Effects of Floating Ring Bearing Manufacturing Tolerance Clearances on the Dynamic Characteristics for Turbocharger

The inner and outer oil film dynamic characteristic coefficients of floating ring bearings（FRBs） change due to the manufacturing tolerance of the floating ring, journal and intermediate, which leads to high-speed turbocharger＇s vibration too large and even causes nonlinear vibration accident. However, the investigation of floating ring bearing manufacturing tolerance clearance on the rotordynamic characteristics is less at present. In order to study the influence law of inner and outer clearance on turbocharger vibration, the rotor dynamic motion equations of turbocharger supported in FRBs are derived by analyzing the size relations between floating ring, journal and intermediate for the inner and outer oil film clearances, the time transient response analysis for combination of FRBs clearance are developed. A realistic turbocharger is taken as a research object, the FE model of the turbocharger with FRBs is modeled. Under the conditions of four kinds of limit state bearing clearances for inner and outer oil film, the nonlinear transient analyses are performed based on the established FE dynamic models of the nonlinear rotor-FRBs system applied incentive combinations of gravity and unbalance force, respectively. From the waterfall, the simulation results show that the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different under the four kinds of bearing manufacturing tolerance limit clearances, and fractional frequency does not appear in the turbocharger and the amplitude is minimum under the ODMin/IDMax bearing manufacturing tolerance clearances. The turbocharger vibration is reduced by controlling the manufacturing tolerance clearance combinations of FRBs, which is helpful for the dynamic design and production-manufacturing of high-speed turbocharger.

Effects of Semi-floating Ring Bearing Outer Clearance on the Subsynchronous Oscillation of Turbocharger Rotor

Semi-floating ring bearing（SFRB） is developed to control the vibration of turbocharger rotor. The outer clearance of SFRB affects the magnitude and frequency of nonlinear whirl motion, which is significant for the design of turbocharger. In order to explore the effects of outer clearance, a transient finite element analysis program for rotor and oil film bearing is built and validated by a published experimental case. The nonlinear dynamic behaviors ofrotor-SFRB system are simulated. According to the simulation results, two representative subsynchronous oscillations excited by the two hearings respectively are discovered. As the outer clearance of SFRB increases from 24 ~tm to 60 pro, the low-frequency subsynchronous oscillation experiences three steps, including a strong start, a gradual recession and a combination with the other one. At the same time, the high-frequency subsynchronous oscillation starts to appear gradually, then strengthens, and finally combines. If gravity and unbalance are neglected, the combination will start starts from high rotor speed and extents to low rotor speed, just like a ＂zipper＂. It is found from the quantitative analysis that when the outer clearance increases, the vibration amplitude experiences large value firstly, then reduction, and suddenly increasing after combination. A useful design principle of SFRB outer clearance for minimum vibration amplitude is proposed： the outer clearance value should be chosen to keep the frequency of two subsynchronous oscillations clearly separated and their amplitudes close.

Effect of Supported Bearing Clearance on Load-Sharing Characteristics of a Double-Row Planetary Gear System

Few studies were focused on the load-sharing characteristics of double-row planetary gear(DRPG)systems with bearings.Meanwhile,the supported bearing has an important influence on the transmission characteristics of the entire system.To overcome this problem,a multi-body dynamic(MBD)model of the DRPG system fully considering the influences of bearing parameters is established.Dynamic loads among contacting gear pairs have been obtained to calculate the load-sharing coefficient(LSC)of the system.The LSC of each gear tooth pair has been compared to study the effect of the supported bearing clearance on the load-sharing characteristics.These methods are based on Hertz contact theory.The liner stiffness and damping are used in the model.The results show that the supported bearing clearance has a greatly effect on the LSC of the DRPG system.Choosing appropriate clearance parameters of supported bearing can help suppress the uneven load distribution of the DRPG system.The results can provide some guidance to find new method to study the LSC and increase the service life of planetary gear systems.

NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE

Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.

The influence of rolling bearing clearances on diagnostic signatures based on a numerical simulation and experimental evaluation

This paper presents investigations into the influences of bearing clearances on the diagnostic features of monitoring rolling-bearings. A nonlinear dynamic model of a deep groove ball bearing with five degrees of freedom is developed for numerical analysis under increased radial clearances which are due to not only the scenarios of bearing grades but also gradual wear with bearing service lifetime. The model incorporates local defects and clearance increments in order to gain the insight into the bearing dynamics under different fault cases along with clearance changes. Numerical results show that the vibrations at fault characteristic frequencies exhibit clear inconsistency with common understandings for different cases of increased clearances. This study highlights that it has to take into account the clearance effect, especially for the inner race fault, in order to avoid the under-estimate of fault sizes which may be indicated by the feature amplitude reduction.

Bifurcation and chaos study on transverse-torsional coupled 2K-H planetary gear train with multiple clearances

A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.

Contact Force Distribution and Static Load-carrying Capacity of Large Size Double Row Four-point Contact Ball Bearing

Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.

An Approach to Stability Analysis of Sliding Motion in a Clearance Joint of a Four-Bar Mechanism

The sliding motion refers to the case when the pin of a revolute joint is in contact with the bush, following all or a segment of the circular trajectory inside the bearing. The equation of the sliding motion is obtained based on Lagrangian approach. By use of the classical continuation method, the stationary points can be calculated, and their local stability is determined with the theory of stability. This paper focuses its analysis on the joint connecting the rocker of a four bar mechanism to the ground. The results show that there are some relations between the local stability of sliding motion and contact loss

TEHL analysis of high-speed and heavy-load roller bearing with quasi-dynamic characteristics

In this paper, the aero-engine mainshaft roller bearing D1842926 under typical operating conditions is taken as a case study, a new integrated numerical algorithm of quasi-dynamics and thermal elastohydrodynamic lubrication（TEHL） is put forward, which can complete the bearing lubricated analysis from global dynamic performance to local TEHL state and break out of the traditional analysis way carried out independently in their own field.The 3-D film thickness distributions with different cases are given through integrated numerical algorithm, meanwhile the minimum film thickness of quasi-dynamic analysis, integrated numerical algorithm and testing are compared, which show that integrated numerical results have good agreements with the testing data, so the algorithm is demonstrated available and can judge the lubrication state more accurately.The parameter effects of operating and structure on pv value, cage sliding rate, TEHL film pressure, thickness and temperature are researched, which will provide an important theoretical basis for the structure design and optimization of aero-engine mainshaft roller bearing.

Friction moment analysis of space gyroscope bearing with ribbon cage under ultra-low oscillatory motion

This paper presents the model of calculating the total friction moment of space gyroscope ball bearings which usually work under ultra-low oscillatory motion and are very sensitive to the friction moment. The aim is to know the proportion of the friction moment caused by each frictional source in the bearing＇s total friction moment, which is helpful to optimize the bearing design to deduce the friction moment. In the model, the cage dynamic equations considering six degree-of-freedom and the balls dynamic equations considering two degree-of-freedom were solved.The good trends with different loads between the measured friction moments and computational results prove that the model under constant rate was validated. The computational results show that when the speed was set at 5 r/min, the bearing＇s maximum total friction moment when oscillation occurred was obviously larger than that occurred at a constant rate. At the onset of each oscillatory motion, the proportion of the friction moment caused by cage in the bearing＇s total friction moment was very high, and it increased with the increasing speed. The analyses of different cage thicknesses and different clearances between cage pocket and ball show that smaller thickness and clearance were preferred.

径向游隙对深沟球轴承疲劳寿命影响精细分析

采用Romax Designer工程分析软件,应用ISO/TS 16281寿命计算方法,根据经典的滚动轴承理论,对某风机用电机轴深沟球轴承,在不同径向游隙时的轴承内部载荷分布、接触应力、套圈滚道当量动载荷和ISO/TS 16281寿命进行了大量的计算,重点对轴承的疲劳寿命进行了精细分析,分析了径向游隙对轴承ISO/TS 16281寿命的影响。研究结果表明,径向游隙对寿命的影响不仅仅是通过对轴承内部载荷分布、接触应力和套圈滚道当量动载荷的影响而对寿命产生影响,还通过对寿命修正系数等因素的影响而对寿命产生影响;相同工况条件下,存在一个相对最优的径向游隙,由于所研究电机的两个轴承所受载荷不同,因而相对最优的径向游不同。研究结果可为深沟球轴承的优化设计提供参考。

考虑外圈变形和轴承座支承作用的球轴承动力学研究

高速、重载或薄壁球轴承等情况下的外圈结构弹性变形和柔性外圈与轴承座的配合支承特性对轴承及其系统的动力学性能有着重要的影响。采用等效刚体单元和Timoshenko梁单元建立了柔性外圈等效力学模型,考虑钢球与柔性外圈的分段滚道之间、柔性外圈与轴承座之间的动态接触作用,建立了计及外圈结构弹性变形和轴承座支承作用的球轴承多体接触动力学模型。运用广义-α方法计算分析了外圈弹性变形和轴承座支承作用对轴承载荷分布规律和动态配合特性的影响规律,获得了不同配合间隙、内部游隙、外圈厚度和径向力等因素下球轴承的动态作用力、载荷分布角和相对位移等动力学结果。结果表明:外圈增加至一定厚度,球轴承内部载荷分布与刚性套圈理论具有很好的一致性,刚性外圈与刚性轴承座的支承接触区域相对较小;随着外圈壁厚的减小,柔性外圈与轴承座的支承接触力逐渐由平滑曲线变为典型的多点极值和非光滑分布的动态变化规律,且相邻极值的差值,随着外圈壁厚的减小,配合间隙、内部游隙和径向力的增加而明显增加;随着配合间隙或内部游隙增大,球轴承载荷分布范围和轴承座的支承接触区域总体上呈现减小趋势;不同的配合间隙、内部游隙或径向载荷下薄壁外圈更容易发生近似对称的压缩、扩张、拉伸或压扁等不同形式的结构弹性变形。提出的动力学模型为滚动轴承及其系统的动力学研究和动态设计提供新方法。

水润滑轴承衬套装配间隙对轴系振动的影响

水润滑尾轴承通常安装在美人架和尾轴管中,轴承衬套的安装间隙大小直接影响到轴承刚度,从而对轴系振动产生影响,极大程度影响到舰船隐身性能。通过试验验证过盈配合和间隙配合2种安装结构的轴承在静载条件下的摩擦特性与振动特性。结果表明,2种安装间隙下的水润滑轴承的摩擦扭矩的变化趋势一致,均随载荷的增大而增大,随转速的升高而减小,间隙配合轴承的扭矩大于相同工况条件下过盈配合轴承的扭矩;在振动性能上,间隙配合轴承的振动幅值大于过盈配合的轴承,且相比于过盈配合轴承有更大机率出现高频特征频率。在相同工况条件下,过盈配合的轴承的摩擦特性和振动特性均优于间隙配合的轴承。

第三代轮毂轴承保证轴向游隙的动态选配方法

针对保证第三代轮毂轴承完成自动装配后的轴向游隙在规定范围的问题,首先根据装配线上轮毂轴承的实际测量推导出轴向游隙公式;其次,以满足轮毂轴承单元轴向游隙为目标,把增加的工艺生产功能转换为约束条件;最后,通过仿真模拟装配机床的合套过程,采用动态路径规划算法获取高精度组件的自动选择性装配方法,实现轮毂轴承钢球与外圈、内圈、法兰自动选配的最优合套方案。该方法提高了轴承轴套率,降低零件的报废率,可进一步推广到分析其他类型的轴承合套问题。

圆柱滚子轴承滚子对数修形优化研究

为了提高轴承的疲劳寿命,采用Romax Designer工程分析软件,在充分考虑径向游隙和内外圈相对倾斜量(影响轴承寿命的主要因素)对修形效果影响的基础上,对某大兆瓦风电机组齿轮箱输出轴轴承进行了对数修形优化分析。首先,对国际标准ISO/TS 16281寿命计算方法进行了简要分析;然后,对不同径向游隙情况下对数修形的效果进行了分析;最后,对不同内外圈相对倾斜量情况下对数修形的效果进行了分析。研究结果表明:以轴承最大接触应力最小为优化目标和以国际标准ISO/TS 16281寿命最长为优化目标的轴承对数修形,其最佳修形量不同,相应的ISO/TS 16281寿命有很大不同;在该轴承的具体条件下,以ISO/TS 16281寿命最长为优化目标的最佳修形凸度量对应的ISO/TS 16281寿命比以最大接触应力最小为优化目标的最佳修形凸度量对应的ISO/TS 16281寿命长2.39%~10.63%;以ISO/TS 16281寿命最长为优化目标的最佳修形凸度量对应的ISO/TS 16281寿命比未修形的ISO/TS 16281寿命长111.47%~1054.88%,建议以ISO/TS 16281寿命最长为优化目标对轴承进行修形优化设计。该研究结果可为滚子类轴承的优化设计提供参考。

含轴承间隙复摆颚式破碎机动态性能分析

在复摆颚式破碎机中,轴承间隙对其稳定性及轴承寿命均有一定影响。为分析轴承间隙对复摆颚式破碎机动态性能的影响,采用拉格朗日乘子法,建立含轴承间隙复摆颚式破碎机的动力学模型,分析了不同偏心轴转速及间隙值对破碎机动态性能的影响;并通过试验验证了其准确性。结果表明,增加偏心轴转速与减小间隙值均可减小破碎机动颚轴承滚子与内外滚道的碰撞力,增强运行稳定性及提高轴承寿命;增加偏心轴转速还可减少轴承的不规则磨损。对于PE150×250颚式破碎机,在提高生产率的同时减弱破碎机中的冲击现象,选择38 rad/s的转速最佳。

全陶瓷球轴承最佳原始游隙的研究与分析

游隙对于滚动轴承服役过程中的振动噪声、载荷分布及温升等均有重要影响。为获得适用于全陶瓷球轴承游隙的计算方法,将轴承装配、高速离心效应及热膨胀系数等因素统一为有效过盈量并对轴承游隙进行分析、总结计算公式,同时对氮化硅及轴承钢材料进行拉伸变形计算,研究发现氮化硅材料的延展性为轴承钢的67.7%,以此对过盈量引起游隙变化公式进行优化,并进行轴承装配实验验证优化结果。以7007C氮化硅全陶瓷球轴承为例,计算最佳原始游隙,结果表明在影响轴承径向游隙的因素中,离心效应影响程度最大,其次是轴承装配,再次为热膨胀系数,影响程度最小的为温差;随着转速及载荷的增加,离心效应及热膨胀系数的影响程度在所有影响因素中所占比重也会逐渐增加。

电机轴承振动特性试验

针对电动机支承轴承的振动问题,以某型变压器鼓风机中电动机非传动端支承轴承为研究对象,在分析转子临界转速的基础上,搭建电动机振动测试系统研究转速、升速率、保持架类型、预载荷和配置游隙等因素对轴承振动特性的影响,试验结果表明:电动机在小于临界转速的工况下运行时,轴承振动频率以电动机转频为主;随着电动机转速的升高,x,y,z方向的振动值均随转速提高而增大,转速对x方向振动的影响最大,对z方向振动的影响最小;电动机启动过程对轴承振动有明显影响,应尽量减小达到工作转速所需时间以避免电动机产生过大的振动;轴承游隙对其振动也存在一定影响,非传动端轴承宜采用CN游隙组;相对于钢制冲压保持架,电机轴承采用尼龙保持架时运转稳定性更好;过大或过小的预载荷均不利于轴承稳定运转。

球柱联合转盘轴承的寿命特性

为研究球柱联合转盘轴承的寿命特性,建立了轴承的力学模型与疲劳寿命计算模型,采用牛顿-拉弗森方法对模型进行求解,分析了轴承结构参数和工况参数对轴承寿命的影响,结果表明,轴承疲劳寿命随着轴承轴向游隙的增大先增大后减小,随轴向排每列钢球数的增加呈明显上升趋势,随径向排滚子数的增加仅小幅提高,随外载荷作用距离的增加和外载荷的增大明显降低。