Bifurcating self-excited vibrations of a horizontally rotating viscoelastic shaft

Summary Self-excited postcritical vibrations of a rotating geometrically non-linear shaft caused by internal friction are analysed in this paper using the Hopf bifurcation theory. Stable periodic vibrations bifurcate from the non-trivial equilibrium which becomes unstable itself. Ordinary differential equations of motion are obtained by means of Galerkin's method. Bifurcating periodic solution is constructed in a parametric form due to Iooss and Joseph.

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Verzweigende selbsterregte Schwingungen eines horizontal gelagerten viskoelastischen Rotors

Übersicht Die von der inneren Reibung abhängigen selbsterregten Schwingungen einer drehenden geometrisch nichtlinearen Welle werden in dieser Arbeit mit Hilfe der Hopfschen Bifurkationstheorie analysiert. Die stabilen periodischen Schwingungen verzweigen sich ausgehend von der Gleichgewichtslage, die selbst instabil wird. Die Bewegungsgleichungen werden mit Hilfe der Galerkinschen Methode ausgewertet. Verzweigungslösungen werden in parametrischer Form nach Iooss und Joseph konstruiert.

     

On plane self-excited vibrations of a cantilever suspended wheel

Torsional vibrations of a wheel about its leg axis arising in the carriage rectilinear motion were dubbed the shimmy phenomenon. Because of insufficient understanding of dry friction laws in the case of point contact, the causes of the shimmy phenomenon were explained by specific features of tyre deformation [1–3].     

Suppression of self-excited vibrations by a random parametric excitation

Previous theoretical and experimental studies have shown that some vibrating systems can be stabilized by zero-averaged periodic parametric excitations. It is shown in this paper that some zero-mean random parametric excitations can also be useful for this stabilization. Under some conditions, they can be even more efficient compared to the periodic ones. Two-mass mechanical system with self-excited vibrations is considered for this comparison. The so-called bounded noise is used as a model of the random parametric excitation. The mean-square stability diagrams are obtained numerically by considering an eigenvalue problem for large matrices.     

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...     

Calculation of inviscid secondary flows in hydromachinery blade systems

The equations of the problem of calculating secondary flows in hydromachinery blade systems are obtained for the quasi-three-dimensional flow approximations. The results of calculating these flows for a Francis turbine and the pumping regime of a pumpturbine are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhdkosti i Gaza, No. 5, pp. 10–15, September–October, 1993.     

Theoretical analysis of self-excited vibrations in a machine-tool,isolated mounting-base system

Summary This paper describes the theoretical analysis of the dynamic performance of a machine-tool isolated mounting-base system when unstable behaviour of the moving slider — stick slip motion — occurs owing to low driving speed. The equations of motion are derived from Lagrange's equation when the basic energy expressions of such a system are known.Numerical examples are calculated by making use of the digital computer in order to clarify the relation between the principal parameters governing the behaviour of the vibrating system so that the factors that influence the design and operational conditions of a machine tool supported by a vibration-isolating base may be more clearly understood and specifically identified. By this method a detailed analysis is carried out of the performance of an experimental rig fixed to a concrete mounting base supported on helical springs, in order to investigate the mechanism of frictional damping of machine tool slideways.

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Sommario Nell'articolo è effettuata l'analisi teorica del comportamento dinamico di un sistema costituito da una macchina utensile con relativa fondazione, quando il moto rettilineo della slitta, alle basse velocità, manifesta condizioni instabili dipendenti dall'insorgere di vibrazioni autoeccitate. Le equazioni del moto sono ottenute dalle equazioni di Lagrange una volta calcolate le espressioni energetiche del sistema.Mediante un calcolatore digitale sono stati elaborati alcuni esempi numerici per definire la relazione esistente tra i principali parametri da cui dipende il comportamento del sistema vibrante, in modo da valutare la complicata interdipendenza dei fattori che influenzano il progetto e le condizioni operative di una macchina utensile vincolata ad una fondazione isolata dal terreno con supporti elastici.Con il metodo numerico proposto è stato studiato il comportamento dinamico di un'apparecchiatura sperimentale, fissata ad una fondazione in cemento sostenuta da molle elicoidali, predisposta per valutare gli effetti combinati dello smorzamento e dell'attrito nelle guide di una macchina utensile.

     

On the self-excited vibrations of bluff bodies suspended with a narrow clearance in a vertical pipe

The results of an experimental study of the flow past a sphere suspended with a narrow clearance in a circular cylindrical pipe and allowed only lateral movement, are presented. The study was limited to the case of intense vibrations accompanied by impacts between the sphere and the pipe wall. The experiments were conducted in steel and copper pipes at Reynolds numbers varying from 10⁴ to 10⁵ and several values of the sphere mass and the clearance between the sphere and the pipe wall. The self-excited vibration frequency was measured by a newly developed method based on registering the frequency only in the resonance modes which set in when the sphere and pipe vibration eigenfrequencies coincide. The flow was photographed and filmed at various values of the water flow rate. The major nondimensional parameters characterizing the phenomenon considered were revealed, and a universal relation between them and the nondimensional self-excited vibration frequency was established with acceptable accuracy. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 136–143, March–April, 2000. The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00152).     

Prediction of losses in the flow through the last stage of low‐pressure steam turbine

In this paper, the numerical modelling of the flow through the low‐pressure steam turbine last stage was presented. On the basis of predicted wet steam flow‐field, the aerodynamic as well as thermodynamic losses were estimated. For calculations of the wet steam steady flow‐field three numerical methods were employed. The first method was a streamline curvature method (SCM). The commercial CFD code (CFX‐TACflow) and an in‐house code, both solving the 3‐D RANS equations, were the next two methods. In the wet steam region, by means of all three methods, the equilibrium flow was modelled. Additionally, the in‐house CFD code was used for modelling of the non‐equilibrium steam condensing flow. In this work, the comparison of the cascade loss coefficient for stator and rotor and selected flow parameters for the stage were presented, compared and discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 1 of this two-part paper,firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investigate the APES technique.Then steady and unsteady simulations are conducted in a transonic compressor stage.The results from both simulations are compared to highlight the significance of the unsteady interactions.Furthermore,the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial correlations (SC).Lastly,steady and time-averaging (employing APES with DC) simulations for the downstream stator alone are conducted employing DC derived from the unsteady results.The results from steady and time-averaging simulations are compared with the time-averaged unsteady results.The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.     

Asymptotic analysis of self-excited and forced vibrations of a self-regulating pressure control valve

Nonlinear Dynamics - Pressure vibrations in hydraulic systems are a widespread problem and can be caused by external excitation or self-exciting mechanisms. Although vibrations cannot be completely...     

An inviscid model for the base pressure of transonic turbine cascade

An inviscid base pressure model for transonic turbine blade has been presented. It has been shown that for a given back pressure the base pressure at the trailing edge, and the profile loss of a turbine blade are fixed according to the model and the base pressure can be calculated with the help of an inviscid numerical scheme. A parameteric study on the model shows that a blade profile with positive curvature downstream of the throat is advantageous for generating less loss, whilst the worst situation is when the exit flow reaches the sonic condition.     

Turbulent kinetic energy balance measurements in the wake of a low-pressure turbine blade

The turbulent kinetic energy budget in the wake generated by a high lift, low-pressure two-dimensional blade cascade of the T106 profile was investigated experimentally using hot-wire anemometry. The purpose of this study is to examine the transport mechanism of the turbulent kinetic energy and provide validation data for turbulence modeling. Point measurements were conducted on a high spatial resolution, two-dimensional grid that allowed precise derivative calculations. Positioning of the probe was achieved using a high accuracy traversing mechanism. The turbulent kinetic energy (TKE) convection, production, viscous diffusion and turbulent diffusion were all obtained directly from experimental measurements. Dissipation and pressure diffusion were calculated indirectly using techniques presented and validated by previous investigators. Results for all terms of the turbulent kinetic energy budget are presented and discussed in detail in the present work.     

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2: influence of deterministic correlations on time-averaged flow prediction

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study was to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 2 of this two-part paper,the influence of DC on the time-averaged flow field was systematically studied.Several time-averaging computations were conducted with various boundary conditions and DC for the downstream stator in a transonic compressor stage,by employing the CFD solver developed in Part 1 of this two-part paper.These results were compared with the time-averaged unsteady flow field and the steady one.The study indicated that the circumferentialaveraged DC can take into account major part of the unsteady effects on spanwise redistribution of flow fields in compressors.Furthermore,it demonstrated that both deterministic stresses and deterministic enthalpy fluxes are necessary to reproduce the time-averaged flow field.     

3-D DEM simulation of cohesive soil-pushing behavior by bulldozer blade

A numerical simulation based on discrete element method (DEM) was conducted on the excavation and pushing processes of soil by a bulldozer blade. Soil contains water and the resistance acting on the bulldozer blade is largely influenced by the cohesive force due to liquid bridges formed among soil particles. In the present study, a cohesive bond force model proposed by Utili and Nova [5] was introduced in which the microscopic behavior of cohesive force was modeled analogously with macroscopic shear failure characteristics. The dependency on the magnitude of microscopic cohesive force was verified. The behavior of particles changed greatly by taking into account the cohesive bond force. The characteristic behavior of excavated soil aggregates, such as rolling motion and intermittent collapsing, were observed in front of the blade surface.     

Dynamic study of a wind turbine blade with horizontal axis

The study of the dynamic behavior of a wind turbine with horizontal axis can be undertaken by various methods of analysis. The effects of the change of the aerodynamic flow (in the steady and unsteady cases), the variation of parameters of the cinematic movement (angle of attack, pitch angle and yaw angle) and the definition of subsystems characteristics that makes the wind turbine (blade, nacelle and pylon) allow one to characterize the structural dynamic behavior of the wind turbine. It is therefore necessary to develop these items. Once this is done, the structural dynamic behavior of the system can be improved. The term `improve' means the increase of the life duration by mastering the fatigue effects and the reduction of cost without sacrificing the aerodynamic output. The present study aims to examine the behavior of the blade, which is the main part of the wind turbine in that it that transmits forces to all other parts of the structure. The model is based on the theory of three-dimensional beams, under the assumption of variable sections of the type NACA 4415 airfoil, and takes into account membrane, transversal shear, flexion and free torsion effects. With regards to the aerodynamic loads (the lift, the drag and the pitching moment), a validation has been undertaken by considering experimental data and numerical results obtained by a CFD code (Fluent). The forces are obtained by means of a parametric CAD method interpolation of the aerodynamic poles by Bézier patch under geometrical constraints solved by a Simplex type algorithm. The emphasis is put on dynamic aspects by a complete processing of the dynamic equilibrium equation, applied to the wind turbine blade with horizontal axis.     

涡轮叶片的持久寿命预测模型

镍基高温合金用于制造发动机的高压涡轮叶片.为了提高涡轮叶片持久寿命设计参数选取和设计方法的可靠性,从涡轮叶片代表性部位取材并设计、加工试验试件,进行持久寿命试验.试验过程中记录试件的变形量,进而推算出其蟠变应变,然后利用修正θ-Project Concept法来建立其持久寿命预测方程,并对其进行验证.