Improved model of a ball bearing for the simulation of vibration signals due to faults during run-up

In this paper an improved bearing model is developed in order to investigate the vibrations of a ball bearing during run-up. The numerical bearing model was developed with the assumptions that the inner race has only 2 DOF and that the outer race is deformable in the radial direction, and is modelled with finite elements. The centrifugal load effect and the radial clearance are taken into account. The contact force for the balls is described by a nonlinear Hertzian contact deformation. Various surface defects due to local deformations are introduced into the developed model. The detailed geometry of the local defects is modelled as an impressed ellipsoid on the races and as a flattened sphere for the rolling balls. With the developed bearing model the transmission path of the bearing housing can be taken into account, since the outer ring can be coupled with the FE model of the housing. The obtained equations of motion were solved numerically with a modified Newmark time-integration method for the increasing rotational frequency of the shaft. The simulated vibrational response of the bearing with different local faults was used to test the suitability of the envelope analysis technique and the continuous wavelet transformation was used for the bearing-fault identification and classification.     

空心圆柱形永磁体内径对单畴GdBCO超导块材磁悬浮力的影响

通过对空心圆柱形永磁体与单畴GdBCO超导体磁悬浮力的实验测量,研究了空心圆柱形永磁体内径(d)的变化对超导体磁悬浮力的影响.结果发现,当空心圆柱形永磁体内径从0 mm增加到26 mm时,超导磁悬浮力大小与空心圆柱形永磁体内径有着密切关系(最小测量间距Z=2 mm),所有超导磁悬浮力曲线都存在磁滞现象.随着空心圆柱形永磁体内径的增大,最小间距处超导磁悬浮力逐渐减小,从d=0 mm时的14.8 N减小为d=26 mm时的-0.1 N,d≥20 mm时,最小间距处超导磁悬浮力出现负值;当0 mm≤d5 mm时,超导体最大磁悬浮力出现在最小间距处,d≥5 mm时,超导磁悬浮力先增大后减小,最大超导磁悬浮力产生的位置随着内径的增大而变大.研究表明:只有科学合理地设计永磁体结构参数,才能获得较大的磁场强度,提高超导磁悬浮力特性.该结果对设计并优化磁悬浮轴承系统、环形轨道和超导体的实际应用具有一定的指导意义.     

拟柱面激光二极管阵列端面泵浦方式提高固体激光器性能

就高功率激光二极管阵列端面泵浦大口径放大器提出一种新的耦合方式:激光二极管阵列拟柱面排布,即所有激光二极管面阵成1维圆弧型排列,圆弧的圆心在增益介质的几何中心,其后紧接一个空心导管进行耦合传输。建立了3维光线追迹程序对这种新耦合方式的特性进行模拟。模拟计算结果表明:这种耦合方式中二极管阵列排布方式灵活,当二极管阵列面阵单元以1×12(圆弧方向)、2×6(圆弧方向)、3×4(圆弧方向)这3种排布方式排布时,在较大的圆半径变化范围内均能实现高的输出耦合效率和高的能量沉积效率;当增益介质紧贴导管输出放置时,3种方式排列均能在增益介质中实现均匀平顶分布;当快轴方向所排阵列个数与慢轴方向所排阵列个数之比接近慢轴发散角与快轴发散角之比时,能获得更好的耦合效果。     

The measurement of structural mobilities of a circular cylindrical shell

Structural mobility is useful for the estimation of structural power flows in coupled systems. Although the methods of measuring structural mobilities are easily found for one-dimensional beam structures, few are available for cylindrical shells. In this paper, a new method is proposed for the measurement of the structural mobilities of a circular cylindrical shell. A point force excitation is used instead of circumferential modal forces which are difficult to implement in practice. This method utilizes the least squares technique to obtain the transfer function components of different circumferential modes from the measured data. Experiments were carried out on a circular cylindrical shell with different end conditions excited by a point force to verify the feasibility of this proposed method.     

Active control of low-frequency sound radiation by cylindrical shell with piezoelectric stack force actuators

A novel active control method of sound radiation from a cylindrical shell under axial excitations is proposed and theoretically analyzed. This control method is based on a pair of piezoelectric stack force actuators which are installed on the shell and parallel to the axial direction. The actuators are driven in phase and generate the same forces to control the vibration and the sound radiation of the cylindrical shell. The model considered is a fluid-loaded finite stiffened cylindrical shell with rigid end-caps and only low-frequency axial vibration modes are involved. Numerical simulations are performed to explore the required control forces and the optimal mounting positions of actuators under different cost functions. The results show that the proposed force actuators can reduce the radiated sound pressure of low-frequency axial modes in all directions.     

基于ANSYS的高温超导混合磁轴承悬浮力分析

基于商用电磁场有限元软件ANSYS以及Bean临界态模型,对由圆柱形高温超导块材、永磁体和超导线圈组成的新型高温超导混合磁轴承的电磁场分布及悬浮力进行了仿真分析,研究了超导线圈对高温超导混合磁轴承悬浮力的影响,同时还通过实验测试了悬浮力。结果表明:仿真与实验具有较好的一致性,使用软件仿真方便可行,其结果较为准确可靠,可为高温超导混合磁轴承的设计和优化提供理论依据。     

An Evershed type superconducting flywheel bearing

The objective of this work is to develop a bearing using high temperature superconductors (HTSs) for use in an energy storage flywheel. The experimental apparatus includes a cylindrical rotor levitated with the Evershed design in which the majority of the levitation force is provided by a permanent magnet arrangement and the stabilization of the system is achieved by HTS elements. The design characteristics and dynamics of the bearing associated with the rotor part are presented. The instrumentation measures the out of balance force and magnetomechanical stiffness associated with the rotor. A study of the rotational losses was performed using free spin down experiments associated with magnetic field variation measurements. The results are consistent with the loss being caused by hysteresis in the superconductor due to magnet inhomogeneity.     

Rotor–stator contact dynamics using a non-ideal drive—Theoretical and experimental aspects

The possible contact between rotor and stator is considered a serious malfunction that may lead to catastrophic failure. Rotor rub is seen as a secondary phenomenon caused by a primary source, i.e. sudden mass unbalance, instabilities generated by aerodynamic and hydrodynamic forces in seals and bearings among others. The contact event gives rise to normal and friction forces exerted on the rotor at impact events. The friction force plays a significant role by transferring some rotational energy of the rotor to lateral motion. A mathematical model has been developed to capture this for a conventional backup annular guide setup. It is reasonable to superpose an impact condition to the rub, where the rotor spin energy can be fully transformed into rotor lateral movements. Using a nonideal drive, i.e. an electric motor without any kind of velocity feedback control, it is even possible to stop the rotor spin under rubbing conditions. All the rotational energy will be transformed in a kind of “self-excited” rotor lateral vibration with repeated impacts against the housing. This paper studies the impact motion of a rotor impacting a conventional backup annular guide for the case of dry and lubricated inner surface of the guide. For the dry surface case, the experimental and numerical analysis shows that the rotational energy is fully transformed into lateral motion and the rotor spin is stopped. Based on this study this paper proposes a new unconventional backup bearing design in order to reduce the rub related severity in friction and center the rotor at impact events. The analysis shows that the rotor at impacts is forced to the center of the backup bearing and the lateral motion is mitigated. As a result of this, the rotor spin is kept constant.     

Acoustic radiation from a shell-encapsulated baffled cylindrical cap

An exact study of radiation of an acoustic field due to radial/axial vibrations of a baffled cylindrical piston, eccentrically positioned within a fluid-filled thin cylindrical elastic shell, into an external fluid medium is presented. This configuration, which is a realistic idealization of a liquid-filled cylindrical acoustic lens with a focal point inside the lens when used as a sound projector, is of practical importance with a multitude of possible applications in underwater acoustics and ocean engineering. The formulation utilizes the appropriate wave field expansions along with the translational addition theorems for cylindrical wave functions to develop a closed-form solution in the form of an infinite series. Numerical results reveal the key effects of excitation frequency, cap angle, radiator position (eccentricity), dynamics of the elastic shell, and cap surface velocity distribution on sound radiation.     

Acoustic signature of a submarine hull under harmonic excitation

The structural and acoustic responses of a submarine under harmonic force excitation are presented. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The far-field radiated sound pressure is then calculated by means of the Helmholtz integral. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is clearly observed. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model.     

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.     

Formation of a quasi-hollow beam of high-energy heavy ions using a multicell resonance RF deflector

The generation of matter in an extreme state with precisely measurable parameters is of great interest for contemporary physics. One way of obtaining such a state is to irradiate the end of a hollow cylindrical shell at the center of which a test material is kept at a temperature of several Kelvin by an annular beam of high-energy heavy ions. Under the action of the beam, the shell starts explosively expanding both outwards and inwards, compressing the material to an extremely high pressure without subjecting it to direct heating. A method of producing a hollow cylindrical beam of high-energy heavy ions using a resonance rf deflector is described. The deflection of the beam in two transverse directions by means of an rf electric field allows it to rotate about the longitudinal axis and irradiate an annular domain on the end face of the target.     

Casimir Effect in Hemisphere Capped Tubes

In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2 + 1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.     

Unsteady fluid dynamic forces on a simply-supported circular cylinder of finite length conveying a flow,with applications to stability analysis

An exact analytic expression for the unsteady fluid pressure acting on the internal walls of a simply-supported circular cylindrical tube of finite length, carrying flow, is presented. The generalized force coefficients corresponding to specific modes of deformation are given explicitly. The results are applied to two problems: (1) the interaction of flow and buckling of thin-walled cylindrical shells subjected to lateral pressure and/or end thrust; (2) the aeroelastic stability of the shells. The second problem is aimed at resolving some controversy about post-divergence flutter oscillation of cylindrical shells or plates exposed to a subsonic flow. The shell equation, of the Morley type, is solved by Galerkin's method and an analytic approach is used to examine the stability of the system. It is important that damping be taken into account in the analysis. The undeformed configuration is always unstable when the flow speed exceeds the minimum divergence boundary.     

Consistent projection methods for variable density incompressible Navier–Stokes equations with continuous surface forces on a rectangular collocated mesh

Two consistent projection methods of second-order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density Navier–Stokes equations with a continuous surface force. Instead of the original projection methods (denoted as algorithms I and II in this paper), in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not guaranteed solenoidal, the consistent projection methods (denoted as algorithms III and IV) obtain the cell center velocity based on an interpolation from a conservative fluxes with velocity unit on surrounding cell faces. Dependent on treatment of the continuous surface force, the pressure gradient in algorithm III or the sum of the pressure gradient and the surface force in algorithm IV at a cell center is then conducted from the difference between the updated velocity and the intermediate velocity in a consistent projection method. A non-viscous 3D static drop with serials of density ratios is numerically simulated. Using the consistent projection methods, the spurious currents can be greatly reduced and the pressure jump across the interface can be accurately captured without oscillations. The developed consistent projection method are also applied for simulation of interface evolution of an initial ellipse driven by the surface tension and of an initial sphere bubble driven by the buoyancy with good accuracy and good resolution.     

Mechanics of a magnet and a Meissner superconducting ring at arbitrary position and orientation

The force and torque exerted by a magnetic dipole on a superconducting ring (or hollow cylinder) in the Meissner state at arbitrary position and orientation are calculated using a Maxwell-London model previously proposed by the authors. The center of the ring is an unstable equilibrium point for the magnet. At this point the ring tends to align the magnet but tends to expel it for any small axial deviation from the center. There is also a non-monotonic and oscillatory dependence of the forces and torques on the position caused by the finiteness of the ring and a torque arises when the magnet is displaced both radially and axially from the center of the cylinder which corresponds to the experimental data. Therefore, the use of a magnet in a Meissner superconducting ring as a self aligning bearing requires a centered position and that the axial unstability to be compensated by additional mechanical means.     

Selective cap opening in carbon nanotubes driven by laser-induced coherent phonons

We demonstrate the possibility of a selective nonequilibrium cap opening of carbon nanotubes as a response to femtosecond laser excitation. By performing molecular dynamics simulations based on a microscopic electronic model we show that the laser-induced ultrafast structural changes differ dramatically from the thermally induced dimer emission. Ultrafast bond weakening and simultaneous excitation of two coherent phonon modes of different frequencies, localized in the spherical caps and cylindrical nanotube body, are responsible for the selective cap opening.     

广义平面应变锂离子电池柱形梯度材料颗粒电极中扩散诱导应力分析

柱形梯度材料是最有潜力的锂离子电池电极之一. 为了研究恒压充电过程中柱形梯度材料颗粒电极下力学机理, 以Li_1.2(Mn_0.62Ni_0.38)_0.8O₂为例, 讨论弹性模量、扩散系数和偏摩尔体积三个重要材料参数对应力场影响. 并推导出非均匀柱形颗粒电极的扩散方程和力学方程. 结果表明, 柱形梯度材料纳米电极, 沿着半径方向Mn 的材料组分升高Ni 的材料组分降低, 其材料结构有利于降低最大径向应力和环向拉应力, 有效地避免电极的力学失效现象. 并根据计算结果, 对梯度材料电极提出材料结构优化建议.     

Electrostatic force acting on conductive ball between electrodes II: Cylindrical upper electrode with hemispherical tip for capturing/releasing conductive ball

The electrostatic force between a conductive ball on a plane electrode and a cylindrical electrode with a hemispherical tip is analyzed. A cylindrical electrode with a dielectric film for realizing a new LSI bonding system is proposed. The force on the ball increases with increasing diameter of the cylindrical electrode. When a dielectric film is placed under the cylindrical upper electrode with a fixed gap between the electrodes, the force acting on the ball increases with increasing dielectric film thickness. Capture of the ball was experimentally confirmed. This study provides a useful foundation for electrostatic manipulation of a conductive ball.     

胶体中排空作用的耦合效应

通过Monte Carlo模拟和接受率方法研究了限制在圆柱形管道中大胶球之间以及大胶球与管壁之间排空作用的耦合效应.研究发现,当两个大胶球靠近时,大胶球之间的排空作用因与大胶球与管道壁之间的排空作用耦合而得到加强,同样当大胶球与管道壁靠近时,大胶球与管道壁之间的排空作用也因与另一大胶球之间排空作用的耦合而得到了加强.此外,研究还发现,随着圆柱形管道直径的减小,胶球之间、胶球与管道壁之间的排空作用的耦合效应是增强的. 关键词： 排空作用的耦合效应 接受率方法 Monte Carlo模拟