Linear and non-linear control techniques applied to actively lubricated journal bearings

The main objectives of actively lubricated bearings are the simultaneous reduction of wear and vibration between rotating and stationary machinery parts. For reducing wear and dissipating vibration energy until certain limits, one can use the conventional hydrodynamic lubrication. For further reduction of shaft vibrations one can use the active lubrication action, which is based on injecting pressurized oil into the bearing gap through orifices machined in the bearing sliding surface. The design and efficiency of some linear (PD, PI and PID) and a non-linear controller, applied to a tilting-pad journal bearing, are analysed and discussed. Important conclusions about the application of integral controllers, responsible for changing the rotor-bearing equilibrium position and consequently the “passive” oil film damping coefficients, are achieved. Numerical results show an effective vibration reduction of unbalance response of a rigid rotor, where the PD and the non-linear P controllers show better performance for the frequency range of study (0-80 Hz). The feasibility of eliminating rotor-bearing instabilities (phenomena of whirl) by using active lubrication is also investigated, illustrating clearly one of its most promising applications.     

铜微颗粒碰撞阻尼特性

碰撞阻尼在机床、机器人、透平机械、飞机以及运载火箭等领域具有重要的应用价值. 在碰撞阻尼器中加入微颗粒材料, 可以利用颗粒的细化和塑性变形而有效地吸收振动能量, 为碰撞阻尼的研究和发展开辟了一条新途径. 本文讨论了带有中值粒度为50 μm的铜颗粒碰撞阻尼器在96 h内对正弦激励悬臂梁的阻尼减振特性. 研究表明, 在所考察的时间段内, 主系统的响应经历了先上升、再下降和再上升的过程. 这三个阶段的响应对应着铜颗粒微观结构变化的三个阶段. 在初始阶段, 铜颗粒主要表现为弹性变形, 能耗较低, 而钢球的次谐波共振可能将部分能量返回给主系统, 使主系统响应随时间呈现近似线性的上升; 在第二阶段, 当主系统响应增加到一定程度时, 钢球对铜粉的冲击力超出铜颗粒的屈服应力, 铜颗粒发生屈服, 不可逆能耗使主系统的响应震荡下降; 到了第三阶段, 铜颗粒在钢球冲击下发生硬化, 其应变和层错概率上升, 应变能和层错能下降, 主系统的响应再次持续震荡上升. 本文的结果对振动的被动控制以及材料塑性变形机理研究具有参考 意义. 关键词： 振动控制 碰撞阻尼 颗粒减振剂 微结构分析     

碳纳米管与石墨烯协同提高导热硅脂热性能

以甲基硅油为基础油,碳纳米管、石墨烯或碳纳米管/石墨烯混杂物为导热填料,制备复合导热硅脂.研究结果表明:以碳纳米管为单一导热填料,碳纳米管管径越小,管长越长,越有利于导热硅脂的导热性能提升。当总填充量在6%、碳纳米管和石墨烯配比为2:1时,导热硅脂的热导率提高19%。碳纳米管对石墨烯纳米片起到了分隔和桥连的作用,提高了石墨烯纳米片的分散性,有利于三维热传导网络的形成,进而提高导热硅脂的热传导性能。     

Vibration analysis of a rotating system due to the effect of ball bearing waviness

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modelled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian contact theory is applied to calculate the elastic deflection and non-linear contact force, while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the non-linear governing equations of the rotor, which are solved by using the Runge–Kutta–Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e., the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing, but also between those of two or more ball bearings constrained by the rotor.     

某纯电动汽车驱动轴异响分析与优化

针对某纯电动前驱汽车在急加速时驱动轴出现的异响问题,测试了异响产生时的振动和噪声数据,并利用希尔伯特变换识别了异响源的优先级,锁定异响至驱动轴。然后,结合驱动轴的三销轴式万向节、球笼式万向节的工作特性和轮心振动的分析结果,识别异响来源于球笼式万向节内部高速运动时的挤压摩擦。最后,通过改善润滑油脂的成分比例,提升润滑油脂的润滑性能,保证万向节内部润滑油膜具有一定厚度,结合实车验证了该方案的有效性,可为后续排查此类问题提供参考。     

THE APPLICATION OF BALL-TYPE BALANCERS FOR RADIAL VIBRATION REDUCTION OF HIGH-SPEED OPTIC DISK DRIVES

This study is dedicated to the design of a ball-type balancer system installed on the high-speed disk drive in order to reduce radial vibrations of rotors caused by eccentricities of disk's center of gravity and circular runway of the ball balancer. The ball balancer is a promising candidate due to its low cost and capability to completely eliminate radial vibrations under the conditions that runway eccentricity, damping and friction are not present. A mathematical model was established first for the analysis of the dynamics of a rotor-balancer system. The influence of concerned parameters, e.g., runway eccentricity and rolling resistance, on residual vibrations was then explored through solving the equations for steady state solutions. The results were used to evaluate the performance of balancers in terms of vibration reduction. The design guidelines for minimizing the vibrations by controlling the aforementioned concerned parameters were provided based on the parametric analysis conducted. Finally, experimental study was orchestrated and performed to verify the validity of the mathematical model and demonstrate balancer capability for reduction of radial vibrations.     

Design and Dynamics Investigation for a Silicone Rubber Shock Absorber

A new kind of coupling-type silicone rubber shock absorber was prepared. Vibration and static stiffness tests were carried out to investigate the characteristics of vibration control. A mechanical model of the shock absorber was established, and the working principle of the shock absorber was studied by comparing the vibration test with simulation results. The dynamic results show the shock absorber has excellent vibration control performance. The coupling characteristics originate from the contact of inner and outer silicone rubber. It is shown that the stiffness and damping coefficients in the coupling process are critical for vibration control of the shock absorber.     

磁流变体的制备及性能

对以羰基铁粉、硅油和烃类油为悬浮相和悬浮介质,通过适当添加剂和工艺制备的磁流变体材料,制备方法、磁流变性能及影响因素进行了研究,认为是具有良好综合性能的磁流变体材料。制备的磁流变体具有较低的零场粘度（0．4－1．5Pas),较高的剪切应力（τ=50-75kPa)和良好的稳定性及阻尼性能。     

An approach for including the stiffness and damping of elastohydrodynamic point contacts in deep groove ball bearing equilibrium models

This work presents a methodology for including the Elastohydrodynamic (EHD) film effects to a lateral vibration model of a deep groove ball bearing by using a novel approximation for the EHD contacts by a set of equivalent nonlinear spring and viscous damper. The fitting of the equivalent contact model used the results of a transient multi-level finite difference EHD algorithm to adjust the dynamic parameters. The comparison between the approximated model and the finite difference simulated results showed a suitable representation of the stationary and dynamic contact behaviors. The linear damping hypothesis could be shown as a rough representation of the actual hysteretic behavior of the EHD contact. Nevertheless, the overall accuracy of the model was not impaired by the use of such approximation. Further on, the inclusion of the equivalent EHD contact model is equated for both the restoring and the dissipative components of the bearing?s lateral dynamics. The derived model was used to investigate the effects of the rolling element bearing lubrication on the vibration response of a rotor?s lumped parameter model. The fluid film stiffening effect, previously only observable by experimentation, could be quantified using the proposed model, as well as the portion of the bearing damping provided by the EHD fluid film. Results from a laboratory rotor–bearing test rig were used to indirectly validate the proposed contact approximation. A finite element model of the rotor accounting for the lubricated bearing formulation adequately portrayed the frequency content of the bearing orbits observed on the test rig.     

Spontaneous formation of densely packed shear bands of rotating fragments

Appearance of self-similar space-filling ball bearings has been suggested to provide the explanation for seismic gaps, shear weakness, and lack of detectable frictional heat formation in mature tectonic faults (shear zones). As the material in a shear zone fractures and grinds, it could be thought to eventually form a conformation that allows fragments to largely roll against each other without much sliding. This type of space-filling "ball bearing" can be constructed artificially, but so far how such delicate structures may appear spontaneously has remained unexplained. It is demonstrated here that first-principles simulations of granular packing with fragmenting grains indeed display spontaneous formation of shear bands with fragment conformations very similar to those of densely packed ball bearings.     

Consistency-dependent optical properties of lubricating grease studied by terahertz spectroscopy

The optical properties of four kinds of lubricating greases (urea, lithium, extreme pressure lithium, molybdenum disulfide lithium greases) with different NLGL (National Lubricant Grease Institute of America) numbers were investigated using terahertz time-domain spectroscopy. Greases with different NLGL grades have unique spectral features in the terahertz range. Comparison of the experimental data with predictions based on Lorentz--Lorenz theory exhibited that the refractive indices of each kind of lubricating grease were dependent on the their consistency. In addition, molybdenum disulfide (MoS₂) as a libricant additive shows strong absorption from 0.2 to 1.4 THz, leading to higher absorption of MoS₂-lithium grease than that of lithium grease.     

高温超导磁悬浮轴承动态测试平台

为了研究高温超导磁悬浮轴承样机的动态旋转特性,介绍了由振动分析仪、转速计和位移传感器组成的动态测试平台。该测试平台不仅可以测试高温超导磁悬浮轴承的共振频率、刚度和阻尼系数等基本动态参数,而且可以实时测试旋转轴承的转速和振动偏移等运行参数。通过脉冲激励实验和自由衰减实验证实测试实验数据真实可靠。该平台的搭建将为本小组在轴对称式高温超导磁悬浮技术(轴承、飞轮等)的应用研究和开发奠定基础。     

Linear parameter varying control design for rotating systems supported by journal bearings

Linear parameter varying (LPV) control is a model-based control technique that takes into account time-varying parameters of the plant. In the case of rotating systems supported by lubricated bearings, the dynamic characteristics of the bearings change in time as a function of the rotating speed. Hence, LPV control can tackle the problem of run-up and run-down operational conditions when dynamic characteristics of the rotating system change significantly in time due to the bearings and high vibration levels occur. In this work, the LPV control design for a flexible shaft supported by plain journal bearings is presented. The model used in the LPV control design is updated from unbalance response experimental results and dynamic coefficients for the entire range of rotating speeds are obtained by numerical optimization. Experimental implementation of the designed LPV control resulted in strong reduction of vibration amplitudes when crossing the critical speed, without affecting system behavior in sub- or super-critical speeds.     

Vibration and damping analysis of multilayered rectangular plates with constrained viscoelastic layers

Governing equations of motion for vibrations of a general multilayered plate consisting of an arbitrary number of alternate stiff and soft layers of orthotropic materials are derived by using variational principles. Extension, bending and in-plane shear deformations in stiff layers and only transverse shear deformations in soft layers are considered as in conventional sandwich structural analysis. In addition to transverse inertia, longitudinal translatory and rotary inertias are included, as such analysis gives higher order modes of vibration and leads to accurate results for relatively thick plates. Vibration and damping analysis of rectangular simply supported plates consisting of alternate elastic and viscoelastic layers is carried out by taking a series solution and applying the correspondence principle of linear viscoelasticity. The damping effectiveness, in term of the system loss factor, for all families of modes for three-, five- and seven-layered plates is evaluated and its variations with geometrical and material property parameters are investigated.     

Detection of acoustic oscillations of single gold nanospheres by time-resolved interferometry

We measure the transient absorption of single gold particles with a common-path interferometer. The prompt electronic part of the signal provides images for diameters as small as 10 nm. Mechanical vibrations of single particles appear on a longer time scale (period of 16 ps for 50 nm diameter). They reveal the full heterogeneity of the ensemble, and the intrinsic damping of the vibration. We also observe a lower-frequency mode involving shear. Ultrafast pump-probe spectroscopy of individual particles opens new insight into mechanical properties of nanometer-sized objects.     

Dynamic instability of supercritical driveshafts mounted on dissipative supports—Effects of viscous and hysteretic internal damping

The case of a rotating shaft with internal damping mounted either on elastic dissipative bearings or on infinitely rigid bearings with viscoelastic suspensions is investigated in order to obtain the stability region. A Euler-Bernoulli shaft model is adopted, in which the transverse shear effects are neglected and the effects of translational and rotatory inertia, gyroscopic moments, and internal viscous or hysteretic damping are taken into account. The hysteretic damping is incorporated with an equivalent viscous damping coefficient. Free motion analysis yields critical speeds and threshold speeds for each damping model in analytical form. In the case of elastic dissipative bearings, the present results are compared with the results of previous studies on finite element models. In the case of infinitely rigid bearings with viscoelastic suspensions, it is established that viscoelastic supports increase the stability of long shafts, thus compensating for the loss of efficiency which occurs with classical bearings. The instability criteria also show that the effect of the coupling which occured between rigid modes introducing external damping and shaft modes are almost more important than damping factor. Lastly, comparisons between viscous and hysteretic damping conditions lead to the conclusion that an appropriate material damping model is essential to be able to assess these instabilities.     

器壁滑动摩擦力对受振颗粒体系中冲击力倍周期分岔过程的影响

颗粒物质由离散的固体颗粒组成, 受到周期性振动时可以表现出复杂的动力学行为. 这些行为往往受众多因素的影响, 如空气阻力和器壁摩擦力等. 针对受振颗粒体系中冲击力的倍周期分岔现象, 通过抽真空或将容器底镂空消除空气阻力, 单独研究器壁滑动摩擦力的影响. 结果表明在仅有器壁摩擦力作用的情况下, 倍周期分岔过程仅受约化振动加速度的控制, 与颗粒的尺寸、颗粒层数及振动频率无关. 将器壁摩擦力处理成一个大小恒定、方向与颗粒和器壁相对速度反向的阻力, 并包含到完全非弹性蹦球模型中, 能够对所观察到的现象给出很好的解释. 通过对倍周期分岔点测量平均值的拟合, 得到器壁滑动摩擦力的大小约为颗粒总重量的10%. 关键词： 颗粒物质 器壁摩擦力 倍周期分岔 冲击力     

On the non-linear dynamic behavior of elastohydrodynamic lubricated point contact

The complex dynamic concepts of mechanical systems are regarded each day as new barriers to be overcome. One of the most complex systems, despite its common construction design, is the rolling element bearings. The interactive dynamic interfaces of such bearings are normally disregarded by engineering analysis on the day to day basis due to its complexities. This paper intends to propose a new approach to the characterization of the elastohydrodynamic lubricated point contacts on such components, in order to fully depict its non-linear dynamic behavior, avoiding the use of rough hypothesis on a systemic procedure. A multi-level method was used to solve the coupled lubrication-deformation problem, alongside a Newmark-ß integrator of the motion equation for the contact system. A range of dynamically similar contacts were evaluated, so as to characterize its nonlinear dynamic behavior. A least-squares method was applied to the multi-level algorithm results, fitting the displacements-force relation to a linear and also to a third order polynomial stiffness. The fitting results were compared, clearly showing the nonlinear behavior of such contacts. Also, the oil film damping was regarded as viscous, leading to good overall response. Some peculiarities of the proposed adjust method are also considered.     

布谷鸟搜索的润滑脂特征红外光谱波段优选技术

针对润滑脂分类,提出了基于布谷鸟搜索的红外光谱波段筛选方法,有效剔除了易受噪声等环境影响的红外光谱区域、实现了对庞大光谱数据进行特征选择和降维处理、通过筛选光谱最优波段建立了更加准确高效的润滑脂分类模型。以三类不同稠化剂润滑脂的红外光谱数据为研究对象,采用主成分分析法(PCA),对不同波段的红外光谱数据进行压缩,以提取的红外光谱主要成分作为输入,润滑脂稠化剂类别作为输出,通过布谷鸟搜索法(CS),对主要成分权重和分类核参数进行准确度寻优训练,建立分类识别预测模型。对所建立的模型再进行分类准确性测试,得到模型测试结果准确度,建立红外光谱波段和测试准确度之间的联系,得到润滑脂最优类别识别模型和最优分类波段。对所建立的模型再进行分类准确性测试,结果显示：经过布谷鸟搜索法训练加权后的主要特征呈现明显聚类现象,可以得到分类核,实现对润滑脂种类的准确识别;在搜索过程中提供了区分不同润滑脂的推荐波段和特征峰,使对润滑脂的正确鉴别概率由全波段建立分类模型的94.44%提高到筛选后特征波段建立分类模型的100%,并减少了运算时间、提高了搜索运行效率。     

Non-linear dynamics of flexible multi-bearing rotors

A general analysis has been developed to computer simulate steady state and transient vibration phenomena of complex rotor-bearing-support systems. A central feature of this analysis is a proper handling of various highly non-linear effects (most notably journal bearings) which dominate the dynamic phenoména encountered during large amplitude rotor-bearing vibrations. There are a number of potential causes of large amplitude rotor vibration, such as high rotor imbalance (e.g., loss of turbine blades at running speed), critical speed operation, journal bearing dynamic instability (oil whip), earthquakes, and shock. Failure mode analysis requires the evaluation and understanding of such potentially large dynamic forces and displacements. The paper presents development of the analysis, comparison with experiment and examples of its use in industrial applications.