andfriction coefficient to wheel/rail contact static characteristic. The wheel/rail rolling contactfinite element model for steady analysis is constructed by using mixed Lagrangian/Eulerianmethod. The rolling of wheel is described with Eulerian, and Lagrangian method is used todescribe rail. There is no relative movement between wheel mesh and rail mesh. The steadyanalysis of wheel/rail rolling contact is computed by implicit method. The results of steadyanalysis as initial conditions, the finite element model for transient analysis of wheel/railrolling contact is established with Lagrangian method and computed with explicit method.Through static, steady and transient analysis results show that the friction coefficient influenceon the longitudinal shear stress and transverse shear stress of wheel/rail contact patch strongly.Their values change ratably with wheel/rail friction coefficient. So it should be attachedimportance to the wheel/rail rolling contact fatigue life analysis and simulation of crackpropagation.
(3) Considering the influence of friction coefficient to wheel/rail rolling contact tangentialcharacteristic, the ratcheting finite element model is established. In this model, the functionalfriction coefficient replace conventional constant friction coefficient. The ratcheting analysisfor wheel/rail rolling contact is done by using metal plasticity constitutive model integrated in the nonlinear finite element software-ABAQUS. Based on the ratcheting analysis results, thewheel/rail rolling contact fatigue life analysis is done by using fatigue life prediction model ofJiang-Sehitoglu. The fatigue life analysis results are compared with wheel/rail contact fatigueanalysis results of the Japanese scholar AKAMA M and Swedish scholar Ringsbergrespectively. It is found that the results in this paper are close to the results by Japanesescholars due to wheel/rail material parameters and conditions parameters roughly same tocalculation parameters of Japanese scholar AKAMA M.
(4) The extended finite element method is presented for solving discontinuous mechanicsproblem. It is no need high density mesh refinement to crack tip in solving crack problem andremeshing for crack in simulating crack growth. Based on wheel/rail rolling contact fatigueanalysis, the extended finite element crack model of wheel/rail contact is constructed. Theinfluence analysis of wheel/rail friction coefficient, crack location and size on the contactsurface crack growth are mainly done. The results show that J-integral value is large whenwheel/rail surface crack size of about8mm. It is beyond the fracture toughness of rail materialat room temperature. In this condition, crack propagation is so easy, may lead to lateral fractureof the rail. It is coincide with the results of the field observation.
The existing wheel/rail functional friction coefficient can reflect the real state of thefriction between wheel and rail to a certain extent. However, for high speed wheel/rail, thereare coupling third mediums, such as water, oil, magnetic field. So it is need to conduct morein-depth studies to reveal friction behavior of high-speed wheel/rail and construct moreaccurate functional friction coefficient between wheel and rail. In addition, the wheel/railrolling contact fatigue life and surface crack propagation is also associated with multiplefactors. It is need to systematic study wheel/rail rolling contact surface damage by effectivelycombining test method and the numerical method.
引文
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