重型燃机转子的热弯曲变形及振动响应分析

转子的热弯曲变形是透平旋转机械热启动出现较大振动的原因之一。燃机停机后,转子在静置过程中与周围空气通过自然对流进行热交换,由于转子上下部冷却的热效率不对称,轴截面将产生温度梯度,转子发生热弯曲变形。分析了停机后的静置过程中,转子在自然对流冷却条件下截面的温度分布、温差变化及热弯曲变形。结果表明:随着静置时间延长,轴截面的温差和转子的热弯曲变形都先增大后减小,但二者的峰值时刻并不相同;若静置时间足够长,最终温差将趋于零,热弯曲变形消失。进一步通过求解弯曲转子的运动方程分析了不同时刻热弯曲变形转子热启动时的振动响应,给出了热弯曲转子热启动时,发生可接受振动水平的允许静置时间。同时验证了转子在发生最大热弯曲变形时刻热启动时,低速盘车对热弯曲变形的有效消除作用。计算结果对燃机转子的正常启停及安全运行具有现实参考意义。     

磁悬浮轴承转子热弯曲振动影响因素分析

为了研究磁悬浮轴承转子系统中热弯曲振动的影响因素,根据磁悬浮轴承转子热弯曲振动机理,提出了一种迭代计算方法,不断更新计算条件,反复迭代计算,直到振动收敛或发散,由此得到转子工作时电控参数和转子结构参数对热弯曲振动的影响。计算结果表明：电控参数中,改变偏置电流和积分系数对热弯曲振动无明显影响,而提高比例系数和微分系数会使热弯曲振动的影响增大;转子结构参数中,增大非悬臂侧轴段长度和悬臂侧轴段长度会降低热弯曲振动的影响,而增大悬臂长度和外挂圆盘半径会轻微增大热弯曲振动的影响。由此可知,电控系统和转子自身的幅频特性决定热弯曲的影响程度,二者的相频特性决定热弯曲振动的变化趋势。     

轴类零件的动态特性和设计应用

以简单均质轴为例，分析了轴类零件弯曲振动的基本参数，简要介绍了动态特性的影响因素及其计算方法。轴类零件的纵向与扭转特性和弯曲振动的分析方法是类似的。对于结构复杂的轴，差异仅在于动态参数的计算方法有所不同。     

转子-机匣系统振动特性研究

采用传递矩阵法计算转子－机匣系统的临界转速、不平衡响应及初始弯曲响应，计算转子－机匣系统临界转速及稳态响应时的位能与位能分配，提出了借助转子－机匣的位能分配判断各阶临界转速的分析方法，并研究了机匣对系统振动特性的影响。     

柔性转子不平衡响应及初始弯曲振动特性研究

以悬臂式热弯曲转子、Jeffcott转子、双简支光轴转子为对象研究单转子初始弯曲及不平衡响应的振动特性 ,采用传递矩阵法计算了临界转速、初始弯曲响应及不平衡响应 ,得出了普遍的规律。计算了双简支等截面光轴转子偏心距按各阶振型分布的不平衡响应 ,证实了柔性转子振动主振型正交性的性质 ,介绍了一套有助于柔性转子模态平衡法理论分析的通用程序     

旋转机械动静碰摩耦合振动分析

针对摩擦转子系统动力特性建立一种耦合分析模型。结合摩擦热冲击温度方程和转子热弯曲方程,推导转子热弯曲与温度直接相关的微分方程,进而建立摩擦转子动力方程与热冲击温度方程耦合的时变方程。该耦合方程既包括摩擦力冲击和热冲击对转子动力特性的影响,也包括振动特性对摩擦热量的影响。运用该耦合模型,分析某实际发电机转子摩擦情况下的振动特性。给出摩擦截面碰摩力、温度、转子弯曲变形和振动波形随摩擦时间的变化情况,结合频谱图分析不同碰摩情况下振动谐波成分,得到振动随时间逐渐发散和波动的过程。给出碰摩位置和转速对摩擦振动的影响。运用分析结论解释某实际机组发生的摩擦现象。     

基于分段啮合刚度的双圆弧斜齿轮转子系统的振动响应分析

以双圆弧斜齿轮平行轴转子系统为研究对象,结合其啮合过程的变形特点,导出了其动能和势能的计算公式,根据拉格朗日方程建立了齿轮啮合的动力学模型;根据转子系统齿轮多点和多齿的啮合特点,采用分段式的方法计算其啮合刚度,将其与动力学模型相结合,采用有限元法,求解平行轴转子的弯曲振动和弯扭耦合振动特征值,并分析了系统在不平衡力作用下随激振频率变化的振动响应曲线.研究表明,采用分段式计算啮合刚度的方法来分析双圆弧齿轮是可行的,以此为根据求解的响应曲线符合转子动力学的振动规律,可为双圆弧齿轮平行轴转子系统的动力学分析提供理论基础.     

核电厂电动主给水泵热启动的振动特性试验

试验研究了某国产压水堆核电机组(CPR 1000)电动主给水泵压力级转子热启动过程的振动特性,并提出优化运行措施。采用高采样率的振动数据采集设备,测试电动主给水泵在50%负荷、100%负荷联锁启动及再循环工况热启动时压力级泵的振动信号,发现启动过程中压力级转子存在振动较快上升然后缓慢下降至稳定的现象。通过分析振动趋势图、振动频谱图及振动轴心轨迹图等认为这属于渐变性强迫振动,振动变化至稳定的时间约为20min。根据压力级转子的结构特点,建立带初始热弯曲的Jeffcott转子动力学模型,分别研究弯曲变形和质量偏心的影响,认为压力级转子热备用期间存在暂态热弯曲是导致渐变性热致振动的主要原因,且通过实测壳体端面的热成像图得到验证。电动主给水泵的振动特性表明,热启动过程中应分别设置瞬态振动延时保护与稳定运行期间的振动定值保护。     

由精密齿轮传动链轴弹性弯曲变形产生的回差

对于精密齿轮传动链，轴弹性变形也是影响回差计算的主要因素。现行计算方法仅计入轴弹性扭转变形对回差的影响，因此存在较大误差。通过分析及计算，导出了包括轴弹性扭转变形及弹性弯曲变形在内的轴弹性变形产生回差的计算公式。研究表明。轴弹性弯曲变形对轴弹性变形产生回差的影响不容忽视。     

阶梯轴弯曲固有振动分析及应用

给出阶梯轴弯曲固有振协精确的分析方法,该法亦可用于工程中阶梯梁弯曲固有振动分析。我们用该方法计算了硅压阻式加速度传感顺五阶梯硅梁固频率和振型。     

Vibration analysis on the rolling element bearing-rotor system of an air blower

Air blowers are widely used in industry. The vibration of the rolling bearing-rotor is a key factor in the blower’s performance because it significantly influences the security and working life of the whole system. In previous research on the vibration characteristics of the air blower, the supporting rolling element bearing was always simplified as a particle on a shaft with radial stiffness and damping coefficient. Such simplification neglects the effects of the bearing structure on the vibration performance of the rotor system. In this paper, a numerical model of the bending stiffness of the tapered roller bearing was established through mechanics and deformation analysis. On the base of the model, a new TMM (transfer matrix method) for bearing-rotor system was established; the new TMM considers the influences of the bearing structure on the vibration of the rotor system. Furthermore, modal analysis on an air blower rotor system was carried out by using the new TMM, and the mode shape, critical speed and unbalance response of the air blower system were obtained. The same blower rotor was also analyzed by FEM to verify the validation of the new TMM, showing that the new method proposed in this paper for vibration characteristics calculation of an air blower is credible.     

Stability analysis of a rotor bearing system due to surface waviness and number of balls

In the paper, the stability analysis of a rigid rotor supported by ball bearings has been studied. In the analytical formulation, the contacts between balls and races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the nonlinear differential equations iteratively. The effects of surface waviness and the varying number of balls on stability of rotor bearing system are observed. All results presented in form of fast fourier transformations show that the vibration characteristics of the rotor and its bearings change, when the bearings operate in different regions of their nonlinear load deflection characteristics. From the analysis, it is implied that the number of balls and number of waves in the ball bearing are two important governing parameters affecting its dynamic behavior.     

碰摩转子弯扭耦合振动特性分析

在给出单盘转子弯扭耦合振动的一般理论模型后 ,对碰摩转子的弯扭耦合振动动力特性进行了理论分析。在给出几个基本概念和碰摩转子弯扭耦合振动的激振力形式、刚度与阻尼的变化后 ,建立了碰摩转子的非线性弯扭耦合振动微分方程。然后对弯扭耦合振动转子的碰摩特性进行了数值分析 ,得出了若干结论 ,找出了扭转对弯曲的影响特征。     

发电机转子不稳定振动的分析与处理

针对某机组在安装调试阶段出现振动超标问题,应用多通道信号采集系统测量轴系振动特性,进行故障机理与相关因素分析,采用转子动平衡的措施校正补偿发动机转子热不平衡响应,有效地抑制了机组振动发散超标现象。     

温度载荷下夹芯板蜂窝微结构构型与尺度对结构刚度的影响研究

建立了求解正交各相异性材料等效性能的能量法。数值模拟实验中,在材料组分比一定的情况下,通过缩放因子改变单胞尺寸,研究同种蜂窝微结构对结构力学性能影响的尺度效应;同时验证了不同多孔材料微结构构型对结构刚度的影响;在稳态温度载荷的作用下,热变形引起弯曲变形,利用微结构的构型差异和尺度效应共同作用实现结构最大挠度的控制。     

Unbalance Response of a Super-Critical Rotor Supported by Foil Bearings—Comparison with Test Results©

This article compares theoretical and experimental results on the unbalance response of a super-critical rotor supported by two kinds of gas foil bearings. Analysis of the super-critical rotor is performed with viscoelastic foil bearings (VEFB) and conventional bump foil bearings and compared with early published experimental data. The vibration orbits obtained by theoretical investigation on the viscoelastic foil bearings (VEFB) and the conventional bump foil bearings are compared with the experimental vibration orbits of the super-critical rotor supported by both foil bearings. A numerical analysis program can calculate the static and dynamic characteristics of the elastically supported gas foil bearing using the measured stiffness and damping of the elastic foundation. After the stiffness and damping of both foil bearings are calculated using the perturbation method, vibration orbits of the flexible rotor modeled by the finite element method are calculated. Vibration orbits calculated by numerical analysis agree well with experimental data when the vibration amplitude is small and the rotating speed is below the bending critical speed. The numerical results also show that the enhanced structural damping of the elastic foundation reduces vibration near the bending critical speed.     

Evaluation of the influence of the initial deflection curve shape of a two-span rotor with residual imbalance on its vibroactivity during rundown

This work is devoted to the evaluation of the influence of the curve shape of the ineradicable initial deflection of a two-span rotor with the residual imbalance on the transition vibration amplitudes at low critical speeds under the rundown. The model corresponds to a high-pressure rotor–combined mid-low-pressure rotor (HPR–MLPR) system of a turbine unit. It is assumed that rotors are connected by a rigid coupling and installed on anisotropic elastic damper supports. It is supposed that the resulting deflection (bend) of this system is formed as a result of the fact that a high-pressure rotor acquires the initial deflection during the operation or because of abnormal launch conditions, the curve shape of which for a load-free rotor is known. The influence of the mutual arrangement of the residual imbalances of rotors and the imbalances caused by the resulting deflection of shafting in a system on the amplitudes of its transition vibration under the rundown of a turbine unit has been studied for two shapes of the initial rotor deflection curve that have the highest and lowest values of the shape parameter. The values of the initial rotor bending deflection and the residual imbalance of both rotors have been set equal to the maximum acceptable values for the operation of a turbine unit. Amplitude calculations have been performed for rotors of a K-300-23.5 Leningrad Mechanical plant (LMZ) turbine.     

Mixed-lubrication analysis of marine stern tube bearing considering bending deformation of stern shaft and cavitation

A mixed-lubrication model has been developed to study tribological characteristics of a marine stern tube bearing. The finite difference method is employed to obtain numerical solutions of the Reynolds equation using combined Newton–Raphson and iterative relaxation methods. The differential equation of deflection curve of the propeller shaft is used to describe the bending deformation of propeller shaft. The displacement superposition method is used to solve the differential equation of deflection. The influences of cavitation and different boundary conditions, the Reynolds boundary condition and Jacobsson–Floberg and Olsson (JFO) boundary condition, as well as the bending deformation of shaft, on the Stribeck Curves are discussed in this paper.     

柔性转子加速过临界瞬态响应特征分析

对于工作一阶或多阶临界转速以上的转子系统,转子如何安全平稳越过临界转速已成为研究热点。本文中建立了考虑变速转子运动微分方程以及越过临界转速时瞬态动挠度随速度变化的新模型,通过Newmark-β积分法得到越过临界转速的动挠度、进动角速度随加速度和阻尼系数变化的曲线,得出加速度和阻尼系数会影响进动角速度及动挠度波动频率和幅度。小阻尼系数会加剧转子过临界的波动并产生反进动以及反进动与动挠度变化的对应关系,阻尼系数大到一定数值能使转子平稳越过临界转速等一系列规律。