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.

Super-harmonic resonance of gear transmission system under stick-slip vibration in high-speed train

This work deals with super-harmonic responses and the stabilities of a gear transmission system of a high-speed train under the stick-slip oscillation of the wheel-set.The dynamic model of the system is developed with consideration on the factors including the time-varying system stiffness,the transmission error,the tooth backlash and the self-excited excitation of the wheel-set.The frequency-response equation of the system at super-harmonic resonance is obtained by the multiple scales method,and the stabilities of the system are analyzed using the perturbation theory.Complex nonlinear behaviors of the system including multi-valued solutions,jump phenomenon,hardening stiffness are found.The effects of the equivalent damping and the loads of the system under the stick-slip oscillation are analyzed.It shows that the change of the load can obviously influence the resonance frequency of the system and have little effect on the steady-state response amplitude of the system.The damping of the system has a negative effect,opposite to the load.The synthetic damping of the system composed of meshing damping and equivalent damping may be less than zero when the wheel-set has a large slippage,and the system loses its stability owing to the Hopf bifurcation.Analytical results are validated by numerical simulations.

Experimental Investigation of the Deformation of Helical Gears with Double－Circular－Arc Tooth Profile Using Linear Variable Differential Transformer

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三圆弧齿廓谐波齿轮的负载啮合性能仿真

为揭示负载工况下谐波齿轮传动的多齿啮合状态,提升负载传动性能,建立三圆弧空间齿廓实体单元谐波齿轮有限元模型。定义柔轮与波发生器、齿面间的面-面接触关系,对刚轮施加逐步增大的转角位移,模拟空载、额定转矩至瞬间容许最大转矩时齿面的啮合状态,提取轮齿啮合力和齿面接触压力大小及分布;分析不同工况下轮齿啮合力周向分布和齿面接触压力的变化规律,评估柔轮齿向修形的三圆弧空间齿廓谐波齿轮的负载啮合性能。结果表明:三圆弧空间齿廓在波发生器的长轴区设置最小初始侧隙,形成的凸-凹啮合区可以以更低的接触压力承载更大的负载转矩;利用齿向修形设置从中截面向后截面逐渐增大的初始侧隙有利于形成轴向更宽的齿面接触区;随负载增大,最大啮合力向长轴右侧偏移,右侧啮合力增幅快,呈平台分布;最大接触压力沿周向呈3个峰值分布,且最大值发生在有波发生器径向支撑的中截面,可有效增加负载刚度,提升承载能力。

双参变量下单级齿轮系统动态特性界域结构分析

为了研究含间隙齿轮系统幅值跳跃与齿面冲击的关联关系,用谐波平衡法建立了单级齿轮系统动力学方程组,用Broyden秩2拟牛顿法和拟弧长延续算法求解获得了系统幅频特性的参数界域结构。分析齿侧间隙、静态综合误差、时变啮合刚度、阻尼和频率等参数界域结构中的多值解/齿面冲击特性,探索了参数对系统幅值跳跃、多值解和啮合冲击特性的影响。结果表明,系统的幅值跳跃响应出现在共振频率附近,受齿侧间隙的影响在无间隙的轴承支承处也出现了非线性跳跃;当间隙b>1.55时,间隙对系统多值解/齿面冲击特性不敏感;系统的多值解/齿面冲击特性随时变啮合刚度和静态综合误差的增加而加剧;阻尼能有效抑制系统幅值跳跃和齿面冲击特性,当阻尼ξ>0.3时系统表现出线性特征。

成型滚刀误差对谐波齿轮大变位柔轮精度影响

开展成型滚刀误差引起谐波齿轮大变位柔轮加工误差的仿真计算,定量分析滚刀误差对柔轮几何精度的影响,以更好地控制滚齿精度而提高柔轮的加工质量。建立综合考虑滚刀齿形误差、切削刃螺旋线误差和滚刀径向圆跳动误差的成型滚刀误差模型,进行大变位柔轮滚齿仿真及理论加工误差计算,分析滚刀误差对大变位柔轮齿形误差、基节误差的影响。经研究发现,滚刀切削刃螺旋线误差引起的柔轮齿形误差和基节误差均较大,引起的基节误差值与滚刀切削刃一转内螺旋线误差值大致相同;滚刀齿形误差和径向圆跳动误差对柔轮基节误差影响非常小,滚刀径向圆跳动误差引起的柔轮齿形误差平均值约为滚刀跳动值的40%。

轻载装载机变速箱振动特性分析与试验

为了给装载机变速箱减振降噪提供依据,通过集中参数和有限元法相结合的方式对变速箱进行振动分析。综合考虑液力变矩器激励、齿轮系统内部激励等因素,建立装载机变速箱传动系统的弯-扭耦合动力学模型,求解得到各轴承的动态支反力;建立箱体有限元模型,进行模态分析,以轴承动态支反力为激励,在模态的基础上进行箱体谐响应分析,得到箱体在激励下的振动响应,选择箱体表面的振动测点,分析测点的振动加速度,找到并分析振动峰值及对应振型;最后进行变速箱振动试验,验证仿真的正确性。结果表明:传动系统的激励主要集中在输入和输出平行轴齿轮处,传动系统和箱体振动的峰值频率均和齿轮啮合频率相近,变速箱箱体振动较大的位置位于箱体的底部。试验与仿真对比,试验中存在和仿真相近的峰值频率,仿真和试验所得的振动加速度均方根误差值小于20%,验证了仿真的正确性。

一次性谐波齿轮的裂纹扩展仿真与啮合刚度研究

将航空航天等领域中使用过一次后不再重复利用的机械设备称为一次性机械。柔轮的失效是影响一次性谐波减速器性能的最主要因素,而啮合刚度的变化又可以反映谐波传动的故障特征。以一次性谐波齿轮为研究对象,从应用环境和结构区分一次性谐波齿轮与常规谐波齿轮,分析了一次性谐波传动中柔轮的裂纹萌生位置;基于扩展有限元法,建立了一次性谐波齿轮传动的损伤模型,观察了柔轮裂纹的扩展路径,并据此建立了一次性谐波齿轮传动的裂纹刚度模型;最后,分析了裂纹对一次性谐波传动啮合刚度的影响。研究结论可为一次性谐波齿轮的故障诊断和寿命预测提供理论支撑。

谐波齿轮大变位柔轮滚齿成形机理及误差分析

文中基于滚齿仿真计算研究大变位齿轮成形机理,分析柔轮齿面理论加工误差值及产生原因,为滚齿工艺参数选择提供指导,以改善大变位柔轮滚齿精度。建立滚刀系列切削刃参数化方程,并结合滚齿参数及滚齿时滚刀和工件相互运动关系建立变位齿轮滚切成形数学模型,基于滚齿多刃切削成形特征建立齿面理论加工误差评价模型进行滚齿加工误差仿真计算,还进行了滚齿加工试验验证仿真计算的正确性。对大变位柔轮滚齿成形过程及产生的齿面拓扑误差、齿形和齿向误差进行仿真计算发现:增大滚刀长度可有效减小因齿顶处切削不足而产生的加工误差,计算得到完全切削的滚刀最小长度;减小滚刀轴向进给量可显著减小齿面误差,计算得出齿向误差最大值与滚刀轴向进给量的关系曲线。

谐波减速器柔轮齿形修形啮合性能分析

为探究柔轮齿形修形对谐波减速器啮合性能的作用,建立了中空型谐波减速器的装配模型,采用有限元法分析了柔轮与刚轮啮合情况。以双圆弧齿形的在空载、负载过程中等效变形与等效应力作为对比条件。综合考虑柔轮齿形齿顶修形量,同时调整柔轮齿形轴向的齿高倾角,计算同等边界条件下齿形修形后的等效变形应力情况。对比结果表明,空载与负载条件下,提取柔轮轮齿前缘与后缘的中性层曲线,柔轮的等效变形基本不变,但最大等效应力分别降低至80%与76.6%,啮合性能得到提升。相关研究为谐波减速器的设计、评估及传动性能优化提供有益尝试和参考依据。

谐波齿轮大变位柔轮滚齿误差分析及滚刀设计

基于滚齿仿真计算研究大变位柔轮成形机制,分析其齿面理论加工误差值及产生原因,重新设计滚刀以提高大变位柔轮滚齿精度。建立滚刀系列切削刃参数方程,根据滚刀与工件的几何参数及加工参数确定滚刀与工件相互位置和空间运动关系,进行滚齿切削仿真;根据滚刀多刃切削的成形特点,建立齿面理论加工误差评价模型,对滚齿误差进行仿真计算;基于滚齿加工时滚刀与齿轮法向基节相等原理,重新设计滚刀以减小滚齿齿面偏差。研究发现,标准滚刀加工齿数较多的大变位柔轮时,会因滚刀切削刃数不足而在齿顶处出现欠切削,致使加工误差大;模数、压力角不同于标准滚刀的新滚刀仅需较少切削刃即可实现大变位柔轮的完全切削,且齿面加工误差比标准滚刀完全切削齿面时产生的加工误差略小。研究结果可为大变位柔轮滚齿精度控制研究及滚刀参数选择等提供重要参考。

导引头伺服机构消隙齿轮系统动力学特性分析

消隙齿轮广泛应用于导引头伺服机构惯性稳定平台传动系统中,用于消除回程误差,提高传动精度。目前,对消隙齿轮传动系统的动力学分析大多采用数值方法,然而在求解含时变啮合刚度和间隙的强非线性系统时耗时较长。本文利用集中质量法建立考虑时变啮合刚度的消隙齿轮系统动力学模型,通过对模型的无量纲及归一化处理,运用分段的增量谐波平衡法对消隙齿轮传动系统进行分析,并利用四阶Runge-Kutta法进行数值验证,研究了不同参数对消隙齿轮系统动力学特性的影响规律。结果表明:随扭簧刚度的提高,系统谐振频率也提高,且共振幅值降低;随内部激励的增加、阻尼比的减小,系统由周期运动逐渐变为混沌运动,且共振幅值增大。

A method for detection and quantification of meshing characteristics of harmonic drive gears using computer vision

A lack of accurate description of the meshing characteristics and the corresponding frictional mechanism of the harmonic drive gear has limited progress toward modeling the hysteresis stiffness. This paper presents a method for detection and quantification of the meshing characteristics of the harmonic drive gear based on computer vision. First, an experimental set-up that integrates a high speed camera system with a lighting system is developed, and the image processing is adopted to extract and polish the tooth profiles of the meshed teeth pairs in each acquired video sequence. Next, a physical-mathematical model is established to determine the relative positions of the selected tooth pair in the process of the gear engagement, and the combined standard uncertainty is utilized to evaluate the accuracy of the calculated kinematics parameters. Last, the kinematics analysis of the gear engagement under the ultra-low speed condition is performed with our method and previous method, and the influence of the input rotational speed on the results is examined. The results validate the effectiveness of our method, and indicate that the conventional method is not available in the future friction analysis. It is also shown that the engaging-in phase is approximately a uniform motion process, the engaging-out phase is a variable motion process, and these characteristics remain unchanged with the variation of the input rotational speed. Our method affords the ability to understand the frictional mechanism on the meshed contact surfaces of the harmonic drive gear, and also allows for the dynamic monitoring of the meshing properties.

Deformation analysis of the flexspline of harmonic drive gears considering the driving speed effect using laser sensors

Accurate description of the elastic deformation of the flexsphne is the foundation for optimization design of the structure and conjugate profiles of the harmonic drive gear.This paper proposed an experimental method to investigate the effect of the driving speed on the deformation characteristics of the flexspline.First,an experimental apparatus that integrates a special-fabricated micro-displacement platform and a pair of laser displacement sensors is developed,and the radial displacement of the flexsphne is measured in vertical and horizontal directions.Next,the deformation analyses of the flexsphne at different driving speeds are performed with our method and the conventional method,and the comparison results reveal that the radial displacement of the flexsphne is actually composed of both harmonic and random components,and the amplitude decreases and tends to zero with the increase of the driving speed,especially near the closed end of the flexsphne.Last,the mechanisms of the inherent multi-frequency and amplitude attenuation characteristics of the radial displacement of the flexsphne are discussed.It is indicated that the impact and friction existing in the flexible bearing of the wave generator is likely responsible for the existence of the random component,and the assumption of linear distribution of the flexsphne deformation along the rotating axis is invalid under high speed condition.Our research promotes the further study on the contact-impact problem of the flexible bearing of the wave generator and the transfer characteristic of the elastic deformation of the flexsphne.

Magnetic Field Analytical Model for Magnetic Harmonic Gears Using the Fractional Linear Transformation Method

Magnetic harmonic gears with high gear ratios exhibit high torque densities.However,the revolution and rotation of the eccentric rotor makes the magnetic field analysis complex.In this study,an analytical model of magnetic fields for magnetic harmonic gears is developed by using the fractional linear transformation method.The transformation formula is accurate in theory and suitable for the analysis of magnetic fields with large eccentricity.The rotor eccentricity region in the z-plane is mapped onto a uniform region in the w-plane.The magnetic field solutions are obtained by modulating the magnetic field distributions without rotor eccentricity with the relative permeance function derived from the effect of rotor eccentricity.The torque of magnetic harmonic gears is calculated from the radial and tangential components of the air-gap magnetic fields.Results of the finite element method and prototype test confirm the validity of the analytical prediction.

基于改进运动学法和瞬态动力学的谐波齿轮新型齿廓设计研究

为了提升谐波减速器的啮合性能、改善机器人的工作性能,提出了基于改进运动学法和瞬态动力学的谐波齿轮新型齿廓设计方法。首先,针对公切线双圆弧齿廓和S型齿廓的特点,提出了由S型齿廓和公切线双圆弧齿廓相结合的新型柔轮齿廓;其次,基于改进运动学法计算了共轭刚轮的齿廓,并运用瞬态动力学方法对比分析了在不考虑塑形变形情况下齿廓谐波齿轮的啮合侧隙和柔轮应力。对比分析发现,在不考虑塑形变形情况下,新型齿廓谐波齿轮具有更小的啮合侧隙和等效应力,最小啮合侧隙仅为0.0036 mm,给定负载工况下最大等效应力仅为1211.6 MPa,与双圆弧齿廓柔轮、S型齿廓柔轮、公切线双圆弧齿廓相比都明显降低;新型齿廓设计方法可有效改善谐波齿轮的传动性能,为高性能谐波齿轮设计奠定了理论基础。

谐波转矩对机车传动系统动态特性的影响研究

牵引电机谐波转矩对由牵引电机、齿轮传动、轮轨接触等组成的铁路机车传动系统动态载荷、振动噪声等动态特性有着重要影响。本文基于国内某交流电力机车牵引电机的结构参数和功能特点,通过虚位移原理获得了脉动谐波转矩,并将其作为激励输入到建立的考虑齿轮传动系统动态啮合的车辆-轨道垂-纵耦合动力学模型中,研究了牵引电机谐波转矩对机车传动系统动态特性的影响规律。研究结果表明,谐波转矩会加剧传动系统齿轮动态啮合力和动态传递误差的幅值波动,从而进一步导致轮轨动态相互作用力波动程度加剧,但受轴重转移影响,轮轨黏着系数均方根值增载位轮对小于减载位轮对,且增载位轮对受谐波转矩影响较小,而减载位轮对受谐波转矩影响较大。

双圆弧谐波齿轮齿形参数化设计仿真与验证

谐波减速器的应用领域对产品性能的要求日益提高,尤其是机器人行业,要求谐波减速器具备高寿命、高精度、高转矩容量等。传统的渐开线齿形由于同时啮合齿对数较少,传动能力有限,难以达到使用要求。而双圆弧谐波齿形能满足上述要求。但目前国产谐波减速器主要还是以渐开线齿形为主,对双圆弧谐波齿形的设计原理基本没有掌握。首先介绍了谐波减速器的研究概况,然后讲述了双圆弧谐波减速器齿轮传动的基本原理和双圆弧齿形计算机辅助设计软件的开发,提出了几种齿形设计中如何提高啮合精度的方法和基于复杂柔轮有限元变形分析的中性曲线的三次样条模型。通过理论计算模型开发出了双圆弧谐波齿轮计算机辅助设计软件,极大地提升了设计开发效率,降低了开发成本。通过有限元分析模拟了柔轮的真实变形,有限元模拟出的柔轮变形齿廓能与刚轮齿廓精确啮合,与理论计算出的刚柔轮齿廓能精确啮合达成一致,证明理论模型计算出的双圆弧齿廓是准确无误的。

行星齿轮传动非线性动力学方程求解与动态特性分析

发展了单自由度解析谐波平衡法的应用。对行星齿轮传动系统的多自由度非线性动力学微分方程组，在考虑刚度波动的情况下，推导了行星齿轮系统微分方程组的解析谐波平衡法的计算公式，并采用Ｂｒｏｙｄｅｎ迭代方法求解非线性代数方程组。给出一个算例，用上述方法进行求解，得到了行星齿轮传动的非线性频响特性，与相应的线性系统进行了比较。并研究了时变啮合刚度、误差和齿侧间隙对系统非线性动力学行为的影响。

谐波齿轮传动技术发展概述

简要介绍了谐波齿轮传动的传动原理、特点及应用,着重介绍分析了国内外谐波传动技术的发展现状及重点研究内容,提出了未来需进一步开展的研究工作。