Compression stiffness of infinite-strip bearings of laminated elastic material interleaving with flexible reinforcements

The closed-form solutions to the compression stiffness of the laminated elastomeric bearings of infinite-strip shape with flexible reinforcements are derived. The effect of bulk compressibility in the elastic layer and the effect of boundary condition at the ends of the bearing are considered. Three types of the elastic layers bonded to flexible reinforcements are studied. The first type simulates the interior elastic layers of the bearings with shear-free ends. The second type simulates the exterior elastic layers of the free-end bearings. The third type simulates the elastic layers in the bearings which ends are bonded to rigid plates. The theoretical solutions to the compression stiffness of the bearings are extremely close to the results obtained by the finite element method, which proves that the displacement assumptions utilized in the theoretical derivation are reasonable.     

Deformation analysis of infinite-strip bearings of laminated elastic material interleaving with tension-only reinforcements

Bonding with fiber reinforcements can increase the stiffness of elastic layers only when the elastic layer is compressed. Fiber loses its rigidity when it is not stretched. The procedure to include this ‘tension-only’ nonlinearity in the deformation analysis of the fiber-reinforced bearing is developed. In the elastic layers bonded with tension-only reinforcements, the responses to the compression force and the bending moment are coupled unless the reinforcements are entirely in tension. The coupled relation, which is not linear, depends on the length of the tension zone in the reinforcement. Increasing the compression force on the bearings will extend the tension zone in the reinforcements and enhance the stiffness of the bearing, but the compression force may add more bending moment to the bearings and increase the lateral deformation. The vertical buckling load of the bearings with tension-only reinforcements varies with the lateral force and is smaller than the buckling load of the bearings with linear reinforcements.     

Static and dynamic behavior of disk bearings for OSPG railway bridges under railway vehicle loading

The aim of the present study is to investigate the static and dynamic behavior of disk bearings under railway vehicle loadings. A disk bearing is operated as an elastic bearing in the vertical direction and is composed of a Polyether Urethane (Polyurethane) disk for elastic support and Polytetrafluoroethylene (PTFE) to accommodate lateral movements. Static tests are conducted in a laboratory to determine the static behavior of a Polyurethane disk. Finite Element (FE) analysis is also performed to assess the friction and the role of the pin inside a disk bearing. For dynamic behavior, four disk bearings having the identical Polyurethane disk, which are used in the static tests, are installed in a real railway bridge and tested under a running locomotive. From the test results, the static and dynamic stiffness of disk bearings are estimated and compared with each other. The estimated static stiffness of the disk bearing is almost half of that under dynamic loading. In addition, under relatively light loads the dynamic stiffness of a fixed disk bearing is approximately 80% greater than that of an expansion disk bearing since the PTFE deflects and the gap is closed in the expansion bearing. Deformation of the disk bearings in the real bridge is measured with varying locomotive speeds. The deformation of the disk bearings does not vary significantly with changes in the locomotive’s speed.     

两端弹性支承输流管道固有特性研究

输流管道广泛应用于航天航空、石油化工、海洋等重要的工程领域, 其振动特性尤其是系统固有特性一直是国内外学者研究的热点问题. 本文研究了两端弹性支承输流管道横向振动的固有特性, 尤其是在非对称弹性支承下的系统固有特性. 使用哈密顿原理得到了输流管道的控制方程及边界条件, 通过复模态法得到了静态管道的模态函数, 以其作为伽辽金法的势函数和权函数对线性派生系统控制方程进行截断处理. 分析了两端对称支承刚度、两端非对称支承刚度、管道长度以及流体质量比对系统固有频率的影响规律, 重点讨论了管道两端可能形成的非对称支承条件下固有频率的变化规律. 结果表明, 较大的对称支承刚度下管道的第一阶固有频率下降较快; 当管道两端支承刚度变化时, 管道的各阶固有频率在两端支承刚度相等时取得最值; 对于两端非对称支承的管道而言, 两端支承刚度越接近, 第一阶固有频率下降的越快, 而且相应的临界流速越小; 流体的流速越大, 其对两端非对称弹簧支承的管道固有频率的影响更为明显.      

Dynamics and stability of elastic shaft-bearing systems with nonlinear bearing parameters

The dynamics and stability of a continuously elastic spinning shaft mounted on two dissimilar end bearings possessing nonlinear anisotropic and cross coupling stiffness and damping coefficients are analyzed. Sufficient conditions of system stability in the sense of Liapunov are derived. The developed stability criteria of the considered system have been shown to reduce to that of simpler models found in the pertinent literature. The effects of nonlinearity of bearing stiffness and damping parameters together with shaft stiffness parameter and other system parameters on the dynamic stability of the system are investigated. Several graphs demonstrating parametrically the influence of various system nondimensionalized parameters on system stability boundaries for typical cases are presented. Received on 26 October 1998     

L形柱在反复荷载作用下的非线性分析

在平截面假定的前提下,将钢筋混凝土L形柱划分为两端弹塑性区、中间为弹性区的三分段杆单元模型。将应用于平面剪力墙的多垂直杆单元模型拓展为空间的多垂直杆单元模型,推导了拓展的多垂直杆单元模型单元刚度矩阵,经静力凝聚为三分段杆单元模型刚度矩阵,该单元模型可用于各种截面形式的钢筋混凝土异形柱、剪力墙墙肢和梁的非线性分析,计算工作量较小。讨论了目前垂直杆的轴向拉压滞回模型,提出了轴向拉压滞回曲线考虑骨架曲线下降段的简化处理方法。最后提供了算例,结果表明本文方法计算的滞回轴线与在反复加载下L形柱的试验结果吻合较好。     

基于概率密度演化理论的LRB隔震支座时变可靠度研究

铅芯橡胶隔震支座LRB （Lead Rubber Bearing）的等效水平刚度是隔震建筑物的重要力学指标,橡胶材料由于其复杂活跃的化学组分,在使用过程中极易发生老化,是LRB支座中随时间变化的活跃因素。考虑铅芯橡胶隔震支座中橡胶材料退化的时变性和随机性,引入时变变异系数。基于概率密度演化方法,得到LRB支座等效水平刚度的概率密度演化曲线和时变可靠度。结果表明,随着时间的增长,支座等效水平刚度产生增大的趋势,支座的可靠度发生非线性降低,老化对支座等效水平刚度的离散性产生了明显的影响。     

Compression analysis of rectangular elastic layers bonded between rigid plates

An elastic layer bonded between two rigid plates has higher compression stiffness than the elastic layer without bonding. While the finite element method can be applied to calculate the stiffness, the compression stiffness of bonded rectangular layers derived through a theoretical approach in this paper provides a convenient way for parametric study. Based on two kinematics assumptions, the governing equation for the mean pressure is derived from the equilibrium equations. Using the approximate shear boundary condition, the mean pressure is solved and the compression stiffness of the bonded rectangular layer is then established in an explicit single-series form. Through the solved pressure, the horizontal displacements are derived from the corresponding equilibrium equations, from which the shear stress on the bonding surface can be found. It is found that the effect of the rectangular aspect on the compression stiffness is significant only when Poisson’s ratio is near 0.5. For the smaller Poisson’s ratio, the compression stiffness of the rectangular layer can be approximated by the formula for the infinite-strip layer of the same shape factor.     

基于电子万能试验机的新型压杆稳定实验装置

本文介绍了一种基于电子万能试验机开发的新型压杆稳定实验装置。该装置利用电子万能试验机自身传感设备,通过测量压杆两端受力与绘制端部轴向位移曲线来确定压杆失稳荷载。装置包括上、中、下三个约束部分与压杆试样部分,可实现两端固支、两端铰支、一端固支一端铰支和一端固支一端自由等4种不同端部约束型式,并且能够施加中部固支约束与压杆初始偏心。本文同时讨论了两种铰支型式,即刀刃铰支与轴承铰支对测试精度的影响。实验表明,轴承铰支测量精度比刀刃铰支高。该套装置的整体测量精度高,与理论值的相对误差最高为2%。     

分析弹性支承输流管道的失稳临界流速

研究了两端弹性支承输流管道静态失稳和动态失稳临界流速. 根据梁模型横向弯曲振动模态 函数,由两端弹性支承的边界条件得到了其模态函数的一般表达式. 根据特征方程具体分析 了弹性支承刚度、质量比、流体压力和管截面轴向力等主要参数对失稳临界流速的影响. 数 值计算结果表明,管道在弹性支承下的动力稳定性比较复杂,在较小的弹性支承刚度和较小 的参数范围内,管道主要表现为动态颤振失稳;在较大的弹性支承刚度和较大的参数作用下, 管道的失稳形式主要表现为静态失稳;并且失稳临界流速随流体压力和管截面轴向压力的增 加而下降,随管截面轴向拉力的增加而上升.     

永磁向心轴承承载能力与刚度的计算

目前，尽管磁浮轴承技术的研究与开发应用已经受到国内外学者的广泛重视，但在永磁向心轴承承载能力的研究方面，却还存在着两个尚待解决的问题：一是将环形磁体作为无限长条形磁体处理，二是只能对轴承承载能力进行估算。针对这种情况，根据等效磁荷理论，在圆环状态下对轴向控制的永磁向心轴承的承载能力和刚度进行了研究，建立了永磁向心轴承承载能力数学模型，并对其计算结果作了试验验证，同时还提出了利用刚度系数建立的可供工程设计应用的永磁轴承承载能力和刚度的计算公式。结果表明，承载能力的计算值与实测值相当吻合；在偏心距的实际应用范围内，永磁向心轴承的径向刚度是个常量；内外磁环的轴向位移对磁轴承的承载能力和刚度都有明显的影响．因此，为了最大限度地提高这种轴承的承载能力和刚度，就要在设计其结构的过程中注意尽力保证内外磁环轴向对齐。     

油膜轴承负荷特性的数值解析

轧机油膜轴承频繁出现巴氏合金剥落、龟裂等现象，直接影响到油膜轴承的使用寿命和轧制生产的正常进行，应用三维弹性接触问题的边界元法对宝钢2050支承辊油膜轴承载荷分布进行分析研究，建立了油膜轴承的接触模型，模拟真实的约束与受力，结果轴承出现严重偏载现象，通过改善约束条件，在自位情况下轴承偏载现象大幅度降低，同时接触应力也在一定程度上减小，从而使得轴承的承载能力得到提高，由于考虑了弹性变形的影响，该方法具有计算精度高，收敛速度快等优点。     

基于阻抗法的矩形截面均压槽气浮支承静态性能分析

针对CFD仿真方法效率低下的状况,提出利用阻抗法来提升气浮支承承载性能的计算速度. 以矩形截面均压槽气浮支承为研究对象,研究了当均压槽高度、角度、数量、半径和供气压力变化对气浮支承承载性能的影响. 结果表明:与CFD仿真方法相比,阻抗法在保证计算结果精度的前提下可提高气浮支承承载力的计算速度. 当均压槽高度、角度、数量、半径和供气压力增大时,阻抗比会增加,气浮支承的承载力和刚度峰值对应的阻抗比也会增加. 当气膜厚度增加时,阻抗比会增加,但承载力会相应地减小. 本文作者通过阻抗法推导了气浮支承承载力简化计算公式,解决了气浮支承在均压槽方向上简化计算的难点,并为阻抗法在均压槽中的研究与应用提供了理论依据.      

Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

惯性平台轴承预紧力及其刚度的分析计算

本文对惯性平台中框架支承的角接触球轴承的预紧力、刚度和摩擦力矩进行了分析，并结合实际轴承给出了初步的计算。     

角钢约束混凝土中长柱轴压力学性能试验及承载力计算

为了研究角钢约束混凝土中长柱在轴压荷载作用下的力学性能,以长细比、缀板间距、混凝土强度等级为变化参数,完成了8个试件的静力加载试验。通过试验观察了试件的破坏形态,获取了其极限承载力、刚度、位移延性和耗能系数等力学性能指标;分析了各变化参数对力学性能指标的影响,利用统一强度理论、极限理论和叠加理论对试件的承载力进行计算。研究结果表明:长细比越小越容易发生柱端破坏,长细比加大后易发生柱中破坏;减小缀板间距,试件的极限承载力和变形能力均得到提高。随着混凝土强度等级的提高,试件的极限承载能力和初始弹性刚度得以提高,但位移延性和耗能能力有所降低。采用统一强度理论的计算值略大于试验值,采用极限分析理论和叠加理论的计算值均小于试验值。     

Buckling of short beams with warping effect included

A beam theory for the stability analysis of short beam that includes shear deformation and warping of the cross-section is developed. The warping of the cross-section is taken to be an independent kinematics quantity and corresponding force resultants are defined. For the beam subjected to the external loading only at the ends of the beam, equilibrium equations have been obtained by the principle of virtual work. The variations of lateral displacement, rotational angle of the cross-section and the multiplier of the warping shape along the beam axis are solved in closed form and expressed in terms of deformation quantities at the ends of the beam. Based on this beam theory, the lateral stiffness of the beam sustained an axial compression force and a lateral shear force at one end is explicitly derived, from which the equation of the buckling load is established and the buckling load can be solved. When the effect of cross-section warping is neglected, the derived lateral stiffness and buckling load converge to the solutions of the Haringx theory.     

Study of milling stability with Hertz contact stiffness of ball bearings

This present work examines the stability and nonlinear responses of a spindle milling system supported by ball bearings. A shaft finite element based on Timoshenko beam theory is employed to model the spindle, and modal reduction method is therefore adopted for saving the numerical calculating time. The issues of evaluating the effects of the ball bearing Hertz contact stiffness are consequently addressed. It is found that suitable constant bearing stiffness can be adopted to replace the nonlinear nonsmooth Hertz stiffness in prediction of the critical cutting depth of the milling system in certain bearing configuration conditions. For the constant bearing stiffness can be obtained by experiment, this replacement will undoubtedly simplify the spindle-bearing milling system. But with the increase in the bearing clearance, the spindle milling system will present obvious nonlinear behaviors, and the nonlinear Hertz contact bearing stiffness will take over. Isolated islands of chatter vibration, which are induced by the nonlinear nonsmooth bearing Hertz stiffness, can be found exist in milling processes in large bearing clearance conditions.     

Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries.Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli(EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.     

计及机体变形的内燃机主轴承弹性流体动力润滑分析

针对某四行程四缸内燃机曲轴主轴承,考虑机体变形因素的影响,进行了曲轴轴承弹性流体动力润滑分析.计算中采用动力学法进行曲轴轴承的润滑分析,采用变形矩阵法计算油膜压力作用下轴承表面的变形.结果表明,与不考虑机体变形影响相比,计入机体变形影响时轴承轴心轨迹基本没有改变,在1个工作循环中的大部分时间轴承最大油膜压力、最小油膜厚度、端泄流量和轴颈摩擦系数几乎没有变化,仅在某些时刻附近轴承最大油膜压力略有减少,轴承最小油膜厚度略有增加.因此在计算精度要求不是非常高的情况下,曲轴主轴承润滑分析可以不考虑轴承表面因油膜压力作用产生的弹性变形的影响.