Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Method for solving dynamic equilibrium equations based on displacement excitation

Mode superposition is a widely used method for solving the dynamic equilibrium equation in structural dynamic analysis.However,the accuracy of this method may be reduced when the dynamic equilibrium equations are set up using displacement excitation.A new method for developing solutions for dynamic equilibrium equations based on displacement excitation is introduced.The dynamic equilibrium equation is decomposed into two parts,namely displacement excitation and velocity excitation,and precise integration and mode superposition methods are combined to solve the equation.Ritz vectors are then used to calculate the static response of the truncated modes of the structure,and a method for determining the number of participating modes is obtained.Using multi-degree-of-freedom systems as two computational examples,the differences in the structural responses obtained from the displacement excitation and acceleration excitation are compared and analyzed.It is shown that the new solution method generates consistent accuracy between the displacement excitation and acceleration excitation.

Study on the Sliding Displacement of a Sliding Structure Subjected to Multi directional Earthquake Excitation

Transient dynamic analysis is used to study the effect of the bidirectional interaction of friction on the response of sliding displacement of a sliding structure subjected to bidirectional earthquake ground motion. The analysis varies the parameters of amplitude ratio of earthquake excitation, the period of the superstructure, and the coefficient of friction in the sliding support. Numerical results show that the sliding structure is significantly influenced by the interaction of frictional forces. So the sliding displacement may be underestimated and the acceleration of the superstructure may be overrated if the bidirectional interaction of frictional forces is neglected.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

Some Properties of Two-mode Displaced Excited Squeezed Vacuum States

In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.

大体积混凝土板微振动控制能力的测试与分析

精密大科学设施具有十分严格的微振动控制要求。为研究某大型精密设施内大体积混凝土底板对微振动的控制效果并为类似项目建设提供参考,在该设施建设现场进行了冲击激励、跑车激励和环境激励下的测试。通过对实测速度时程数据的处理,得出测点1~100 Hz内1 s的位移有效值。分析结果表明,在环境激励下,该设施中试验大厅底板表面的微振动水平能够达到控制要求;在冲击激励下,试验大厅底板表面微振动信号主要分布在5~30 Hz的频带内;场地内的车辆开动会对场地的微振动水平产生明显的影响;环境激励下,整个建设场地的微振动水平基本一致。研究结果对该精密大科学装置及类似工程的防微振设计具有重要的理论及参考价值。

考虑内、外圈复合故障的角接触球轴承振动特性研究

为描述考虑内、外圈复合故障角接触球轴承的振动特性,建立了角接触球轴承内、外圈复合故障时变位移激励模型;基于非线性Hertz接触理论,建立了角接触球轴承时变刚度模型;提出了考虑内、外圈复合故障的角接触球轴承动力学计算方法,研究了不同参数和工况条件下复合故障轴承的振动响应规律。研究结果表明:随着故障尺寸和轴承载荷的增大,复合故障轴承的振动特征频率不变,但其幅值增大;随着轴承转速的增大,复合故障轴承的振动特征频率及其幅值均增大;故障位置的变化将对复合故障轴承的振动特征产生很大影响,故障处越接近承载区,轴承的负载越大,振动特征越明显。

基于有限元软件海水置换泵连接管线机械激励振动分析

受动设备产生机械激励的影响,管道往往会出现振动问题,对海上平台的安全生产造成严重威胁。通过分析产生机械激励的原因,探究了管道产生机械激励振动的机理,可将其分为动设备自身问题和管道系统设计缺陷两种类型。对当前机械激励振动有限元分析方法进行了梳理,总结出完整且可靠的机械激励振动分析流程,并以某海上平台海水置换泵连接管线为例,采用有限元分析软件进行管线三维建模、模态分析和谐波响应分析。通过对计算结果进行分析评估,得到了共振频率下管道的振动结果,并针对振动较大位置采取了减振措施。经有限元软件再次分析检验,验证了处理机械激励振动问题时对振幅较大管段添加约束形式支架方案的切实可行性,为实际管道振动中处理机械激励振动的相关问题提供了参考。

基于绝对位移法的曲线梁桥多维多点弹塑性随机响应分析

针对当前地震动空间效应下曲线梁桥地震反应分析多采用确定性激励输入且忽略桥梁非线性的情况,采用了多维多点非平稳随机激励对曲线连续梁桥进行弹塑性响应分析。建立非线性有限元模型并降维解耦非平稳地震动非平稳演化功率谱(energy power spectral density,EPSD)矩阵,采用绝对位移法对桥梁进行非线性时程分析。考虑不同视波速、场地条件、相干性以及平稳与非平稳地震激励,综合分析了曲线连续梁桥的随机响应及其频域特性和时域特性。结果表明,地震动空间效应和地震动的非平稳性对曲线梁桥随机响应影响很大,其中地震动空间效应对桥梁随机响应大小及其频域分布有显著影响,而非平稳性会对随机响应大小及其时变响应趋势产生重要影响。因此,在曲线连续梁桥抗震分析中需充分考虑地震动空间效应和地震动非平稳性,以避免错误估计桥梁抗震性能。提供了全面的分析结果,对加强曲线连续梁桥的抗震设计和评估,从而提高其抗震性能和可靠性具有重要意义。

Research of transient rotor dynamic characteristic of magnetic liquid double suspension bearing in double collision state

During the operation of magnetic liquid double suspension bearing(MLDSB),due to rotor resonance,assembly error and other factor,the vibration amplitude of the rotor in resonance state exceeds the original design clearance,resulting in the collision damage between the rotor and the stator,the rotor and the casing.This paper presents a method to simulate the influence of different factors on the dynamic characteristics of 5 degrees of freedom(DOF)rotor based on the dynamic model of MLDSB.Firstly,according to the second Lagrange equation,the dynamic equation of 5 DOF rotor is derived,and the mathematical model is established.Then,based on 5 DOF rotor dynamic equation,the rotor transient dynamic equation under collision state is obtained,and the rotor transient collision dynamic simulation model is established.Finally,the key influencing factors of rotor dynamic characteristics are extracted,and the influence mapping relationship of rotor displacement,axis locus and stress distribution under different factors is simulated by using ANSYS Workbench software.The experimental results show that this method can effectively reflect the influence of various factors on the dynamic characteristics of the rotor.This method can provide theoretical reference for the design and control of MLDSB.

地震作用下时滞位移反馈对AMD振动控制效果的影响

在传统被动TMD的基础上引入时滞位移反馈控制,将TMD转变为AMD。在AMD系统中,将时滞和反馈增益系数作为可调的控制参数。首先,建立AMD作用下两自由度耦合振动系统力学模型和数学模型;然后,采用特征值分析法判断控制参数平面上系统的稳定性;最后,以位移响应峰值、加速度响应峰值、位移均方根和加速度均方根为评价指标,基于Simulink仿真,分析控制参数对El Centro波作用下AMD振动控制效果的影响。研究结果表明,当系统物理参数固定时,控制参数取值决定了系统振动稳定性;相较于TMD作用的情况,合理的控制参数取值,可使AMD达到更佳的振动控制效果,主结构和阻尼器地震响应均在不同程度上得到抑制;在控制参数取值不合理的情况下,AMD振动控制效果变差。

空气静压轴颈轴承力学性能的分析优化

为提升小孔节流空气静压轴颈轴承的静、动力学性能,针对轴承间隙的流场特性与轴承的承载力、位移阻抗性能进行分析与优化。采用数值仿真方法分析轴承间隙的流场特性,并在参数设计中消除了气膜流场中的超音速区,以避免微振动;分析轴承气膜的刚度、阻尼性能,并采用ESA-CFD(Engineering Simplification Algorithm-Computational Fluid Dynamics)方法计算轴承振动系统的位移阻抗。结果表明,气膜压力自小孔至外边界逐渐衰减,小孔出口出现激波可导致漩涡流动并引起微振动,微振动形成机制与止推轴承相似。建立优化设计数学模型,以轴颈轴承的位移阻抗、承载力为设计目标,并消除轴承微振动,其中考虑多组偏心率与激励频率的组合。通过优化设计,提升了轴颈轴承的力学性能,相关优化、分析过程可为工程应用中空气静压轴颈轴承的设计提供参考。

电涡流位移传感器的仿真分析与验证

为了研究基于印制电路板(PCB)设计的电涡流位移传感器结构参数对性能的影响,应用Ansys仿真软件,建立电涡流位移传感器模型,分析传感器的线圈激励频率、线圈与被测目标间隙等参数对系统等效阻抗以及感应电压的影响。根据优化模型制作传感器样机,搭建试验平台,将仿真结果与实测结果进行误差分析,试验结果表明,经优化后的系统在全量程范围内的误差达到±1.5%,验证了模型的准确性和可行性,对电涡流位移传感器的开发应用提供了理论依据。

Simulation of spatially coupling dynamic response of train-track time-variant system

There exist three problems in the calculation of lateral vibration of the train-track time-variant system athome and abroad and the method to solve them is presented. Spatially coupling vibration analysis model of train-track time-variant system is put forward. Each vehicle is modeled as a multi-body system with 26 degrees of freedomand the action of coupler is also considered. The track structure is modeled as an assembly of track elements with 30degrees of freedom, then the spatially coupling vibration matrix equation of the train-track time-variant system is es-tablished on the basis of the principle of total potential energy with stationary value and the "set-in-right-position"rule. The track vertical geometric irregularity is considered as the excitation source of the vertical vibration of thesystem, and the hunting wave of car bogie frame is taken as the excitation source of lateral vibration of the system.The spatially coupling vibration matrix equation of the system is solved by Wilson-θ direct integration method. Theapproximation of the calculated results to the spot test results demonstrates the feasibility and effectiveness of thepresented analysis method. Finally, some other vibration responses of the system are also obtained.

滚动轴承内圈局部故障渐变动力学建模与分析

当滚动轴承内圈出现局部故障时会产生复杂的振动响应,从滚动轴承内圈实际故障形貌的渐变性和非规则性的客观实际出发,引入位移激励函数定性分析滚动体通过故障区域时球心位置的渐变规律,采用随机数列表征故障底部形貌非规则性的特点,综合考虑轴承的径向载荷和滚动体通过故障区域时的打滑率等因素,建立了一种内圈局部故障渐变的轴承动力学模型。通过对比分析不同转频条件下实验和仿真数据的故障特征频率值,验证了局部故障渐变动力学模型的准确性。

场地相关的非平稳相干函数及其工程应用

依据蒙特卡洛方法和连续小波变换得到非平稳相干函数,采用四阶傅里叶级数拟合非平稳相干函数,分析场地条件和站点间距对参数的影响,验证模型有效性,并合成多点地震动。以一输电塔线体系为研究对象,对比分析了一致与非一致地震激励作用下输电塔最大层间位移角,研究结果表明:①建立的傅里叶非平稳相干函数模型,能够较好地模拟相干函数非平稳特性及场地变化,且拟合精度较高;②场地条件影响傅里叶非平稳相干函数模型的五个参数,站点间距影响傅里叶非平稳相干函数模型的三个参数,应考虑场地条件和站点间距的影响;③与一致地震激励作用输电塔最大层间位移角超出限值的极限峰值加速度相比,非一致地震激励作用下的极限峰值加速度较小,表明输电塔较早发生破坏,输电塔线体系地震响应分析应考虑非一致地震激励的影响。

非平稳激励下绝对位移直接求解非线性结构的时频分析

强震作用下地震动能量的时-频演变特性对迟滞非线性的结构有着极大影响,然而通用有限元软件现有的计算模块进行频域分析时不能对非线性结构输入解耦的EPSD矩阵,限制了随机振动理论对大型复杂结构的仿真计算。将绝对位移直接求解的虚拟激励法引入多维多点的非线性动力方程,通过APDL的外部程序调用接口对非平稳地震动EPSD矩阵进行解耦与降维处理,并转化为独立于时间变量的四维均匀调制激励矩阵,实现对非线性结构精确高效的非平稳激励动态输入与随机动力响应的计算求解。最后以一座中承式三跨钢管混凝土系杆拱桥为例,计算拱肋、拱脚和桥面系响应的时变功率谱及方差。结果表明,绝对位移直接求解的激励输入方式很好地模拟了非线性结构体系所带来的时滞现象,为通用有限元软件实现非线性结构多维多点非平稳激励随机响应的求解与分析提供了可行性依据。

适应动态加速度场的压电-液压串联复合激振装置研制

为了实现动态加速度与时变振动环境的综合模拟,研制了一套适应动态加速度场的轻量宽频激振装置。首先提出了压电-液压串联复合激振方法和装置构型,解决了传统激振方法“宽频不轻量、轻量不宽频”的难题。设计了六单元并联压电激振模块,建立了精密装调工艺,并联激振效率达到74.2%。为满足动态加速度环境下的宽频激振需求,提出液压内嵌式定中方案,研制了具有“缸中缸”构型的液压激振模块。基于分频器,提出了串联复合激振系统的分频控制方法,实现了压电、液压激振模块的协调工作、均衡出力。以力平衡控制结合零位移反馈补偿控制,提出了液压激振模块定中控制方法,实现了动态加速度环境下的精确定中。提出了变增益、长时波形再现两种时变振动控制方法,研制了一体化的控制系统。测试结果表明,串联复合激振装置在离心加速度不低于60 g、加速度变化率不低于15 g/s工况下,分别实现了50 kg负载下的6 grms振动加速度、10~2 000 Hz频率范围的宽频激振。该装置已应用于多项惯性器件、组件和系统的环境试验考核,载荷控制效果良好。相比飞行试验,本文成果为飞行器制导、控制系统功能性能考核提供了高效经济的实验室手段,特别在大样本数据获取方面具有优势。

位移激励下含负刚度的惯容减振系统参数优化解析研究

为抑制位移激励下主结构的振动,提出了三种含有负刚度的惯容减振系统(N‑ISD),推导了各系统分别在H∞和H_(2)优化准则下设计参数的解析解,探究了不同形式N‑ISD系统振动控制的特点。建立位移激励下减振系统的动力学方程,得到结构的传递函数。针对简谐位移激励下的振动幅值,采用固定点理论推导了以H∞范数为优化准则的设计参数解析解;针对随机激励下位移均方值,采用极值理论推导了以H2范数为优化准则的设计参数解析解。通过与基于遗传算法的数值优化解对比,验证了上述最优设计参数解析解的有效性及优越性。对最优状态下的减振系统进行减振效果分析,结果表明:负刚度的引入能有效降低主结构的振幅放大因子和均方值,简谐激励下N‑SPIS‑Ⅱ型惯容系统反共振峰值更低,共振峰值间距更大,减振效果及稳定性更好;随机激励下N‑SPIS‑Ⅰ和N‑SPIS‑Ⅱ型惯容系统位移均方值均小于N‑SIS型惯容系统,表现出更好的减振性能。

滚动轴承局部故障动力学建模与振动分析

针对传统轴承动力学模型采用单一的固定位移激励或半正弦函数位移激励,提出了一种与滚动体实时位置相关且考虑故障底部的非规则形貌的时变位移激励函数来对滚动轴承外圈故障进行描述。建立了滚动轴承外圈局部故障四自由度动力学模型,并对所建立的模型进行了仿真计算,仿真结果显示外圈故障频率在包络谱中清晰可辨,并与实验结果相吻合,验证了模型的准确性。基于此模型分析了故障宽度对故障特征指标的影响,随着故障宽度的增加,峰值和均方根均呈现增大的趋势,峭度指标呈现出无规律的波动趋势,波形因子几乎无变化。