结合有限元法和接触理论的内齿轮副啮合刚度计算方法

提出了一种将有限元方法和接触理论相结合的内啮合齿轮副啮合刚度计算方法。该方法通过齿轮整体和局部有限元模型分离出啮合点宏观变形,利用线接触变形解析公式计算啮合点接触变形,求解非线性啮合平衡方程后得到齿轮副时变啮合刚度和载荷分布。该方法相比一般有限元法具有更高的计算效率和稳定性,同时克服了解析方法难以考虑斜齿轮和不同齿圈结构影响的缺点。最后,分析了内齿圈不同支撑数目和齿圈厚度对啮合刚度的影响。该方法可为内齿轮副强度及动态特性设计提供有效指导。     

盾构机刀盘四齿轮并联驱动的载荷均衡性仿真

建立了盾构机刀盘四齿轮并联驱动系统的动力学方程,运用UG软件建立了该系统的三维模型,并利用ADAMS软件对该系统进行了动态仿真,分析了啮合阻尼、啮合刚度、齿侧间隙和主动齿轮布置方式等因素对齿轮副载荷均衡性的影响。研究表明,各个齿轮副啮合刚度和啮合阻尼相差越大,载荷分配就越不均匀;齿侧间隙在驱动载荷变化时对载荷均衡性影响较大;主动齿轮不同布置方式对传动系统的传动平稳性有较大影响。分析结果可为多齿轮并联驱动系统的设计与制造提供理论依据。     

斜齿面齿轮齿面接触问题的有限元-线性规划解法

提出了一种基于有限元及线性规划计算斜齿面齿轮齿面接触区域载荷分布及啮合刚度的方法。建立了斜齿面齿轮齿面的数学模型,基于matlab实现其齿面及接触轨迹的可视化;基于有限元思想,并结合线性规划改进的单纯形算法,得到齿面接触区域各点载荷分配;根据接触区域平均变形量和载荷计算了啮合齿对的啮合刚度;计算了接触区域最大压应力,并与Hertz理论的计算结果进行对比,验证该线性规划算法的有效性。     

高重合度摆线内齿轮副时变啮合刚度计算与齿间载荷分配研究

高重合度摆线内齿轮副时变啮合刚度计算和齿间载荷分配是其动力学分析和强度设计的基础,由于是多齿啮合,齿间载荷分配非常复杂,属于静不定问题。结合现有文献,考虑了真实的过渡曲线和精确的轮齿建模,采用更为准确的齿面赫兹接触刚度计算方法,基于势能法建立了与摆线齿形相适应的单轮齿对啮合综合刚度模型,针对该齿轮副的传动特点,构建了其变形协调方程,提出了多齿啮合齿间载荷分配模型。为验证所建模型的正确性并提高仿真分析效率,在ABAQUS中利用Python脚本编程进行二次开发,实现了精确化建模、参数化分析和自动化操作,根据齿轮加载接触分析结果和基于有限元法的轮齿对受载啮合刚度计算方法,得到了不同负载转矩作用下单轮齿对、多轮齿对的啮合综合刚度和轮齿啮合力。对比表明,计算结果趋势吻合、数值接近,验证了建模分析的正确性,可为动力学分析和强度计算提供基础。     

斜齿轮轮齿接触有限元分析的新方法研究

提出一种新的基于斜齿轮啮合特性的有限元网格单元划分方法,使得啮合过程中接触线依次通过各单元节点,求解齿面柔度系数矩阵。建立斜齿轮轮齿接触分析模型,考虑参与及未参与啮合点的相互影响,通过引入边界条件及变形协调条件,建立及求解载荷平衡方程。计算一组斜齿轮副算例的时变啮合刚度、齿面变形及齿面载荷分布,且与按GB/T 3480—1997计算的啮合刚度进行对比,证明该方法的可靠性。     

大功率高速行星齿轮减速器啮合刚度计算研究

针对某NGW型大功率高速行星齿轮减速器,运用自编程序生成内、外啮合齿轮副的精确啮合节点坐标,结合三维建模软件和有限元计算软件,将各啮合节点坐标导入仿真环境下生成真实齿面上的各个有限元节点,通过依次在各啮合节点上施加单位载荷进行变形计算,提取各啮合结点的综合变形结果并组装得到内、外齿啮合齿面的柔度系数矩阵,进而得到各啮合齿面的啮合刚度。根据此减速器内、外啮合齿面在各啮合位置的啮合刚度值及齿面啮合周期内的啮合刚度波动规律,对减速器的齿轮参数选取的优劣做出判断。     

齿轮轮齿误差对啮合刚度影响规律研究

建立了斜齿圆柱齿轮承载接触分析模型,综合考虑齿距偏差、齿廓偏差和螺旋线偏差,提出了考虑轮齿误差时齿轮啮合刚度计算方法。分析了在不同精度等级和载荷作用时,斜齿轮啮合刚度和接触线总长度的变化规律。计算结果表明:啮合刚度曲线在一个啮合周期内的变化趋势和实际接触线总长度变化趋势基本一致。在同一精度等级下,随着载荷的增大,含误差的齿轮啮合刚度逐渐增大,并最终趋近于理想齿轮啮合刚度。而在相同载荷下,由于误差的存在,齿轮精度等级越高,其啮合刚度越大。     

大功率高速行星齿轮减速器啮合刚度计算研究

针对某NGW型大功率高速行星齿轮减速器,运用自编程序生成内、外啮合齿轮副的精确啮合节点坐标,结合三维建模软件和有限元计算软件,将各啮合节点坐标导入仿真环境下生成真实齿面上的各个有限元节点,通过依次在各啮合节点上施加单位载荷进行变形计算,提取各啮合结点的综合变形结果并组装得到内、外齿啮合齿面的柔度系数矩阵,进而得到各啮合齿面的啮合刚度.根据此减速器内、外啮合齿面在各啮合位置的啮合刚度值及齿面啮合周期内的啮合刚度波动规律,对减速器的齿轮参数选取的优劣做出判断.     

随机风载下含裂纹故障风机增速箱动力学研究

裂纹故障会导致齿轮时变啮合刚度发生变化,进而引起系统振动响应改变.以风机增速箱为研究对象,考虑基圆和齿根圆不重合,采用改进能量法分别计算了各级齿轮副的时变啮合刚度,并计算、分析了太阳轮裂纹故障对啮合刚度的影响.风机增速箱运行于自然风载荷环境中,受时变转速和转矩激励,综合考虑齿侧间隙、时变啮合刚度、啮合误差等因素,利用集...     

斜齿圆柱齿轮轮齿动态响应的研究(第二部分,载荷分布与啮合刚度)

根据[1]所提出的计算方法,本文计算了一对斜齿圆柱齿轮轮齿啮合过程的载荷分布和啮合刚度。与[1]的计算结果对比发现,斜齿圆柱齿轮轮缘与轮辐对斜齿轮在啮合过程中的载荷分布和啮合刚度波动影响很大。因此,在计算斜齿圆柱齿轮的变形时,应选择合理的计算模型。     

A semi-analytical method of time-varying mesh stiffness in concentric face gear split-torque transmission system

Concentric face gear split-torque transmission system (CFGSTTS) has great applied value in the field of aeronautical transmission due to the characteristic of high integration. Mesh stiffness, as one of the most primary sources of vibration, is vitally important for the dynamic performances of gear transmission system. The existing finite element method (FEM) and analytical method (AM) are not suitable for tackling the mesh stiffness calculation of closed-loop multi-branch system such as CFGSTTS. Thus, a semi-analytical method (SAM) is presented and verified, which combines the high precision of FEM with the high efficiency of AM. Additionally, the differences between the mesh stiffness of independent face gear drive and that of the same gear pair in CFGSTTS under accordant load is researched by applying SAM. The influence rules of distribution angle and load condition on the mesh stiffness of gear pairs considering system structure are also studied. Results demonstrate that the mesh stiffness of gear pairs in CFGSTTS is time-varying and tends to be consistent with each other by adjusting load parameters.     

时变刚度渐开线直齿轮啮合冲击响应的研究

由于渐开线齿轮啮合刚度的时变性，传动齿轮的振动具有非线性振动的性质。文章将啮合冲击区分成若干微区段，视各微区段啮合刚度为定值，采用时域方法辨识出相应模态参数，用直线拟合固有频率分布曲线，从而提出一种新的计算啮合冲击响应的方法，其计算结果与实验值相符，并给出了用固有频率作敏感因子诊断轮齿裂纹故障的例子。     

考虑齿距偏差的直齿轮转子系统振动特性分析

针对工程实际中的齿轮存在齿距偏差,主要研究齿距偏差对齿轮系统振动特性的影响。考虑齿距偏差,建立了齿轮啮合刚度和传递误差模型,在此基础上,建立了通用齿轮啮合动力学模型,将该模型与转子系统有限元模型进行耦合,得到了齿轮转子系统有限元模型,分析了齿距偏差对系统振动响应的影响。研究结果表明:由于齿距偏差的存在,齿轮双齿啮合区刚度降低,无载荷传递误差增大,齿轮系统振动增大,频谱图中出现啮合频率及其高次谐波的边频带成分,这些边频带主要由主动和从动齿轮的转频及其倍频组成。减小齿距偏差和增大作用扭矩均能降低齿距偏差引起的边频带幅值。研究结果可为含齿距偏差的齿轮振动分析提供理论依据。     

含侧隙齿轮副的动载荷分析

以振动理论为基础，提出一种考虑齿轮拍击振动的齿轮动载荷的数值计算方法。建立计算动载荷的齿轮冲击模型，在模型中考虑了齿轮正、反冲击时实际的啮合刚度，并给出啮合柔度的计算方法。分析在考虑静态传递误差、啮合刚度、侧隙、摩擦力及外部扭矩变化等多种激励时，作用在轮齿上的动态载荷以及整个齿轮上的综合动态载荷的计算公式。最后通过实例分析作用在轮齿上的动态载荷、综合动态载荷变化规律以及相关激励参数对动态载荷的影响。     

输入转矩对驱动桥系统动力学特性的影响

在驱动桥系统中,滚子轴承是连接轴系与壳体的关键部件,其刚度具有各向耦合性和非线性特性,且与输入转矩有关。为准确高效地分析输入转矩对驱动桥系统动力学特性的影响,基于非线性轴承理论、有限元法和模态综合方法,建立包含主减速器总成、差速器总成、轮毂总成和桥壳等部件的完整驱动桥系统动力学分析模型,根据输入转矩大小的不同,定义轻载、中载和重载三种典型工况,分别计算各工况下的非线性轴承刚度,分析轴承刚度随输入转矩大小变化的特点,对驱动桥系统进行单位谐波传动误差激励下的动力学分析,研究输入转矩对驱动桥系统动力学特性的影响,分析不同工况下准双曲面齿轮动态啮合力的频响特性。计算结果表明,驱动桥系统动力学特性随输入转矩大小变化具有一定规律,能有效指导驱动桥系统的减振降噪设计,避开危险工况。     

On modeling and vibration of gear drives influenced by nonlinear couplings

Gear drives are one of the most common parts in many rotating machinery. When the gear drive runs under lower torque load, nonlinear effects like gear mesh interruption can occur and vibration can be accompanied by impact motions of the gears. This paper presents an original method of the mathematical modeling of gear drive nonlinear vibrations using modal synthesis method with degrees of freedom number reduction. The model respects nonlinearities caused by gear mesh interruption, parametric gearing excitation caused by time-varying meshing stiffness and nonlinear contact forces acting between journals of the rolling-element bearings and the outer housing. The nonlinear model is then used for investigation of gear drive vibration, especially for detection of nonlinear phenomena like impact motions, bifurcation of solution and chaotic motions in case of small static load and in resonant states. The theoretical method is used for investigation of two-stage gearbox nonlinear vibration.     

双压力角非对称齿廓渐开线齿轮的振动分析

基于非对称渐开线圆柱齿轮传动时的啮合机理和齿轮系统动力学。同时考虑到齿轮系统时变啮合刚度和静态传递误差的影响，建立了齿轮动力学模型，利用数值积分和数值仿真方法对其进行了非线性振动研究。比较了标准齿轮与非对称齿轮的振动特性，分析了齿轮系统各参数对系统动态特性的影响。仿真结果对考虑动载荷情况下的油膜厚度计算提供了基础数据，为进一步研究非对称渐开线的各种特性提供了理论依据。     

Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear

Gear wear is one of the most common gear failures, which changes the mesh relationship of normal gear. A new mesh relationship caused by gear wear affects meshing excitations, such as mesh stiffness and transmission error, and further increases vibration and noise level. This paper aims to establish the model of mesh relationship and reveal the vibration characteristics of external spur gears with gear wear. A geometric model for a new mesh relationship with gear wear is proposed, which is utilized to evaluate the influence of gear wear on mesh stiffness and unloaded static transmission error (USTE). Based on the mesh stiffness and USTE considering gear wear, a gear dynamic model is established, and the vibration characteristics of gear wear are numerically studied. Comparison with the experimental results verifies the proposed dynamic model based on the new mesh relationship. The numerical and experimental results indicate that gear wear does not change the structure of the spectrum, but it alters the amplitude of the meshing frequencies and their sidebands. Several condition indicators, such as root-mean-square, kurtosis, and first-order meshing frequency amplitude, can be regarded as important bases for judging gear wear state.     

Influences of friction and mesh misalignment on time-varying mesh stiffness of helical gears

As one of the most important excitation sources of vibration, time-varying mesh stiffness of helical gear pairs need accurately calculated. Compared with spur gears, friction in helical gears is significant. This work for the first time presents an improved calculation method for the mesh stiffness of helical gears with effect of friction incorporated. Firstly, helical gear is sliced into number of pieces along its axis direction and each piece could be regarded as spur gear. Then forces applied to each piece including friction force are analyzed. Potential energy method is employed to develop time-varying mesh stiffness of each piece pair of both kinds of helical gears with different transverse and axial contact ratios. Furthermore, influences of various working conditions and misalignment on mesh stiffness are also investigated. Results indicate that effect brought by friction on total mesh stiffness should be not neglected. The reduction amount of stiffness increases with lower speed, heavier load and rougher surface. The stiffness difference between cases with and without friction is affected by gear geometry and mounting parameters like module, helix angle and mounting misalignment. This work provides an essential tool for comprehensive dynamics analysis with consideration of the relationship between stiffness and working conditions.     

含间隙的斜齿轮副扭振分析与试验研究

建立了科齿轮副的间隙型非线性扭振模型，其中考虑了斜齿轮副的啮合综合误差，齿侧间隙和时变啮合刚度。采用三维有限元法计算了斜齿轮副啮合刚度，用三次样条插值拟合得到时变啮合刚度函数。用数值积分方法对系统的非线性动力学微分方程进行了求解，获得了斜齿轮副在外转矩作用下受静态传动误差激励的非线性稳态强迫响应，并对系统的动态响应进行了测试，试验和理论计算结果了一致性证实了本文所提出模型和解法的正确性。