Coefficient of friction of a starved lubricated spur gear pair

The frictional power loss issue of gear pairs becomes an important concern in both industry and academia due to the requirement of the energy saving and the improvement of power density of gear drives. A thermal starved elastohydrodynamic lubrication model is developed to study the tribological performance of a spur gear pair under starved lubrication conditions. The contact pressure, the film thickness, the temperature rise, the frictional power loss, as well as the coefficient of friction are evaluated by considering the variation of the curvature radius, the sliding/rolling motion, and the load distribution of gear tooth within the meshing period. Effects of lubrication starvation condition, load and speed on the coefficient of friction are studied.

     

WN齿轮传动弹流润滑及接触摩擦效率研究

应用WN齿轮接触摩擦与弹流润滑机制结合的方法进行效率分析.依据WN齿轮副啮合原理,创建该齿轮动力润滑与混合摩擦分析模型,分析了啮合中载荷与弹性接触对油膜厚度的影响,探讨油膜形成机制和承载特性;通过啮合过程中的接触摩擦分析,推导出WN齿轮啮合时动力传动效率计算新方程;分析齿轮运转速度、负载及润滑等对传动效率的影响.结果表明:在高速下WN齿轮的传动效率高于渐开线齿轮而在低速下却相反;旋转速度对传动效率的影响要比载荷的影响更大.通过实例计算和试验分析验证了本方法的有效性.     

Behavior of lubricant fluid film in gears under dynamic conditions

This paper presents a new method for modeling the fluid film lubrication in gears, considering the actual meshing conditions and gear dynamics. The model takes into account both the elastohydrodynamic lubrication (EHL) and the dynamic load between the mating tooth pair. The EHL film is described as a fully flooded elliptical contact.The present approach is validated by means of comparison with other methods found in the literature, in which dynamic effects were neglected. The effect of the gear dynamics on the fluid film is investigated. It is shown that pressure and film thickness are strongly modified by the dynamics of the gear pair.The dependence of the dynamic gear lubrication on dimensionless parameters is investigated: a new dimensionless inertia parameter is added to the standard Moes' parameters. These parameters are useful to describe the lubrication conditions in gear pairs.     

Analysis on Isothermal Elastohydrodynamic Lubrication of Orthogonal Face Gear

Face-gear drives have been applied in aviation transmissions, in particular, helicopter transmissions, and the lubrication characteristics are an important indicator for estimating the load-carrying capacity of face-gear teeth. In order to analyze the lubrication performance of the face gear under load, equations for the contact path of the face gear loaded tooth contact analysis (LTCA) were established on the basis of the load equivalent error of alignment (LEEA) and the load distribution among the teeth was calculated. Then a method for calculating the contact area and tooth surface velocity of face-gear drives was studied. Face-gear isothermal elastohydrodynamic lubrication (EHL) dimensionless equations are presented. A multigrid algorithm was used to complete the solution of the minimum film thickness and film pressure of face-gear drives. The lubricant film thickness and film pressure variation in the mesh cycle are expressed using example calculations that provide a theoretical basis for face-gear lubrication design.     

含侧隙齿轮副的动载荷分析

以振动理论为基础，提出一种考虑齿轮拍击振动的齿轮动载荷的数值计算方法。建立计算动载荷的齿轮冲击模型，在模型中考虑了齿轮正、反冲击时实际的啮合刚度，并给出啮合柔度的计算方法。分析在考虑静态传递误差、啮合刚度、侧隙、摩擦力及外部扭矩变化等多种激励时，作用在轮齿上的动态载荷以及整个齿轮上的综合动态载荷的计算公式。最后通过实例分析作用在轮齿上的动态载荷、综合动态载荷变化规律以及相关激励参数对动态载荷的影响。     

摩擦作用下周期双参变激励齿轮系统非线性振动响应研究

研究了周期双参变激励齿轮系统在摩擦作用下的动力学响应,建立了考虑轮齿时变啮合刚度和齿间摩擦的单自由度扭转非线性振动模型,研究了摩擦因子、重合度、惯量比、刚度因子、阻尼因子、载荷分配系数等参数对齿轮系统非线性振动响应的影响。研究结果表明:摩擦对周期双参变激励齿轮系统非线性振动有重要的影响。     

Transient thermo‐elastohydrodynamic lubrication of gear teeth

During a gear mesh cycle, load, rolling and sliding velocities, curvature, and temperature change rapidly. In this paper, a transient, thermo‐elastohydrodynamic lubrication model is presented that has been used to study the lubrication parameters at 250 contact points along the path of a contact. The working flanks were assumed to be smooth. The line load was calculated at every contact point, using the finite‐element method. Dynamic loading was not considered. The steady‐state temperature field of the working flanks was used to obtain the surface temperature at the inlet of each contact point, determined by an experimental‐analytical method presented previously. In this model, the lubricant is considered to follow the Ree‐Eyring constitutive equation. The influences of both pressure and temperature on density, thermal conductivity, and specific heat of the lubricant are also taken into account. Results are presented for an FZG type A gear pair lubricated with an FVA No. 4 reference oil; these include film shape, pressure and temperature distributions, as well as friction coefficient.     

变位斜齿轮的热弹流润滑数值分析

运用斜齿轮有限长线接触数学模型,对渐开线变位斜齿轮进行热弹流润滑数值分析;分析正变位、负变位、等变位3种变位系数下斜齿轮的热弹流润滑状态,计算不同变位系数下斜齿轮的油膜压力、膜厚及温升,并与标准斜齿轮传动计算结果进行比较。结果表明:热弹流润滑条件下,斜齿轮的变位对油膜压力影响不大,对膜厚有较大的影响;变位斜齿轮正传动时,随变位系数的增大,压力减小,膜厚增大;沿最长接触线时,与标准斜齿轮的传动相比,变位斜齿轮正变位系数下压力最小、膜厚最大、温度最低,因此,选择正变位系数更有利于斜齿轮的润滑。     

Study on Starved Lubrication Performance of a Cycloid Drive

The lubrication performance of cycloid drives affects the dynamic characteristics, mechanical efficiency, and contact fatigue behavior. Starved lubrication performance of a cycloid gear drive is studied using a numerical thermo-starved elastohydrodynamic lubrication model. The parameter of the inlet oil film thickness is chosen to represent the starvation degree. Effects of the inlet film thickness on the central film thickness, friction coefficient, frictional power loss, starting position of the effective film thickness, and lubrication efficiency are investigated. The optimum inlet film thickness is defined and is calculated under different rolling–sliding ratios, speeds, and loads. Finally, the optimum inlet film thickness during the meshing process of a cycloid drive is calculated.     

核电循环泵行星齿轮热弹流润滑研究

核电齿轮箱的良好润滑性能是核电循环泵可靠运行的重要保障,充分考虑齿面形貌和齿廓修形等因素对内/外啮合齿轮副的影响是准确评估其润滑特性的前提。建立典型工况下核电循环泵行星传动系统斜齿轮热弹流润滑模型,首先将斜齿轮副的啮合状态几何等效为圆锥滚子的接触问题,然后考虑斜齿轮接触变形和齿廓偏差,计算得到内/外啮合齿轮副接触区域不同位置的油膜厚度、承载压力、摩擦应力和闪温等参数。考虑齿面磨合作用,采用移动平均滤波方法对未经磨合的初始形貌进行光滑处理,分析了齿面形貌对润滑行为的影响,最后采取齿廓修形改善润滑特性。结果表明：粗糙度和齿廓修形均会对润滑特性产生明显的影响,齿面粗糙形貌会造成油膜厚度减小,进而影响其润滑特性,弱化润滑油膜的承载能力;通过齿廓修形可以改善齿轮啮合边界处的几何过渡,降低该区域的应力集中和表面温度,从而明显改善啮合线终端的润滑状态。     

Sliding friction effect on dynamics of crossed beveloid gears with small shaft angle

We propose a new method of incorporating the gear sliding friction model and loaded mesh model into an analytical nonlinear crossed beveloid geared vibration model to evaluate the mesh and dynamic characteristics. A 3-dimensional quasi-static loaded tooth contact analysis is employed and the derivation of distributed sliding friction forces and synthesis of frictions to the effective form is applied in the nonlinear dynamic analysis. Using the proposed method, the excitation effects of frictions on tooth mesh and dynamic responses at different load levels are found and investigated. The analysis results show that the existence of sliding frictions between the engaged teeth indeed tends to affect the contact pattern, normal load distribution and maximum contact pressure, but it is unsubstantial. The torque load effect of friction is found with greater degressive influence on mesh stiffness and transmission error at heavier load case. The magnitude and directionality of sliding friction on effective total engaged teeth exhibit less obvious variations than on each tooth due to the contributions from multiple teeth effect. Also, friction excitations tend to decrease the dynamic mesh force slightly for both light and heavy load cases.     

渐开线直齿轮瞬态微观热弹流润滑分析

考虑了瞬态效应、轮齿表面油膜温度场和轮齿表面纵向粗糙度等因素,对渐开线直齿圆柱齿轮的弹流润滑问题进行研究。载荷由双齿或单齿承担,根据实际载荷谱简化的轮齿载荷曲线,利用压力求解的多重网格法和弹性变形求解的多重网格积分法以及温度求解的逐列扫描技术,得到渐开线直齿轮瞬态微观热弹流润滑问题的完全数值解,讨论了轮齿间油膜的厚度、压力、温度沿啮合线的变化规律。数值计算结果表明,齿轮表面纵向粗糙度对轮齿间油膜的压力、膜厚、温升都有较大影响。考虑轮齿表面粗糙度后,油膜压力和温升明显增大,并随压力的增加而影响越来越显著,粗糙峰使油膜压力分布和温度分布产生振荡,轮齿表面的粗糙峰对摩擦因数影响较小,摩擦因数和最高温升在节点两侧最大。     

乏油工况下斜齿轮热弹流润滑特性研究*

建立斜齿轮的乏油热弹流润滑模型,并讨论供油量、转速和齿面粗糙度对润滑性能的影响。结果表明:乏油工况下增大入口区供油量,润滑区的膜厚增大而摩擦因数、温升和次表面应力幅值降低;随着供油量增大,乏油润滑特性逐步趋于全膜润滑状态下特性;随着转速升高,润滑膜厚增大但幅度有限,相应温度场增大和次表面应力场增大;齿面粗糙度会使油膜压力出现剧烈的波动,在油膜压力峰位置的次表面会出现应力集中。     

齿轮几何参数对齿轮传动弹流润滑性能的影响

本文采用热弹性流体动力润滑理论对渐开线直齿轮传动进行热弹流数值分析;计算分析了在给定传动比和中心距条件下,齿轮模数、齿数以及变位系数等几何参数对齿轮润滑性能的影响,获得了齿轮传动沿啮合线的中心油膜厚度、压力、温度以及轮齿表面摩擦系数等分布规律。     

Fluid-solid interaction model for hydraulic reciprocating O-ring seals

Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators,especially in high parameter hydraulic systems.Only elastic deformations of hydraulic reciprocating seals were discussed,and hydrodynamic effects were neglected in many studies.The physical process of the fluid-solid interaction effect did not be clearly presented in the existing fluid-solid interaction models for hydraulic reciprocating O-ring seals,and few of these models had been simultaneously validated through experiments.By exploring the physical process of the fluid-solid interaction effect of the hydraulic reciprocating O-ring seal,a numerical fluid-solid interaction model consisting of fluid lubrication,contact mechanics,asperity contact and elastic deformation analyses is constructed with an iterative procedure.With the SRV friction and wear tester,the experiments are performed to investigate the elastohydrodynamic lubrication characteristics of the O-ring seal.The regularity of the friction coefficient varying with the speed of reciprocating motion is obtained in the mixed lubrication condition.The experimental result is used to validate the fluid-solid interaction model.Based on the model,The elastohydrodynamic lubrication characteristics of the hydraulic reciprocating O-ring seal are presented respectively in the dry friction,mixed lubrication and full film lubrication conditions,including of the contact pressure,film thickness,friction coefficient,liquid film pressure and viscous shear stress in the sealing zone.The proposed numerical fluid-solid interaction model can be effectively used to analyze the operation characteristics of the hydraulic reciprocating O-ring seal,and can also be widely used to study other hydraulic reciprocating seals.     

链条套筒与销轴铰链副冲击载荷-往复运动的弹流润滑数值模拟

数值模拟链传动中销轴与套筒之间的定载荷和变载荷弹流润滑接触问题,套筒相对于销轴做纯滑动往复运动。定载荷是假定往复运动过程中载荷恒定不变;变载荷是假定链节在啮入和啮出链轮过程中存在的冲击载荷按正弦函数规律变化。比较在定载荷和变载荷加载条件下线接触往复运动工况的弹性润滑油膜变化情况,分析在动载荷加载条件下不同行程长度对弹性流体动力润滑特性的影响。研究发现,动载荷对油膜的压力、膜厚影响较大:随着动载荷的增加,油膜中压力急剧增大,膜厚减小;但加载方式对摩擦因数的影响不大;在相同的加载方式下,随着行程长度的增加,油膜压力减小,中心膜厚和最小膜厚显著增加。     

Application of Transient Elastohydrodynamic Lubrication Analysis for Gear Transmissions

Transient elastohydrodynamic lubrication theory which deals with the lubrication of gear transmission is presented. A numerical procedure was developed to solve the governing equations for the transient EHL with variable load, curvature, and rolling velocity along the line of action. The compressibility of the fluid is taken into consideration. Results are presented for the pressure distribution and the film thickness successively along the line of action as a function of time. A parametric study was conducted to investigate the effects of geometry factors on the lubrication behavior of a gear transmission. Parameters of interest are gear ratio, central distance, gear tooth module, and profile shift of gear tooth. The results of extensive simulations for gear tooth lubrication show that the equivalent curvature radius of gear teeth plays an important role on the EHL film formation.     

微观形貌表征对直齿轮跑合弹流润滑的影响

高斯分布粗糙度函数相比余弦粗糙度函数,能更贴近地描述跑合前齿面粗糙轮廓曲线幅度分布。研究高斯分布的齿面粗糙度对齿轮跑合过程中轮齿间油膜压力和膜厚的影响,探讨瞬态效应对轮齿润滑的影响,利用多重网格技术求得齿轮瞬态微弹流润滑的完全数值解。结果表明：采用高斯分布粗糙度时油膜压力变化明显,更符合啮合点出现粗糙峰而形成的轻微冲击对轮齿间油膜的影响,而采用余弦粗糙度时油膜压力则变化相对比较缓和;采用高斯分布粗糙度的最大油膜压力明显大于采用余弦粗糙度的最大油膜压力,故按照余弦粗糙度计算的最大油膜压力与实际最大油膜压力可能有较大偏差。     

考虑系统变形的电驱动桥齿轮啮合效率研究

传动效率是电驱动桥重要性能指标之一,实际使用条件下,由于齿轮、轴、轴承以及壳体等部件的负载变形,齿轮副之间存在啮合错位。为了准确预测电驱动桥传动系的啮合效率,提出了一种考虑系统变形的电驱动桥齿轮啮合效率计算方法。首先基于传动系等效啮合模型,计算不同载荷工况下传动系每个齿轮副之间的啮合错位量,采用考虑摩擦的齿轮加载接触分析方法(FLTCA)和混合润滑摩擦系数模型对齿轮副的齿面接触力和齿面摩擦系数分布进行计算,得到系统功率损失及啮合效率。然后,与商用有限元软件计算结果进行对比,验证了计算方法的准确性。最后,针对不同载荷工况和不同转速分析了考虑和不考虑系统变形的系统啮合效率,结果表明：随着转矩的增加,系统变形增大,齿轮副之间的错位量增加,导致齿轮副之间发生偏载,齿面摩擦系数增加,系统啮合效率呈下降趋势。