Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

Tooth surface error correction of hypoid gears machined by duplex helical method

In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.

Virtual System Solution of CNC Machine for Spiral Bevel and Hypoid Gears

A virtual computerized numerical control C CNC） processing system is built for spiral bevel and hypoid gears. The pre-designed process of the solution to locate the way of realization is investigated. A kind of combined programming method and principle of solid modeling are chosen. Multienvironmental programming thought and the inter-connected mechanisms between different environments are applied in the proposed system. The problems of data exchange and compatibility of modules are settled. Environment of the system is founded with object oriented programming thought. AutoCAD is located as the graphic environment. Matlab is used for editing the computation module. Virtual C ＋＋6.0 is the realization environment of the main module. Windows is the platform for realizing the multi-environmental method. Through establishing the virtual system based windows message handling mechanism and the component object model, the application of multienvironmental programming is realized in the manufacture system simulation. The virtual gear product can be achieved in the accomplished software.

NC METHOD FOR GENERATION OF CONJUGATING HYPOID GEARS BASED ON NC’S FLEXIBILITY

It is known that manufacture of hypoid gears is difficult and complicated,the reason lies on the limitation of traditional mechanical machine tools. With the development ofNC machine tools, there should be new ways of cutting this kind of gear. Therefore, an idea togenerate gears with conjugating tooth surfaces is proposed, based on the 'flexibility'characteristic of NC that means various motions, in a sense, can be performed, arbitrarily on NCmachine tools. Using this method, the direction of the contact path on tooth surfaces can becontrolled, and also, theoretically, the generated tooth surfaces can transmit motion at specifictransmission ratio curve.

Application and dynamical performance simulation of tooth surface measured data of hypoid gear

The tooth surface shape of hypoid gear is very complicated, and tooth surface accuracy of hypoid gear can be measured by using the latticed measurement and scanning measurement. Advantages and disadvantages of the two measurement patterns are compared and application of their measurement data on hypoid gear＇s quality management is analyzed. How to use these measurement data to simulate the dynamical performance of hypoid gear is researched, and the intelligent predicton of the dynamical performance indexes of contact spot, root stress, vibration exciting forces and load distribution and hertz contact stress on the tooth surface are carried out. This research work has an important guiding sense to design and ma- chine hypoid gear with low vibration and noise.

NEW DESIGN METHOD FOR HYPOID GEARS

A digital model is presented for the purpose of design, manufacture and measurement of hypoid gear, based on the non-uniform rational B-spline surface （NURBS） method. The digital model and the function-oriented active design technique are combined to form a new design method for hypoid gears. The method is well adaptable to CNC bevel gear cutting machines and CNC-controlled gear inspection machines, and can be used to create the initial machine tool cutting location data or program measurement path. The presented example verifies the method is correct.

Accurate Modeling of the Spiral Bevel and Hypoid Gear with a New Tooth Profile

Distinguishing with traditional tooth profile of spiral bevel and hypoid gear, it proposed a new tooth profile namely the spherical involute. Firstly, a new theory of forming the spherical involute tooth profile was proposed. Then, this theory was applied to complete parametric derivation of each part of its tooth profile. For enhancing the precision, the SWEEP method used for formation of each part of tooth surface and G1 stitching schema for obtaining a unified tooth surface are put forward and made the application in the accurate modeling. Lastly, owing to the higher accuracy of tooth surface of outputted model, it gave some optimization approaches. Given numerical example about the model can show that this designed gear with spherical involute tooth profile can achieve fast and accurate parametric modeling and provide a foundation for tooth contact analysis （TCA） in digitized design and manufacture.

TOOTH CONTACT FINITE ELEMENT ANALYSIS OF SPIRAL BEVEL AND HYPOID GEARS

A very useful new method of tooth contact finite element analysis(TCFEA) for spiralbevel and hypoid gears is presented, combines 3-d finite element contact stress analysis withLTCA (Loaded Tooth Contact Analysis). The TCFEA uses mixed finite element method to ana-lyze the 3-d contact stress. The related formulas are derived and an efficient analyzing method asseveral pairs of teeth in contact occurs is presented, which greatly reduce the computationalamount. It is of great significance that the tooth stress. geometry. contact condition and load areall considered in the same model. Finally the related experimental results are used to verify thesolution of TCFEA .

Evaluation of Important Factors Affecting Quench Distortion of Carburized Hypoid Gear with Shaft by Using Computer Simulation Methods

To minimize quenching distortion and dispersion, carburizing and quenching process conditions must be optimized; this includes the parts racking design used for quenching. We investigated some factors affecting carburized quenching distortion with an experiment using a hypoid gear having a shaft and with numerical simulation methods. The experimental results and those obtained from simulation were generally in agreement. Focusing on the surface temperature distribution in the gear, we studied quenching distortion characteristics in terms of changes in tooth profile and helix deviation. In our experiments, distortions occur during quenching in 373 K oil after austenitized temperature treatments conducted with various attitudes. We calculated the distortions by simulating the carburized oil-quenching process for the hypoid gear. Our results show large differences between the cooling rates of the tooth toe, middle section, and heel edges, and these greatly influence the change in tooth profile and helix deviation. We found that reducing the differences in temperatures on the gear surfaces during quenching is most important for minimizing the quench distortion of the hypoid gear.

Numerical Simulation of the Churning Power Losses in the Automotive Hypoid Gear Reducer

Improving vehicle transmission efficiency and reducing vehicle fuel consumption is currently one of the main objectives in the automotive field. Reducing gear churning power losses has significant influence on the decreasing vehicle fuel consumption. Based on the two phase flow theory, a 2D two-phase model of the simplified hypoid gear is established to predict the churning losses in different conditions, the VOF method is introduced to track the volume fraction of the free surface, a standard k-ε model is also built to calculate complex turbulence. The oil distributions at the different rotational speed, the different immersion depth and the different viscosity as well as the churning losses of the hypoid gear are obtained and discussed in detail. In general, the churning power losses increase with the increase of the speed, the immersion depth and the viscosity, while the rotational speed shows the greatest influence on the churning losses. It is hoped that this investigation will be helpful in automotive industry applications.

Parametric relationship between hypoid gear teeth and accurate face-milling cutter

The cutter systems of hypoid gear cutting machines contain groups of inside and outside blades.In these cutter systems,the side cutting edges of the blades machine the convex and concave gear teeth while rotating about the cutter rotation axis.The side cutting edges lay on the rake face formed through the blade,rake,and relief angles;hence,the normal cross-section of the cutter swept surface forms hyperboloid gear teeth.Using the accurate geometry of the cutter system,a relationship between the pressure and spiral angles of the gear tooth and the parameters of the cutter system is developed for the FORMAT machining of a hypoid gear.A new parameterization of the gear tooth surfaces is introduced to determine these angles for the accurate gear tooth by the accurate cutter system.A numerical example with different cutter systems and blade parameters is presented,demonstrating the effects of rake and relief angles over the pressure and spiral angles on mea n point projections and gear tooth surface.Finally,the change in pressure and spiral angles with respect to the rake and relief angles are plotted,and the results are analyzed.Finally,it is concluded that the pressure and spiral angles are changed up to a few seconds of a degree in the operating area of the tooth with the change in the back and side rake angles.The side relief angle exhibited little or no effect over the geometry of the gear tooth.

双重螺旋法准双曲面齿轮啮合性能研究

针对采用双重螺旋法(全工序法)加工的准双曲面齿轮副,运用数值分析的方法研究了安装误差、螺旋运动系数与啮合性能之间的作用规律。利用矢量法建立切齿加工数学模型,求得齿面方程并建立齿轮副装配数学模型,利用齿面接触分析(TCA)研究含多种安装误差的齿面接触特征;建立齿面失配数学模型,分析螺旋运动系数对齿面接触特征、几何形貌的影响规律,揭示双重螺旋法对轮齿工作面、非工作面不同的修形原理;结合刀具与齿坯之间的相对位置关系,阐述了展成线的求解过程,研究了螺旋运动系数对展成线位置的影响规律。对准双曲面齿轮副(7×43)进行磨齿和滚检实验,与数值分析结果进行对比验证了分析模型的正确性。

驱动桥摆线准双曲面齿轮啮合效率优化设计

基于齿轮摩擦加载接触分析(FLTCA)方法,提出了摆线准双曲面齿轮啮合效率优化设计方法。首先,通过预设空载传动误差峰峰值和接触区位置,实现了对摆线准双曲面齿轮正、反车齿面的修形设计。然后基于修形面设计,以行驶工况下齿轮啮合效率最大为优化目标,并综合考虑齿轮副加载传动误差峰峰值、双侧齿面满载接触印迹分布以及最大接触应力建立了优化分析模型。为了提高优化模型的求解速度,采用Kriging代理模型结合多岛遗传算法对优化模型进行了求解。最后,对某型号商用驱动桥摆线准双曲面齿轮副进行了实例设计和试验验证,通过空载接触印迹试验和整桥传动效率试验验证了所提优化方法的有效性。

延伸外摆线准双曲面齿轮啮合特性分析

为了研究延伸外摆线准双曲面齿轮的啮合特性,基于有限元仿真和试验,分析了齿面接触斑点、齿根弯曲应力、重合度和传动误差等啮合特性。结果表明,某一时刻齿面接触区域近似为椭圆形,齿轮啮合过程中,单个齿面上的椭圆形接触面积先增大后减小;大小齿轮齿根危险点均主要承受拉应力,小齿轮危险点先承受拉应力,再承受压应力,而大齿轮危险点则相反;齿轮重合度随载荷的增加而逐渐增大;齿轮传动误差受载荷影响较大,小载荷下传动误差较大,随载荷的增加先减小后增大,最后缓慢减小趋于稳定。文章的研究内容对准双曲面齿轮的设计和使用具有一定指导意义。

驱动桥准双曲面齿轮传动系统振动特性分析

驱动桥是微车传动系统的核心部件之一,承受复杂的载荷,影响整车的安全、舒适和动力,其振动和噪声对整车舒适性(NVH)性能有重要影响。为掌握驱动桥振动响应的影响规律,实现驱动桥动态特性的主动控制,本文以驱动桥准双曲面齿轮传动系统为研究对象,考虑主从齿时变啮合刚度、阻尼、传动误差和冲击等激励,基于集中质量法构建驱动桥齿轮传动系统的多变参数耦合振动模型,并依据牛顿第二定律推导其振动微分方程组,采用RK算法求解方程组;对比准双曲面齿轮修形优化前后主、从动齿轮的垂直、扭转和轴向振动数值解,并讨论输入转速和加载扭矩的改变对系统振动特性的影响规律。结果表明:优化后的齿轮运转振动值减小;主从齿的垂直和轴向振动规律复杂,处于近似混沌运动状态;扭转方向上呈现拟周期运动;输入转速和加载扭矩的改变对主从齿轴向振动影响最大,垂直方向次之,扭转方向最小。进一步对驱动桥总成进行振动测试分析,结果表明,新状态样件的动态性能更优,测试数据的趋势与理论分析结果符合较好。该研究成果可应用于分析驱动桥的关键激励因素,预测振动响应,提升产品的动态性能。

Plücker Coordinate System of Screws and the Study of Generating Gears

After an introductiou of the Plucker coordinate geometry, a discussion is made of the expression of screws in Plucker coordiuates and the addition of screws’ As a result, the geometry or geuerating gears is re-studied and a formula is derived for calculating the axode leugth or hypoid gears’

采用曲面综合法的复杂齿面微分修形与拓扑结构设计

针对高减比准双曲面(HRH)齿轮空间曲面极端扭转、曲率修正难度大的问题,提出了刀具双向修形点接触齿面修正方法。利用ease-off曲面综合法、齿面微分修形、拓扑结构精益化设计,实现了点接触齿面啮合质量的精确控制。建立了曲面综合法齿面微分精益化设计计算流程,给出了轻修形、内对角重修形、内对角轻修形三种拓扑结构设计形式;利用齿面承载接触分析(LTCA)方法,对比了上述三种形式的齿面啮合刚度、传动误差及载荷分布特性,其中内对角轻修形方式的接触性能最好。进行了HRH齿轮动态啮合性能试验,齿面接触斑点检验了点接触齿面ease-off梯度特征。研究结果表明,实测振动特性变化规律与啮合刚度、承载传动误差(LTE)理论仿真分析一致。齿轮在较宽转速与载荷范围运转平稳,验证了所设计HRH齿轮的齿形关系正确,微分精益化修形控制良好。

一种基于刀倾全展成法滚切准双曲面齿轮的数学模型

以通用型摇台式切齿机的坐标系统为基础,推导出基于刀倾全展成法(Spiroflex)滚切准双曲面齿轮的数学模型。首先,对通用型摇台式机床的机械设定进行转换,使其适用于当前新式6轴齿轮切齿机的坐标系统;然后,计算出6轴齿轮切齿机的机械坐标,编制出准双曲面齿轮刀倾全展成法滚切加工的加工程序;最后,用VERICUT仿真软件模拟准双曲面齿轮的滚切加工,并比较模拟齿轮与理论齿轮间的齿面误差。结果表明,模拟齿轮与理论齿轮间的齿面点位置误差及齿厚误差值均小于50μm,验证了该数学模型在6轴CNC齿轮切齿机上实施准双曲面齿轮的刀倾全展成法加工具有较高的准确性。

准双曲面齿轮实际齿面接触分析与调整计算

为了对准双曲面齿轮实际齿面的接触区进行调整修正,基于齿面测量结果,对大、小轮齿面进行了双三次样条曲面拟合。采用齿面点二维黄金分割加密方法,编制了离散齿面接触分析算法,获得了实际齿面的啮合信息和接触印痕调整参数,为机床加工参数的反调修正提供了依据。对某车桥准双曲面齿轮副进行了实际齿面滚检试验,仿真分析与实际滚检结果基本一致,验证了所提出算法的可行性和正确性。

纵向变位HRH齿轮等高成形法制式设计

研究了准双曲面齿轮的节锥和轮齿收缩的形成与演变规律,分析了刀盘半径、齿根角、节锥等参数之间的耦合关系。根据节点纵向变位原理,提出了等高成形法高减比准双曲面(High reduction hypoid, HRH)齿轮的制式设计方法;通过纵向变位系数和刀盘半径的恰当匹配,确定了适合等高成形法HRH齿轮的节锥角、齿根角的几何可行域,其中等径刀盘设计为工程应用提供了便利。给出了3种HRH齿轮等高成形法的几何制式设计样例,完成了3∶60、1∶60两种HRH齿轮加工、滚检与动态性能试验,试验所设计HRH齿轮齿形与啮合关系正确,接触性能良好。证明了所提出的纵向变位HRH齿轮等高成形法设计方法的可行性。