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.

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.

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.

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.

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.

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.

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.

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 .

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’

高减速比准双曲面齿轮滑动率的计算方法研究

根据GLEASON准双曲面齿轮齿坯计算卡提出一种从大轮推导小轮齿坯参数的高减速比齿坯计算新方法,得出相应的齿坯基本参数公式。基于空间齿轮啮合原理对点接触齿轮副运动规律进行分析,推导出基本滑动率公式。然后结合高减速比准双曲面齿轮传动基本原理,对齿面节点进行运动分析,推导得出以高减速比齿坯设计参数为自变量的滑动率公式。计算了两对高减比齿轮副的滑动率,并取其中一对进行验证计算。该研究对高减速比齿坯的设计计算提供了新的计算方法,为高减速比齿轮的磨损分析和优化提供了理论基础。

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。

计算机辅助设计在准双曲面齿轮数控化加工中的应用

介绍了准双曲面齿轮数控化加工中计算机辅助设计的应用 ,给出了计算机图形仿真系统的基本算法和具备通用性质的拟合齿面的接触分析方法 .通过使用计算机进行辅助设计 ,减少了传统加工中的试切 ,降低了加工过程中参数调整对经验的依赖性 ,缩短了设计周期 .

准双曲面齿轮非线性振动分析

本文建立一个准双曲面齿轮单自由度非线性振动方程。方程中考虑了时变啮合刚度、传动误差和间隙,用打靶法和参数化法得到了周期解。

Ease-off拓扑修正的准双曲面齿轮齿面修形方法

为了提升驱动桥准双曲面齿轮传动的啮合性能,针对准双曲面齿轮刀倾半展成法(HFT)提出一种Ease-off拓扑修正方法。在建立齿面共轭啮合数学模型的基础上,推导出小轮基准齿面方程,通过计算小轮实际齿面与基准齿面之间的偏差,构建出Ease-off拓扑。借助二阶多项表达式对Ease-off拓扑分解,计算出齿面失配系数,通过调整齿面失配系数构建出修正Ease-off拓扑。通过比较当前Ease-off拓扑与修正Ease-off拓扑,消除小轮当前齿面与修正齿面之间的偏差,反求出小轮加工参数。最后以一对准双曲面齿轮为例进行齿面拓扑修形与磨齿加工,实际齿面印痕与仿真结果一致,验证了齿面拓扑修形方法的有效性。齿面加载接触分析结果表明,修形后齿面接触应力分布得到了改善,实际载荷下齿面接触重合度增加,从而验证了修形方案的合理性。

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荷分布和齿间载荷分配合理 ,接触印痕受安装误差的影响较小 。

准双曲面齿轮的齿面优化设计

基于局部综合法的准双曲面齿轮加工参数设计方法,经过近几年来的改进和发展,已经显示出其可预控性以及计算简洁等优点。本文对刀倾法加工准双曲面齿轮过程中可选加工参数以及预控参数进行优化,有效地消除准双曲面齿轮的三阶接触缺陷,实现准双曲面齿轮的质量控制。