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.

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.

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.

ANALYSIS OF TOOTH FORM ERROR OF EQUAL BASE CIRCLE BEVEL GEAR

The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute

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.

Research on theory of gearing for epicycloidal bevel gear

The engaged feature of a pair of gears was determined by the geometrical characteristics of their tooth surfaces. Through an analysis of gearing theory on epi-cycloidal bevel gears, the method to examine if there exists undercut during manufacturing of epicycloidal bevel gears, the approximate formulae to calculate the gap between the convex and concave tooth surfaces in meshing so as to guarantee against the occurrence of point-contact for tooth surfaces even in maximum angle of inclination are derived in this paper. Those formula derived are simple, compact and have practical value to the design and production of epicycloidal bevel gears.

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。

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。

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。

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。

基于平面共轭对数的弧齿锥齿轮齿面设计研究

为了提高弧齿锥齿轮建模模拟在承载工作的情况下所得出数据的准确性,在球面渐开线弧齿锥齿轮齿面成形设计原理的基础上,引入平面共轭对数对球面渐开线弧齿锥齿轮齿面形成理论进行进一步的研究与改进,建立与法向截面圆弧齿形点位相接触的弧齿锥齿轮数学模型,并利用修改后的齿面设计理论进行弧齿锥齿轮工作齿面、齿顶根曲线及齿根过渡曲面的齿面精确数学建模,使大小轮之间的共轭曲面啮合精度得到提升,从而提高弧齿锥齿轮在循环啮合过程当中的接触强度与稳定性,并对原先球面渐开线理论中所具有的对弧齿锥齿轮传动时的轴角可分性进行分析,进行存在轴角误差时对该设计下齿轮的传动误差的影响。

弧齿锥齿轮系统行波共振特性分析与验证

以某航空发动机弧齿锥齿轮系统为研究对象,提出了一套锥齿轮系统级行波共振特性分析方法。基于设计参数和加工参数,创建具有精确齿面的弧齿锥齿轮副三维模型;对弧齿锥齿轮系统开展静力学分析,保证齿轮副接触正常;对弧齿锥齿轮系统进行预应力模态分析,得到齿轮系统的模态特性;基于行波共振理论,进行锥齿轮系统行波共振预测;通过预测结果与试验结果的对比,判断行波共振预测的准确性和有效性。结果表明,理论分析与试验结果具有较好的一致性,研究为弧齿锥齿轮系统的行波共振预测提供了有价值的参考方法。

高阶滚比修正系数对弧齿锥齿轮齿面形状的影响规律

基于弧齿锥齿轮齿面数学模型,引入高阶滚比修正系数,采用矢量运算与二元迭代的方法,对齿面进行了离散化处理,计算了各离散点的齿形偏差。分析了各阶滚比修正系数的改变对弧齿锥齿轮齿面形状的影响规律,绘制了齿面误差拓扑图,表示了误差齿面相对于理论齿面的偏离方向以及误差值的大小。基于齿面误差的模型,采用最小二乘法,计算了弧齿锥齿轮齿面在各阶滚比修正系数改变下的敏感系数,分析了各阶滚比修正系数对齿面形状的影响类型和程度,为弧齿锥齿轮实际加工过程中齿面几何形状的调整和齿形误差的修正提供了理论依据。通过实际的磨齿加工和测量,验证了齿面数学模型与齿面误差拓扑图结果的正确性。

小模数弧齿锥齿轮半滚切切齿加工方法研究

为了大幅度提高齿轮传动性,解决传统机械结构弧齿锥齿轮滚切双面法铣齿加工(即双重双面法)齿面啮合质量难以控制的问题。这里提出了小模数弧齿锥齿轮半滚切加工方法,详细地介绍了加工的相关理论计算和机床的刚性改造,分析了机床带有对刀装置的结构能保证均匀的齿切加工余量。通过生产实践,结果表明:该加工方法将有助于提高小模数弧齿锥齿轮加工效率,提高齿面啮合质量,降低生产能耗,对小模数弧齿锥齿轮的加工有一定的借鉴作用。

车桥锥齿轮加工误差修正方法

针对车桥锥齿轮的齿面几何精度和传动质量难以有效控制问题,本文提出了一种基于一维测头的车桥锥齿轮加工误差数字化修正方法,从数学分析和工程反求角度实现了齿面几何偏差的极小化。通过建立理论设计齿面、实际加工齿面与偏差齿面之间的数学关系,推导出机床加工参数与齿面偏差的映射关系,构建了机床加工修正模型,采用数值迭代逆向求解的方法实现了齿面偏差的极小化。通过某车桥锥齿轮小轮齿面加工误差的修正实验,验证了本文所提基于一维测头的齿轮加工误差修正方法的正确性和实用性。实验结果表明:经过修正后,小轮凸面和凹面加工误差的最大偏差分别从0.1349 mm降低至-0.0127 mm,从0.2411 mm降低至0.0316 mm,小轮齿面的总体偏差趋势得到了有效的降低。

直齿锥齿轮分岔脱啮特性参数解域界结构

为研究含间隙直齿锥齿轮系统周期运动与齿面冲击、脱啮、动载间的耦合转迁关系,基于胞映射原理构建了时变啮合刚度和频率比双参平面,采用改进的CPNF(continuous-Poincaré-Newton-Floquet)法求解了系统胞元的周期、冲击、脱啮、动载特性解域界结构.仿真结果表明,在双参解域界内系统存在鞍结、Hopf、倍化、激变及周期3等分岔方式和3种齿面冲击共存现象,随时变啮合刚度系数递增其冲击和混沌现象加剧.齿面脱啮、齿背接触及动载系数受齿面冲击和周期分岔的影响而发生突变,在同一界域内随频率比增加而降低,随刚度系数增加而加剧.

格里森制摆线齿锥齿轮齿面失配分析与轮齿接触仿真

为了能够对格里森制摆线齿锥齿轮啮合性能进行综合评判,提出集齿面失配分析、齿面接触仿真和齿面加载接触仿真于一体的系统性评价方法。构建刀盘数学模型和刀倾法切齿加工数学模型,获得理论齿面。研究与大轮齿面完全共轭的小轮基准齿面及齿面Ease off拓扑计算方法。在此基础上,基于齿轮啮合数学模型,研究齿面接触分析解析计算方法,构建齿面加载接触分析有限元仿真流程。最后以一对格里森制摆线齿锥齿轮为例进行了齿面失配分析和轮齿接触仿真,算例仿真结果与格里森软件一致,验证了齿面接触仿真算法的正确性,同时也表明采用有限元方法进行齿面加载接触分析在啮合性能评价方面具有较大的直观性。

弧齿锥齿轮参数建模及有限元接触分析

针对高精度弧齿锥齿轮在啮合过程中齿面接触动态变化问题,分析了弧齿锥齿轮齿面加工原理,建立了弧齿锥齿轮齿面方程,计算创建模型所需要的齿面离散点方程,准确求解出齿面各点的坐标,建立了弧齿锥齿轮的三维模型。构建弧齿锥齿轮有限元模型,采用瞬态动力学模块分析弧齿锥齿轮啮合过程中齿面接触应力的动态变化,得到弧齿锥齿轮大轮凹面接触印痕,与实验得到的弧齿锥齿轮大轮齿面接触印痕进行对比分析。结果表明,仿真和实验得到的接触印痕都符合设计准则中接触区域的范围,能够满足弧齿锥齿轮实际使用要求。

螺旋运动系数对弧齿锥齿轮齿形的影响规律

为探究螺旋运动系数对弧齿锥齿轮齿形的影响规律,充分发挥数控机床的万能运动特性,使齿轮设计人员及机床调整人员更好地运用高阶运动实现齿面的修形以及齿面接触区的调整,基于弧齿锥齿轮加工原理,通过引入一至六阶螺旋运动系数,建立了齿面数学模型。基于齿面数学模型,采用矢量运算与二元迭代的方法,计算了实际齿面相对于理论齿面在其各离散点法线方向上的齿面误差。分析了各阶螺旋运动系数的改变对弧齿锥齿轮齿面形状的影响规律,以图像的方式表示了实际齿面相对于理论齿面的偏离方向以及误差值的大小。采用最小二乘法,计算了弧齿锥齿轮轮齿齿面在各阶螺旋运动系数改变下的敏感系数,分析了各阶螺旋运动系数对齿面形状的影响类型和程度。通过实际的磨齿加工和测量验证,结果表明各阶螺旋运动系数对齿面形状的实际影响与理论分析结果一致。