准双曲面齿轮齿面接触应力过程计算

针对准双曲面齿轮疲劳破坏中出现几率最高的齿面接触疲劳强度问题,在齿面接触分析（TCA）和承载接触分析（LTCA）的基础上,采用弹性力学中2个空间曲面弹性接触计算方法,计算了齿轮副在整个啮合过程中齿面最大接触应力的变化过程,指出了最大接触应力所在的齿面位置,这一点与现有的强度计算方法不同,为实际工程中准双曲面齿轮的接触强度设计与校核提供了更为准确的方法。     

Design and simulation of meshing of new type of worm-gear drive with localized contacts

The design and simulation of meshing of a single enveloping worm-gear drive with modified surfaces is presented. Generally worm-gear is generated by the hob which is identical, to the worm. This process guarantees the conjugation between the worm and the gear but results in a line contact at every instant which is very sensitive to misalignment. The localization of bearing contact is necessary to reduce the sensitivity of the worm-gear drive to misalignment. Practically this localization is achieved by application of an oversized worm type hob to cut the worm-gear. The oversized hob approach is very practical and effective to localize bearing contact but can not provide the conjugation between the worm and the modified worm-gear. This work proposes an analytical procedure to make the worm surface conjugate to the worm-gear which is cut by the oversized hob. The developed computer program allows the investigation of the influence of misalignment on the shift of the bearing contact and the determination of the transmission errors, the contact ratio and the principle curvatures. The developed approach has been applied for ZK type of single-enveloping worm-gear drives and the developed theory is illustrated with a numerical example.     

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.     

Multi-objective optimization modification of a tooth surface with minimum of flash temperature and vibration acceleration RMS

The minimum of tooth surface flash temperature and vibration acceleration RMS design is proposed and analyzed. The tooth contact analysis (TCA) and the load tooth contact analysis (LTCA) method and multi-objective optimization are also detailed. Satisfying design variables in multiple physical quantities leads to the minimum of multi-objective optimization. Considering the tooth surface loading conditions are uniform or not, the optimal modification of the tooth surface for improving gear comprehensive characteristics under various load bearing conditions is improved. The tooth surface flash temperature and vibration acceleration root mean square (RMS) values in different transmission modes of marine ship power rear gears drive system are derived. This research considers the multi-objective optimization modifications of tooth surface, and its main purpose is to propose an approach to help design tooth corrections to simultaneously optimize several objective physical quantities.     

一种弧齿锥齿轮安装误差变动范围的确定方法

提出一种接触印痕位置参数分析法,用于确定弧齿锥齿轮安装误差的可变动范围。根据设计要求的啮合性能,采用局部综合法,设计弧齿锥齿轮加工参数,得到弧齿锥齿轮副齿面。在齿面参考点处的压入深度为0.006 35 mm的条件下,计算小轮驱动力矩。在此力矩作用下,进行安装误差状态下的轮齿加载接触分析(Loaded tooth contact analysis,LTCA),获得描述承载齿面接触印痕的位置参数。以接触印痕边界点到齿面边界的距离为设计目标,分别以不同类型的单因素安装误差为设计变量,采用优化设计方法确定接触印痕在齿面有效边界内变动时,对应的安装误差的变动范围。以某航空发动机附件传动系统中的弧齿锥齿轮为对象,依据上述方法,确定出不同类型安装误差的可变动范围,验证上述方法的有效性。所提出的方法为合理确定弧齿锥齿轮副安装误差的变动范围提供一种参考。     

变位非正交面齿轮副小轮齿向修形轮齿接触分析

建立了变位非正交面齿轮的加工坐标系和啮合坐标系,推导了变位小轮及变位非正交面齿轮的齿面方程,计算得到了面齿轮数值齿面,分析了变位对非正交面齿轮齿宽的影响。在变位的基础上研究了对小轮进行齿向鼓形修形,而面齿轮不修形的修形方式。分别对未变位、变位、变位加小轮齿向修形的三种非正交面齿轮传动形式进行考虑安装误差的轮齿接触分析。研究表明：随着变位系数增大,非正交面齿轮最小内半径、最大外半径及极限齿宽均减小;变位不影响非正交面齿轮副的接触规律;小轮齿向修形能降低接触轨迹对安装误差的敏感性,会引起幅值较小的直线型传动误差。     

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载体分布、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的分配合理，接触印痕受安装误差的影响较小，具有较高的强度和较好的动态特性。     

Tooth contact analysis of face-gear drives

Based on the face-gear generation process, the analytical geometry of the face-gear drive and its mathematical model for tooth contact analysis of the face-gear and the spur pinion meshing were derived. The tooth contact paths and the transmission errors due to assembly error along the axis of face-gear, misalignment of crossed and angular displacements between axes of spur pinion and face-gear were analyzed. Furthermore, the conditions of undercutting and pointing in the generation process were studied. Several design charts were then developed. Finally, the conditions of undercutting and pointing for a face-gear drive were all identified in meshing with and without assembly error along the direction of the axis of face-gear and misalignment of angular displacement between axes of spur pinion and face-gear. Several numerical examples were also presented.     

高齿弧齿锥齿轮的承载啮合仿真和动态性能试验

研究了高齿弧齿锥齿轮和普通弧齿锥齿轮的加载接触过程，对比了二者在载荷作用下的齿面载荷分布、齿面加载接触印痕和承载传动误差，计算了齿根弯曲应力。在台架试验台上测定了高齿弧齿锥齿轮和普通弧齿锥齿轮的噪声和振动量，实验证明高齿弧齿锥齿轮齿面载荷分布合理，弯曲应力较小，具有较低的噪声和较好的动态特性。     

含安装误差的鼓形齿轮承载接触分析

基于齿轮范成原理，建立修形后直齿的鼓形面数学模型，并根据齿轮接触分析（Tooth contact analysis，TCA）结果进行齿面接触线上接触点的离散。基于Weber能量法，求解齿间载荷分布，并利用线性规划法，求解齿向载荷分布。在得出齿面的实际载荷分布后，建立鼓形齿面的圆柱体模型。利用赫兹原理，对含安装误差的鼓形齿面进行齿面接触应力分布求解。分析结果发现垂直平面误差较轴平面误差对接触应力分布影响更大，起鼓修形后齿面载荷分布虽然得到明显改善，但接触应力值会有所增大。接触应力分布结果与有限元方法结果规律相一致，证明了该方法的合理性，为齿轮承载接触分析（Loaded tooth contact analysis，LTCA）提供了新的简便方法。     

Computerized design of low-noise face-milled spiral bevel gears

An advanced design methodology is proposed for the face-milled spiral level gears with modified tooth surface geometry that provides a reduced level of noise and has a stabilized bearing contact. The approach is based on the local synthesis of the gear drive that provides the “best” machine-tool settings. The theoretical aspects of the local synthesis approach are based on the application of a predesigned parabolic function for absorption of undesirable transmission errors caused by misalignment and the direct relations between principal curvatures and directions for mating surfaces. The meshing and contact of the gear drive is synthesized and analyzed by a computer program. The generation of gears with the proposed geometry design can be accomplished with existing equipment. A numerical example that ilustrates the proposed theory is presented.     

Ease-off修形准双曲面齿轮齿面动态抗磨设计与分析

为了改善准双曲面齿轮动态性能、减小齿面磨损提出齿面动态抗磨修形设计与分析方法。小轮修形齿面表示为共轭齿面与法向Ease-off曲面两个矢量的和,Ease-off曲面通过预置抛物线修形参数及几何传动误差参数表达。提出考虑磨损深度影响的齿面承载接触分析（Tooth contact analysis with wear,WLTCA）数值方法,该方法通过承载接触分析（Tooth contactanalysis,LTCA）方法获得啮合刚度及齿面静载荷,在此基础上根据动力学分析获得齿面动载荷,结合Archard磨损公式进一步获得齿面磨损量,将齿形更新时的同时啮合齿对的磨损量叠加到齿对的初始间隙,为磨损后的LTCA计算提供准确的参数,重复以上循环可得到齿形更新后齿面上任一点的磨损深度及次数。以无磨损时法向相对振动加速度均方根最小、齿面磨损量最小进行修形优化获得最优Ease-off曲面;分析齿面磨损与系统动态响应之间的耦合作用。结果表明最优Ease-off齿面主要通过齿廓修形减少了磨损量,有效改善了系统动态响应。该方法充分考虑了齿面修形、磨损、动态响应的耦合性且计算效率较高,为高性能准双曲面齿轮齿面抗磨、减振设计与分析提供理论参考。     

弧齿锥齿轮的齿面主动设计及试验验证

齿面印痕和传动误差对齿轮传动的性能起着决定作用,根据齿面印痕的位置、方向及传动误差幅值的要求,在齿面上设计三个啮合点,通过对这三个啮合点的控制,达到对齿面啮合质量的全程控制。在此基础上,为了满足不同的加工要求,又提出按照给定的垂直轮位的值对齿面进行再设计,保证传动误差的幅值不变且接触迹线仅有较小的改变,为弧齿锥齿轮副设计提供了新的方法和途径。最后在磨齿机上加工了一对齿轮,通过印痕检测验证了本文设计方法的正确性。     

高齿准双曲面齿轮的研究

研究基于局部综合法的高齿准双曲面齿轮ＨＦＴ法切齿参数的设计,给出用ＨＦＴ法加工准双曲面齿轮副的齿面接触分析方法,并在此基础上,比较了普通齿和高齿２种准双曲面齿轮副的传动误差曲线和啮合区。结果表明,高齿准双曲面齿轮副具有较好的啮合性能。     

轴线不平行度对人字齿轮齿面啮合性能的影响分析

人字齿轮传动由于加工安装误差、轴承支撑布置无法对称等条件,不可避免会产生轴线的微量不平行。因人字齿轮齿宽较大、啮合刚度高、标准渐开线齿面线接触等特点,微量的轴线不平行度就会导致严重的齿面偏载,影响齿轮传动的平稳性和可靠性。因此,采用了小轮较大轴向浮动的轴承支撑结构,并研究了小轮轴向浮动的人字齿轮齿面承载接触仿真(LTCA)方法,通过大、小轮轴向固定和小轮轴向浮动两种不同轴承支撑结构的仿真比较,说明小轮轴向自位浮动可以有效改善齿面偏载,为人字齿轮传动系统的设计提供了参考。     

弧齿锥齿轮的齿面主动设计

齿面印痕和传动误差对齿轮传动的性能起着决定作用,针对齿面印痕和传动误差,提出弧齿锥齿轮点啮合齿面主动设计的方法。该方法突破了传统齿轮设计的局限性,采用“局部共轭原理”和“局部综合法”,并依据弧齿锥齿轮的加工原理,使齿轮设计人员能够按照要求的传动性能来设计齿面的形状,并可在摇台结构的铣齿机进行加工。齿面主动设计能保证齿面在整个啮合过程中满足预先设计的传动误差和齿面接触路径的要求,从而达到对齿面啮合质量的全程控制,它为弧齿锥齿轮副设计提供新的方法和途径,这对于高速和重载齿轮以及有特殊要求的齿轮的设计具有十分重要的意义。     

LUBRICATION AND LOADED TOOTH CONTACT ANALYSIS FOR SPIRAL BEVEL AND HYPOID GEARS

ＬＵＢＲＩＣＡＴＩＯＮＡＮＤＬＯＡＤＥＤＴＯＯＴＨＣＯＮＴＡＣＴＡＮＡＬＹＳＩＳＦＯＲＳＰＩＲＡＬＢＥＶＥＬＡＮＤＨＹＰＯＩＤＧＥＡＲＳＬＵＢＲＩＣＡＴＩＯＮＡＮＤＬＯＡＤＥＤＴＯＯＴＨＣＯＮＴＡＣＴＡＮＡＬＹＳＩＳＦＯＲＳＰＩＲＡＬＢＥＶＥＬＡＮＤ...     

人字齿轮直线型对角修形设计及成形磨原理

为了降低承载传动误差波动产生的振动激励，提出了成形磨人字齿轮直线型对角修形优化设计。根据ISO对角修形定义，计算齿顶、齿根修形起始线在旋转投影面上的螺旋角，将修形曲线设计为直线型，给定最大修形量，确定对角修形的齿面方程。利用齿面接触分析和轮齿承载接触分析，以工作载荷下人字齿轮承载传动误差波动量最小为优化目标，采用遗传算法优化对角修形参数。确定以目标修形齿面法向偏差的平方和最小的目标函数，以螺旋角、模数、压力角为设计变量，采用遗传算法分别对齿顶和齿根修形区域进行逼近，从而实现对角修形的成形磨加工。结果表明，人字齿轮直线型对角修形可以将承载传动误差波动量降低到36.65%；采用三截面砂轮成形磨的理论误差控制在1μm以内，获得较高的齿面精度；试验人字齿小轮齿的检测结果控制在4级精度以内，并进行了齿轮副的滚检试验，从而验证该方法的有效性。     

弧齿锥齿轮几何传动误差的设计与分析

提出基于传动误差设计的概念和方法。通过TCA和LTCA对传动误差曲线的设计进行啮合仿真分析的结果表明 ,根据工作载荷合理地确定传动误差转换点处的幅值与总的幅值 ,可降低弧齿锥齿轮对误差的敏感性 ,可使工作载荷下传动误差波动幅值最小 ,同时可有效地避免或减轻边缘接触。     

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.