The photoelastic-coating technique for plastic-elastic contact

Steel models coated with thin birefringent layers representing transverse sections through British-Standardinch keyed shafts and hubs have been loaded in torsion. Models with two different steel shafts and clearance fits between key and keyways and between shaft and hub have been analyzed over a large range of torques. Large plastic strains occurred at six contact positions where there are discontinuities of profile and surface contact of the chamfered key or the shaft. Contact strains have been measure, corrected for shear lag and normalized. Plastic-elastic SCF's are lower than corresponding elastic values.     

Reduction of elastic stress concentrations in end-milled keyed connections

Frozen-stress, three-dimensional models were used to study the elastic stress distribution in both metric and inch rectangular, parallel, standard keys, shafts and hubs with end-milled keyways, loaded in torsion. The coefficient of friction between the shaft and the hub was measured and the surface conditions were arranged to simulate typical prototype friction. Positions and magnitudes of the peak shear stresses were determined in the prismatic part and at the ends of keys and keyways. The axial position of torque application to the hub, the key length and key-end shape were altered to investigate their effects on the stress distributions. The maximum shear stresses in the shaft occur in the keyway end if the key is not chamfered. The maximum stress in the standard metric shaft is 25 percent greater than in the inch standard. Changing the axial position of torque application from the middle to the front increases the peak stresses by about 13 percent. Doubling the length of hub and key reduces the stresses by about 25 percent. Filing off parts of the key to prevent contact at the keyway end reduces the maximum stresses by 11 percent.     

Keyway stresses when torsional loading is applied by the keys

Guided by failure of large-diameter shafts, photoelastic measurements were made of stresses near the inboard ends of keyways containing keys which provided the forces necessary to place the shaft in torsion. Tensile-stress concentrations not previously reported were found at or near the inboard ends of these keys and keyways. The locations and magnitudes of these stress concentrations correlate well with fractures which have been found to begin at or near these same locations in large marine and compressor shafts.     

Strength of cylinder joint adhesively bonded by coupling

Summary A method of joining two metal cylindrical shafts with adhesive coupling is proposed. Two cylindrical shafts with the same diameter are connected by bonding through a cylindrical coupling with epoxy resin. The strength of the shaft joint under tensile loading and torsional loading is investigated analytically and experimentally. The stress and strain distributions of the shaft joint is analyzed by the finite element method. The analyzed strain distributions in the joint are compared with experimental values. The joint strength is predicted by applying the strength laws of shafts, coupling, adhesive layer and adhesive interface between shaft and adhesive coupling. The effects of the coupling dimension on the joint strength are examined. It is shown that the adhesive shaft joint can transfer the load by which the cylindrical shafts are plastically deformed.This paper was refined by the author, K. Ikegami, during statying at Technische Universität München under the support of Deutscher Akademischer Austauschdients. The author is grateful to Professor Lippmann of Technische Universität München who is the host professor of the support.     

Extension of Lagrangian–Hamiltonian mechanics for continuous systems—investigation of dynamics of a one-dimensional internally damped rotor driven through a dissipative coupling

In this paper, the extended Lagrangian formulation for a one-dimensional continuous system with gyroscopic coupling and non-conservative fields has been developed. Using this formulation, the dynamics of an internally and externally damped rotor driven through a dissipative coupling has been studied. The invariance of the extended or so-called umbra-Lagrangian density is obtained through an extension of Noether’s theorem. The rotor shaft is modeled as a Rayleigh beam. The dynamic behavior of the rotor shaft is obtained and validated through simulation studies. Results show an interesting phenomenon of limiting behavior of the rotor shaft with internal damping beyond certain threshold speeds which are obtained theoretically and affirmed by simulations. It is further observed that there is entrainment of whirling speeds at natural frequencies of the rotor shaft primarily depending on the damping ratio.     

高速列车穿越有竖井隧道流场的特性研究

给出了高速列车穿越隧道压力波的三维粘性流场数值模拟过程,控制方程为三维粘性、可压缩、等熵和非定常流的Navier-Stokes方程,空间离散采用了中心有限体积法格式,时间采用预处理二阶精度多步后差分格式进行离散,对隧道壁面采用壁面函数处理。在模拟中考虑了竖井的位置、竖井的断面积、竖井的数目等因素对隧道内压力及压力梯度的影响。计算结果表明,竖井的存在改变了压缩波的波前形状,从而使得隧道内的压力变化的最大值降低,因而能够降低隧道内的压力梯度最大值,但它并不能延长压力上升的时间。     

A shrink-fit shaft subject to torsion

The problem studied is an elastic, circular shaft, fitted into a cavity normal to the free surface of a half-space. The cavity is smaller than the shaft, so that there is a residual radial stress. A torque is applied to the shaft, giving rise to a region of slip between the shaft and the socket. Its extent is determined by forming an integral equation whose kernel is given by a circular ring dislocation, which has a Burgers vector whose magnitude is constant, oriented in the tangential direction. The problem has direct application to the study of shrink fitted shafts in wheels, whose diameter is large compared with the shaft.     

Dynamic stability of a viscoelastic rotating shaft under parametric random excitation

This paper deals with dynamic stability of a viscoelastic rotating shaft subjected to a parametric random axial compressive thrust, by using moment Lyapunov exponents and the largest Lyapunov exponents as indicators. The equation of motion for the shaft is derived, which is a system of gyroscopic stochastic differential equations. The method of stochastic averaging is used to decouple the governing equations into Itô equations, from which the moment Lyapunov exponent is obtained by using mathematical transformations only. The largest Lyapunov exponent is obtained through its relation with moment Lyapunov exponents. The effects of various parameters on the stochastic dynamic stability are discussed. The approximate analytical results are confirmed by Monte Carlo simulation.     

A Universal Expression for Bounds on the Torsional Rigidity of Cylindrical Shafts Containing Fibers with Arbitrary Transverse Cross-Sections

We derive upper and lower bounds for the torsional rigidity of host shafts containing a number of cylindrical fibers. The transverse cross-sections of the host shaft and the fibers are simply connected, but could be arbitrary in shape. Utilizing the fact that the torsion solution of a homogeneous host shaft with simply connected cross-section can be known, we propose a method to construct statically and kinematically admissible fields interior to the matrix and to the fibers. Previous developments on bounding the torsional rigidity of composite shaft so far are confined to circular fibers. Here we try to simulate fibers with non-circular cross-section and incorporate the interactions of the cross-sectional shapes of the host shaft and the fibers at the same time. Proceeding from extremal principles of elasticity, together with propositions of some domain integration procedures, we provide a universal expression for bounds on the torsional rigidity of the composite shaft. The exact expressions depend on the constituent information of the fibers and the host shaft, which could offer useful information to tailor the shape and the arrangement of the constituents to achieve an optimal value.     

秦岭公路隧道2号竖井地应力与岩爆分析

利用水平圆柱形激波管对激波驱动的可压缩性气固两相流进行了试验研究. 利用压电式压力传感器、电荷放大器、示波器及计算机组成的压力信号测试系统, 对激波 与颗粒作用前后的气相参数进行测量及分析. 试验中测得了激波在管中的传播速 度, 波后气流的压力, 反射激波、透射激波的压力和速度等. 分别考察颗粒、装载 比、驱动气源以及入射激波马赫数等因素的差异对气相参数的影响. 试验结果表明: 激波与颗粒群相互作用时, 会产生反射激波和透射激波, 其强度与驱动气源、颗粒大小、颗粒装载比等参数有关; 激波衰减率随着装载比、马赫数的增大而减小. 研究指出, 在颗粒群被激波加速的初始阶段, 颗粒间的弹性碰撞起着重要的作用.     

Bifurcation of a shaft with hysteretic-type internal friction force of material

IntroductionItwasfoundlongtimeagothattheinternalfrictionofmaterialcancauseinstabilityofrotatingshaft.Soitisalwaysoneoftheimportantsubjectsinrotordynamics[1].Earlyinvestigationswerefocusedonthedynamicalstabilityproblemofrotorinfluencedbythelinearinternalfrictionofmaterial,aimingtoobtainthecriterionofstability[2～4 ].Asthedevelopmentofnonlineardynamics,moreandmoreattentionswerepaidtothestudyoftheself_excitedmotionofrotatingshaft,thatisthebifurcation .Thestabilityregionsandbifurcationsofbothanau…     

轴电流作用下电机轴承润滑脂研究进展

发电机和电动机是最普遍使用的动力设备之一,电机轴承润滑脂是保证电机稳定、高效运转的关键,电机轴承在轴电流作用下润滑脂性能退化,会导致轴承失效. 作者在本文中介绍了电机轴承轴电流的产生和危害,同时对电机轴承润滑脂性能和作用进行了分析, 重点介绍了如何防止和抑制轴电流对轴承的损伤,并指出电机轴承润滑脂需要解决的问题和未来发展的趋势.      

INSTABILITY OF SHAFT EXCAVATION AND MECHANISM OF ROCKBURST

基于稳定性理论和弹塑性厚壁筒的解析解,研究了竖井开挖过程的平衡路径,并将屈服后的井壁压力--位移平衡路径曲线应用到围岩的稳定性分析.研究表明,竖井围岩的不稳定及其岩爆的发生不仅取决于岩石材料应力应变全过程曲线的峰后特性,还取决于竖井开挖过程对应的平衡路径曲线的类型.平衡路径曲线能够描述围岩结构加载屈服后的力学行为.平衡路径的曲线形状只可能有两种类型,一种曲线上的点都处于稳定的平衡状态,虽有塑性变形的累积,但不会失稳崩落;另一种曲线则发生极值点型井壁失稳并伴有位移突跳.竖井开挖过程的平衡路径曲线是判定围岩岩爆发生的关键因素.极值点型失稳和位移突跳是均质围岩中岩爆可能发生的一种力学机制.     

Suppressing chaos in crystal growth process using adaptive phase resonant perturbation

Chaos occurs in the flexible shaft rotating-lifting (FSRL) system of crystal growth process. Chaotic swing does harm to the quality of mono-silicon crystal production. Therefore, it must be suppressed. Previous studies have proposed impulse control method to suppress the chaos in crystal growth process. However, the impulses require sudden and intermittent changes to the rotation speed, which are difficult to implement through the soft rope connection. In this work, a small amplitude resonant perturbation to the rotation speed is being proposed to suppress chaos in the FSRL system. The system state, given by the swing angle between the rotation center on the vertical axis and the soft shaft, is observed by measuring the force on the soft shaft and by using the untraced Kalman filter. The control parameters are selected by calculating the Lyapunov exponent. As compared with the previous impulse control methods, the proposed small amplitude resonant perturbation method engenders a small continuous change instead of the sudden change in the rotation speed. In addition, the proposed method does not alter the average rotation speed, which complies with the crystal growth technique requirement. The effectiveness of the proposed chaos control method is validated by numerical simulations.

     

竖井开挖的不稳定性和岩爆的力学机制

基于稳定性理论和弹塑性厚壁筒的解析解,研究了竖井开挖过程的平衡路径,并将屈服后的井壁压力--位移平衡路径曲线应用到围岩的稳定性分析.研究表明,竖井围岩的不稳定及其岩爆的发生不仅取决于岩石材料应力应变全过程曲线的峰后特性,还取决于竖井开挖过程对应的平衡路径曲线的类型.平衡路径曲线能够描述围岩结构加载屈服后的力学行为.平衡路径的曲线形状只可能有两种类型,一种曲线上的点都处于稳定的平衡状态,虽有塑性变形的累积,但不会失稳崩落;另一种曲线则发生极值点型井壁失稳并伴有位移突跳.竖井开挖过程的平衡路径曲线是判定围岩岩爆发生的关键因素.极值点型失稳和位移突跳是均质围岩中岩爆可能发生的一种力学机制.      

Bifurcation of the electromechanically coupled subsynchronous torsional oscillating system with hysteretic behavior

In subsynchronous resonance (SSR) systems where shaft systems of turbine-generator sets are coupling with electric networks, Hopf bifurcation will occur under certain conditions. Some singularity phenomena may generate when the hysteretic behavior of couplings in the shaft systems in considered. In this paper, the intrinsic multiple-scale harmonic balance method is extended to the nonlinear autonomous system with the non-analytic property, and the dynamic complexities of the system near the Hopf bifurcation point are analyzed. The project supported by the National Natural Science Foundation of China (as a key project) and the State Education Committee Pre-research Foundation.     

深井提升动力学研究

随着浅部煤炭资源的日益枯竭, 我国煤炭开采朝着深部化和大型化方向发展, 新建和改扩建的大型立井年生产能力已达1000万吨, 开采最大深度已达1500 m. 千米深井在提升过程中, 造成提升钢丝绳、容器振荡, 特别是自由悬挂平衡尾绳大幅度摆动, 严重影响多绳摩擦提升系统向高速度、深度化发展. 在国家重点研发计划“深地资源勘查开采”重点专项“煤矿深井建设与提升基础理论及关键技术”支持下, 建立了单元数量自动调整的自由悬挂平衡尾绳提升系统动力学模型, 揭示了传统提升系统诱发平衡尾绳大摆动的机理; 提出了深井SAP提升新模式, 构建了多元耦合下的SAP提升系统动力学模型与非光滑动力学模型, 揭示了多参数影响下系统的非光滑动力学特性及非线性振动演化规律; 研发了适用于深部提升的SAP提升技术与装备, 开展了SAP提升技术与装备的现场研究, 解决了大强煤矿立井提升系统运行过程中尾绳大摆动、提升容器大振动等关键问题, 提高了提升系统高速运行的安全性, 消除了尾绳大摆动难控制的问题.      

轴同期涡动和轴承座激振对轴承油膜稳定性的影响

在自行设计的轴承试验台上研究了轴颈同期涡动和轴承座激振对油膜层流失稳的影响 .结果表明 :随着轴颈偏心的增大 ,涡动倾向增强 ,流体出现层流失稳 ;当涡动倾向较弱时 ,影响油膜层流失稳的主要因素是轴承激振的强度以及低频激振 ,而高频激振对其影响较小 ;但当涡动倾向较强时 ,轴承激振的强度以及激振频率对油膜层流的失稳几乎没有影响     

Model based online diagnosis of unbalance and transverse fatigue crack in rotor systems

A model based technique for online identification of malfunctions in rotor systems is discussed. Presence of fault changes the dynamic behavior of the system. This change is taken into account by equivalent loads acting on the undamaged system model. Equivalent loads are fictitious forces and moments acting on the undamaged system model, which generate a dynamic behavior identical to that of the real damaged system. The mathematical representation of equivalent loads is referred to as Fault Model. The work focuses on developing a fault model for a transverse fatigue crack in shaft and testing it through simulated studies. The basic principle of the technique is validated for unbalance identification, through numerical simulations as well as by experiments on a real rotor system.     

Viscoelastic blood flow through arterial stenosis—Effect of variable viscosity

Current theoretical investigation deals with mathematical model of unsteady non-Newtonian flow of blood through a stenosed artery. The flowing blood is considered as a viscoelastic fluid having shear-thinning rheology and characterized by generalised Oldroyd-B model. The arterial wall is considered to be rigid having cosine shaped stenosis in its lumen. The governing equations of motion accompanied by appropriate choice of the initial and boundary conditions are solved numerically by MAC (Marker and Cell) method and the results are checked for numerical stability with desired degree of accuracy. The quantitative analysis has been carried out finally which includes the respective profiles of the flow-field. The key factors like the wall shear stress and flow separation are also examined for further qualitative insight into the flow through arterial stenosis. The present results show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.