大功率循环泵行星齿轮箱耦合动态特性分析

综合考虑齿轮时变啮合刚度及轮齿误差等内部激励作用下,建立了某大功率循环泵行星齿轮箱齿轮-传动轴-轴承-箱体系统耦合动力学模型。对齿轮箱系统有限元模型进行耦合模态分析,采用模态叠加法对齿轮箱的动态响应进行求解,得出齿轮箱各点振动位移和速度时频域响应历程,为大功率循环泵行星齿轮箱系统的动态性能优化提供了理论依据。     

真实啮合状态面齿轮副时变啮合刚度计算及系统振动特性分析

为了获得面齿轮传动系统真实啮合状态的时变啮合刚度,提出一种能够综合考虑齿面修形和安装误差,运用面齿轮轮齿接触分析(TCA)及承载接触分析(LTCA)技术的时变啮合刚度精确计算方法。构建了面齿轮副的TCA和LTCA模型,采用有限元和数学规划的方法获得轮齿接触变形及齿轮啮合力,计算得到面齿轮副精确时变啮合刚度,进而研究了修形参数对面齿轮系统时变啮合刚度的影响规律;在此基础上,建立了考虑时变啮合刚度以及综合传递误差等内部激励的面齿轮传动系统动力学模型,仿真了精确时变啮合刚度激励下的面齿轮传动系统振动响应,为面齿轮传动系统的动态设计提供了理论参考。     

齿轮传动系统的动态模拟

针对齿轮副非线性振动问题展开研究,综合分析了啮合冲击激励、时变啮合刚度和误差激励对齿轮系统振动的影响。根据扭转啮合刚度定义,分别建立了无齿面缺陷和有齿面缺陷的齿轮三维接触仿真分析模型。计算了两种运行状态下,不同接触位置上的扭转啮合刚度。在进行齿轮副非线性振动的分析时,综合考虑了啮合冲击激励、时变啮合刚度和误差激励等非线性因素,建立了齿轮副非线性动力学模型,采用变步长四阶Runge-Kutta数值积分方法求解了系统的动态响应。     

一种面齿轮传动时变啮合刚度数值计算方法

准确计算时变啮合刚度是齿轮动力学研究的基础。提出了一种面齿轮传动时变啮合刚度数值计算新方法。以直齿圆柱齿轮为例,建立合理的有限元模型,得到直齿圆柱齿轮的时变啮合刚度曲线,并将其与ISO6336方法计算结果进行对比,验证了该啮合刚度计算方法的正确性及有限元模型的精确性。应用该数值计算方法,研究面齿轮传动时变啮合刚度变化规律,得到了精确的面齿轮传动时变啮合刚度曲线。研究结果为面齿轮传动的动力学分析及设计提供参考。     

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。     

考虑安装误差的斜齿轮啮合刚度计算与分析

斜齿轮啮合刚度的分析计算是进行齿轮动力学研究的基础。根据齿轮啮合原理及坐标变换理论利用数值分析方法建立了含有安装误差的斜齿轮啮合有限元模型,提出了考虑安装误差时斜齿轮啮合刚度的有限元计算方法。将安装误差参数化,利用有限元软件仿真分析不同安装误差下斜齿轮啮合刚度的变化,用准静态过程模拟动态行为的方式,得到时变啮合刚度,分析了不同安装误差下时变啮合刚度波动的变化规律。分析结果表明,安装误差会降低啮合刚度,尤其是角度偏差影响更为严重,同时角度偏差对啮合刚度的影响具有一定规律的耦合作用。不同安装误差对啮合刚度的影响具有不同的规律,且轻载条件下的影响较重载明显。     

变风速运行控制下风电传动系统的动态特性

基于齿轮系统动力学的方法对风电传动系统进行研究。运用基于自回归模型的线性滤波法(Auto-regressive,AR)建立的风速模型对实际风场的随机风速进行模拟;根据风力发电机在实际情况中的运行控制策略获得风力发电机齿轮传动系统的时变输入转矩激励;综合考虑风力发电机齿轮传动系统中各个齿轮副的时变啮合刚度、各个滚动轴承的刚度、各个轮齿综合啮合误差等内部激励,采用集中参数质量法建立风力发电机齿轮传动系统的耦合动力学模型;在此基础上建立风力发电机齿轮传动系统的动力学微分方程并进行仿真计算,分别求解风力发电机齿轮传动系统的固有频率、振动响应、动态啮合力和滚动轴承动态轴承力。研究结果为风力发电机传动系统的动态性能优化设计和可靠性设计奠定了基础。     

基于动态啮合刚度的直齿圆柱齿轮动态特性研究

齿轮系统转速直接影响齿轮系统的动态特性,然而在啮合刚度的计算中该因素却被许多学者们忽略。为了研究转速对啮合刚度的影响,基于有限元框架使用平均加速度法提出了一种计算与转速相关的动态啮合刚度的算法,同时对不同转速下的动态啮合刚度进行仿真计算与分析,最后进一步探究了受动态啮合刚度影响后的齿轮系统所具有的相关动态特性。分析表明,动态啮合刚度始终围绕着静态啮合刚度上下波动;随着转速的增加,其波动幅度增加,振荡次数减少;随着转速的变化,动态啮合刚度计算的动态传动误差振幅相对于静态啮合刚度而言大小关系不一致,且计算的齿轮系统共振转速区间或超前或滞后于静态啮合刚度模型;动态啮合刚度影响特定转速区间的齿轮系统的振动周期。对与转速相关的动态啮合刚度的研究可为直齿圆柱齿轮传动性能的改善及减振降噪提供参考。     

齿轮啮合内部动态激励数值根据

把具有内部激励和时变刚度齿轮系统非线性微分方程变换为近似的线性微分方程,把时变刚度激励、误差激励、啮合冲击激励作为右端顶。时变刚度曲线用轮齿三维接触有限元方法求得,啮合冲击激励力用轮齿三维 冲击－动力接触有限元混合法求得。误差激励按精度等级确定的齿轮偏差进行模拟。把激励力作用在整个齿轮系统的三维有限元模型上,以便求得其振动响应。     

变载荷激励下故障半直驱风电行星齿轮传动系统的动力学特性

半直驱风力发电机凭借良好的综合性能,已得到较广泛的技术推广,前景广阔,其关键机械部件——传动系统的动力学问题依然突出。文中针对半直驱风力发电齿轮传动系统,在考虑时变外部激励、齿根裂纹、啮合误差等条件下,运用集中参数法建立了含故障的半直驱风电行星齿轮传动系统动力学模型,计算得到了齿轮传动系统的固有频率及振型。针对随机风场中,风速变化复杂的特点,采用线性滤波AR模型,模拟了脉动风速时程曲线,获得了半直驱风电行星齿轮传动系统的外部激励;利用改进能量法对含裂纹齿轮的啮合刚度进行了数值模拟,获得故障齿轮的时变啮合刚度;引入随机风载及故障动态参数激励,仿真分析了系统的动态响应,研究了时变载荷激励下含故障的行星齿轮系统的动力学特性,为风电齿轮传动系统的故障分析、诊断提供了理论依据。     

RV减速器传动系统动力学特性分析

为深入研究工业机器人用RV减速器动力学特性,采用集中参数法,综合考虑啮合阻尼、时变啮合刚度以及综合啮合误差,建立了RV传动耦合扭转动力学模型,通过数值解法对建立的动力学方程进行求解,得到其振动位移、振动角速度响应及各齿轮副动态啮合力。基于UG与ADAMS建立RV减速器动力学模型,进行仿真分析实验,验证动力学模型的正确性。通过改变啮合刚度分析了啮合力的变化,随着啮合刚度的增加,在一定范围内,传动过程中的啮合力更加稳定,为RV减速器的故障诊断和优化设计奠定基础。     

齿轮系统动态传递误差和振动稳定性的数值研究

建立了计及轮齿时变啮合刚度、啮合阻尼、支承刚度和阻尼的齿轮系统扭转-横向振动耦合的3自由度动力学模型。用数值仿真方法,研究了重合度、支承刚度、啮合阻尼和支承阻尼对齿轮动态传递误差和动力稳定性的影响。研究结论对于高速、精密齿轮传动的动力学设计具有积极意义。     

Effects of dynamic transmission errors and vibration stability in helical gears

Transmission error is an important reason for instability in helical gears. A six-degree-of-freedom dynamic model coupled flexional, torsional and axial motion of a helical gear transmission system, which includes time varying mesh stiffness, bearing supporting stiffness, mesh damping and backlash, is developed, after taking into account the dynamic characteristics and vibration responses of helical gear in three dimensions. Influences of involute contact ratio, bearing supporting stiffness, mesh damping and backlash on the dynamic transmission errors and vibration stability of the helical gear system are investigated using numerical simulation technique. The effects on dynamic transmission errors and stabilities by contact ratio, supporting stiffness and mesh damping as well as gear backlash are analyzed. The intrinsic relationship between above parameters and dynamic transmission errors and stabilities for helical gear system are presented. The stable and unstable regions under different parameters are given. The results in this paper can be helpful to the dynamic and stable design of a helical gear transmission system.     

一种舰船用齿轮传动的动态优化设计方法

舰船用宽斜齿轮副的动态特性直接关系到舰船轮机系统的整体性能。本文考虑单自由度齿轮传动动态特性，以接触线长度的变化代替啮合刚度的变化，求解一对啮合齿轮副的综合啮合刚度及轮齿啮合刚度，以啮合线方向上加速度最小为优化目标函数，给出了基于动力学研究的舰船用齿轮副动态优化设计方法。     

Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations

This paper presents a 26 degree of freedom gear dynamic model of three shafts and two pairs of spur gears in mesh for comparison of localised tooth spalling and damage. This paper details how tooth spalling and cracks can be included in the model by using the combined torsional mesh stiffness of the gears. The FEA models developed for calculation of the torsional stiffness and tooth load sharing ratio of the gears in mesh with the spalling and crack damage are also described. The dynamic simulation results of vibration from the gearbox were obtained by using Matlab and Simulink models, which were developed from the equations of motion. The simulation results were found to be consistent with results from previously published mathematical analysis and experimental investigations. The difference and comparison between the vibration signals with the tooth crack and spalling damage are discussed by investigating some of the common diagnostic functions and changes to the frequency spectra results. The result of this paper indicates that the amplitude and phase modulation of the coherent time synchronous vibration signal average can be effective in indicating the difference between localised tooth spalling and crack damage.     

行星传动动态均载特性分析

从动力学角度建立2K-H型行星传动系统的计算模型.针对各构件的制造和安装误差,运用当量啮合误差原理和动力学分析方法,推导行星传动的运动微分方程,建立系统的动力学分析模型,分析系统的动态均载特性和各误差的参数变化对系统均载特性的影响,此方法计算结果与已有试验结果十分吻合.分析结果表明,浮动太阳轮对系统的均载特性有很大的改善:装配误差和安装误差共同对系统的均载特性起作用,只减少某一个误差值达不到良好的均载效果;转速对系统的均载有较大的影响.     

复杂多级齿轮-转子-轴承系统的动力学建模和数值仿真

以啮合线与水平线的夹角作为参考角度,总结了该参考角度在不同象限时沿着啮合线的相对位移的求解方法,根据此方法可以方便地求出多级齿轮系统的动态啮合力.建立了复杂多级齿轮-转子-轴承系统的动力学模型,模型中考虑了时变啮合刚度、静态传动误差、不平衡质量、轴承刚度和弹性轴的影响.采用数值仿真方法求解了系统的动态响应,得到了转频、啮合频率及其边频带、啮合频率之间的组合频率及其边频带.为工程实践中的多级齿轮-转子-轴承系统的振动特性分析和故障诊断提供了依据.     

Load-related dynamic behaviors of a helical gear pair with tooth flank errors

This study focused on the effects of tooth manufacturing errors (MEs) on the dynamic behaviors of a helical geared system. The composite mesh error is introduced and calculated, which is taken as error excitation in the dynamic model. A combined finite element method (FEM) and analytical contact model is used to investigate the interaction of mesh stiffness and MEs. The dynamic model is developed based on the finite element method and its effectiveness has been verified. By introducing stiffness excitation and error excitation, the effects of mesh stiffness and MEs can be easily distinguished in the total excitation. The influence degrees of these two factors are obtained at different torque levels by simulating the quasi-static and dynamic responses of the system. The results show that the composite mesh error will have great changes under light load conditions, and larger dynamic factors as well as decreased resonance speed will be brought. The excitation produced by manufacturing errors is dominate in the total vibration excitation in a light loading, while the excitation produced by mesh stiffness is becoming the dominating one in a heavy loading.     

Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form

The mesh stiffness is close to rectangular stiffness, and the first harmonic approximate term of rectangular stiffness is generally adopted in the nonlinear gear dynamic analysis. The differences between the rectangular stiffness and its approximate form are analyzed in detail. The frequency response and dynamic factor are calculated by a numerical method, to illustrate the dynamic characteristics of the gear nonlinear system with different mesh stiffness forms. The results show that: The trends of frequency response of gear dynamic system with rectangular stiffness and its approximate form are identical. The jump phenomena are detected in both cases. Without the effect of static transmission error, the dynamic factor with rectangular mesh stiffness is larger than that with approximate mesh stiffness. Under design power and speed condition, the result with approximate mesh stiffness function may deduce reasonless suggestions for a designer. The static transmission error will enlarge the vibration amplitude and dynamic factor when the approximate mesh stiffness is adopted, but the effects on the response of gear system with rectangular mesh stiffness are fractional. The mesh stiffness may excite the odd subharmonic resonance, and the static transmission error may excite the even sub-harmonic resonance respectively.