Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system

This research studies the effects of axial preload on nonlinear dynamic characteristics of a flexible rotor supported by angular contact ball bearings. A dynamic model of ball bearings is improved for modeling a five-degree-of-freedom rotor bearing system. The predicted results are in good agreement with prior experimental data, thus validating the proposed model. With or without considering unbalanced forces, the Floquet theory is employed to investigate the bifurcation and stability of system periodic solution. With the aid of Poincarè maps and frequency response, the unstable motion of system is analyzed in detail. Results show that the effects of axial preload applied to ball bearings on system dynamic characteristics are significant. The unstable periodic solution of a balanced rotor bearing system can be avoided when the applied axial preload is sufficient. The bifurcation margins of an unbalanced rotor bearing system enhance markedly as the axial preload increases and relates to system resonance speed.     

Dynamic Behavioral Analysis of an Antiseismic Support under an External Kinematic Disturbance

Study is made of the dynamic behavior of an antiseismic support, which is a heavy homogeneous ball rolling within a cycloidal cavity between mobile upper and lower slabs, subjected to an external kinematic disturbance. The equations of motion are derived for the heavy ball moving in the cycloidal cavity without slipping, and the dynamic effects in this, new earthquake-protective system are analyzed numerically.     

A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint

Impact affects the dynamic characteristics of mechanical multi-body systems and damages those rotating parts, such as the joint rolling element bearings, which are high-precision, defect intolerant components. Based on multi-body dynamic theory, Hertzian contact theory, and a continuous contact model, this study proposed a modelling method that can describe the dynamic behaviour of planar mechanical multi-body systems containing a rolling ball bearing joint under impact. In this method, the rigid bodies and bearing joint were connected according to their joint force constraints; the impact constraint between the multi-body system and the target rigid body was constructed using a continuous contact force model. Based on this method, the reflection relationship between the external impacts of the mechanical multi-body system and the variation law governing the dynamic load on the rolling bearing joint were revealed. Subsequently, an impact multi-body system, which was composed of a sliding–crank mechanism containing a rolling ball bearing joint and the target rigid body with an elastic support, was analysed to explore the dynamic response of such a complex discontinuous dynamic system andthe relevant relationship governing the dynamic load on the rolling bearing joint. In addition, a multi-body dynamic simulation software was used to build a virtual prototype of the impact slider–crank system. Compared with the theoretical model, the prototype had an additional deep groove ball bearing. That is to say, the prototype model took account of the specific geometric structural characteristics and the complex contact relationship of the inner and outer races, rolling balls, and bearing cage. Finally, the effectiveness of the theoretical method proposed in this study was verified by comparative analysis of the results. The results suggested that the external impact of a mechanical multi-body system was prone to induce sudden changes in the equivalent reaction force on its bearing joint and the dynamic load carried on its rolling balls. This study provided an effective method for exploring the distribution characteristics of dynamic loads on rolling ball bearing joints under working impact load conditions. Moreover, it offered support for the parameter optimisation of geometric structure, performance evaluation, and dynamic design of the rolling ball bearings.     

Influences of wear on dynamic characteristics of angular contact ball bearings

Wear between balls and races has significant effects on the dynamic characteristics of bearing, which is the main reason to cause bearing failure. Some existing contact stiffness models were established to study the dynamic characteristics of bearing. However, the wear of bearing has been rarely investigated due to the complexities of contact load and wear mechanism. This paper presents a new dynamic wear simulation model of angular contact ball bearings mounted in pairs to solve this problem. A final contact stiffness model is established based on the wear model. The effects of running distance, horizontal load, preload, initial contact angle, number and diameter of balls on wear performances are analyzed. A generalized time-varying and piecewise-nonlinear dynamic model of angular contact ball bearings is established to perform an accurate investigation on its dynamic characteristics, especially considering the coupling effects of wear and rolling contact. The effects of wear on the contact stiffness and nonlinear dynamic characteristics are analyzed according to the dynamic model. Additionally, the variations of the contact stiffnesses and frequency responses with different preloads are discussed and the results indicate that parameter selection has significant effects on the wear and nonlinear response.

     

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

Stability and dynamic characteristics of a ball 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 Floquet 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.     

考虑转速影响的滚珠丝杠副摩擦系数计算与试验研究

针对目前滚珠丝杠副摩擦系数选取多以轴承经验值为依据的现状,基于滚珠丝杠副的结构特点建立滚珠与滚道的运动学及动力学模型,得到滚珠丝杠副摩擦系数与预紧力及摩擦力矩之间的关系,并推导出滚珠丝杠副摩擦系数计算公式.通过新型设计的预紧力可调机构可实现对双螺母滚珠丝杠副预紧力的任意加载与实时监测.利用该机构,结合摩擦力矩测量系统便可实现对滚珠丝杠副摩擦力矩和预紧力的直接测量,从而计算不同预紧力和转速下的实际摩擦系数.由于测量系统转速限制,试验在转速400 r/min以下的低速条件进行,最终得到摩擦系数随转速与预紧力的变化规律,并给出了滚珠丝杠副低速下摩擦系数的选用范围.通过试验得到合理的滚珠丝杠副摩擦系数取值对今后研究其摩擦特性有着重要的意义.     

THE DYNAMIC ANALYSIS OF THE INTERESTING EXPERIMENT OF ROLLING BALL

本文定量分析了"瑞利球"实验的动力学过程。"瑞利球"实验中构建了一个"怪坡",通过对两导轨的控制,使均质圆球看起来像在"爬坡"。文中据刚体运动原理构建了物理模型,并分析系统的受力情况和运动过程,导出了均质圆球"爬坡"的最大高度的公式。在忽略空气阻力与摩擦力情况下,当两导轨杆初始距离远小于圆球半径、小球刚好不能掉落时突然合拢两导轨使其平行、两导轨初始夹角等于两倍导轨倾斜角时,均质圆球可以达到最大高度和最远距离。     

滚动轴承-偏置转子系统动力特性数值分析与实验研究

应用有限元法建立偏置转子的计算模型,采用考虑轴承Hertzian接触力和内间隙等非线性因素的二自由度滚动轴承模型,建立了滚动轴承-偏置转子系统的非线性动力学模型.通过数值仿真和实验研究分析了转子系统的非线性动力特性.实验数据和有限元模型计算结果是一致的,证实了所建立滚动轴承-转子系统非线性模型的合理性.发现由于滚动轴承非线性因素的影响,当转速达到系统共振转速的两倍附近时,激起了系统亚谐共振.     

Nonlinear dynamics of a system of rigid bodies with controlled electromagnetic dampers

A nonlinear mathematical model of a system of n rigid bodies undergoing translational vibrations under inertial loading is constructed. The system includes ball supports as a seismic-isolation mechanism and electromagnetic dampers controlled via an inertial feedback channel. A system of differential dynamic equations in normal form describing accelerative damping is derived. The frequencies of small undamped vibrations are calculated. A method for analyzing the dynamic coefficients of rigid bodies subject to accelerative damping is developed. The double phase–frequency resonance of a two-mass system is studied     

Penetration of Solid Bodies into Concrete

The results of an experimental study of quasistatic and dynamic penetration of solids into sand concrete are presented.Cylindrical bodies with conical tips and a ball were used. The resistance forces are compared for the taper angles of 180?, 90?, 60?, 30?, 9.5? and a ball. The flow character in the quasistatic immersion regime and in dynamic immersion due to inertia is determined.     

An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems

This study is focused on dynamic modeling of planar multibody systems with multiple deep groove ball bearing joints, in which the radial clearance, contact deformation, and bearing kinematics are included. By using the approach presented, the variation of the joint reaction force and the dynamic load on each ball element in bearings can be simulated. The deep groove ball bearing joints are modeled by introducing a nonlinear force system, which takes into account the contact elastic deformations between the ball elements and the raceways. The contact force is calculated by the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. A planar slider-crank mechanism with two deep groove ball bearing joints is chosen as an example to demonstrate the application of the methodologies presented in this paper. In this model, one bearing locates at the joint between the ground and crank, while the other one locates at the joint between the crank and connecting rod. By numerical calculation, the dynamic load distribution characteristics of bearings under real mechanism movement conditions are simulated. From the results, it can be concluded that the dynamic load on each rolling element varies differently and belongs to a variable load with the change of mechanism configuration. Load characteristic analysis is the foundation of developing research on the fatigue life and reliability of bearings. This study will provide a key mechanical support for the performance evaluation, dynamic design, and geometrical parameter optimization of the joint rolling element bearings.     

An experimental testing of a simplified model of a ball bearing: stiffness calculation and defect simulation

This paper presents an experimental verification of a simplified model of a nonlinear stiffness ball bearing in both static and dynamic modes and testing its capabilities to simulate accurately fault’ effects.     

Subharmonic resonance of a symmetric ball bearing–rotor system

The performance of a ball bearing–rotor system is often limited by the occurrence of subharmonic resonance with considerable vibration and noise. In order to comprehend the inherent mechanism and the feature of the subharmonic resonance, a symmetrical rotor system supported by ball bearings is studied with numerical analysis and experiment in this paper. A 6DOF rotordynamic model which includes the non-linearity of ball bearings, Hertzian contact forces and bearing internal clearance, and the bending vibration of rotor is presented and an experimental rig is offered for the research of the subharmonic resonance of the ball bearing–rotor system. The dynamic response is investigated with the aid of orbit and amplitude spectrum, and the non-linear system stability is analyzed using the Floquet theory. All of the predicted results coincide well with the experimental data to validate the proposed model. Numerical and experimental results show that the resonance frequency is provoked when the speed is in the vicinity of twice synchroresonance frequency, while the rotor system loses stability through a period-doubling bifurcation and a period-2 motion i.e. subharmonic resonance occurs. It is found that the occurrence of subharmonic resonance is due to the together influence of the non-linear factors, Hertzian contact forces and internal clearance of ball bearings. The effect of unbalance load on subharmonic resonance of the rotor system is minor, which is different from that of the sliding bearing–rotor system. However, the moment of couple has an impact influence on the subharmonic resonances of the ball bearing–rotor system. The numerical and experimental results indicate that the subharmonic resonance caused by ball bearings is a noticeable issue in the optimum design and failure diagnosis of a high-speed rotary machinery.     

头部与大挠度弹性板的撞击响应特性分析

在行人与汽车碰撞的研究中，头部-汽车发动机罩撞击损伤是重要的内容．把此问题简化为柔性球体与大挠度弹性板的大变形撞击响应问题，采用有限元方法分析了头部与汽车发动机罩撞击的动态响应特性，得出了相关因素对撞击响应的影响特点，并提出了具有行人保护作用的发动机罩的设计原则．为非线性动态响应力学问题的研究提供参考．     

硬脂酸钾固体润滑薄膜的制备及其摩擦磨损性能研究

采用浸渍-提拉法制备出硬脂酸钾薄膜,用DF-PM型静-动摩擦磨损试验机和UMT-2MT型摩擦磨损试验机考察了在低速滑动和高速滑动条件下硬脂酸钾薄膜的摩擦磨损性能,采用扫描电子显微镜和X射线能量色散谱仪观察分析了薄膜及偶件磨损表面的形貌及其典型元素的面分布情况.结果表明,以GCr15钢球为偶件在高速滑动和以氮化硅球作为偶件在高、低速滑动条件下,薄膜具有较好的摩擦磨损性能.由于钢球和氮化硅陶瓷球表面粗糙度及其化学状态存在差异,硬脂酸钾更容易在氮化硅球表面形成转移膜,从而具有更低的摩擦系数和更长的耐磨寿命.     

Nonlinear dynamic characteristics of ball screw feed system under thermal deformation

In this study, a novel kinetic model is established to investigate the dynamic characteristic of the ball screw feed system by considering the thermal deformation of bearing joints, screw-nut joints and screw shaft. Based on the Hertz contact theory, the relationship between elastic restoring force and axial deformation of bearing joints and screw-nut joints is obtained, respectively. Then the dynamic characteristics of the kinetic equation are analyzed by Runge–Kutta method. The vibration characteristics of the feed system with and without thermal deformation are analyzed, and the results indicate that the amplitude becomes larger when thermal deformation is considered. The motion state of the feed system at different frequencies is analyzed, and the results show that with the change of frequency, the motion state of the system will appear period-doubling motion, quasi-periodic motion and chaotic motion. Finally, the influence of different parameters on the vibration characteristics of the system is discussed.

     

航空发动机整机耦合动力学模型及振动分析

面向航空发动机整机振动, 建立了航空发动机转子-滚动轴承-机匣耦合动力学模型. 该模型具有如下特点: (1)考虑转子、滚动轴承及机匣之间的耦合作用; (2)考虑了实际航空发动机的弹性支承及挤压油膜阻尼效应; (3)将转子考虑为等截面自由欧拉梁模型, 运用模态截断法进行分析; (4)考虑了滚动轴承间隙、非线性赫兹接触力以及变柔性VC(Varyingcompliance)振动; (5)考虑了转子与机匣之间的碰摩故障. 运用数值积分方法研究了航空发动机的整机振动规律, 包括: 滚动轴承VC振动分析、弹性支承刚度对耦合系统临界转速的影响、转轴模态截断阶数NM对系统响应的影响分析、挤压油膜阻尼器参数对系统响应的影响分析、突加不平衡的瞬态响应分析以及转静碰摩故障特性分析等.      

Finite-Element Dynamic Analysis of a Rotating Shaft with or without Nonlinear Boundary Conditions Subject to a Moving Load

A C ⁰ continuity isoparametricfinite-element formulation is presented for the dynamic analysis of arotating or nonrotating beam with or without nonlinear boundaryconditions subject to a moving load. The nonlinear end conditions arisefrom nonlinear rolling bearings (both the nonlinear stiffness andclearance(s) are accounted for) supporting a rotating shaft. The shaftfinite-element model includes shear deformation, rotary inertia, elasticbending, and gyroscopic effect. Lagrange's equations are employed toderive system equations of motion which, in turn, are decoupled usingmodal analysis expressed in the normal coordinate representation. Theanalyses are implemented in the finite-element program DAMRO 1.Dynamic deflections under the moving load of rotating and nonrotatingsimply supported shafts are compared with those obtained using exactsolutions and other published methods and a typical coincidence isobtained. Samples of the results, in both the time and frequencydomains, of a rotating shaft incorporating ball bearings are presentedfor different values of the bearing clearance. And the results show thatsystems incorporating ball bearings with tight (zero) clearance have thesmallest amplitude-smoothest profile dynamic deflections. Moreover, fora system with bearing clearance, the vibration spectra of the shaftresponse under a moving load show modulation of the system naturalfrequencies by a combination of shaft rotational and bearing cagefrequencies. However, for a simply supported rotating shaft, the firstnatural frequency in bending dominates the response spectrum. The paperpresents the first finite-element formulation for the dynamic analysisof a rotating shaft with or without nonlinear boundary conditions underthe action of a moving load.     

力锤敲击作用下内嵌自主移动钢球欧拉梁碰撞减振性能研究

结合内嵌自主移动质量子系统梁／板实验平台实验结果,对力锤敲击作用下,内嵌自主移动钢球欧拉梁碰撞减振系统进行研究。采用线性弹簧-阻尼模型模拟钢球与梁之间的碰撞机制,通过分析建立了整个碰撞系统的分段线性动力学方程;运用无量纲化、假设模态法及高阶模态截断等方法导出系统的状态空间方程。数值计算结果表明,内嵌自主移动钢球对欧拉梁...     

CONTACT ELECTRIFICATION DUE TO THE OBLIQUE IMPACT OF CHEMICALLY IDENTICAL BALL AND PLATE

报道了同种材料球板斜碰带电量实验和理论研究, 发现同种材料球和板斜碰后球板会带电,带电量的极性与材料有关,带电量的大小与板的倾角有关,随着倾角的增大先增加后减小,当倾角约50°时,碰撞电量达到最大,是正碰撞电量的6~8 倍. 通过球板斜碰过程的动力学分析,发现球板碰撞后球的带电量与碰撞过程中球与板的摩擦面积成正相关.