Friction-induced vibration of an elastic slider on a vibrating disc

The in-plane vibration of a slider-mass which is driven around the surface of a flexible disc, and the transverse vibration of the disc, are investigated. The disc is taken to be an elastic annular plate and the slider has flexibility and damping in the circumferential (in-plane) and transverse directions. The static friction coefficient is assumed to be higher than the dynamic friction. As a result of the friction force acting between the disc and the slider system, the slider will oscillate in the stick-slip mode in the plane of the disc. The transverse vibration induced by the slider will change the normal force on the disc, which in turn will change the in-plane oscillation of the slider. A numerical method is used to solve the two coupled equations of the motion. Results indicate that normal pressure and rotating speed can drive the system into instability. The rigidity and damping of the disc and transverse stiffness and damping of the slider tend to suppress the vibrations. The in-plane stiffness and damping of the slider do not always have a stabilizing effect. The motivation of this work is the understanding of instability and squeal in physical systems such as car brake discs where there are vibrations induced by non-smooth dry-friction forces.     

Vibration analysis of a ferromagnetic plate subjected to an inclined magnetic field

The magnetic traction on a deformable ferromagnetic material is deduced based on the classical magnetoelastic model. The vibration frequency of a ferromagnetic beam subjected to an inclined magnetic field is analyzed by employing formulations of the magnetic force. The result for the condition of longitudinal magnetic field is the same trend as that of the previous experiment carried out by Takagi et al. [Analysis and experiment of dynamic deflection of a thin plate with a coupling effect. IEEE Transactions on Magnetics 1992;28(2):1259–62]. Moreover, experimental tests have been carried out to study the free vibration of a magnetic plate subjected to an inclined magnetic field.     

磁弹性传感器励磁电源的设计

磁弹性传感器是用于测量轧机轧制力、钢带张力的一种测力传感器,为保证其输出信号稳定、精确,要求励磁电流具有高稳定性。本文着重探讨了产生励磁信号的信号发生器和恒流输出的功率放大器。励磁信号发生器输出标准正弦波的频率和幅值非常稳定,从而在信号源上确保励磁电流信号的稳定性和精确度。双闭环设计的恒流功率放大器,输出电流密切跟随励磁信号,在磁弹性传感器内建立起稳定的磁场,从而保证被测力值的准确性。     

Moving interfacial crack between two dissimilar soft ferromagnetic materials in uniform magnetic field

This paper presents the dynamic magnetoelastic stress intensity factors of a Yoffe-type moving crack at the interface between two dissimilar soft ferromagnetic elastic half-planes. The solids are subjected to a uniform in-plane magnetic field and the crack is opened by internal normal and shear tractions. The problem is considered within the framework of linear magnetoelasticity. By application of the Fourier integral transform, the mixed boundary problem is reduced to a pair of integral equations of the second kind with Cauchy-type singularities. The singular integral equations are solved by means of a Jacobi polynomial expansion method. For a particular case, closed-form solutions are obtained. It is shown that the magnetoelastic stress intensity factors depend on the moving velocity of the crack, the magnetic field and the magnetoelastic properties of the materials.     

导弹滑行出箱过程中颤动现象的建模与分析

为了深入研究导弹在发射箱内滑行产生的颤动现象,建立了基于Stribeck摩擦模型的质量块-传输带干摩擦动力学模型,利用静、动摩擦转换时摩擦力降落引起的负阻尼力激发系统的自激颤动现象。通过对运动方程进行稳定性分析,得到平衡点失去渐进稳定特性并产生自激颤动的临界速度。利用数值方法求解常微分方程得到相平面内的相轨迹,仿真证明系统存在稳定的极限环、发生了自激颤动。通过试验曲线与仿真曲线的对比,阐明了导弹发动机燃气喷流、发射箱内燃气绕流和发射车底盘振动等强干扰因素对不稳定周期运动的影响。最后,给出了工程上切实可行的摩擦控制、颤动抑制的方法,这对地面箱/轨式发射导弹具有较大的参考价值。     

弹性地基上输送振荡流粘弹性管道的动力稳定性

基于线粘弹性理论,建立了弹性地基上输送振荡流粘弹性管道的运动微分方程,采用Galerkin法和解初值问题的Runge-Kutta法对含有周期系数的偏微分方程进行了求解。根据Floquet理论,研究了材料的量纲一延滞时间、量纲一流速以及量纲一刚度比对输送振荡流Kelvin-Voigt粘弹性管道动力不稳定区域的影响,给出了在这些参数变化时,频率比与激励参数平面上管道的动力稳定性区域和不稳定区域。     

微机械电磁阻尼结构分析

提出采用电磁阻尼结构来提高微机械角度调节装置的响应速度.通过建立结构模型和分析结构参数对阻尼效果的影响,给出具体设计实例以及制作工艺,证实该阻尼结构的有效性和可行性.     

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.     

Magnetoelastic Stability of Magnetic Axial Bearings

Permanent magnet bearings offer no wear and no mechanical friction. Recently, Rare Earth (RE) permanent magnets have been used, which give rise to force fields 20 times greater than those of common magnets. RE also allows to build magnets suitable for bearings of every shape. RE bearings are then profitable. On the other hand, permanent magnet bearings are unstable. For example, the levitated ring of the axial bearing with opposite magnetic fields of Fig. 1 is stable axially, but unstable radially. It has been, however, verified that a permanent magnet system may become stable under peculiar conditions. As an example, if the above-mentioned levitated ring is subjected to a parametric axial excitation, its radial instability can be removed. In our opinion, it may also be possible that stability is obtained by exploiting microstructural properties of ferromagnetic materials, especially of RE, like dimensional and magnetic changes if subjected to mechanical stresses. Then, in this paper, the stability of the levitated member of an RE axial ring bearing is investigated by a suitable exploitation of magnetoelastic properties of the ring.

Parametric combination resonance instability characteristics of laminated composite curved panels with circular cutout subjected to non-uniform loading with damping

The dynamic instability of laminated composite doubly curved panels with centrally located circular cutout, subjected to non-uniform compressive in-plane harmonic edge loading is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to simple resonances in parametrically excited antisymmetric angle-ply and symmetric cross-ply laminated composite doubly curved panels with central circular cutout. The method of multiple scales is used to obtain analytical expressions for the simple and combination resonance instability regions. It is shown that other cases of the combination resonance can be of major importance and yield a significantly enlarged instability region in comparison to the principal instability region. The effects of non-uniform edge loading, centrally located circular cutout, damping, number of layers, orthotropy, the static load factor and the width-to-thickness ratio on dynamic instability behavior of simply supported laminated composite doubly curved panels are studied. The results show that under localized edge loading, combination resonance instability zones are as important as simple resonance instability zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which doubly curved panels cannot become dynamically unstable. A central circular cutout has the destabilizing effect on the dynamic stability behavior of laminated composite doubly curved panels subjected to non-uniform edge loading. This example of simultaneous excitation of two modes, each oscillating steadily as its own natural frequency, may be of considerable interest in vibration testing of actual structures.     

考虑激振频率的可倾瓦推力轴承动特性理论与试验研究

为了研究激振频率对可倾瓦推力轴承动特性的影响,提出考虑激振频率的动特性建模方法和试验方法。依据可倾瓦轴承刚度和阻尼定义,将激振频率引入可倾瓦推力轴承动特性计算过程,通过建立轴向扰动下的膜厚方程、雷诺方程及瓦块运动方程,推导出包含激振频率的可倾瓦推力轴承动特性数学模型,计算分析刚度和阻尼随扰动频率(激振频率与主轴转频的比值)、转速及载荷的变化规律;采用脉冲激振法在可倾瓦推力轴承试验台进行动特性试验,得到不同激振频率、转速及载荷条件下刚度、阻尼的试验结果,并和相应的理论计算值进行对比分析。结果表明：当扰动频率较小时,可倾瓦推力轴承刚度随其增加而逐步增大,阻尼随其增加而逐步减小;当扰动频率增加到一定程度后,其刚度和阻尼逐步趋于稳定。此外,转速和载荷对其刚度和阻尼随扰动频率的变化幅度基本无影响。     

MAGNETIC-ELASTIC BUCKLING OF A THIN CURRENT CARRYING PLATE SIMPLY SUPPORTED AT THREE EDGES

The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic equation, physical equations, geometric equations, the expression for Lorenz force and the electrical dynamic equation, the magnetic-elasticity dynamic buckling equation is derived. The equation is changed into a standard form of the Mathieu equation using Galerkin＇s method. Thus, the buckling problem can be solved with a Mathieu equation. The criterion equation of the buckling problem also has been obtained by discussing the eigenvalue relation of the coefficients 2 and r/ in the Mathieu equation. As an example, a thin plate simply supported at three edges is solved here. Its magnetic-elasticity dynamic buckling equation and the relation curves of the instability state with variations in some parameters are also shown in this paper. The conclusions show that the electrical magnetic forces may be controlled by changing the parameters of the current or the magnetic field so that the aim of controlling the deformation, stress, strain and stability of the current carrying plate is achieved.     

Effects of dynamic transmission errors and vibration stability in helical gears

Transmission error is an important reason for instability in helical gears. A six-degree-of-freedom dynamic model coupled flexional, torsional and axial motion of a helical gear transmission system, which includes time varying mesh stiffness, bearing supporting stiffness, mesh damping and backlash, is developed, after taking into account the dynamic characteristics and vibration responses of helical gear in three dimensions. Influences of involute contact ratio, bearing supporting stiffness, mesh damping and backlash on the dynamic transmission errors and vibration stability of the helical gear system are investigated using numerical simulation technique. The effects on dynamic transmission errors and stabilities by contact ratio, supporting stiffness and mesh damping as well as gear backlash are analyzed. The intrinsic relationship between above parameters and dynamic transmission errors and stabilities for helical gear system are presented. The stable and unstable regions under different parameters are given. The results in this paper can be helpful to the dynamic and stable design of a helical gear transmission system.     

A novel nonlinear model of rotor/bearing/seal system and numerical analysis

A novel nonlinear model of rotor/bearing/seal system based on the Hamilton principle is proposed for steam turbine systems in power plants. The Musznyska model and unsteady bearing oil-film force model were applied to describe the nonlinear steam excitation force and oil-film force. The Runge-Kutta method was used to solve the motion equation of the rotor/seal/bearing system. The dynamic characteristics of the rotor/bearing/seal system were analyzed with bifurcation diagrams, time-history diagrams, trajectory diagrams, Poincare maps and frequency spectrums. The numerical analysis indicates that the seal force and the oil-film force influence the nonlinear dynamic characteristics of the rotor system. With the increase of rotation speed, the rotor system exhibits rich forms of periodic, double-periodic, multi-periodic, quasi-periodic and chaotic motion. The combined impact of steam excitation force and bearing oil-film force may cause a severe vibration which seriously affects the safety and stability of the rotor. The presented model provides a theoretic foundation for further research on the ultra-supercritical steam turbines.     

考虑PMSM转子偏心作用的EV动力传动系统非线性扭振特性分析

针对在路面激励,系统阻尼以及惯性负载作用下,纯电动汽车（Electric vehicle,EV）动力传动系统呈现复杂的非线性扭转振动特性,造成EV动力传动系统失稳的问题,考虑永磁同步电机（Permanent magnet synchronous motor,PMSM）制造和安装引起的静态偏心和路面激励引起的动态偏心的影响,建立EV动力传动系统非线性扭振模型,求解并分析无扰动Hamilton系统的平衡点,采用控制变量法分别研究路面激励波动,系统阻尼渐变以及惯性负载跃变对EV动力传动系统非线性扭振特性的影响,得到EV动力传动系统失稳的具体途径和机理。研究表明：分别取路面激励f₁、系统阻尼μ₁及惯性负载m₁作为单一变量,当f₁ < 0.23,μ₁ > 0.2或0 < m₁ < 0.3时,EV动力传动系统表现为稳定的一周期运动;当0.23 < f₁ < 0.52,0 < μ₁ < 0.2或0.3 < m₁ < 0.5时,EV动力传动系统由倍周期分岔通往混沌运动;当0.52 < f₁ < 0.62或0.5 < m₁ < 0.6时,EV动力传动系统由混沌运动转变为三周期运动;随着路面激励f₁或惯性负载m₁的进一步增大,即0.62 < f₁ < 0.8或0.6 < m₁ < 0.85时,EV动力传动系统表现为倍周期运动与混沌运动交替的运动状态,而随着系统阻尼μ₁进一步增大,即μ₁ > 0.2时,系统始终表现为稳定的一周期运动。     

基于分数阶阻尼的超磁致伸缩致动器非线性动力学研究

为进一步揭示超磁致伸缩致动器(Giant magnetostrictive actuator, GMA)系统非线性运动过程中的内在机理和动力学特征,基于分数阶微积分理论,将GMA动力学系统模型拓展至分数阶,建立含有分数阶阻尼的非线性GMA系统动力学方程,基于平均法分析系统主共振,得到系统的幅频响应方程;使用幂级数方法求解系统的数值解,通过Matlab数值模拟分析不同激励幅值和阻尼阶次对GMA系统的影响机理,从定性和定量的角度研究系统的分岔和混沌运动现象。结果表明：激励幅值和阻尼阶次对系统的幅频特性有显著影响;阻尼阶次对系统的分岔和混沌行为影响较大;不同阻尼阶次下由激励幅值变化引起系统的动力学行为相似但混沌区域不同。该研究有助于更好地了解GMA系统动力学特性,对工程实践中控制GMA系统稳定运行提供新的视角。     

Subharmonic resonance oscillations of impact oscillator

The motion of a damped impact oscillator under the action of harmonic force is studied. The conditions of existence and stability of periodic resonance modes are investigated.     

Dynamic stability of cross-ply laminated composite cylindrical shells

The dynamic stability of thin, laminated cylindrical shells under combined static and periodic axial forces is studied using Love’s classical theory of thin shells. A normal-mode expansion of the equations of motion yields a system of Mathieu–Hill equations. Bolotin’s method is then employed to obtain the dynamic instability regions. The present study examines the dynamic stability of antisymmetric cross-ply circular, cylindrical shells of different lamination schemes. The effect of the magnitude of the axial load on the instability regions is also examined.     

Stability improvement and vibration suppression of the thin-walled workpiece in milling process via magnetorheological fluid flexible fixture

In aerospace industry, thin-walled workpiece milling is a critical task. Also, the machining vibration is a major issue for the accuracy of the final part. In this study, a new dynamic analytical model is proposed to determine the effect of damping factor on the dynamic response of thin-walled workpiece in machining. A complex structure workpiece is equivalent to a thin plate. The fixture constrains and the damping factor are crucial elements of this thin plate. Therefore, the magnetorheological fluid flexible fixture is designed to suppress the machining vibration in machining process. Then, the general dynamic cutting force model and the damping force model are proposed for the key dynamic equation for the prediction of dynamic response to evaluate the stability of the milling process with and without the damping control. Finally, the feasibility and effectiveness of the proposed model is validated by machining tests. The predicted values match on the experiment results.     

Dynamic instability characteristics of laminated composite plates subjected to partial follower edge load with damping

The study of vibration and dynamic instability behaviour of laminated composite plates subjected to partially distributed non-conservative follower forces is presented by using the finite element technique. The first-order shear deformation theory is used to model the plate, considering the effects of shear deformation and rotary inertia. The modal transformation technique is employed to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping to study the significance of damping on stability characteristics. The effects of load width, boundary condition, aspect ratio, ply orientation, direction control of the load and damping parameters are considered for the stability behaviour of the plates. The results show that under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending on system parameters.