An optimised short bearing theory for nonlinear dynamic analysis of turbulent journal bearings

An approximate method for nonlinear dynamic analysis of turbulent journal bearings supporting an unbalanced rigid shaft is proposed. The method is based on two assumptions: the separation of variables for pressure and a parabolic pressure distribution in the axial direction of the bearing. To take into account inertia effects, the well-known algebraic turbulent model based on the Prandtl mixing length hypothesis is used. Using the Constantinescu's approach, the pressure equation is modified by introducing two turbulent coefficients which are depending on the local Reynolds number. The nonlinear equations of motion for the rotor-bearing system are solved by means of the Euler's scheme, and the journal centre trajectories are examined for cases with and without unbalance forces. To illustrate the validity of the present study, three cases of journal bearings are analysed. The accuracy of the minimum film thickness, the dynamic transmissibility coefficient and the peak-to-peak displacement amplitudes obtained by the proposed methodology are comparable to the more elaborate and time consuming 2-D finite difference solution, while the turbulent journal centre orbits are comparable to those obtained experimentally.It is concluded that the optimised short bearing theory shows the advantage of minimising the computation time required for nonlinear dynamic analysis of laminar and turbulent journal bearings without any significant loss of accuracy.     

变阶梯结构自适应径向滑动轴承的研究

分析了变阶梯结构自适应径向滑动轴承膜压力的形成机理,并建立了二段油膜形耦合变形阶梯结构的流量控制方程,采用有限差分法交叉循环迭代求解了油压力的雷诺方程和变阶梯结构的流量控制方程,比较了设计参数对这咎径向滑动轴承的最小油膜厚度、压力分布、承载能力、摩擦阻力等性能和温升的影响,研究结果表明;合理地选择设计参数可以使得这种滑动轴承具有较好的润滑性能和承载特性。     

计及轴颈倾斜的径向滑动轴承湍流润滑分析

分析了轴颈倾斜状态下，径向滑动轴承的湍流润滑性能. 基于轴颈倾斜的统一Reynolds方程和能量方程，应用有限差分法求解了不同轴颈倾斜方位角、轴颈倾斜度、偏心率和平均雷诺数下的径向滑动轴承湍流润滑性能. 结果表明:轴颈倾斜方位角α=0°时，随着轴颈倾斜度的增大，轴承油膜的压力峰向轴承一端移动，轴承一端的轴向油膜温度梯度增大；α=90°时，随着轴颈倾斜度的增大，轴承油膜压力逐渐出现双峰分布，且向轴承两端移动，轴承两端的轴向温度梯度也不断增大. 在相同轴颈倾斜度增量下，轴承最大油膜压力、最高油膜温度、承载力和稳定工作力矩的增量随轴承中央截面偏心率的增大而增大. 相同轴颈倾斜度增量下，轴承最大油膜压力增量、最高油膜温度增量、承载力增量、摩擦系数减量和稳定工作力矩增量随平均雷诺数的增大而增大. 可见，径向滑动轴承湍流润滑分析中有必要考虑轴颈倾斜因素的影响.      

水润滑高速动静压轴承试验研究

研究了动静压轴承在水介质润滑和高速、高压极端工况条件下,最小液膜厚度和流量等性能参数的变化情况,并将其与理论预测结果进行比较.结果表明,水润滑动静压轴承在高速时能够稳定运行,且形成完整的润滑液膜,没有出现明显的汽化及汽蚀现象,试验后轴承表面涂层基本完好.试验结果显示出轴承的承载能力和流量主要取决于供水压力,这与理论预测结果基本一致.     

多个滑动轴承支承的转子系统稳定性研究

本文研究了多支承转子系统的稳定性以及支承不对中对稳定性的影响,提出求支承负荷分配的选代算法,按照求系统特征方程根的分析系统稳定性的方法。分析了国产某型200MW汽轮发电机组的稳定性,和支承不对中对稳定性的影响,为该型机组转子系统的改型设计和运行机组稳定性的改善提供了理论依据。     

Parameter variation and data mining of oil-film bearings: a stochastic study on the Reynolds’s equation of lubrication

The modeling and simulation process of oil-film bearing dynamics constitutes a rather essential task integrated in the workflow of various mechanical products. Specifically, in the turbo charger industry, the correct capture and understanding of the associated nonlinear rotating dynamics is of utmost importance, since the system’s efficiency and lifetime span depends on it. The root cause of the nonlinear rotordynamic effects is the oil-film concentrated in the rotor’s journal bearings. Its behavior is highly coupled with both the system’s geometric and dynamic configuration. The dynamics of the oil-film are described by the well-known Navier–Stokes equation, which under a series of assumptions and simplifications results to the, so-called, Reynolds equation. In this paper, the Reynolds equation is numerically solved based on a finite difference scheme and several parameter variation studies are conducted in an effort to pinpoint the most influential parameters—journal bearing geometric dimensions, oil-film properties and rotor-velocity-driven inputs—with respect to designated responses—friction, oil-film pressure force, minimum oil-film thickness and boundary oil-flow—all of which are regarded as important in terms of the aforementioned system’s efficiency and lifetime span. Based on multivariate analysis algorithms, correlation outcomes and global sensitivity results are presented. In an effort to capture possible nonlinear phenomena, which might not be possible via linear data mining tools, the Spearman rank-order coefficient and self-organizing maps methodology are applied.     

Vibration characteristics of a hydraulic generator unit rotor system with parallel misalignment and rub-impact

The object of this research aims at the hydraulic generator unit rotor system. According to fault problems of the generator rotor local rubbing caused by the parallel misalignment and mass eccentricity, a dynamic model for the rotor system coupled with misalignment and rub-impact is established. The dynamic behaviors of this system are investigated using numerical integral method, as the parallel misalignment, mass eccentricity and bearing stiffness vary. The nonlinear dynamic responses of the generator rotor and turbine rotor with coupling faults are analyzed by means of bifurcation diagrams, Poincaré maps, axis orbits, time histories and amplitude spectrum diagrams. Various nonlinear phenomena in the system, such as periodic, three-periodic and quasi-periodic motions, are studied with the change of the parallel misalignment. The results reveal that vibration characteristics of the rotor system with coupling faults are extremely complex and there are some low frequencies with large amplitude in the 0.3–0.4× components. As the increase in mass eccentricity, the interval of nonperiodic motions will be continuously moved forward. It suggests that the reduction in mass eccentricity or increase in bearing stiffness could preclude nonlinear vibration. These might provide some important theory references for safety operating and exact identification of the faults in rotating machinery.     

An Analysis of Journal Orbits for Nonlinear Dynamic Bearing Systems

An analysis of journal centre orbits is presented in this paper based on a non-isothermal non-Newtonian fluid model for dynamically loaded bearing systems. A spectral element approach is used to solve a full set of coupled equations (kinematics and constitutive) governing the flow of the lubricant, and an operator-splitting spectral element technique is used to evaluate the dynamic energy equation. The motion of the journal is calculated on the basis of Newtonian mechanics incorporated with a simple cavitation model. The stability of the journal orbits is investigated under a wide range of the rotation speeds of journal. The unstable orbits arise as a sub-harmonic motion when the journal rotation speed is increased beyond a critical value. The influences of the oscillation speeds of the applied loads on the journal orbits are examined. The numerical simulations demonstrate that both the rotation speed of the journal and the oscillation speed of the applied load play an important role in determining the pattern of the journal orbits. The effects of square-wave and rotating applied loads on the journal orbits are also investigated. Received 22 April 1998 and accepted 26 May 1999     

Performance of hydrodynamic journal bearing under the combined influence of textured surface and journal misalignment: A numerical survey

A wisely chosen geometry of micro textures with the favorable relative motion of lubricated surfaces in contacts can enhance tribological characteristics. In this paper, a computational investigation related to the combined influence of bearing surface texturing and journal misalignment on the performances of hydrodynamic journal bearings is reported. To this end, a numerical analysis is performed to test three texture shapes: square “SQ”, cylindrical “CY”, and triangular “TR”, and shaft misalignment variation in angle and degree. The Reynolds equation of a thin viscous film is solved using a finite differences scheme and a mass conservation algorithm (JFO boundary conditions), taking into account the presence of textures on both full film and cavitation regions. Preliminary results are compared with benchmark data and are consistent with a positive enhancement in misaligned bearing performances (load carrying capacity and friction). The results suggest that the micro-step bearing mechanism is a key parameter, where the micro-pressure recovery action present in dimples located at the second angular part of the bearing (from 180° to 360°) can compensate for the loss on performances caused by shaft misalignment, while the micro-pressure drop effect at the full film region causes poor performances. Considering the right arrangement of textures on the contact surface, their contours geometries can have a significant impact on the performance of misaligned journal bearings, particularly at high eccentricity ratios, high misalignment degrees and when the misalignment angle α approaches to $0\mathrm{°}$ or $180\mathrm{°}$.     

推力轴承对轴承－转子系统的耦合作用研究

研究了推力轴承对轴承－转子系统的耦合作用。在传递矩阵法的基础上，提出一种研究考虑推力轴承影响的轴承－转子系统的动力学的通用方法。研究中考虑了如下几个因素：（１）推力盘的静态倾斜；（２）转子的静变形；（３）径向轴承中负荷的重新分配；（４）偏载对径向轴承性能的影响；（５）推力轴承对系统稳定性的影响。研究结果表明，在某些情况下，推力轴承对径向轴承的动特性、转子的静挠度、系统稳定性等具有显著的影响     

滑动轴承二维动态摩擦接触的分析研究

应用边界单元法研究了滑动轴承动态摩擦时的接触力学性质,揭示了接触压力分布的不对称性;讨论了载荷,摩擦系数等因素对不对称性的影响,认为摩擦系数可使峰值接触压力降低和接触面积增加,增大载荷会使接触压力分布的不对称性更为明显,接触压力分布的不对称意味着磨损分布的不对称。同时分析了实际工作中滑动轴承摩擦副间的当量摩擦系数,指出在滑动试验研究中应采了当量摩擦系数。     

四瓦可倾瓦径向滑动轴承动力特性的实验研究

采用在线分析方法考察了300MW汽轮发电机可倾瓦轴承的静、动力特性,探讨了载荷、轴颈转速以及动态激振力频率等参数变化对可倾瓦轴承的静、动态性能的影响,比较试验结果与理论计算结果发现,在不同频率激振力作用下,理论计算所得到的可倾瓦轴承动特性参数与试验结果有较大的差异。     

Synthesis of thermal effects in misaligned hydrodynamic journal bearings

The analysis presented herein deals with the evaluation of pressure and temperature fields which are generated in thin fluid films of varying thickness. The particular problem of a misaligned journal bearing has been studied by solving simultaneously the Reynolds and energy equations, which also include the effects of viscous dissipation and the variation of fluid viscosity with temperature. The method has been used to predict pressure and temperature fields as well as global performance parameters for a typical journal bearing operation.     

随动耦合变阶梯径向滑动轴承动力特征及稳定性的研究

用有限差分法循环迭代求解了随动耦合变阶梯结构径向滑动轴承油膜压力的雷诺方程和两阶段油膜耦合变阶梯结构的流量控制方程。在分析轴承油膜压力形成机量及静力特性的基础上,采用对位移和速度的小扰动法计算了轴承的动力特性系数,考察了运转参数对这种轴承承载特性、动力特性系数、等效刚度、界限涡动比以界限失稳转速的影响,结果发现合理地选择设计参数可以使这种轴承具有较好的静力特性、动力特性和稳定性。     

Surface roughness effects in a short porous journal bearing with a couple stress fluid

In this paper, a theoretical study of the effect of surface roughness in hydrodynamic lubrication of a porous journal bearing with couplestress fluid as lubricant is made. The modified Reynolds equations accounting for the couple stresses and randomized surface roughness structure are mathematically derived. The Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effects of surface roughness on the static characteristics of a short porous journal bearing with couplestress fluid as lubricant. Further, it is assumed that, the roughness asperity heights are small compared to the film thickness. It is observed that, the effects of surface roughness on the bearing characteristics are more pronounced for couplestress fluids as compared to the Newtonian fluids.     

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.     

Numerical investigation on the influence of surface texture on the performance of hydrodynamic journal bearing

Many researchers have adopted various techniques for improving the performance characteristics of journal bearing. Apart from other parameters, incorporation of different forms of surface texture (sinusoidal, dimple, spherical etc.) on bearing or shaft also helps to increase the load carrying capacity and reduce the friction coefficient etc. in the journal bearing. Present study investigates the influence of different forms of surface texture on finite journal bearing which has been considered in the form of negative texture (micro cavities) at different locations of bearing surface. The Governing equations are solved numerically through finite difference approach for analysis of texture effects on bearing characteristics. It has been observed that the presence of micro cavities at different locations of bearing surface help in enhancing the bearing performance. It has also been found that the negative half wave texture enhances the bearing performance more in comparison to full wave texture on bearing surface.     

圆锥滚子轴承润滑与动力学耦合研究

为准确分析圆锥滚子轴承润滑和动力学耦合性能,建立了基于油膜刚度与阻尼的圆锥滚子轴承动力学耦合方程,并对方程进行了验证和数值求解. 数值结果表明:与不考虑润滑相比,考虑润滑后轴承内圈轴向运动更加稳定,轴向位移变小;在不同的滚子端面球半径和挡边倾角下,润滑效应能够使内圈径向振动加速度级减小1.71到2.07 dB;同时滚子个数的增加会使轴承内圈滚道和内圈挡边的平均最小油膜厚度分别增加7.97%和4.43%.      

电流变“Smart”轴承动态特性分析

本文采用作者提出的二次规划法为基础的双线性流变有限元方法分析了电流变“Ｓｍａｒｔ”轴承的动态特性,给出了在不同偏心率下轴承油膜八项动态特性系数随电压改变的曲线。通过对轴承－转子系统的稳定性分析,发现若加大油膜电压将会提高轴承的稳定性     

复合表面径向滑动轴承的概念和性能预报

近年来的研究发现固液界面的滑移可以减小表面摩擦,但也会造成流体动力效应下降甚至消失.本文提出了复合表面滑动轴承的概念,轴套表面由具有不同吸附和滑移特性的复合表面组成,发现复合表面轴承比普通轴承有许多优点.通过改变轴套表面的滑移特性可以改变和优化轴承的各种性能,例如摩擦系数、承载力、润滑剂流量、承载角等.数值解表明,在轴承高压区改变轴套表面滑移特性,轴承的整体性能会有大幅度提高.例如,本文给出的初步优化设计方案使得摩擦系数降低50%以上,同时承载力可提高20%,并且承载角可以降低33%.本文提出的设计理念不但可用于设计出具有更优异特性的径向滑动轴承,而且可以设计出具有复合表面的轴向滑动轴承或滑块轴承.复合表面滑动轴承在降低轴承摩擦、提高承载能力方面有很大的空间可以探索.