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 tad 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 3μm 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.

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

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.

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 .

Mathematical modeling and characteristics analysis for the nutation gear drive based on error parameters

We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double circular arc tooth profile and based on the equal tooth strength principle. The nutation drive meshing coordinate system was set up by introducing the cone vertex error, tilt error, nutation angle error and spiral angle error. The tooth profile equations of the double circular arc external and internal spiral bevel gears were further obtained based on the crown gear tooth profile equation concerning above mentioned error parameters. The influences of the nutation gear reducer tooth contact conditions were analyzed with the gear tilt error and axial misalignment error. Finally, the correctness of the theoretical analysis was verified by the contact spot test.

Modification Design Method for an Enveloping Hourglass Worm Gear with Consideration of Machining and Misalignment Errors

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

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.

A Method for Identification and Compensation of Machining Errors of Digital Gear Tooth Surfaces

In order to generate the digital gear tooth surfaces(DGTS)with high efficiency and high precision,a method for identification and compensation of machining errors is demonstrated in this paper.Machining errors are analyzed directly from the real tooth surfaces.The topography data of the part are off-line measured in the post-process.A comparison is made between two models:CAD model of DGTS and virtual model of the physical measured surface.And a matching rule is given to determine these two surfaces in an appropriate fashion.The developed error estimation model creates a point-to-point map of the real surface to the theoretical surface in the normal direction.A“pre-calibration error compensation”strategy is presented.Through processing the results of the first trail cutting,the total compensation error is predicted and an imaginary digital tooth surface is reconstructed. The machining errors in the final manufactured surfaces are minimized by generating this imaginary surface.An example of ma- chining 2-D DGTS verifies the developed method.The research is of important theoretical and practical value to manufacture the DGTS and other digital conjugate surfaces.

The Analysis of the Untwisting and Retwisting Methods in Determining the Twist of OE Yarn

The twists of twelve kinds of the cotton OE yarns in different machine twists and different yarn linear density have been determined by one time back twisting and twisting method, triple twisting method and double twisting method. The quantitative analysis of the measurement principles of all the untwisting and retwisting methods has been made by the writers. It is theoretically and practically concluded that for twelve kinds of the cotton OE yarns the difference between the twist determined by triple twisting method and machine twist is the lowest and there is measuring method error in determining the twist of OE yarn by all the untwisting and retwisting methods.

样品尺寸对脉冲穿透法声速测量误差的影响

岩心的声速测量能够提供关键的储层地质信息,对储层评价和地质模型构建具有实际应用价值。脉冲穿透法是一种常用的声速测量方法,但它要求样品尺寸远大于波长(约10倍)。当特殊场景如需在测井信号主频8~20 kHz下测量样品声速时,被测样品长达数米,不仅制备困难,还存在声波信号衰减大的问题。关于试样尺寸能否缩小或能缩小到什么程度的定量研究很少见到公开报道。该文将数值模拟和实验测量相结合,系统定量地研究了圆柱状样品长度及直径与波长之间的比值对脉冲穿透法声速测量精度的影响。研究表明:为确保脉冲穿透法声速测量的准确性,建议样品沿传播方向上的长度不低于4倍声波波长,横向尺寸不低于2倍波长。研究结果突破了传统脉冲穿透法要求样品尺寸远大于波长的限制,为优化声速测量方法和提高测量精度提供了理论支持。

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。

齿向修鼓和轴向错位直齿轮副刚度的计算方法

针对齿向修鼓和轴向错位直齿轮副刚度激励的问题,提出了一种通用的时变啮合直齿轮副刚度的解析方法。首先,建立了直齿轮齿向修鼓与轴向错位模型,导出了轮齿副总误差计算式;然后,结合了弹性力学理论、齿接触分析(TCA)以及加载齿接触分析(LTCA),对齿向修鼓和轴向错位的直齿轮副加载状态下的啮合特征进行了计算;基于势能法以及切片理论,建立了改进的几何刚度、耦合刚度、赫兹接触刚度以及齿基刚度模型,并进一步推导了齿向修鼓和轴向错位的直齿轮副时变啮合刚度改进解析式;最后,将该方法的计算结果与有限元结果进行了对比分析,对该解析模型进行了验证,并分析了不同鼓形量与错位量对直齿轮副刚度激励的影响。研究结果表明:提出的齿向修鼓和轴向错位直齿轮副刚度计算方法的计算误差为3%,能够准确且有效地分析齿向修鼓和轴向错位直齿轮副的啮合刚度,为齿轮副传动系统的修形设计提供了理论基础。

固定式双向体积管清洗效果影响因素研究

本文以长庆油田某油库固定式双向体积管的清洗工作为例,介绍了清洗工艺,并详细剖析了结污情况、清洗介质、设备器具、操作运行四个方面对体积管清洗效果的影响,提出相应建议。通过本次标定容积值较上一次结果的对比,论证了分析的成效,证明了研究的必要性和可靠性。

非接触式纵梁折弯高度检测方法研究

随着变宽度车架使用越来越多,各种非接触式测量方案应用越来越广泛。借助非接触式距离测量设备,快速检测变宽度车架的Z型面高度差,在此基础上通过多点测量、统计数据极大似然估计,构建数学模型,运用最小二乘法拟合直线,并利用计算点与直线的距离来快速判断测量平面与基准平面的间距的方案。通过多次测量以及统计学分析,可实现使用低精度设备达到高精度测量的思路,系统误差约为原来的2/3。研究结果可为快速检测车架纵梁折弯高度提供依据,在大幅度提升测量效率的同时保持较高的稳定性。

增量数字图像相关方法的误差分析及应用考量

增量数字图像相关方法(digital image correlation, DIC)常应用于变形后图像中被测物体出现大变形、环境光变化剧烈以及采用激光散斑追踪变形等容易发生图像退相关的场景。增量DIC充分利用局部图像序列的相关性,通过更新参考图像计算增量变形,再进行累加以获得整体变形,可解决采用固定参考图像的传统DIC方法在出现图像退相关时计算失效的问题。但是,由于DIC计算变形时存在系统误差,在增量计算以累加增量位移的过程中会导致误差累积。为实现更准确高效的增量DIC分析,需明确这一误差的累积规律并提出抑制误差的方法。本文通过模拟和真实实验研究了采用不同增量策略的增量DIC方法在不同场景下的误差累积规律。结果显示:为减少参考图像更新带来的累积误差,应采用条件增量计算策略以尽量减少参考图像的更新次数;同时,自适应参考图像子区平移策略和图像高斯低通预滤波方法可以显著降低插值带来的系统误差,应与增量DIC方法配合使用。

基于多边法的多轴转台相交度测量方法

随着导航、光电跟测和飞行仿真等技术的飞速发展,对多轴转台的测量精度要求越来越高。轴线相交度是多轴转台重要的技术指标,为此,提出一种基于多边法的激光跟踪干涉仪测量多轴转台相交度的方法。该方法首先对激光跟踪干涉仪位置进行自标定,构建坐标系;其次将靶球依次安装于双轴转台(方位轴和俯仰轴)的测量平面,利用多台激光跟踪干涉仪跟踪靶球,分别测量两轴的转动轨迹,采用最小二乘法对获取的轨迹进行拟合,通过所有轨迹点建立双轴转台回转轴线相交度的求解方程,以实现其相交度测量;最后重点分析了测量方法的主要误差来源,对测量不确定度进行评价。实验表明:所提方法相较传统测量方法测量误差更小,减小了动态测量盲区,无需辅助工件,且不受轴数限制,能够无接触、高精度测量。

考虑齿对耦合的直齿锥齿轮啮合刚度计算方法

为了解决直齿锥齿轮时变啮合刚度计算效率和准确性问题,提出了一种考虑齿对耦合效应的直齿锥齿轮啮合刚度切片计算方法。基于切片离散方法,将锥齿轮轮齿和轮体分别沿齿宽方向和轴线方向离散为若干宽度相等的薄片,并基于背锥等效原理将薄片展开,当薄片宽度足够小时,锥齿轮可近似为一系列直齿圆柱齿轮,可通过能量法计算各薄片啮合刚度;为考虑多齿啮合时齿对间耦合效应,在双齿啮合刚度计算中引入轮体刚度修正系数,减少了双齿啮合刚度计算误差;建立误差状态下锥齿轮啮合刚度模型,计算了理想和装配误差条件下直齿锥齿轮啮合刚度、各薄片中心点角位移与齿面载荷分布;最后,通过与有限元计算结果对比,验证了本文方法的准确性和高效性。

基于声测法的齿轮行波共振测试方法

针对航空发动机由行波共振导致的中央传动锥齿轮断裂故障,提出了一种基于声测法的齿轮行波共振转速测试方法,建立了非接触齿轮行波共振测量系统,该测试方法简便易行,不需要对转子件进行测试改装,直接引出测试部位的声信号进行分析研究。基于声测法开展了航空发动机中央传动锥齿轮行波共振试验,研究中央传动锥齿轮行波共振特性,获取了从动锥齿轮行波共振频率、危险转速范围。通过动应力同步测量试验进行对比验证,结果表明:该测试方法和系统可以精准识别和有效监测航空发动机中央传动锥齿轮行波共振频率和共振转速,行波共振频率误差小于0.025%,共振转速误差小于0.018%。该方法同时适用于其它齿轮和盘轴的行波共振故障分析,为相关类型齿轮共振试验及故障诊断提供了一种非接触、长时间监控疲劳试验的测量方法。

基于中点弦测法的中低速磁浮轨道不平顺误差研究

中低速磁浮轨道10 m弦测值作为评价轨道几何平顺性的标准时,由于弦测值在幅频范围内存在畸变并受基准线选取的影响而产生较大误差。本文推导了弦测法“以小推大”的传递函数,进一步定义了“以小推大”及其逆推算法的误差放大系数;分析了弦长、矩阵维度对误差积累特性的影响,结合传递函数分析不同波长对误差的敏感性差异,并通过数值模拟进行验证。结果表明:“以小推大”算法及其逆推算法在传递函数为0的波长范围内误差积累较严重,轨道不平顺功率谱密度出现阶跃信号;随着矩阵维度的增加,“以小推大”逆推算法的误差快速积累,推得的小弦长越小则误差积累越小。应用“以小推大”算法时应减小大小弦长比值;对于“以小推大”逆推算法,要减小采样步长、可换算最小弦长以及矩阵维度。

基于齿面位姿-几何误差模型的大规格滚齿机关键误差识别

为研究影响大规格滚齿机加工精度的关键几何误差,提出了一种基于齿面位姿-几何误差模型结合Sobol法的机床关键几何误差识别方法。首先,基于齐次坐标变换理论,建立了刀具位姿-几何误差模型,通过求解滚齿双参数包络方程,获得了加工齿面接触迹点坐标值,建立了机床齿面位姿-几何误差模型;然后,考虑几何误差的随机性和互耦性,利用Sobol法对该模型进行敏感性分析,计算了几何误差的敏感度系数以识别出关键几何误差;最后,进行了关键几何误差虚拟仿真修正和对比验证。研究结果表明,所提方法能有效识别大规格滚齿机的关键误差项。