油润滑渐开线斜齿轮摩擦动力学特性及疲劳寿命预估
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摘要
渐开线斜齿轮因传动平稳、承载能力强被广泛应用于高速重载传动。随着传动系统对转速和转矩的大幅度提高，斜齿轮传动的啮合平稳性、效率特性及疲劳寿命等问题成为高速重载齿轮研究的重点和热点。在高速大功率运行工况下，齿轮传动表现出强非线性动力学特征。齿面在大范围变滑滚比状态下作高速剪切运动并产生瞬时高温，导致润滑油粘度大幅度降低，油膜厚度显著减小，润滑状态复杂多变。本文全面考虑了渐开线斜齿轮在混合润滑状态下的弹流润滑特性、热效应以及摩擦学特性与动力学行为的耦合关系，建立了齿轮的摩擦动力学模型；考虑残余应力和硬度梯度的影响以及裂纹在不同阶段的生长机制建立了齿轮接触疲劳寿命的全过程预估模型。
本文首先建立了啮合接触区二维有限长线接触混合弹流润滑模型，基于最小弹性势能原理确定了低速稳态工况的载荷分布规律，并对弹流润滑模型进行数值求解，获得了接触区的稳态润滑特性。在求解过程中，采用Reynolds方程的统一差分格式解决了混合弹流润滑中粗糙峰接触区的判定问题，应用多重网格积分法加速了表面弹性变形的计算，并对多重网格法和Gauss-Seidel松弛迭代法联立求解，获得了接触区的润滑特性，揭示了齿面粗糙峰的峰值、方向相关特征和分布密度等因素对润滑特性的影响规律。
当齿轮在高速大转矩工况下工作时，由于润滑油膜内部的高剪切作用以及混合润滑状态下粗糙峰间的摩擦剪切作用，接触区将产生大量的热。在弹流润滑状态下，入口区的剪切热将降低润滑剂的粘度，并导致由卷吸速度带入接触区的油量减少，从而使油膜厚度减薄。为了对齿面进行热分析，将能量方程、移动点热源法和热流分配系数相结合，建立了齿面温升模型，并与弹流润滑方程相耦合，通过求解获得了油膜中层温升和两齿面的温升分布特征，进而揭示了热流在齿面不同位置的传导规律。
在实际运转中，尤其在高速工况下，由于齿形和装配误差的存在，以及油膜的瞬态挤压效应，齿轮啮合副在运动过程中将不可避免地产生动态传递误差，进而引起载荷冲击和振动。为了深入剖析润滑特性与动力学行为的耦合关系，综合考虑啮合刚度的时变特性、油膜瞬态挤压效应，齿面形貌特征以及摩擦转矩对动力学行为的影响，建立了渐开线斜齿轮的摩擦动力学模型。在数值求解过程中，建立了油膜变形量的解析模型，实现了动力学方程与弹流润滑方程的解耦，以相对线位移满足啮合周期性的假设为依据，确定了动力学方程的边界约束条件。对摩擦动力学模型进行迭代求解，获得了啮合过程中动态啮合力的变化特征以及接触区油膜压力和温升分布的动态变化过程，揭示了动态工况下斜齿轮接触区的润滑规律。
从齿轮失效形式来看，点蚀、剥落等接触疲劳失效是最常见的失效形式，其失效机理较为复杂，与基体材料的晶体组织结构、材料缺陷以及局部应力分布有关。本文针对渗碳淬火齿轮的表面材料属性，考虑残余应力和硬度梯度的影响，以次表面最大剪切应力为评价参数，基于风险疲劳累积理论建立了裂纹萌生寿命模型，用以预测沿齿面深度方向微裂纹的萌生位置和形核寿命。在裂纹扩展寿命模型中，考虑裂纹在晶粒内部的非线性扩展规律以及相邻晶粒间的非连续扩展特征，建立了短裂纹扩展模型。综合考虑疲劳裂纹扩展速率的不同阶段，建立了长裂纹扩展的统一方程，进而完成了对齿轮接触疲劳寿命的预估。
Helical gears are widely employed in high-power transmission due to the advantage ofsteady operating performance and heavy-load capability. With the increasing requirementfor high speed and heavy load, the meshing performance, high efficiency and fatigue life ofinvolute gear become critical and gradually are focused on by many researchers. Under thecondition of high speed and power, the gear tooth exhibits strong non-linear behaviors. Dueto the high shear effect of sliding velocity, amount of heat generates from tooth surface,which greatly reduces the viscosity of lubricant and leads to more complicated lubricatingcondition. Therefore, the author aims to build up a tribo-dynamic model that covering thecoupled influences of elastohydrodynamic lubrication (EHL) characteristics, the thermaleffects and dynamic behaviors. Based on this pressure-solving model, a new fatigue lifemodel is proposed including the factors of residual stress, the hardness gradient and thecrack growing process in different propagation stage.
First, a two-dimensional finite line contact EHL model is built and a steady model ofthe non-uniform load distribution is proposed for helical gear based on the minimum elasticpotential energy criterion, which is combined with the mixed EHL to obtain the film shapeand pressure distribution in contact area. In numerical solution, a unified discrete formationis established to determine the asperity contact region, and the multilevel integrationmethod is introduced to speed up the calculation of surface simultaneously. Besides, theGauss-Seidel iteration and multilevel method are used to obtain the lubricatingcharacteristics. Accordingly, the influence disciplinarianof asperity roughness, direction anddensity on local pressure and film distribution are revealed.
When the gear is working in high speed or heavy torque conditions, the high shearbehaviors of oil film and asperity frictions in contact region will generate amount of heat.Under the condition of elastohydrodynamic lubrication, the shear heating effect at inlet willdecrease the viscosity of oil film, which would lead to less volume of lubricant beingentrained by rolling velocity. Consequently, the film thickness becomes thinner. Therefore,the energy equation is combined with moving point heat source method using the heatpartition coefficient to obtain the temperature distribution in mid-layer film and tooth surfaces. Accordingly, the heat transferring mechanism in different meshing position isanalyzed.
Due to the profile and assembly error, the dynamic transmission error and loadingimpact are unavoidable during rotating process especially under high speed conditions. Todiscover the coupled relationship between the lubricating performance and dynamicbehaviors, a tribo-dynamic model is built up considering the influences of time-varyingmeshing stiffness, the transient film squeezing effect, the surface topography and frictiontorque. In numerical solution, the film temperature is taken as the most outer iterative cycle.In order to uncouple the dynamic motion equation and the EHL model, an analyzed modelof film elastic deformation is proposed to simplify the calculation of film stiffness. Besides,based on the assumption that the relative displacement satisfies the periodicalboundarycondition, the dynamic meshing force is solved. Finally, the solved dynamic pressure andtemperature in contact region are obtained in dynamic model.
In terms of the gear failures, the contact failures such as pitting and case crushing aremost common forms. The contact failure occurs at the spot where either the material defectsor shear stress peak exists. The maximum shear stress in subsurface is employed by authorto evaluate the fatigue life base on the material inherent properties. Crack initiation modelfor gear contact failure is built according to the risk accumulation theory. In the modelingof short crack propagation, the non-linear and discontinuouscharacteristics are taken intoaccount. Besides, a unified equation for long crack propagation covering various crackswith different scales is proposed to predict the whole fatigue life of gear pair. Consequently,the whole contact fatigue life is predicted by combining the three parts of the fatigue life indifferent stage.
本文首先建立了啮合接触区二维有限长线接触混合弹流润滑模型，基于最小弹性势能原理确定了低速稳态工况的载荷分布规律，并对弹流润滑模型进行数值求解，获得了接触区的稳态润滑特性。在求解过程中，采用Reynolds方程的统一差分格式解决了混合弹流润滑中粗糙峰接触区的判定问题，应用多重网格积分法加速了表面弹性变形的计算，并对多重网格法和Gauss-Seidel松弛迭代法联立求解，获得了接触区的润滑特性，揭示了齿面粗糙峰的峰值、方向相关特征和分布密度等因素对润滑特性的影响规律。
当齿轮在高速大转矩工况下工作时，由于润滑油膜内部的高剪切作用以及混合润滑状态下粗糙峰间的摩擦剪切作用，接触区将产生大量的热。在弹流润滑状态下，入口区的剪切热将降低润滑剂的粘度，并导致由卷吸速度带入接触区的油量减少，从而使油膜厚度减薄。为了对齿面进行热分析，将能量方程、移动点热源法和热流分配系数相结合，建立了齿面温升模型，并与弹流润滑方程相耦合，通过求解获得了油膜中层温升和两齿面的温升分布特征，进而揭示了热流在齿面不同位置的传导规律。
在实际运转中，尤其在高速工况下，由于齿形和装配误差的存在，以及油膜的瞬态挤压效应，齿轮啮合副在运动过程中将不可避免地产生动态传递误差，进而引起载荷冲击和振动。为了深入剖析润滑特性与动力学行为的耦合关系，综合考虑啮合刚度的时变特性、油膜瞬态挤压效应，齿面形貌特征以及摩擦转矩对动力学行为的影响，建立了渐开线斜齿轮的摩擦动力学模型。在数值求解过程中，建立了油膜变形量的解析模型，实现了动力学方程与弹流润滑方程的解耦，以相对线位移满足啮合周期性的假设为依据，确定了动力学方程的边界约束条件。对摩擦动力学模型进行迭代求解，获得了啮合过程中动态啮合力的变化特征以及接触区油膜压力和温升分布的动态变化过程，揭示了动态工况下斜齿轮接触区的润滑规律。
从齿轮失效形式来看，点蚀、剥落等接触疲劳失效是最常见的失效形式，其失效机理较为复杂，与基体材料的晶体组织结构、材料缺陷以及局部应力分布有关。本文针对渗碳淬火齿轮的表面材料属性，考虑残余应力和硬度梯度的影响，以次表面最大剪切应力为评价参数，基于风险疲劳累积理论建立了裂纹萌生寿命模型，用以预测沿齿面深度方向微裂纹的萌生位置和形核寿命。在裂纹扩展寿命模型中，考虑裂纹在晶粒内部的非线性扩展规律以及相邻晶粒间的非连续扩展特征，建立了短裂纹扩展模型。综合考虑疲劳裂纹扩展速率的不同阶段，建立了长裂纹扩展的统一方程，进而完成了对齿轮接触疲劳寿命的预估。
Helical gears are widely employed in high-power transmission due to the advantage ofsteady operating performance and heavy-load capability. With the increasing requirementfor high speed and heavy load, the meshing performance, high efficiency and fatigue life ofinvolute gear become critical and gradually are focused on by many researchers. Under thecondition of high speed and power, the gear tooth exhibits strong non-linear behaviors. Dueto the high shear effect of sliding velocity, amount of heat generates from tooth surface,which greatly reduces the viscosity of lubricant and leads to more complicated lubricatingcondition. Therefore, the author aims to build up a tribo-dynamic model that covering thecoupled influences of elastohydrodynamic lubrication (EHL) characteristics, the thermaleffects and dynamic behaviors. Based on this pressure-solving model, a new fatigue lifemodel is proposed including the factors of residual stress, the hardness gradient and thecrack growing process in different propagation stage.
First, a two-dimensional finite line contact EHL model is built and a steady model ofthe non-uniform load distribution is proposed for helical gear based on the minimum elasticpotential energy criterion, which is combined with the mixed EHL to obtain the film shapeand pressure distribution in contact area. In numerical solution, a unified discrete formationis established to determine the asperity contact region, and the multilevel integrationmethod is introduced to speed up the calculation of surface simultaneously. Besides, theGauss-Seidel iteration and multilevel method are used to obtain the lubricatingcharacteristics. Accordingly, the influence disciplinarianof asperity roughness, direction anddensity on local pressure and film distribution are revealed.
When the gear is working in high speed or heavy torque conditions, the high shearbehaviors of oil film and asperity frictions in contact region will generate amount of heat.Under the condition of elastohydrodynamic lubrication, the shear heating effect at inlet willdecrease the viscosity of oil film, which would lead to less volume of lubricant beingentrained by rolling velocity. Consequently, the film thickness becomes thinner. Therefore,the energy equation is combined with moving point heat source method using the heatpartition coefficient to obtain the temperature distribution in mid-layer film and tooth surfaces. Accordingly, the heat transferring mechanism in different meshing position isanalyzed.
Due to the profile and assembly error, the dynamic transmission error and loadingimpact are unavoidable during rotating process especially under high speed conditions. Todiscover the coupled relationship between the lubricating performance and dynamicbehaviors, a tribo-dynamic model is built up considering the influences of time-varyingmeshing stiffness, the transient film squeezing effect, the surface topography and frictiontorque. In numerical solution, the film temperature is taken as the most outer iterative cycle.In order to uncouple the dynamic motion equation and the EHL model, an analyzed modelof film elastic deformation is proposed to simplify the calculation of film stiffness. Besides,based on the assumption that the relative displacement satisfies the periodicalboundarycondition, the dynamic meshing force is solved. Finally, the solved dynamic pressure andtemperature in contact region are obtained in dynamic model.
In terms of the gear failures, the contact failures such as pitting and case crushing aremost common forms. The contact failure occurs at the spot where either the material defectsor shear stress peak exists. The maximum shear stress in subsurface is employed by authorto evaluate the fatigue life base on the material inherent properties. Crack initiation modelfor gear contact failure is built according to the risk accumulation theory. In the modelingof short crack propagation, the non-linear and discontinuouscharacteristics are taken intoaccount. Besides, a unified equation for long crack propagation covering various crackswith different scales is proposed to predict the whole fatigue life of gear pair. Consequently,the whole contact fatigue life is predicted by combining the three parts of the fatigue life indifferent stage.
引文
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