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.

Pinion Tooth Surface Generation Strategy of Spiral Bevel Gears

Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.

Effect of static transmission error on dynamic responses of spiral bevel gears

The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.

Analysis and modeling of error of spiral bevel gear grinder based on multi-body system theory

Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix (HTM) were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 rad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3 μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.

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

A virtual computerized numerical control (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. Multi-environmental 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 multi-environmental programming is realized in the manufacture system simulation. The virtual gear product can be achieved in the accomplished software.

Research on global form deviations for spiral bevel gear based on latticed measurement

In order to improve the machining ac cu racy of spiral bevel gear,difference surface was adopted to characterize its gl obal form deviations quantifiably and correct its deviations.The theoretical to oth surface model of spiral bevel gear was built,and the actual tooth surface o f spiral bevel gear had been got by using latticed measurement.The equation of difference surface which can characterize the actual tooth surface deviation s was built by means of mathematical method in combination with measurement prin ciple.The quantitative mathematical relationship between the actual tooth surfa ce deviations of spiral bevel gear and the corrected values of the machine-sett ing parameters had been referred,and the theoretical correction formula of the global form deviations had been got by the least square method.Finally,the pinion of spiral bevel gear in the automobile rear axle has been set for an exam ple to account for the effectiveness of the deviation correction by use of the d ifference surface method.

NC Machining of Spiral Bevel Gear and Hypoid Gear Based on Unity Transformation Model

A unity transformation model (UTM) was presented for flexible NC machining of spiral bevel gears and hypoid gears. The model can support various machining methods for Gleason spiral bevel gears and hypoid gears, including generation machining and formation machining for wheel or pinion on a universal five-axis machining center, and then directly produce NC codes for the selected machining method. Wheel machining and pinion machining under UTM were simulated in Vericut 6.0 and tested on a five-axis machining center TDNC-W2000 with NC unit TDNC-H8. The results from simulation and real-cut verify the feasibility of gear machining under UTM as well as the correctness of NC codes.

Influence of cutter diameter on meshing performance in spiral bevel gears

Playing a critical role in transmitting movement and power, the meshing performance of spiral bevel gears has a significant effect on products' operational performance. To evaluate the meshing performance, the accurate three-dimensional(3D) spiral bevel gear models are established through the Pro/E and MATLAB softwares, and the finite element analysis(FEA) methods are applied to the theoretical investigation of the influence of cutter diameter on meshing performance in spiral bevel gears. The results obtained show that the cutter diameter has a significant influence on spiral bevel gears' meshing performance, such as the contact area, contact pressure, bending stress, torsional stiffness and transmission error.

METHOD FOR PRECISE CALCULATION OF ROOT STRESS OF SPIRAL BEVEL GEARS

A method for precise calculation of tooth root stress of spiral bevel gears is presentedand developed. On the basis of the machine settings analysis, tooth geometry anaysis and loadedtooth contact analysis, by using the tooth surface distribution load from tooth load analysis, thecalculation model is established and the root stress is calculated by means of finite element meth-od. The method mentioned is verified by a tested gears example.

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 .

STUDY ON DOUBLE CIRCULAR ARC PROFILE SPIRAL BEVEL GEAR TRANSMISSION

A stepped double arc spiral bevel gear tooth profile is examined. The development ofconjugate tooth surfaee of double are profile spiral bevel gears is described. The design and man-ufacture of the cutter is also discussed. Experimental results show that these gears have high loadcarrying capacity and that they are suitable for heavily loaded transmission. It is asserted thatsuch gears have higher power-to-weight ratios, are longer-lived, and provide more reliable per-formance than ordinary spiral bevel gears.

Reverse Engineering of Machine-tool Settings with Modified Roll for Spiral Bevel Pinions

Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical tooth surfaces and the corresponding machine-tool settings.

高接触比螺旋锥齿面修形方法及动态特性研究

为抑制高接触比螺旋锥齿轮传动的振动,提出一种新的高阶齿面修形方法。根据高接触比螺旋锥齿轮的啮合特点,提出一种新的修形曲线,采用辅助齿面修形方法生成高阶修形螺旋锥齿轮。在考虑齿变形的情况下,计算了高阶修正弧齿锥齿轮传动的载荷传递误差和啮合冲击,在此基础上建立了降低高接触比螺旋锥齿轮传动的载荷传递误差和啮合冲击的优化模型。仿真结果表明:与二阶修形弧齿锥齿轮相比,高阶齿面修形方法不仅可以有效降低高接触比螺旋锥齿的载荷传递误差、啮合冲击和动态负载系数,而且可以提高其在全速范围内的动态性能。

弧齿锥齿轮动力特性分析及其神经网络控制

针对含间隙锥齿轮系统动力学特性转迁及其控制问题,提出了基于胞元映射理论的参数解域结构和基于径向基函数神经网络的控制方法。采用集中质量法建立了7自由度弧齿锥齿轮动力学模型,基于胞元映射理论构建了频率和负载参数平面,采用伪不动点延续追踪算法求解了系统的分岔、齿面冲击、脱啮、齿背接触和动载特性转迁规律,分析发现频率和齿面冲击是影响周期分岔的主要因素,随负载增大其脱啮、冲击减弱,动载系数增大。针对平面中系统混沌现象,设计了参数反馈控制器、基于Poincaré截面欧氏距离构造适应度函数,用自适应引力搜索算法对控制器参数进行优化,从而实现了系统混沌、拟周期和周期运动向周期轨道有效控制。

等距螺旋锥齿轮的精确建模与金属粉末注射成型工艺试制

等距螺旋锥齿轮作为一种新型锥齿轮,其螺旋齿面具有法向等距的特点,适用于金属粉末注射成型工艺批量化生产。根据坐标变换理论推导出球面渐开线和等距圆锥螺旋线的参数方程,再基于齿面形成原理建立齿面数学模型;在MATLAB中对齿面数学模型编程计算出齿面离散点坐标,并通过UG逆向工程完成等距螺旋锥齿轮的精确建模;利用ANSYS仿真分析等距螺旋锥齿轮的啮合接触,得出齿轮的传动性能;最后通过金属粉末注射成型工艺完成等距螺旋锥齿轮的试制。研究结果表明,齿面数学模型结合离散点逆向建模可确保模型的精度,金属粉末注射成型工艺可用于等距螺旋锥齿轮的批量化生产。

基于自助法的弧齿锥齿轮齿面修正

为了降低弧齿锥齿轮在批量加工制造中存在的齿面偏差,提出一种基于自助法的弧齿锥齿轮齿面修正方法。以同一批次小样本弧齿锥齿轮作为研究对象,在自助法统计齿面偏差检测数据的基础上,得到大量的齿面偏差数据;利用NURBS曲面拟合方法构建齿面的均值差曲面,将它作为实际加工齿面,建立齿面偏差的数字化预控补偿模型,对它进行优化求解,得到批量齿面数控加工的机床修正参数,然后不断调整机床加工参数,实现齿面的预控修正补偿;最后对修正前、后齿面偏差作对比分析。结果表明:小轮齿面偏差比修正前降低了76.66%,验证了自助法齿面修正理论的有效性,对指导弧齿锥齿轮批量齿面修正提供了理论依据。

考虑安装误差的弧齿锥齿轮凹凸齿面印痕修正

弧齿锥齿轮作为重型燃气轮机中关键的动力传动部件,其双向传动的运行特点对齿轮凹凸齿面的接触印痕提出了更高的质量要求。为了满足实际需求,通过建立齿面啮合模型,利用考虑安装误差的齿轮接触分析(error tooth contact analysis, ETCA)技术研究了一对弧齿锥齿轮凹面和凸面均为工作面时,接触印痕随安装误差变化的数值规律。同时,以齿面印痕的中点位置、长轴倾角和面积作为印痕参数化处理后的特征值,优化齿轮安装误差调整值,修正印痕的不合理之处,实现凹凸齿面印痕的一致性和重叠性。滚检实验验证了模拟印痕的准确性,该修正规律可以为弧齿锥齿轮副的安装调整提供理论依据。

Delaunay三角剖分的汽车螺旋锥齿轮磨损检测

由于汽车后桥螺旋锥存在耦合竖向振动,导致齿轮磨损难以精准检测,因此提出Delaunay三角剖分的汽车螺旋锥齿轮磨损检测方法。通过扫描式方法测量齿轮表面的离散数据,对相邻扫描线进行Delaunay三角剖分,完成齿面非特征离散数据分块,实现对齿轮表面区域的全面描述。根据数据分块结果,采用基于Hermite插值的LMD算法,遍历计算三角网格的PF分量幅值,完成齿轮磨损故障的检测。实验结果表明,所提出方法的磨损深度与磨损率检测结果与实测结果基本一致,并且能够对齿轮磨损区域面积进行有效检测,检测精度最高达到98.7%。因此,说明所提出方法能够对齿轮磨损进行有效的检测。

尾减速器轴承预紧对锥齿轮接触印痕和齿隙的影响规律研究

尾减速器是直升机传动系统的重要部件,轴承预紧是尾减速器装配的关键环节,直接影响直升机尾旋翼的平稳性、寿命及噪声。根据轴承支撑构型建立预紧螺栓的受力模型,得到螺栓的拧紧力矩及施加在支撑面上的轴向力;基于受力关系建立尾减速器轴承预紧有限元分析模型,根据分析结果提取了锥齿轮副的安装误差,处理得到:弧齿锥齿轮副的齿面间隙随着力矩的增大而减小,印痕位置随着力矩的增大有逐渐向大端移动的趋势;试验结果与有限元计算结果吻合性较强,方法可进一步推广到其他类型减速器中。