Stick-slip vibrations of a self-excited SD oscillator with Coulomb friction

Nonlinear Dynamics - In this paper, the stick-slip vibrations of an archetypal self-excited smooth and discontinuous (SD) oscillator are investigated. The mathematical model of the self-excited SD...     

Analytical investigation of an SDOF building structure equipped with a friction damper

The purpose of this study is to investigate analytically a single-degree-of-freedom (SDOF) building structure equipped with a friction damper for assessing its vibration control effect. Friction dampers are installed between stories to reduce inter-story displacements of building structures subjected to external loading. They are in general regarded to generate damping forces characterized by Coulomb damping, of which the directions are opposite to the inter-story velocities of building structures. Hence, the building structure model with friction dampers can be represented by a mass-spring-viscous-Coulomb damping system. The building response reduction as a result of damper installation can be provided by observing the damping ratio rather than the friction force contributed by the dampers. Since a large friction damper force is required to attenuate the response of the building due to strong excitation, friction force ratio is directly related to building response reduction, which is the friction force of the damper versus external force. Therefore, damping and friction force ratios are key parameters, playing a main role in selecting an optimal friction damper, which satisfies target response reduction. This study first identifies an SDOF building structure installed with a friction damper for free vibration with initial conditions. A?closed-form expression of normalized displacement is derived in terms of friction force ratio in the time domain. Peak and valley of displacements are also found and then the time when the structure stops is derived with recursive interval number. This study is extended to identify steady-state vibration of the structure by deriving closed-form solution in case of resonance in terms of friction force ratio. Then, the dissipated energy balance is identified for both free and steady-state vibrations. Finally, equivalent viscous damping ratios are derived by using friction force ratio based on dissipated energy balance equation. The derived equations in terms of viscous damping ratio and friction force ratio can provide insight to design a friction damper for reducing structural displacement under external loadings.     

Reduction of subsynchronous vibrations in a single-disk rotor using an active magnetic damper

Rotor instabilities in turbomachinery often manifest themselves as a re-excitation of the first rotor critical speed resulting in lateral rotor vibrations at a frequency below the rotor operating frequency. Considerable work exists in the literature involving the analysis of destabilizing mechanisms and passive solutions for reducing subsynchronous vibrations. The authors propose here a novel active control solution utilizing active magnetic bearing (AMB) technology in conjunction with conventional support bearings. The AMB is utilized as an active magnetic damper (AMD) at rotor locations inboard of conventional support bearings. Presented here are initial proof-of-concept experimental results using an AMD for vibration control of subsynchronous rotor vibrations in a high-speed single-disk laboratory rotor. The study shows that subsynchronous vibrations are reducible with an AMD and up to a 93% reduction in the amplitude of subsynchronous vibrations is demonstrated. The study also shows that the AMD can significantly increase synchronous vibration response (up to 218% in one case) by increasing system stiffness and pushing a critical speed closer to an operating speed. The overall results from this work demonstrate that reduction in subsynchronous response is feasible and that full rotor dynamic analysis and design is critical for the successful application of this approach.     

滞回摩擦型调谐惯质阻尼器结构隔震研究

本文研究一种新型非线性阻尼器——滞回摩擦型调谐惯质阻尼器(HFTID)在工程结构抗震控制中的应用。HFTID由调谐惯质阻尼器(TID)和滞回弹簧摩擦元件并联组成。首先通过谐波平衡方法推导了HFTID单自由度系统力与位移的传递率。然后对HFTID进行了最佳调谐参数优化,得到HFTID最优参数的近似表达式,比较了HFTID和TID振动控制系统的减振效果。结果表明,HFTID相比TID可以进一步降低振动控制系统的传递率。最后,以一栋多层隔震结构为例,将HFTID与TID的隔震效果进行了对比,结果表明,HFTID相比TID在降低地震响应峰值和均方根值方面具有更大优势,验证了HFTID在降低地震响应方面的有效性和实用性。HFTID在建筑和桥梁结构抗震、车辆悬挂系统和其他机械隔震问题上具有潜在的应用前景。     

Subharmonic steady vibrations of a non-linear damper with two degrees of freedom and viscous damping

The steady-state. $\text{1}\text{3}$ subharmonic vibrations of a dynamic damper (or vibration absorber) with two degrees of freedom, sinusoidal forcing function and internal viscous damping. are presented. The study of these oscillations leads to the determination of suitable “form functions” of the solutions, by following a methodology recently introduced by Nocilla for studying the harmonic vibrations of non-linear systems with one and two degrees of freedom. The proposed theory. which is valid even if the non-linearity is large, gives satisfactory results in all the cases in which the subharmonic component is predominant in the steady-state oscillation of the system.     

Estimating the dynamic coefficient of friction from experimental data: the motion of a rocket inside a smoothbore launcher

The motion of a spinning rocket inside a smoothbore launcher has drawn some attention in recent years. The inaccuracy of spin-stabilized rockets can be attributed, in part, to the initial motion of the rocket inside the smoothbore launcher. Recently, tests have indicated that a closer examination of the problem is required. The tests were performed to determine the time history of the spin and forward motion of the rocket by Fastax cameras. The evaluation of the data with respect to engineering-design parameters is difficult since the experimental results must be compared with an analytical model of the system. In this paper, the results of one test are reported and a nonlinear analytical model is used which includes both the rotary and forward motion of the rocket. The two motions are coupled through a dynamic friction coefficient. The intent of this paper is to show how an analytical model can be made to fit the experimental data, that is, the initial conditions and the coefficient of friction are found which define the solution giving the best least-square fit to the data.     

Specific impulse losses due to friction and dispersion in a gas-film cooled liquid rocket engine nozzle

Conclusions The proposed method and program for calculating the compressible turbulent boundary layer in rocket engine nozzles with gas film cooling make it possible to determine the specific impulse losses due to friction, the heat fluxes and other characteristics of the flow. The calculations are based on the numerical solution of the equations of gas dynamics in the boundary layer approximation using a three-parameter differential turbulence model.The calculations for nozzles without film cooling showed that the contours occupying a narrow interval between the families of contours with uniform and variational characteristics have the minimum impulse losses due to friction and dispersion. In contrast to the known results, the loss minimum is displaced relative to nozzles with a variational characteristic (Rao nozzles) towards truncated nozzles with a uniform characteristic.The dependence of the maximum heat transfer to the wall in the critical throat section of the nozzle on the rate of flow of fuel into the film has been determined for nozzles with film cooling. It is shown that as the film flow rate increases, the friction losses decrease, and the minimum of the impulse losses due to friction and dispersion is shifted towards the contours with a variational characteristic, which have the minimum dispersion losses. The total impulse losses, which take into account the change in the fuel component ratio in the flow core due to the diversion of part of the fuel into the film, increase with increase in the film flow rate.The results of our numerical investigation of the effect of the contour shape and film flow rate indicate that the contour with a variational characteristic, which has near-minimum specific impulse losses due to friction and dispersion, should be used as the optimum contour for LRE nozzles.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 82–93, May–June, 1993.deceased.The authors wish to thank their colleagues at the Énergomash NPO L. P. Vereshchak and L. K. Danilyuk for assisting with the calculations, the participants in G. A. Lyubimov's seminar for discussing the results obtained, and D. A. Mel'nikov, U. G. Pirumov, and A. A. Sergienko for valuable advice.     

The effect of longitudinal high-frequency in-plane vibrations on a 1-DoF friction oscillator with compliant contact

Nonlinear Dynamics - The effect of vibrational smoothing of dry friction has been studied intensively in the past. High-frequency vibrations have been shown to reduce average friction forces and...     

An analytical study of time-delayed control of friction-induced vibrations in a system with a dynamic friction model

We investigate the control of friction-induced vibrations in a system with a dynamic friction model which accounts for hysteresis in the friction characteristics. Linear time-delayed position feedback applied in a direction normal to the contacting surfaces has been employed for the purpose. Analysis shows that the uncontrolled system loses stability via. a subcritical Hopf bifurcation making it prone to large amplitude vibrations near the stability boundary. Our results show that the controller achieves the dual objective of quenching the vibrations as well as changing the nature of the bifurcation from subcritical to supercritical. Consequently, the controlled system is globally stable in the linearly stable region and yields small amplitude vibrations if the stability boundary is crossed due to changes in operating conditions or system parameters. Criticality curve separating regions on the stability surface corresponding to subcritical and supercritical bifurcations is obtained analytically using the method of multiple scales (MMS). We have also identified a set of control parameters for which the system is stable for lower and higher relative velocities but vibrates for the intermediate ones. However, the bifurcation is always supercritical for these parameters resulting in low amplitude vibrations only.     

某发动机热试车的振动环境预示方法研究

发动机热试车试验在新型运载器的研制过程中起到重要作用,可用于预测运载器在飞行中的振动环境.由于载荷不等效,试验数据量有限,使得难以直接通过试验数据建立同一结构在不同系统下的映射关系模型.本文提出了一种基于试验数据的振动环境预示方法,以某发动机两次热试车试验数据为对象,分别提取了反映结构特性的动力学模型,基于载荷等效原则...     

Design and mechanical characteristics analysis of a new viscous damper for piping system

In this paper, the design of a new viscous damper is presented and its mechanical characteristics are investigated experimentally. The motion equation of a system consisting of a drop machine and the damper is set up. By numerically simulating this equation, the curve of the damper cavity generatrix is obtained on the assumption that the resisting force is constant. Then the new damper with big capacity and high-energy dissipation rate is designed. Drop tests using this damper and a Pro225-damper bought in the market are performed, respectively. On one hand, the experimental resisting forces of the new damper approximate constants, which illustrates that the simulation is viable. On the other hand, some advantages of the new damper over the Pro225-damper are found.     

Influence of inhomogeneity on the nonlinear stabilization of acoustic vibrations of a heat releasing medium in a confined space

The problem of determining the amplitudes of unstable acoustic vibrations when they are stabilized in a confined heat releasing medium by transfer of energy from the unstable mode to the damped mode as a result of their nonlinear interaction has been considered by Artamonov and Vorob'ev [1]. Their treatment applied to a gas with volume heat release filling a channel of finite length under the assumption that the parameters of the gas in the steady state are constant over the volume. In the present paper an investigation is made in the nonlinear approximation of the stability of a weakly inhomogeneous heat releasing gas that fills a channel of finite length with respect to acoustic vibrations propagating along its axis in the direction of the gradients of the steady parameters. It is shown that the spatial inhomogeneity of the gas leads to breakdown of the resonance of the excited acoustic vibrations, which in turn leads to a higher level of the steady vibrations compared with the case of a spatially homogeneous medium.     

用于新型等效原理空间实验检验的静电加速度计设计

等效原理是爱因斯坦广义相对论的基本假设之一,在更高精度上检验等效原理是否成立可以预言新型基本相互作用力。新型等效原理是我国科技工作者提出的一种假设,通过检验两个相同材料但自旋状态不同的宏观物体的自由落体运动来检验等效原理可能存在的破坏。提出了一种面向空间检验新型等效原理的差分静电加速度计设计方案,给出了地面实验用原理样机的结构设计,对结构模态和温度应力进行了有限元仿真;依据支承刚度和量程约束条件,对径向和轴向静电支承控制回路进行了设计和仿真分析;建模分析了高真空下转子静电加转驱动回路的主要性能,仿真结果表明启动过程中达到目标转速(10~4 rpm)的启动时间为36.9 min。