带弹性支承的角接触球轴承动态特性分析

针对航空发动机中的轴承支承模型,在有限元分析和轴承动力学的基础上,采用修正的Craig-Bampton固定界面模态综合法,建立了弹性支承结构与刚性的轴承外圈、轴承座之间的耦合连接,开发了带弹性支承的角接触球轴承动力学分析模型,分析并讨论了不同工况下,弹性支承体对轴承振动特性的影响。结果表明:与刚性支承相比,弹性支承能够降低系统固有频率下的振动幅值。轴承在轴向力作用下,力较小时,增大支承体的刚度能够降低振动幅值,力较大时,采用适当刚度的弹性支承有利于减小振动幅值;轴承在径向力作用下,存在一个合理的弹性支承刚度,使径向振动幅值达到最小。     

三环减速机的弹性动力学建模

综合考虑了三环减速机的输入轴和支承轴的弹性、行星轴承的弹性、输出轴轴承的弹性、齿轮啮合弹性以及输入轴和支承轴偏心套的偏心误差和分度误差 ,建立了三环减速机的弹性动力学方程。分析了三环减速机的固有频率。为系统地分析三环减速机的动力学行为奠定了理论基础     

用分形接触理论研究拉杆转子轴承系统动力学模型

根据分形接触理论,建立了拉杆转子轮盘结合面弹性接触弯曲耦合模型和扭转耦合模型。在此基础上,采用集总参数法,建立了拉杆转子-轴承系统的动力学模型。通过锤击试验,测量了拉杆转子自由状态下的固有频率,验证了该模型的有效性。借助于数值仿真方法,研究了系统横向振动固有频率和扭转振动固有频率随结合面法向载荷的变化规律。研究发现:分形接触理论可以有效地解决拉杆转子轮盘接触表面间的弹性接触问题;结合面法向载荷增大时,系统固有频率同步增大;拉杆转子的固有频率小于相同结构尺寸的连续体转子的固有频率;法向载荷对高阶固有频率影响较大;对滑动轴承支承的拉杆转子轴承系统来说,拉杆转子预紧力对低阶横向振动和扭转振动固有频率影响相对较小。     

基于刚柔耦合的高方平筛动力学建模与振动模态分析

针对高方平筛和其上固结的柔性吊杆组成的动力学系统,进行了刚柔耦合的动力学建模和振动模态分析。将筛体—偏重块系统和吊杆分别作为刚体和弹性的可变形体,建立了筛体稳态圆振动方程和吊杆悬臂梁力学模型,总结出系统固有频率的计算方法。在此基础上,采用有限元方法对系统进行了模态计算和动力学响应分析。结果表明,理论模型能够很好地反映筛体与吊杆之间的动力学耦合关系;以理论分析为基础的载荷和边界条件的设置,使有限元仿真结果较准确地模拟了系统实际的振动特性。     

一边弹性支承三边自由矩形板对接处角刚度的识别

通过试验模态分析,寻找一边弹性支承三边自由对接长方形板的最低阶弯曲振型及对应的固有频率,将对接板的动力学问题转化为一边弹性支承的对接梁来求解,借助计算机代数语言,编写对接梁的传递矩阵法程序,推导出对接处含角刚度作为符号的方程,输入板的最低阶弯曲振型所对应的固有频率就可识别出该处的角刚度,并通过实例验证此法的有效性.     

计及二阶效应的刚柔耦合连杆系统动力学分析

根据虚功原理和达郎伯原理推导了计及二阶效应的柔性单元运动方程,并利用刚化条件得到了刚性梁单元运动方程,给出了刚柔耦合连杆系统动力学建模与分析的方法.对构件刚度相差悬殊的多体系统进行动力学分析时,如若当作多刚体系统分析,会因忽略弹性变形导致结果不准确;当作多柔体系统建模分析求解,则因自由度太多导致方程庞大难求解.可行的方法是:将刚性单元与柔性单元耦合建模,在多柔体系统基础上,引入刚性单元和刚性约束条件,对刚性构件自身的动力学特性进行等效,然后按照一般弹性系统有限元方法集成得到虚拟柔性系统动力学方程,建立过渡坐标与广义坐标关系,消除非独立坐标,得到真实的系统运动方程,降低系统方程维数,提高分析效率.以曲柄滑块机构为例,介绍了计及二阶效应的刚柔耦合系统动力学的建模分析过程.     

无隔振装置内燃机支承系统固有特性影响因素研究

建立了将内燃机视为刚体、支承系统视为柔体的刚-柔耦合有限元模型,利用ADAMS软件计算分析了系统的固有频率及振型,讨论了其设计的合理性。采用正交设计法,研究了支承各参数对系统固有频率的影响规律,为无隔振装置内燃机支承优化设计提供了参考。     

发动机转子-滚动轴承系统的振动性能研究

针对发动机转子 滚动轴承系统建立了有限元模型,将弹性轴段、刚性圆盘和弹性支承的动力方程集结后得到系统振动方程,分析计算了支承刚度对系统固有频率的影响。将转子不平衡惯性力和轴承支反力作为激励,求解了系统的稳定响应,得出了合理设计支承刚度和阻尼,可以改善转子系统的振动特性的结论。通过转子系统模拟实验,对该结论进行了验证。     

齿轮-转子系统的振动特性分析

根据转子动力学和齿轮啮合的基本原理,建立了考虑陀螺力矩的齿轮转子系统的动力学模型,以此求得齿轮转子啮合刚度矩阵和阻尼矩阵。探讨了啮合刚度、支承刚度对系统固有频率以及系统稳定性的影响。结果表明齿轮的啮合刚度对弯曲振动以及弯扭耦合振动固有频率的影响不大,而当啮合刚度介于2×105~2×108之间时,对弯扭耦合振动的相对稳定性却有较大的影响;另增大支承刚度,固有频率相应提高;减小跨距可以提高系统的稳定性。分析结果对工程应用具有重要的意义。     

鼠笼式弹性支承-圆柱滚子轴承-转子系统振动分析

考虑圆柱滚子轴承非线性接触力、保持架能量、鼠笼刚度、转子不平衡以及它们之间的力学耦合关系,基于拉格朗日方程建立鼠笼式弹性支承-圆柱滚子轴承-单转子系统动力学分析模型,结合龙格库塔数值积分方法,并对该模型动力学仿真分析,分析了不同转速区域鼠笼式弹性支承-滚动轴承-转子系统振动响应的分岔特性,结果表明:两支点的鼠笼式弹性支承-圆柱滚子轴承-单转子系统受到组合支承非线性支承力的激励作用下,呈现丰富多样的运动周期变化,相比于高转速区域的系统振动响应,低转速区域的系统振动响应混沌现象更易出现。高转速区间可以对系统建模分析进行线性近似处理,更方便地对系统振动进行控制与优化。     

Investigation on steady state deformation and free vibration of a rotating inclined Euler beam

The steady state deformation and infinitesimal free vibration around the steady state deformation of a rotating inclined Euler beam at constant angular velocity are investigated by the corotational finite element method combined with floating frame method. The element nodal forces are derived using the consistent second order linearization of the nonlinear beam theory, the d'Alembert principle and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The rotating element coordinates rotate about the hub axis at the angular speed of the hub. The equations of motion of the system are defined in terms of an inertia global coordinate system, which is coincident with a rotating global coordinate system rigidly tied to the rotating hub. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady state deformation and natural frequency of the rotating inclined beam.     

三环减速器支撑轴结构的探讨

提出了一种三环减速器支撑轴的改进结构,分析了支撑轴的弹性变形协调条件并建立了这种改进结构的弹性动力学分析文程,对改进结构的支撑轴偏心套的受力和固有频率与原结构进行了对比,分析了这种结构克服机构死点的可行性。     

Coupled couple stress and surface roughness effects on elasto‐hydrodynamic contact

This paper deals with the combined effects of couple stress and surface roughness to inspect the elasto‐hydrodynamic performance of slider bearing systems. On the basis of the couple stress Stokes theory and homogenisation method, the homogenised generalised Reynolds equation including the slider bearing stationary surface deformation is derived. The total deformation include the deformation of smooth surface, taken into account by the elastic thin layer model, and the deformation of roughness corresponding to a sinusoidal normal displacement on an elastic half space of identical wavelength. The governing equations are discretised by the finite difference method, and the obtained algebraic equations are solved using the iterative overrelaxation Gauss–Seidel technique. The load‐carrying capacity and friction coefficient are presented for transverse, longitudinal and anisotropic roughness patterns for different values of the couple stress parameter in both rigid and deformable cases. The simulation results indicate that the interaction between couple stress, surface roughness and elastic deformation effects is significant. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance of flexible shell journal bearings with variable viscosity lubricants

In heavily loaded rotating machines, both the deformation of the elastic bearing shell and the dependence of lubricant viscosity on pressure become significant and may result in an appreciable change in the performance of the journal bearing system. In this paper, stable solutions for bearing deformation and the lubricant flow field are obtained which combine the effects of the elastic deformation of the bearing shell with the pressure-viscosity dependence of the lubricant. Two elastic models were tried for deformation calculations in the bearing. One which was computationally economical and consistent in accuracy was adopted for the detailed computation. The effects of bearing deformation on the performance characteristics of the journal bearing system are reported for both isoviscous and variable viscosity lubricants.     

弹性体线接触副的非线性振动研究

从弹性体线接触振动理论出发,建立了弹性体线接触的非线性振动模型,然后依据该振动模型分析了弹性体线接触振动的非线性特性。建立非线性振动模型时既考虑了滚子与滚道间的Hertz弹性变形,又考虑了弹性流体动力学润滑。理论分析和试验证明,在径向载荷作用下,弹性体线接触副的非线性振动特征明显,表现为第一基频的频率略有减小,振动幅度明显增大,振动向第一基频集中。     

Dynamic response-based characterization of ring-based vibratory angular rate sensors

Dynamic response behaviour of a rotating ring is investigated in order to better understand the achievable performance improvements as well as system limitations. For this purpose, the governing equations that represent the transverse as well as the tangential in-plane motion of a rotating ring are derived via the Hamilton’s principle. These equations are then discretized to represent a two-degree-of-freedom time-varying gyroscopic system. The asymmetry effects are considered important and are included by considering mass mismatch in the system mass matrix. In order to predict dynamic behaviour of a ring system subjected to external excitation and body rotation, time and frequency response analyses are performed. The natural frequency variations due to the gyroscopic coupling presented in the system are first characterized for varying input angular rates. The effects of system parameters such as damping and mass mismatch on the sensor sensitivity and operating range are quantified via suitable time and frequency response analyses.     

In-plane vibration analysis of cantilevered circular arc beams undergoing rotational motion

Equations of motion of cantilevered circular arc beams undergoing rotational motion are derived based on a dynamic modeling method developed in this paper. Kane’s method is employed to derive the equations of motion. Different from the classical linear modeling method which employs two cylindrical deformation variables, the present modeling method employs a non-cylindrical variable along with a cylindrical variable to describe the elastic deformation. The derived equations (governing the stretching and the bending motions) are coupled but linear, so they can be directly used for vibration analysis. The coupling effect between the stretching and the bending motions, which could not be considered in the conventional modeling method, is considered in this modeling method. The effects of rotational speed, arc angle, and hub radius ratio on the natural frequencies of the rotating circular arc beam are investigated through numerical analysis.     

弹性地基上转动功能梯度材料Timoshenko梁自由振动的微分变换法求解

基于Timoshenko梁理论研究弹性地基上转动功能梯度材料（FGM）梁的自由振动。首先确定功能梯度材料Timoshenko梁的物理中面,利用广义Hamilton原理推导出该梁在弹性地基上转动时横向自由振动的两个控制微分方程。其次采用微分变换法（DTM）对控制微分方程及其边界条件进行变换,计算了弹性地基上转动功能梯度材料Timoshenko梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种不同边界条件下横向自由振动的量纲一固有频率,与已有文献的计算结果进行比较,退化后结果一致。最后讨论了不同边界条件、转速、弹性地基模量和梯度指数对功能梯度材料Timoshenko梁自振频率的影响。结果表明：功能梯度材料Timoshenko梁的量纲一固有频率随量纲一转速和量纲一弹性地基模量的增大而增大;在量纲一转速和量纲一弹性地基模量一定的情况下,梁的量纲一固有频率随着功能梯度材料梯度指数的增大而减小。     

传递矩阵法分析平面柔顺机构的振动特性

为了分析柔顺机构的动态性能和力学传递关系,提出一种新型的基于传递矩阵法的振动力学模型。柔顺机构由若干个柔性铰链与杆件顺序联接而成,采用传递矩阵法描述其力学状态量的传递关系。将柔性铰链视为拉伸和弯曲变形的弹性梁,应用材料力学理论建立反映其自振性能的传递矩阵。将杆件视为刚体,采用动量矩定理建立其动力学模型,得到描述振动刚体的传递矩阵。按照柔顺机构的联接形式,将每个元件的传递矩阵进行拼装,得到系统总传递矩阵。总传递方程以柔顺机构的边界点状态矢量为未知变量,矩阵中的元素为机构结构参数和频率的函数。应用边界条件,可得柔顺机构的特征方程,通过求解方程可得系统的固有频率和振型。将外力纳入传递矩阵,建立反映外力激励与系统的关系的扩展传递矩阵以求解系统的频率响应。通过2种常用平面柔顺机构的动态性能分析,结果表明所建立模型的正确性,能精确描述柔顺机构力学传递关系。     

结构参量改变时弹性机构本征特性的研究

研究了改变结构参量对弹性机构内在特性的影响及其规律。首先以平面４Ｒ机构为例分析了机构杆件长度参数变化对机构固有频率和动应力等的动态响应。然后从参量与振动的关系的角度对数值计算结果进行了理论分析，由此得到了机构固有频率与结构参量之间的定性关系，进一步揭示了弹性机构的本征特性