Computerized design of modified helical gears finished by plunge shaving

Among the several types of gear shaving operations, plunge shaving is used for finishing gears in mass-production due to the low cost and short machining time. Plunge shaving may be used to apply surface modifications with the purpose of reducing noise and vibration by the predesign of favorable functions of transmission errors, and modify gear tooth surfaces to avoid edge contacts and increase gear endurance, safety, and service life. A new geometry for helical gear tooth surfaces that combine the advantages of gear drives with lineal and localized contacts is proposed and obtained by plunge shaving. The shaver tooth surfaces are conjugated to those of an ideal helical gear with surface modifications. In this way, the to-be-shaved gear and the shaving cutter will be in line contact, and only a radial feed motion of the shaver is needed to generate the required pressure for the shaver to cut the excess of material on the gear tooth surfaces. A numerical example of design illustrates the advantages of the proposed geometry.     

锥齿轮齿根应力有限元模型和分析

从齿轮加工原理出发,利用渐开线和齿根过渡曲线方程生成轮齿的精确齿形,建立2种等效直齿锥齿轮三维轮齿几何模型,研究渐开线直齿锥齿轮的精确建模方法.分别使用h-单元和p-单元分析计算直齿锥齿轮齿根应力,建立直齿锥齿轮三维轮齿齿根应力有限元计算模型和计算基准.计算结果与ISO国标公式比较,证明模型的正确性、精确性和可靠性.     

Modified involute helical gears: computerized design,simulation of meshing and stress analysis

The contents of the paper cover: (i) computerized design, (ii) methods for generation, (iii) simulation of meshing, and (iv) enhanced stress analysis of modified involute helical gears. The approaches proposed for modification of conventional involute helical gears are based on conjugation of double-crowned pinion with a conventional helical involute gear. Double-crowning of the pinion means deviation of cross-profile from an involute one and deviation in longitudinal direction from a helicoid surface. The pinion-gear tooth surfaces are in point contact, the bearing contact is localized and oriented longitudinally, edge contact is avoided, the influence of errors of alignment on the shift of bearing contact and vibration and noise are reduced substantially. The developed theory is illustrated with numerical examples that confirm the advantages of the gear drives of the modified geometry in comparison with conventional helical involute gears.     

An innovative approach to NC programming for accurate five-axis flank milling of spiral bevel or hypoid gears

To transfer power, a pair of spiral bevel or hypoid gears engages. From beginning to end of two tooth surfaces engaging with each other: for their rigid property, they contact at different points; and for their plastic property, they contact at small ellipses around the points. On each surface, the contact line (or called as contact path) by connecting these points and the contact area by joining these ellipses are critical to driving performance. Therefore, to machine these surfaces, it is important to machine the contact line and area with higher accuracy than other areas. Five-axis flank milling is efficient and is widely used in industry. However, tool paths for flank milling the gears, which are generated with the existing methods, can cause overcuts on the contact area with large machining errors. To overcome this problem, an innovative approach to NC programming for accurate and efficient five-axis flank milling of spiral bevel or hypoid gears is proposed. First, the necessary conditions of the cutter envelope surface tangent with the designed surface along a designed line are derived to address the overcut problem of five-axis milling. Second, the tooth surface including the contact line and area are represented using their machining and meshing models. Third, according to the tooth surface model, an optimization method based on the necessary conditions is proposed to plan the cutter location and orientation for flank milling the tooth surface. By using these planned tool paths, the overcut problem is eliminated and the machining errors of contact area are reduced. The proposed approach can significantly promote flank milling in the gear manufacturing industry.     

基于微分进化算法的非对称弧齿锥齿轮约束多目标优化

根据齿轮啮合原理和现代摩擦学理论,建立了以弧齿锥齿轮传动齿面上瞬时接触线方向与相对滑动速度之间夹角的余切值最小、传动总体积最小和齿面诱导法曲率主值最小为目标函数的约束多目标优化设计数学模型。对当前的微分进化多目标优化算法进行了改进,给出了适用于工程领域的微分进化约束多目标优化算法。借助于改进的微分进化多目标优化算法,通过范例对弧齿锥齿轮传动进行两目标和三目标优化设计。分析了齿面上瞬时接触线方向与相对滑动速度之间的夹角及齿面诱导法曲率主值对齿面接触强度和胶合强度的影响。     

齿轮传动的CAD软件

在机械传动装置中,广泛地应用着齿轮传动。外啮合圆柱齿轮、内啮合圆柱齿轮、圆维齿轮和蜗轮蜗杆传动是齿轮传动的基本形式。我们在长期工作研究的基础上,建立了一套CAD软件。该软件可自动进行以上四种传动形式的优化设计,可通过人机交互完成齿轮的结构设计,用有限元分析计算齿轮的强度,并可在绘图机上绘制齿轮的工作图。该软件适用性强、使用方便,经过简单的修改便可用于其它机械产品的CAD。     

螺旋锥齿轮球面渐开线齿面形成原理及推论

从螺旋锥齿轮的精确齿面形状出发,详细地论述了球面渐开线齿面的基本 组成。基于球面渐开线理论在螺旋锥齿轮方面已取得的研究成果,分析并总结其特点与不足, 提出了螺旋锥齿轮的球面渐开线齿面形成原理。并对球面渐开线齿面形成过程中的关键环节 产形线、工作齿廓和球面渐开线齿面的基本方程进行了推导和论述,为其设计及加工提出了 一些方案,以便为螺旋锥齿轮的研究提供理论基础和思路。     

弧齿锥齿轮传动的CAD系统

本文介绍弧齿锥齿轮传动的CAD系统,该系统能自动完成弧齿锥齿轮传动的优化设计、切齿调整计算、接触分析、V-H分析计算、有限元法应力分析以及弧齿锥齿轮工作图的绘制。该系统将弧齿锥齿轮传动的计算机辅助设计(CAD)、辅助制造(CAM)、辅助检验(CAT)及辅助绘图(CAG)集为一体,为弧齿锥齿轮传动提供了一套全新的设计系统。通过在某航空弧齿锥齿轮传动设计中的应用,证实了本系统的有效性。     

An accurate model of high-performance manufacturing spiral bevel and hypoid gears based on machine setting modification

Machine setting modification especially considering the tooth contact performance is always vital to design and manufacture for the spiral bevel and hypoid gears. With the application of new manufacture concepts and advanced design methods, a closed-loop complex model is established to execute the high-performance manufacture. Firstly, an optimization model of machine settings modification considering the residual ease-off is established by correlating the tooth flank represented by universal machine settings. Furthermore, a trust region algorithm with control strategies concerning: (i) double Dogleg algorithm for the iteration step and (ii) updating damping efficient for the trust region radius is employed to obtain the target flank. Finally, a closed-loop measurement-modification-manufacturing (3M) model for high-performance manufacture of the spiral bevel and hypoid gear is established. Where, it mainly describes the accurate machine setting modification considering tooth contact performances. Some numerical examples in practical application can verify the accuracy and performance of the proposed model.     

Generalized concept of meshing and contact of involute crossed helical gears and its application

A general approach for generation and design of standard and non-standard involute crossed helical gears is proposed. The conjugation of gear tooth surfaces is based on application of two generating rack-cutters with a common normal section. The investigation of the geometry is based on a new approach for presentation of the line of action A (the line of points of contact of tooth surfaces). Line A is represented in a plane Π that is tangent to the pinion base cylinder and position of A is determined analytically. Edge contact of tooth surfaces is avoided by limitation of shift of line of action caused by errors Δγ and ΔE of the crossing angle and the shortest distance, respectively. Simulation of meshing and contact is computerized by developed computer program. Enhanced stress analysis approach is proposed. The developed theory is illustrated with numerical examples.     

Static stress analysis of a composite bevel gear using a three-dimensional finite element method

The possibility of using composite materials for power transmission spur gear, from a static strength point of view, have been proved by the authors in their previous study. In this present work an attempt has been made to study the behaviour of composite bevel gear from a static load point of view using a three-dimensional finite element method. The performance of two composite material bevel gears are presented and compared with a carbon steel gear. From a static strength point of view a glass epoxy bevel gear is slightly closer to a carbon steel bevel gear than a boron/epoxy bevel gear; but from a displacement point of view glass/epoxy deviates from that of carbon steel much more than boron/epoxy, unlike the case of a composite spur gear, where boron/epoxy was better both from strength and displacement points of view. Hence from the results it is concluded that composite materials such as boron/epoxy can be very much thought of as a material for power transmission bevel gears.     

A semi-analytical approach to un-deformed chip boundary theory and cutting force prediction in face-hobbing of bevel gears

Rule-of-thumb based design for cutting tools and machining settings in face-hobbing of bevel gears result in cutting tool failures and quality issues. Lack of a virtual machining environment, to efficiently obtain the instantaneous un-deformed chip geometry and predict cutting forces in face-hobbing, causes undesirable production costs in industries. In the present paper, semi-analytical representation of the projection of the un-deformed chip on the rake face of the cutting blades is presented. The proposed approach is drastically fast and more accurate in comparison with numerical methods and can be implemented in a virtual gear machining environment. The cutting system intricate geometry, multi-axis machine tool kinematic chains and the variant cutting velocity along the cutting edge are taken into consideration to obtain the chip geometry efficiently. Then, cutting forces are predicted during face-hobbing by implementing oblique cutting theory using the derived chip geometry and converting face-hobbing into oblique cutting. The proposed methods are applied on two case studies of face-hobbing of bevel gears, and the chip geometry is derived and the cutting forces are predicted.     

New geometry of face worm gear drives with conical and cylindrical worms: generation,simulation of meshing,and stress analysis

New geometry of face worm gear drives with conical and cylindrical worms is proposed. The generation of the face worm gear is based on application of a tilted head-cutter (grinding tool) instead of application of a hob applied at present. The generation of a conjugated worm is based on application of a tilted head-cutter (grinding tool) as well. The bearing contact of the gear drive is localized and is oriented longitudinally. A predesigned parabolic function of transmission errors for reduction of noise and vibration is provided. The stress analysis of the gear drive is performed, the contacting model is designed automatically. The developed theory is illustrated with numerical examples.     

三维环境下高阶椭圆齿轮副的运动仿真

依据非圆齿轮传动特性,确定啮合齿轮在非圆节曲线上的位置及传动关系式,给出了非圆齿轮三维建模设计方法。利用Visual Basic语言对三维软件Solid Edge进行二次开发,实现了三维环境下椭圆齿轮参数化设计及运动仿真,能直观的观察到齿轮副的啮合状况。系统运行效果良好,为非圆齿轮传动三维设计提供了一种方法.     

基于同步压缩-交叉小波变换算法的齿轮故障诊断研究

齿轮超负荷使用或者在不良环境下使用时,容易造成齿轮失效。齿轮的失效形式主要有断齿故障、齿面点蚀、齿轮磨损等,此外齿轮制造过程中也存在固有误差,传统的齿轮故障诊断通常使用振动加速度传感器或者SCADA数据进行处理,但振动加速度传感器与SCADA通常价格昂贵,且会有大量的数据冗余,不便于后期信号处理。本设计拟采用一种同步压缩-交叉小波变换算法,在齿轮故障机理分析的基础上,设计了故障诊断实验装置,对正常齿轮、断齿和磨损情况下的故障特性进行提取,从而对故障进行准确诊断,经验证,该方法诊断准确度高。     

Data-driven bending fatigue life forecasting and optimization via grinding Top-Rem tool parameters for spiral bevel gears

To establish a bridge between grinding tool parameters and loaded tooth fatigue life, an innovative data-driven root flank bending fatigue life forecasting and optimization via Top-Rem tool parameters was proposed for grinding spiral bevel gears. The recent machine settings modification is extended into grinding Top-Rem tool parameters modification in case that geometric accuracy and root bending fatigue life are integrated into a collaborative optimization. The proposed Top-Rem modification includes three key steps: (I) arc-shaped blade, (II) top part, and (III) top fillet part. Then, while root bending stress is determined by using finite element method (FEM)-based simulated loaded tooth contact analysis (SLTCA), data-driven fatigue life forecasting is developed by correlating with the multiaxial fatigue damage model based assessment. Moreover, data-driven bending fatigue life optimization model is established by using Top-Rem tool parameters modification, where the important constraints in target flank determination includes: (i) root overcutting, (ii) geometric accuracy, and, (iii) fatigue life. For high accuracy and efficiency, two different strategies are proposed: (i) the different parameters modification types; and, (ii) sensitivity analysis of grinding Top-Rem tool parameters. Finally, proposed method can verify that bending fatigue life can be significantly improved by modifying the key Top-Rem tool parameters in early stage of the whole life product development for spiral bevel gears.     

Precise Design and Stress Analysis of Straight Conical Gear

1 Introduction Straight conical gears are widely used in power transmission between perpendicular shafts. In the last few decades, there has been a growing interest in conical involute gears. Apart from being frequently used in anti-backlash schemes, they are, according to Mitome, also used as reduction gears[1], miter gears, trimming gears and differential gears. The conical involute gear, which is also called beveloid gear by some authors, is an involute gear with tapered tooth thickness, t…     

Tooth flank modification theory of dual-torus double-enveloping hourglass worm drives

In this paper, the theory of tooth flank modification is enriched and developed for a double-enveloping toroidal worm drive. The goal and significance of the modification are expounded from the point of view of changing the tooth flank configuration for the worm gear pair. It is pointed out that the constant center distance modification, the constant transmission ratio modification, and the combination of the previous two are the convenient and reasonable modification strategies. All the corrected hourglass worm pairs, attained by employing the preceding modification methodology, can be divided into two fundamental types: the type I worm pair and the type II worm pair, from the perspective of the meshing behavior. The division criterion of the worm drive type is moreover provided on the basis of the value range of the modification parameters in this study. The meshing characteristics of the two types of the modified globoidal worm drive are summarized in detail. The results indicate that the type II worm gearing with slight modification should be the preferred style for the double-enveloping toroidal worm drive.     

Research on Design Method of Non-Circular Gear Pair with Double Generating Angles

In order to enhance the bearing capacity of non-circular gear pair, the non-circular gear pair with double generating angles is proposed based on the design idea of unsymmetrical gear with double pressure angles. The tooth profile is designed by generating cutting theory, the pure rolling mathematic model that the center line of unsymmetrical rack roll along non-circular pitch curve is built, the digital model of non-circular gear with double generating angles is created through the second development method of CAD software, and then the drive characteristic and tooth strength are analyzed. The results show that the design method for double generating angles non-circular gear proposed in this paper is feasible, which is significant to improve the bearing capacity of non-circular gear pair.     

双不确定参数作用下双稳态能量采集系统的随机响应分析

为改善纯电动汽车齿轮传动在整个工况范围内的工作性能,提出一种计及负载扭矩和转速工况影响的齿面修形方法.考虑时变啮合刚度、啮合冲击、齿面摩擦激励,建立了系统动力学分析模型.结合轮齿几何接触分析和承载接触分析,采用遗传算法优化获得全工况最优的齿廓、齿向抛物线修形系数,并对比分析了不同修形方案的抑振效果.结果表明：计及工况影响的齿面修形在全工况下的振动加速度均方根都保持在较低水平,说明这一齿面修形策略具有更好的全局抑振效果.