Three-Dimensional Conjugate Tooth Surface Design and Contact Analysis of Harmonic Drive with Double-Circular-Arc Tooth Profle

A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profle is proposed. The radial deformation function of the fexspline (FS), obtained through Finite Element (FE) analysis, is incorporated into the kinematics model. By analyzing the FS tooth enveloping process, the optimization of the overlapping conjugate tooth profle is achieved. By utilizing the hobbing process, the three-dimensional machinable tooth surface of FS can be acquired. Utilizing the coning deformation of the FS, simulations are conducted to analyze the multi-section assembly and meshing motion of the machinable tooth surface. The FE method is utilized to analyze and compare the loaded contact characteristics. Results demonstrate that the proposed design method can achieve an internal gear pair consisting of a circular spline with a spur gear tooth surface and the FS with a machinable tooth surface. With the rated torque, approximately 24% of the FS teeth are engaged in meshing, and more than 4/5 of the tooth surface in the axial direction carries the load. The contact patterns, maximum contact pressure, and transmission error of the machinable tooth surface are 227.2%, 40.67%, and 71.24% of those on the spur gear tooth surface, respectively. It clearly demonstrates exceptional transmission performance.

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.

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

准双曲面齿轮齿面形状非常复杂,可以用点阵式测量和扫描式测量法对齿轮的齿面精度进行测量。比较了两种测量模式的优缺点,分析了测量数据在齿轮齿面品质管理中的应用,研究了如何利用这些测量数据进行准双曲面齿轮的动态性能仿真,并且对接触斑点、齿根应力、振动激振力以及齿面上的载荷分布、赫芝接触应力等动态性能指标进行智能预测。该项研究对设计与制造低振动噪音的准双曲面齿轮有重要指导意义。

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.

Resolution of Digitized Conjugate Tooth-Face Surface Based on the Theory of Digitized Conjugate Surfaces

According to the principle of meshing engagement and the theory of the digitized conjugate surface, this paper applies the software Conjugater-1.0 that is developed by ourselves to compute, respectively, the digitized conjugate curved surfaces of the straight-tooth surface and drum-tooth surface, which will establish the theoretical and technical foundation for digitized engaging analysis, simulation, and digitized manufacturing technology of the diversified gears.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Optimizing circumferential assembly angle of rotor parts connected by curvic couplings based on acquired tooth surface error data

Due to the excellent self-centering and load-carrying capability,curvic couplings have been widely used in advanced aero-engine rotors.However,curvic tooth surface errors lead to poor assembly precision.Traditional physical-master-gauge-based indirect tooth surface error measurement and circumferential assembly angle optimization methods have the disadvantages of high cost and weak generality.The unknown tooth surface fitting mechanism is a big barrier to assembly precision prediction and improvement.Therefore,this work puts forward a data-driven assembly simulation and optimization approach for aero-engine rotors connected by curvic couplings.The origin of curvic tooth surface error is deeply investigated.Using 5-axis sweep scan method,a large amount of high-precision curvic tooth surface data are acquired efficiently.Based on geometric models of parts,the fitting mechanism of curvic couplings is uncovered for assembly precision simulation and prediction.A circumferential assembly angle optimization model is developed to decrease axial and radial assembly runouts.Experimental results show that the assembly precision can be predicted accurately and improved dramatically.By uncovering the essential principle of the assembly precision formation and proposing circumferential assembly angle optimization model,this work is meaningful for assembly quality,efficiency and economy improvement of multistage aero-engine rotors connected by curvic couplings.

NUMERICAL APPROACH TO DETERMINING INSTANTANEOUS CONTACT REGION FOR CONJUGATE SURFACES

According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to find the instantaneous contact boundary in local coordinate system, a modified Powell＇s hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvatm＇e and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.

<i>In Vitro</i>Evaluation of Bacterial Adhesion to Dental and Stainless-Steel Surfaces

This study aimed to describe the factors associated with biofilms formation in dental pathology by comparison of bacterial growth on dental and stainless-steel surfaces. We studied in vitro the behavior of Staphylococcus aureus Métis in order to observe the capacity of adhesion, to evaluate quantitatively the potential of proliferation and to compare the behavior of this germ in contact with the two surfaces. The biomaterials used were cylinders in Stainless steel (AISI 316L), dental fragments and stainless-steel fragments, all were disinfected for 15 minutes and then sterilized in a wet autoclave at 120˚C for 30 min. Macroscopic observation with a binocular magnifier of bacterial proliferation was carried out regularly after 6 h and 24 h of incubation. Observation by optical microscope based on GRAM staining made it possible to visualize the presence or absence of bacteria and to differentiate them. The adhesion of Staphylococcus aureus Méti S on dental fragments was compared to the one obtained on stainless steel fragments. We also carried a Bacterial count by optical dosing. The results show that the ability of this germ to colonize and develop biofilms on surfaces depends mainly on the characteristics of the surface. Rough surfaces as dental surface are more likely to developing biofilms than smooth surfaces like stainless-steel surface.

LUBRICATION BASIS THEORY OF WORM PAIR AND TEMPERATURE DISTRIBUTION ON WORM GEAR SURFACE

The lubrication basis theory of worm pair is given. The lubrication state of worm gear is analyzed. It is found that the temperature distribution on the tooth surface of worm gear is closely related with the lubrication state and that the temperature on the tooth surface of worm gear is consistent with the characteristic term of mesh and motion of worm pair.

直纹面面齿轮共轭小齿轮的滚齿加工研究

针对直纹面面齿轮与圆柱齿轮不满足共轭关系而限制其在小传动比应用场合的情况,提出与直纹面面齿轮共轭的小齿轮及其滚齿加工方法。首先建立了直纹面面齿轮及其共轭小齿轮的齿面方程,获得共轭小齿轮相比圆柱齿轮的齿面偏差形貌;随后推导了阿基米德齿轮滚刀的齿面方程,并根据滚齿加工运动坐标系和啮合原理建立了圆柱齿轮的数学模型;在滚齿加工圆柱齿轮的运动基础上,通过增加滚刀的径向移动和工件的附加转动使滚刀切削刃逼近共轭齿面,附加运动由泰勒多项式表示,通过建立敏感矩阵方程并采用奇异值分解法迭代求解方程获得附加数控运动多项式系数,最后获得数控加工齿面;为评价直纹面面齿轮副的传动性能,进行了齿面承载接触分析,并与传统面齿轮-圆柱齿轮副进行了对比。研究结果表明:相同参数下,直纹面面齿轮副与传统面齿轮副的承载性能基本相同,完全能够代替传统面齿轮副传动;数值算例和仿真加工对该方法的验证表明,其数值算例误差不超过1μm,仿真结果误差不超过6μm,证明了该方法的可行性和准确性。

含点蚀的行星齿轮系统动力学特性及损伤评估研究

齿面点蚀是一种典型的行星齿轮系统故障。为识别点蚀状态,本文开展动力学特性研究并提出了一种新型的评估指标。首先,虑及过渡曲线和齿间结构耦合效应,利用改进Weber法建立了精确的含点蚀故障齿轮副啮合刚度模型,并研究了故障程度对啮合刚度的影响规律。然后,综合考虑时变啮合刚度、静态传动误差、齿侧间隙和时变振动传递路径等多种因素构建了行星齿轮系统平移-扭转动力学模型,揭示了点蚀程度对系统动态特性的影响规律,并基于振动信号频谱特点提出了边带能量因子(Sideband Energy Factor,SEF)用于损伤评估。最后,利用实验验证了仿真模型的正确性及所提指标的有效性。

难变形金属小模数齿形件电流辅助分形旋压成形工艺优化

目的针对30CrMnSiA合金结构钢小模数齿形件电流辅助分形旋压成形工艺,探究工艺参数对小模数齿形件成形质量的影响规律,分析工艺参数间的相关性,获得优化后的工艺参数组合。方法选取小模数齿形件齿廓偏差、齿距偏差、轮齿饱和度为成形质量响应指标,以电流密度、占空比以及旋轮进给速度为影响因素,设计响应面试验方案;根据有限元模拟结果建立成形质量回归预测模型,分析电流密度、占空比以及旋轮进给速度对小模数齿形件成形质量的影响规律,计算获得最优的参数组合并进行试验验证。结果电流密度、脉冲占空比、旋轮进给速度对小模数齿形件成形质量有显著影响,成形质量随着电流密度与占空比的升高而升高,随旋轮进给速度的升高而先升高后降低;且电流密度与旋轮进给速度、脉冲占空比与旋轮进给速度在对轮齿饱和度的影响上有一定的交互性;通过建立的回归模型预测得到的优化工艺参数如下:电流密度为17.5 A/mm2、脉冲占空比为40%、旋轮进给速度为0.6 mm/min。结论回归模型预测值与试验值的相对误差小于8%,说明所构建的成形质量回归预测模型是准确的,利用优化后的参数可制备出成形质量良好的小模数齿形件。

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。

齿调制作用下转子开槽对永磁电机电磁振动影响

为了研究齿调制作用下转子表面开槽对永磁同步电机电磁振动的影响,以小功率分数槽集中绕组(FSCW)内置永磁同步电机(IPMSM)为研究对象,通过麦克斯韦应力张量法推导径向电磁力波的频率及空间阶数特征。分析齿调制作用在FSCW-IPMSM中将空间高阶电磁力波调制为低阶电磁力波的过程,并给出转子表面开槽在齿调制作用影响下与电磁振动间的联系。研究表明,转子表面开槽结构的改变会使各次谐波磁场发生变化,进而改变以极数阶电磁力波为代表的高阶电磁力波的幅值。在齿调制作用下,这些高阶电磁力波会被调制为幅值较高的低阶电磁力波,并引起不同幅度的低阶振动。然后建立C型、V型两种不同转子表面开槽结构的10极12槽FSCW-IPMSM电磁及结构有限元分析模型并进行仿真分析。结果表明,极数阶即10阶电磁力波会被调制为2阶并引起2阶振动,且两种不同开槽结构间的电磁振动存在着高达22.1%的差异。最后,在一台10极12槽样机上进行振动实验,验证理论与仿真分析结果。

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。

直齿锥齿轮系统动态特性参数解域界结构

为研究含间隙直齿锥齿轮系统的幅值跳跃、齿面冲击特性,用谐波平衡法建立系统动力学方程。在频率与间隙、时变刚度、静态综合误差和负载构建的参数平面内用Broyden拟牛顿法和伪弧长延续算法获得系统参数解域界结构,探索系统幅值跳跃、多值解和啮合冲击特性对参数的敏感性。结果表明在系统啮频和轴频主共振区均出现幅值跳跃和多值解现象,在啮频处动态特性更为复杂丰富。小间隙下存在严重的齿面冲击现象,当间隙b>0.98时系统的跳跃与齿面冲击均趋于稳定,系统动态特性对时变啮合刚度不敏感,在高速轻载、较大齿面误差激励下系统的非线性跳跃和齿面冲击均加剧。参数解域界结构为锥齿轮结构设计提供数据支持。

不同侧隙卸荷槽时齿轮泵理论流量的创新计算

为克服齿轮泵理论流量、排量及脉动系数计算方法的局限性与复杂性,从一个完整啮合齿面所产生的理论齿面流量入手,提出双卸荷槽间距内的理论齿面流量即为泵理论输出流量的新方法。以1.0和0.5代表侧隙的有和无,双卸荷槽对称线相对于齿轮副中心线的无量纲不对称宽度为变量,构建出理论输出流量特性的相关简洁式。结果表明:同等侧隙类型下无卸荷槽与单侧卸荷槽下的理论排量相同,有侧隙、单侧卸荷槽下的类型系数经典式确实有误;无侧隙、对称卸荷槽类型下的理论排量更大,流量脉动更小,但困油现象更严重;尤其单侧卸荷槽下的流量脉动很大和困油现象很严重,不建议采用等。本文提出的新方法原理更清晰,公式更简洁,结果更可靠,通用性更强。

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。

渐开螺旋面的数字化曲面及其计量特征

真实齿面的数字化重建是虚拟仿真与测量的重要基础,提出了基于几何线特征的渐开线齿轮齿面的数字化曲面构造方法,根据渐开线齿轮齿面的渐开线、螺旋线和接触线三条特征线之间的相交关系划分齿面网格点,分别构造出三角面片组成的渐开螺旋面和双三次NURBS渐开线螺旋面。与三角面片集拟合得到的曲面进行面型拟合特征与拟合精度、特征线拟合特征与拟合精度的比对分析、特征线拟合精度与光顺性的分析计算。分析结果表明,两种数字化曲面具有明显不一样的特征,NURBS渐开螺旋面具有良好的精度和光顺性。