齿轮传递系统振动功率流特性研究

从振动噪声传递的经典模型(即振源-路径-接受体)出发，分别对轴、轴承、箱体建立模型，进行动力学分析，其中把轴看作受到广义力作用下的空间梁，应用传递矩阵法推导其导纳矩阵；轴承采用Lim模型，箱体看作一个刚体模型。采用子结构导纳方法，推导了传递到子系统的功率流表达式，研究不同阻尼比对传递到箱体和系统的功率流的影响，为进一步研究齿轮箱类结构振动特性奠定分析基础。     

叶片振动影响下双盘转子-轴承系统的稳定性与分岔

研究叶片与转子-轴承系统的耦合非线性振动,建立了一个带叶片的双盘转子-轴承系统的非线性动力学模型,其中包含一个弹性转轴、两个滑动轴承、两个刚性圆盘和两组弹性叶片.为了分析叶片的惯性影响,将其简化为单摆模型.采用4阶Runge-Kutta法进行了数值模拟,并利用分岔图、三维谱图、轴心轨迹和Poincaré映射图等方法分析了系统的非线性动力学特性.研究发现,随着转速的变化,系统响应演化出了倍周期运动、概周期运动、混沌运动和倍周期分岔等典型的非线性动力学行为.在与忽略了叶片振动的转子系统对比后发现,叶片振动使转子发生混沌运动的转速区域增大.在某些参数条件下,采用不同的叶片刚度,叶片振动可能引起转子系统产生混沌运动.     

固定界面动态子结构方法研究车内噪声问题

随着社会的发展，降低车内噪声越来越受到人们的重视。由于整车结构复杂，本文采用包括软子结构的动态子结构方法，把整车模型划分为多个子结构，包括动力总成子结构、副车架子结构、车身与车内声场耦合子结构、非簧载质量子结构及多个线性和非线性软子结构等。采用固定界面模态综合法，建立整车结构车内声场流固耦合动力学模型。对于车身与车内声场耦合子结构，由于其总质量和刚度矩阵为非对称矩阵，传统的模态叠加法不能应用到耦合系统中，本文引入了左特征向量的概念，用左特征向量左乘原方程，使耦合系统微分方程得到解耦。在已建立的总系统动力学模型基础上，在时域内对前后轴分别激励时汽车振动和车内噪声特性进行仿真模拟，并通过台架试验对仿真结构进行验证。     

一种双转子罗茨鼓风机动力学传递模型

针对罗茨鼓风机振动噪声问题,将风机结构简化为转子、轴承、箱体、隔振器支撑、弹性基础等五个子结构,建立一种简化的空间柔性耦合动力学方程。采用子结构传递矩阵法推导各子系统动态传递矩阵及功率流的表达式;从结构噪声能量传输角度出发,分析了轴承刚度、箱体质量等结构参数变化对风机功率流传递性能的影响。结果表明:减小轴承的刚度,会降低输入到箱体的功率流;通过增加箱体质量,可以降低振动。此结果为具有双转子壳类机器的结构优化与动态设计提供理论基础。     

推力主动磁轴承的动特性参数辨识

针对五自由度刚性非对称磁轴承 -转子系统 ,建立了系统动力学模型 ,在此基础上推导出系统动特性参数辨识公式 ,并用多频电流激励法辨识出参数 .与理论计算结果相比表明 :系统所建模型符合实际 ,辨识方法有效 ;径向轴承在 x和 y方向上的力 -刚度和力 -电流系数相同 ,与推力轴承对应系数相比稍大 ;推力轴承对转子横向振动产生的耦合效应明显影响系统的稳定性 ,在设计系统时必须加以考虑     

爆炸冲击荷载作用下弹性支撑拱结构的动力响应分析

利用数值分析方法,系统研究了爆炸冲击荷载作用下弹性支撑对拱结构动力特性和动力响应的影响。研究表明:弹性支撑使拱结构自振频率减小,随着弹性支撑刚度系数的增加,各阶频率逐渐增大,其中对低阶频率的影响比高阶频率大;弹性支撑临界刚度系数是弹性支撑拱结构动力特性的分界点,此时结构第一阶、第二阶的频率几乎重合,出现模态转向;弹性支撑并不总是具有缓冲减振的效果,弹性支撑刚度系数较小时,缓冲减振效果较好,但会引起较大的拱脚竖向位移,在工程实际中可能并不适用;弹性支撑刚度系数较大时,在爆炸冲击消失以后,由于非线性振动等因素的影响,会出现振动增强,尤其当弹性支撑刚度系数接近弹性支撑临界刚度系数时,结构振动增强最为剧烈,此时设置阻尼支撑可消除振动增强。本文结果表明应综合设置刚度系数较大的弹性支撑和阻尼支撑以提高结构的抗爆承载能力。     

航空发动机整机耦合动力学模型及振动分析

面向航空发动机整机振动, 建立了航空发动机转子-滚动轴承-机匣耦合动力学模型. 该模型具有如下特点: (1)考虑转子、滚动轴承及机匣之间的耦合作用; (2)考虑了实际航空发动机的弹性支承及挤压油膜阻尼效应; (3)将转子考虑为等截面自由欧拉梁模型, 运用模态截断法进行分析; (4)考虑了滚动轴承间隙、非线性赫兹接触力以及变柔性VC(Varyingcompliance)振动; (5)考虑了转子与机匣之间的碰摩故障. 运用数值积分方法研究了航空发动机的整机振动规律, 包括: 滚动轴承VC振动分析、弹性支承刚度对耦合系统临界转速的影响、转轴模态截断阶数NM对系统响应的影响分析、挤压油膜阻尼器参数对系统响应的影响分析、突加不平衡的瞬态响应分析以及转静碰摩故障特性分析等.      

核主泵叶轮间隙的轴向振动特性研究

具有径向流的间隙结构广泛存在于轴承结构与旋转机械中,间隙中的流固耦合作用可能影响整体结构的运动稳定性。基于理论间隙模型和核主泵的实际结构,本文对径向间隙流引起的轴向振动进行了多方面的研究。当间隙的一个壁面产生轴向振动并处于旋转状态时,壁面受到由径向流引起的时变轴向力,因此间隙为叶轮提供附加的轴向刚度和阻尼。通过研究以水为介质的理论间隙模型,发现径向间隙流会引起负的等效轴向动力系数（刚度和阻尼）,并且流道形状是影响间隙轴向动力特性的重要因素。扩张流道和平行流道会产生负的轴向动力系数,特别是负阻尼会引起结构振动发散;而收缩流道间隙具有稳定的轴向动力特性。最后,对AP1000核主泵原型叶轮间隙模型进行分析,结果表明,间隙会引起轴向负刚度,并且在一定工况下出现负阻尼,此时系统轴向稳定性及结构安全运行将受到严重的不良影响。     

基于微分求积有限元法的双层微板系统振动特性研究

基于修正的偶应力理论和两变量精化的剪切变形理论,建立了由Winkler-Pasternak连续弹性夹层连接的双层微板系统的自由振动模型,着重推导了系统异步振动的运动微分方程和势能泛函。融合Gauss-Lobatto求积准则和微分求积准则构造了具有C¹连续性的微分求积有限元。通过与已有文献进行对比,验证了数值方法的有效性。详细讨论了各种因素对系统同步和异步振动特性的影响。结果表明,系统的自由振动特性对材料尺度参数、长宽比、长厚比以及边界条件呈现出依赖性;弹性夹层刚度仅对系统异步振动产生作用;随着模态阶次的增大,材料尺度参数和弹性夹层刚度对异步振动频率和模态的影响变得显著。     

核主泵叶轮间隙的轴向振动特性研究

具有径向流的间隙结构广泛存在于轴承结构与旋转机械中,间隙中的流固耦合作用可能影响整体结构的运动稳定性。基于理论间隙模型和核主泵的实际结构,本文对径向间隙流引起的轴向振动进行了多方面的研究。当间隙的一个壁面产生轴向振动并处于旋转状态时,壁面受到由径向流引起的时变轴向力,因此间隙为叶轮提供附加的轴向刚度和阻尼。通过研究以水为介质的理论间隙模型,发现径向间隙流会引起负的等效轴向动力系数(刚度和阻尼),并且流道形状是影响间隙轴向动力特性的重要因素。扩张流道和平行流道会产生负的轴向动力系数,特别是负阻尼会引起结构振动发散;而收缩流道间隙具有稳定的轴向动力特性。最后,对AP1000核主泵原型叶轮间隙模型进行分析,结果表明,间隙会引起轴向负刚度,并且在一定工况下出现负阻尼,此时系统轴向稳定性及结构安全运行将受到严重的不良影响。     

The mathematical phenomenological mapping in non-linear dynamics of spur gear pair and radial ball bearing due to the variable stiffness

In this paper the philosophy of mathematical phenomenological mapping has been applied to the non-linear dynamics of spur gears and radial ball bearings. The spur gear pair dynamics and rolling element bearing dynamics are analyzed separately, but with a tendency to reduce the both of the systems to the same mathematical model. The different reasonable assumptions are taken in every of these analyzes, but they do not have significant influence to the accuracy of the results. The systems are reduced to the single degree of freedom dynamics model. The total gear stiffness and ball bearing stiffness are recognized as the main influent factor of vibration behavior of these machine elements. Therefore, the special attention was paid to the new approach and procedure for stiffness solving and related problems. A single spur gear pair dynamics is solved and the results for total gear stiffness and vibration are shown. The conclusions emphasize the importance of described parallel analyzes in order to reduce the calculation time in solving different phenomena with usage of the principle of mathematical phenomenology.     

车致桥梁支座动反力频谱特性及影响因素研究

建立频域内的车辆-轨道-桥梁垂向耦合动力学模型,包括1/8车辆模型和CRTS-Ⅱ型板式无砟轨道-桥梁-支座模型两部分,以快速求解100Hz以内的桥梁支座动反力。将CRTS-Ⅱ型板式无砟轨道-桥梁-支座模型简化为4层叠合梁,采用Euler梁模拟钢轨、轨道板、底座板和箱梁,采用具有复刚度的弹簧模拟扣件、CA砂浆层、滑动层和桥梁支座。以32m简支桥梁为研究对象,分析了支座动反力的频谱特性,并讨论了轨道不平顺、扣件刚度和支座刚度对支座动反力的影响规律。结果表明:支座动反力在车轮-轨道系统的固有频率附近出现峰值;轨道不平顺幅值在很大程度上决定了支座动反力幅值,其峰值频率点在支座动反力曲线上得以体现;扣件刚度降低可一定程度上减小轮轨力及支座反力峰值、频段幅值及峰值频率;支座刚度降低可以减小支座反力幅值,同时降低峰值频率,其主要通过改变轨道-桥梁耦合系统的频响特性实现,而轮轨力基本不受其影响。     

Planetary gearbox with localised bearings and gears faults: simulation and time/frequency analysis

Planets bearings of planetary gear sets exhibit high rate of failure; detection of these faults which may result in catastrophic breakdowns have always been challenging. The objective of this paper is to investigate the planetary gears vibration properties in healthy and faulty conditions. To seek this goal a previously proposed lumped parameter model (LPM) of planetary gear trains is integrated with a more comprehensive bearing model. This modified LPM includes time varying gear mesh and bearing stiffness and also nonlinear bearing stiffness due to the assumption of Hertzian contact between the rollers/balls and races. The proposed model is completely general and accepts any inner/outer race bearing defect location and profile in addition to its original capacity of modelling cracks and spalls of gears; therefore, various combinations of gears and bearing defects are also applicable. The model is exploited to attain the dynamic response of the system in order to identify and analyze localized faults signatures for inner and outer races as well as rolling elements of planets bearings. Moreover, bearing defect frequencies of inner/outer race and ball/roller and also their sidebands are discussed thoroughly. Finally, frequency response of the system for different sizes of planets bearing faults are compared and statistical diagnostic algorithms are tested to investigate faults presence and growth.     

Nonlinear behavior analysis of geared rotor bearing system featuring confluence transmission

In this paper, the nonlinear vibration characteristics of geared rotor bearing system and the interactions among gears, shafts, and plain journal bearings were studied. First, with the consideration of backlash, transmission error, time-varying mesh stiffness, and layout parameters, the dynamic model of geared rotor bearing system featuring confluence transmission was proposed. The nonlinear oil-film forces were computed with the Reynolds equation for finite-length journal bearings. Second, the responses of meshing vibration and bearing vibration were discussed. The numerical results revealed that the system exhibited a diverse range of periodic, sub-harmonic, and chaotic behaviors. Under different ranges of rolling frequency, the system got into chaos state through different roads. Moreover, in lower frequency, meshing vibration showed coexist of different periodic motions. Lastly, couplings of nonlinear oil-film force and nonlinear gear mesh force were discussed through a range of rolling frequencies. Gear-bearing dynamic interactions were demonstrated through the analysis of dynamic gear loads and dynamic bearing loads, and the coupling effect behaved different when rolling frequency changed.     

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.     

弹性支承条件下车-桥体系的振动分析

本文研究弹性支承条件下车-桥体系的动力分析方法。给出了弹性支承桥梁和车体的振动方程并通过对具有弹性支座简支梁主振动的分析，得出了梁主振型的解析公式。分析计算了上海高架轨道交通典型区段具有弹性支座高架梁的主振型，并利用龙格-库塔法分析计算了车-桥体系在列车通过时的桥梁和车体的振动。计算结果表明，在上海高架轨道交通实际计算参数条件下，考虑支座弹性后桥梁和车体的振动与刚性支承梁的情况相比变化不明显。本文还计算分析了不同橡胶减震支座的刚度及考虑减震支座后系统阻尼比增大等因素对高架梁振动反应的影响，得出一些有益的结论。     

Nonlinear dynamics of a spur gear pair with force-dependent mesh stiffness

Time-varying mesh stiffness is one of the main excitation sources of a gear system, and it is also considered as an important factor for the vibration and noise of gears. Thus, this excitation is usually taken as an input into the gear dynamic model to obtain the system dynamic responses. However, the mesh stiffness of a gear pair is actually nonlinear with respect to the dynamic mesh force (DMF) that fluctuates during the operation of gears. Therefore, the dynamic model of gears with the quasi-static mesh stiffness calculated under a constant load is not accurate sufficiently. In this paper, a dynamic model of spur gear is established with considering the effect of the force-dependent time-varying mesh stiffness, backlash and profile deviation. Due to the nonlinear relationship between the mesh stiffness and the load for each tooth pair, it needs first to determine the load sharing among tooth pairs and then calculate the overall mesh stiffness of the gear pair. As the mesh stiffness and DMF are related, the mesh stiffness is no longer directly taken into the gear dynamic model as an input, but is jointly solved with the numerical integration process using the gear dynamic model. Finally, the dynamic responses predicted from the established gear dynamic model are compared with the experimental results for validation and compared with the traditional models to reveal their differences. The results indicate that the established dynamic model of spur gear transmission has a wider application range than the traditional models.     

Effect of non-linearities in the identification and fault detection of gear-pair systems

This study investigates issues related to parametric identification and health monitoring of dynamical systems with non-linear characteristics. In the first part, a gear-pair system supported on bearings with rolling elements is selected as an example mechanical model and the corresponding equations of motion are set up. This model possesses strongly non-linear characteristics, accounting for gear backlash and bearing stiffness non-linearities. Then, the basic steps of the parametric identification and fault detection procedure employed are outlined briefly. In particular, a Bayesian statistical framework is adopted in order to estimate the optimal values of the gear and bearing model parameters. This is achieved by combining experimental information from vibration measurements with theoretical information built into a parametric mathematical model of the system. In the second part of the study, characteristic numerical results are presented. First, based on the effect of the system parameters on its dynamics, a solid basis is created for explaining some of the peculiar results obtained by applying classical gradient-based optimization methodologies for the strongly non-linear system examined. Some serious difficulties, associated with the existence of irregular response or the coexistence of multiple motions, are first pointed out. A solution to some of these problems, through the application of a suitable genetic algorithm, is then presented. Special problems, related to more classical identification issues associated with the presence of measurement noise and model error, are also investigated.     

Stochastic Vibration Model of Gear Transmission Systems Considering Speed-Dependent Random Errors

A dynamic and stochastic simulation model is developed for analyzing the vibration of gear transmission systems with consideration of the influence of the time-variant stiffness, loads, and gear transmission errors. The gear transmission system is viewed as a non-linear, time-correlated and stationary stochastic system. The transmission errors of gears are decomposed into harmonic and random components based on the spectral analysis. To simulate the random component, a second order Markov process with time-variant parameters considering influence of rotational speed is proposed and the method to determine the model parameters based on the random error of measured gear transmission error is developed. A simulation system is developed. The input to the simulation system is a white Gaussian noise process and harmonic errors, and the output is the rotational vibration acceleration of gears. Experiments are carried out to verify the proposed model. The influences of the random error on vibration acceleration are examined using the developed simulation system.