准静态与动态载荷下斜齿轮齿面粘着磨损计算

基于反向圆锥滚子等效接触模型和Archard磨损计算通式,提出了一种适用于标准斜齿轮齿面粘着磨损的计算方法。由时变接触线长百分比和弯-扭-轴耦合动力学模型确定齿面载荷,根据等效接触模型和Hertz接触理论计算齿面压力和滑移距离,求出准静态与动态载荷下的齿面磨损量。通过将主动轮磨损曲线与相关文献结果比较,验证了上述方法的正确性。几何与工作参数对磨损量的影响分析显示,齿根与齿顶处的磨损量较大,且齿根的磨损量大于齿顶,节圆处的磨损量趋近于零;齿轮前端面至后端面,主动轮磨损量逐渐减小而从动轮磨损量逐渐增大;宽齿轮的磨损量沿齿宽渐趋均布。参数分析表明：增大模数、传动比、齿宽或减小扭矩均可降低磨损量,增大螺旋角或改变转速对减小齿面磨损的作用不明显。上述研究对于提高齿轮表面质量与传动性能,对于减磨设计具有一定的参考价值。     

带式啮合介质齿轮传动的磨损仿真分析

带式啮合介质齿轮传动中,齿轮副的接触由高模量的齿轮对接触转化为高模量齿轮与低模量介质带的接触,磨损主要发生在柔性介质带上。应用Archard黏着磨损理论,建立带式啮合介质齿轮传动磨损数学模型,用Solid Works三维建模软件建立带式啮合介质齿轮的实体模型,并对其结构静力学进行分析;根据磨损数学模型和接触应力的分布情况,模拟计算出介质带的磨损量。结果表明:带式啮合介质齿轮传动最大接触应力发生在啮合节点处,弹性应变主要发生在介质带上,啮合节点处应变值最大;介质带的磨损量随载荷和滑动距离的增加而增加,最大磨损量发生在啮合节点处,在齿轮啮合线上不同节点处磨损量略有差距,边缘处磨损量最大。     

Ease-off修形准双曲面齿轮齿面动态抗磨设计与分析

为了改善准双曲面齿轮动态性能、减小齿面磨损提出齿面动态抗磨修形设计与分析方法。小轮修形齿面表示为共轭齿面与法向Ease-off曲面两个矢量的和,Ease-off曲面通过预置抛物线修形参数及几何传动误差参数表达。提出考虑磨损深度影响的齿面承载接触分析（Tooth contact analysis with wear,WLTCA）数值方法,该方法通过承载接触分析（Tooth contactanalysis,LTCA）方法获得啮合刚度及齿面静载荷,在此基础上根据动力学分析获得齿面动载荷,结合Archard磨损公式进一步获得齿面磨损量,将齿形更新时的同时啮合齿对的磨损量叠加到齿对的初始间隙,为磨损后的LTCA计算提供准确的参数,重复以上循环可得到齿形更新后齿面上任一点的磨损深度及次数。以无磨损时法向相对振动加速度均方根最小、齿面磨损量最小进行修形优化获得最优Ease-off曲面;分析齿面磨损与系统动态响应之间的耦合作用。结果表明最优Ease-off齿面主要通过齿廓修形减少了磨损量,有效改善了系统动态响应。该方法充分考虑了齿面修形、磨损、动态响应的耦合性且计算效率较高,为高性能准双曲面齿轮齿面抗磨、减振设计与分析提供理论参考。     

Enhanced friction model for high-speed right-angle gear dynamics

The modeling of elastohydrodynamic lubrication friction and the analysis of its dynamic effect on right-angle gears, such as hypoid and spiral bevel types are performed in the present study. Unlike the classically applied empirical constant coefficient of friction at the contacting tooth surfaces, the enhanced physics-based gear mesh friction model is both spatial and time-varying. The underlying formulation assumes mixed elastohydrodynamic lubrication (EHL) condition in which the division and load distribution between the full film and asperity contact zones are determined by the film thickness ratio and load sharing coefficient. In the proposed time-varying friction model, the calculation of friction coefficient is performed at each contact grid inside the instantaneous contact area that is being subjected to mineral oil lubrication. The effective friction coefficient and directional parameters synthesized from the net frictional and normal contact forces are then incorporated into a nonlinear time-varying right-angle gear dynamic model. Using this model, the effect of friction on the gear dynamic response due to the transmission error and mesh excitations is analyzed. Also, parametric studies are performed by varying torque, surface roughness and lubrication properties to understand the salient role of tooth sliding friction in gear dynamics. The simulation results are included. But experimental verification is needed.     

Analytical Study of Surface Loading and Sliding Velocity of Automotive Hypoid Gears

An experimental and analytical study has been undertaken to determine the lubrication environment of automotive hypoid gears under severe dynamic operating conditions. Results of an experimental investigation of gear loading and an analytical study of gear sliding under laboratory and field operating conditions in both automobiles and trucks are presented. The sliding relationships of four representative gears are discussed and the effects of changes in pinion offset and gear ratio on sliding velocity are studied. Increases in pinion offset and gear ratio both tend to increase the sliding velocity of hypoid gears. The present trends in automobile hypoid gear design are toward greater pinion offset and lower gear ratios. These two average trends are of opposite effect on gear sliding and tend to cancel each other. The sliding velocity of any particular gear set would have changed considerably in recent years if the design changes were primarily in one factor.     

Wear simulation of spur gears

This paper deals with prediction of wear in spur gears, which has been calculated using an approach in which the wear depth on a tooth surface is integrated over time using the Euler integration method. Variations in pressure distribution over the surface have been considered, as well as changes in curvature and surface profile of the teeth as they wear. The paper focuses on the use of an appropriate wear model for simulating wear using calculated conditions between high-performance slow-running lubricated spur gears. A numerical model for prediction of surface interaction of spur gears developed earlier by the authors has been applied as the basis for the simulation of wear using different wear models. Owing to the nature of the wear models, methods of calculating the contact temperature have been investigated for the specific case of interacting gear teeth. It was found that a linear wear model, when compared with a more complex oxidation model and with a model based on adsorption of lubricant molecules, satisfactorily predicts wear. It was also found that it is the geometry of the gears that causes sliding velocity to be the dominant wear-inducing factor, and so determines the general nature of the wear behaviour.     

弧齿锥齿轮双重螺旋法切齿原理及齿面接触分析研究

弧齿锥齿轮双重螺旋法具有高效、可实现干切削的特点,是Gleason制弧齿锥齿轮的先进加工方法。为揭示双重螺旋法的切齿原理,以大轮成形法加工的弧齿锥齿轮双重螺旋法为研究对象,以啮合原理和微分几何学为基础,根据刀盘、机床、工件之间的运动位置关系,利用矢量法、基于齿面3个参考点建立切齿数学模型,推导机床调整参数的计算过程;然后,以齿槽中点作为参考点,修正弧齿锥齿轮副的齿坯几何参数;另外,以小轮产形面方程代替其共轭齿面方程,提出新的齿面失配设计新方法,与传统方法相比简化计算过程。以一对7×43的准双曲面齿轮副为例进行设计计算和切齿加工,齿面接触分析与滚动检查结果验证所提出的双重螺旋法切齿原理的正确性,并根据该切齿原理开发弧齿锥齿轮双重螺旋法的设计软件,为该方法在国内的推广提供理论基础与技术支撑。     

Development and Validation of an Automotive Axle Power Loss Model

This study proposes a methodology to predict power losses of automotive axle units, including both load-dependent (mechanical) and load-independent (spin) loss components. This methodology combines a mechanical hypoid gear mesh power loss model, a new tapered roller bearing mechanical power loss model, a gear drag loss model, and empirical viscous bearing power loss formulae to determine the total power loss of an axle unit. The proposed methodology captures the effects of operating conditions (speed and torque and oil temperature and level), contact surface roughness amplitudes, as well as bearing preload on power loss. The model is employed to simulate published axle efficiency experiments. Direct comparisons between measured and predicted power losses are presented to demonstrate the accuracy of the proposed modeling methodology.     

基于有限元法的准双曲面齿轮时变啮合特性研究

准确计算准双曲面齿轮的时变啮合参数是其系统动力学分析的基础。基于接触有限元分析原理,应用有限元分析软件ABAQUS对齿轮进行加载接触分析(Loaded tooth contact analysis,LTCA),准确计算准双曲面齿轮时变等效啮合参数,包括时变等效啮合点位置、时变等效啮合力作用方向、等效啮合力作用方向上的线位移传动误差和时变等效啮合刚度,并研究转矩大小对时变啮合参数的影响。对比有限元法与经典齿轮接触分析(Tooth contact analysis,TCA)方法求得的传动误差曲线,并对比有限元法计算与加载啮合试验获得的齿面啮合印迹,验证有限元模型和计算的正确性。该方法求得的时变等效啮合参数能够准确体现准双曲面齿轮的时变啮合特性,为进一步研究准双曲面齿轮系统动力学特性提供依据。     

销盘滑动磨损试验的仿真建模研究

以销盘滑动磨损为研究对象,建立了表面微凸体接触特性的物理模型和数学模型,由微凸体接触产生的磨屑推导出销盘滑动磨损仿真模型.采用有限元分析软件ANSYS对半球形微凸体接触应力和变形进行了仿真计算,并用销盘滑动磨损试验数据给予验证,证明了所建立的仿真模型是可行的.研究表明,利用ANSYS求解摩擦学接触问题是准确可靠的,建立正确的磨损仿真模型并辅以参数化设计方法是解决摩擦学仿真问题非常有效的方法.     

A Model for Potential Adhesive Wear Particle at Sliding Inception of a Spherical Contact

A new approach for adhesive wear modeling based on physical principles that eliminate the use of any empirical wear coefficient has been presented. The model predicts dimensionless volume of a potential wear particle that can be detached from an elastic-plastic sphere in contact with a rigid flat at sliding inception. An explicit relation between the dimensionless potential wear volume, material properties, and dimensionless normal load is obtained. An empirical expression for predicting wear coefficient which depends on the normal load and material properties is also presented. Some recommendations for a dynamic modeling to allow actual detachment of wear particle rather than prediction of a potential wear particle are indicated.     

齿轮箱磨粒在铁谱片上的识别特征

介绍了铁谱分析的原理、样品的制备方法和铁谱分析的步骤,概括了齿轮箱齿轮、滚动轴承、滑动接触3种主要摩擦副在磨合磨损、正常磨损、异常磨损(过载、过速、疲劳)3个阶段的磨粒的主要识别特征,包括尺寸、尺寸分布、数量、成分和形貌等。     

准双曲面齿轮运动参数和曲率特性的研究

文中根据机床加工调整参数,推导了准双曲面齿轮的齿面数学表达式,建立了准双曲面齿轮的三维模型,并通过数值迭代方法求解了准双曲面齿轮点接触弹流润滑分析所需的相对运动速度、卷吸速度以及瞬时接触椭圆长短轴方向的曲率等参数,为准双曲面齿轮弹流润滑分析奠定了基础。     

钴基合金的滑动磨损行为及仿真预测

以销—盘滑动模型为对象,研究钴基合金的摩擦磨损行为,预测大尺寸接触对的磨损状况。通过自主研发的磨损试验机获得钴基合金Stellite6材料的磨损量随磨程、速度和压力的变化规律;在试验与模拟相结合的基础上,建立滑动磨损过程的预测模型,实现节点移动和单元更新过程的自动递推,完成磨损各个阶段的动态仿真,并构建实现磨损过程全自动数值仿真的平台,应用于大尺寸耳轴—轴套模型的磨损预测。结果表明,基于销—盘滑动试验,采用有限元法来离散磨损过程,通过非线性计算实现的磨损仿真结果具有较高的可靠性和有效性。     

Characterization of wear scar surfaces using combined three-dimensional topographic analysis and contact resistance measurements

In this paper, a technique for the quantitative characterization of wear scar surfaces, using combined three-dimensional topographical analysis and contact resistance measurements, is introduced. Parameters for the characterization of wear surfaces, developed during sliding of pin-on-disk specimens in oxygen at high temperature, such as wear volume, roughness, average wear depth on the disk specimen, surface coverage by wear-protective oxide layers and their distributions over the wear surface, are presented and calculated. Such analyses provide more effective data for the analysis of wear processes and wear mechanisms.This method has been applied to the analysis of dry reciprocating sliding wear of a nickel-base alloy, N80A, at temperatures to 600°C. It was found that there was usually a difference between the wear rates of the pin and the disk. This difference increased with increase in temperature, the wear of the pin being much less than that of the disk at the higher temperatures. Although the total wear of both the pin and the disk decreased considerably with increase in temperature, the damage to the disk, judged by the wear depth of the scar, was much higher at elevated temperatures than at low temperatures. The roughnesses of the wear surfaces generally increased with increase in temperature. Less than 50% coverage of the scar surfaces by wear-protective oxide layers was sufficient for the severe-to-mild wear transition. However, the distribution of the wear-protective layers over the wear surfaces was non-uniform. Most of them were concentrated near the centre of the scar, along the sliding direction, under the present conditions. These features of the wear scar surfaces were mainly related to the adhesion and compaction of wear debris particles onto the wear surfaces, leading to development of the wear-protective layers at the various temperatures.     

高齿准双曲面齿轮的轮齿加载接触分析

给出了准双曲面齿轮齿加载接触分析的数学模型和加载接触分析的求解方法，计算了高齿准双曲面齿轮和普通齿准双曲面齿轮副的加载接触过程，对比了两种齿轮在不同工况和安装误差条件下的齿面印痕、齿面载荷分布、齿间载荷分配和承载传动误差，证明了高齿准双曲面齿轮副齿面载载体分布、齿间载荷分配和承载传动误差，证明了高齿准双曲面齿轮副齿面载荷分布和齿间载荷的分配合理，接触印痕受安装误差的影响较小，具有较高的强度和较好的动态特性。     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

Experimental Analysis and Wear Prediction Model for Unfilled Polymer–Polymer Sliding Contacts

Lifetime prediction of polymer–polymer contacts is a major challenge. Current design methods stemming from metal contact surfaces lack accuracy because polymers behave differently, especially regarding temperature variations. Experiments were performed on a pin-on-disk setup alternating static and rotating elements. Common unfilled engineering polymers, viz. polyoxymethylene (POM), polypropylene (PP), polyamide 6.6 (PA6.6), and polycarbonate (PC) were tested at ambient and elevated temperatures. Material combinations were analyzed regarding the effects of load, velocity, temperature, and the product of contact pressure and sliding velocity (PV limit). The experimental results show that the PV limit is not predictive for polymer–polymer contacts; rather, each material combination has a critical factor that determines the wear and frictional values and thus the contact’s durability and lifetime. The critical factor is the value of contact pressure or sliding velocity or temperature at which there is sudden increase in wear rate. The experimental results also demonstrate that the application temperature in operation has an important influence on the lifetime. A temperature increase can either be beneficial or have a negative impact depending on the material combination. Resulting from the extensive experimental analysis, a new design method, based on the principle of deformation energy, is proposed. The new model is different from existing models because it includes thermal properties of the materials in contact and it makes use of the Péclet number. Because the proposed model requires only data sheet values and design parameters to predict wear volume, the model improves the support of engineers in designing durable polymer–polymer sliding contacts.     

Geometric design of a face gear drive with a helical pinion

The application of face gear drives, which have been used recently instead of bevel and hypoid gears for helicopter transmission, has resulted in renewed interest in such drives. A helical pinion must be utilized to change the composition of the contact surface freely. In this work, the problem of where to place the pinion with respect to a gear is solved by defining a reference point. The effect of the helix angle on the composition of the surface contact lines is clarified. A geometric design method that recognizes meshing singularity is proposed. Two unique lines on which specific sliding becomes infinite are regarded as design indexes. Results show that the contribution of the surface contact lines changes significantly depending on the helix angle, and the offset distances influence the effective tooth width of the gear.