Fadi Dohnal

Damping by Parametric Stiffness Excitation: Resonance and Anti-Resonance

Investigations are presented into the stability of vibration suppression employing variable-stiffness actuators. Systems with an arbitrary number of degrees of freedom are considered, and are subject to both parametric excitation and self-excitation. Analytical conditions of stability and instability are derived by applying a singular perturbation technique. These conditions enable a stability classification that naturally leads to the description parametric anti-resonance. The influence of the symmetry property of the parametric excitation matrix on the location of the parametric anti-resonance is discussed. Additionally, the influence of parametric resonance and anti-resonance on the eigenvalues corresponding to the slow motion of a generic system are analysed. A geometric interpretation is presented, enabling deeper insight into the mechanism of vibration suppression, and leading to the interpretation of coupling modes using parametric anti-resonance and amplification of system damping. The basic results obtained can be used for design of a control strategy for variable-stiffness actuators.

Stability Analysis of Open-loop Stiffness Control to Suppress Self-excited Vibrations

We present stability investigations on vibration cancelling employing three different types of variable-stiffness actuators. A two-mass system is considered, with a base mass attached to the ground and a top mass connected to the base mass. The top mass is subject to self-excitation forces. The stiffness of an actuator connecting the base mass and the ground may change with time, according to a predetermined control frequency, for cancelling vibrations. Numerical simulation is employed as the basic tool to investigate the system and to carry out parameter studies. The stability of the system is determined by calculating the eigenvalues of the state transition matrix. Robustness of the proposed methods for vibration cancelling is discussed with respect to various aspects.

Design of an electromagnetic actuator for parametric stiffness excitation

Purpose – An overview is given on design features, numerical modelling and testing of a novel electromagnetic actuator to achieve a controllable stiffness to be used as a device for parametric stiffness excitation.Design/methodology/approach – In principle, the actuator consists of a current driven coil placed between two permanent magnets. Repellent forces are generated between the coil and the magnets, centering the coil between the two magnets. The 2D finite element analyses are carried out to predict the forces generated by this arrangement depending on coil current and coil position. Force measurements are also made using the actual device.Findings – Actuator forces as predicted by the finite element analyses are in excellent agreement with the measured data, confirming the validity of the numerical model. Stiffness of the actuator is defined as the increase of force per unit of coil displacement. Actuator stiffness depends linearly on the coil current but in a nonlinear manner on the coil displaceme...

Experimental Study on Cancelling Self-Excited Vibrations by Parametric Excitation

This article reports on the experimental verification of an anti-resonance effect obtained by parametric stiffness excitation. From theoretical studies it is known that parametric excitation at non-resonant parametric resonances can improve the damping behavior of a mechanical system and even stabilize an otherwise unstable system. To demonstrate this effect, a test setup was designed, based on a two-mass vibration system, gliding on an air track. Parametric stiffness excitation (PSE) was realized by a mechanical device that creates a time-periodic stiffness by modulating the tension in an elastic rubber band. With this device it was possible to demonstrate the improved damping behavior of the system when the PSE device is operating at or near the first parametric combination resonance of difference type. Also, a simple electro-magnetic device was used to create self-exciting forces. It could be shown for the first time that it is indeed possible to stabilize the unstable system by introducing parametric stiffness excitation.Copyright

Suppressing Flutter Vibrations by Parametric Inertia Excitation

A theoretical study of a slender engineering structure with lateral and angular deflections is investigated under the action of flow-induced vibrations. This aero-elastic instability excites and couples the systems bending and torsion modes. Semiactive means due to open-loop parametric excitation are introduced to stabilize this self-excitation mechanism. The parametric excitation mechanism is modeled by time-harmonic variation in the concentrated mass and/or moment of inertia. The conditions for full suppression of the self-excited vibrations are determined analytically and compared with numerical results of an example system. For the first time, example systems are presented for which parametric antiresonance is established at the parametric combination frequency of the sum type.

Joint uncertainty propagation in linear structural dynamics using stochastic reduced basis methods

Uncertainties in the properties of joints produce uncertainties in the dynamic response of built-up structures. Line joints, such as glued or continuously welded joints, have spatially distributed uncertainty and can be modeled by a discretized random field. Techniques such as Monte Carlo simulation can be applied to estimate the output statistics, but computational cost can be prohibitive. This paper addresses how uncertainties in joints might be included straightforwardly in a finite element model, with particular reference to approaches based on fixed-interface (Craig– Bampton) component mode synthesis and a stochastic reduced basis method with two variants. These methods are used to determine the output statistics of a structure. Unlike perturbation-based methods, good accuracy can be achieved even when the coefficients of variation of the input random variables are not small. Undamped as well as proportionally damped components are considered. Efficient implementations are proposed based on an exact matrix identity that leads to a significantly lower computational cost if the number of joint degrees of freedom is sufficiently small compared with the structure’s overall number of degrees of freedom. A numerical example is presented. The proposed formulation is an efficient and effective implementation of a stochastic reduced basis projection scheme. It is seen that the method can be up to orders of magnitude faster than direct Monte Carlo simulation, while providing results of comparable accuracy. Furthermore, the proposed implementation is more efficient when fewer joints are affected by uncertainty.

Brush seals and labyrinth seals in gas turbine applications

The overall efficiency of gas turbines is strongly affected by the performance of the sealing arrangement between the stationary and rotary components. Maintaining an accurate clearance during nominal and transient operation and providing effective damping is of key importance for seal designers. The implementation of brush seals as an alternative to labyrinth seals in a gas turbine engine is outlined in this article. A review of published literature is performed to analyze the leakage performance of brush seals and labyrinth seals. The emphasis lies on the importance of an accurate clearance control and the subsequent reduction in parasitic flows. Based on a discussion of the performance and integrity of brush seals in gas turbine applications their advantages over labyrinth seals are highlighted. Some attention is drawn into common drawbacks of brush seals and how these were improved over time to become more competitive and reliable. Finally, advanced concepts, technological aspects of the design of the brush seals influencing their leakage characteristics and future applications prospective are discussed. It was shown that one of the key advantages of brush seals over conventional labyrinth seals is their positive rotordynamic characteristic. The rotordynamic force coefficients demonstrate very low and generally negative cross-coupled stiffness thereby positively affecting the turbomachine operability in industrial gas turbine applications. The review concluded the need for further work on studying rotordynamic behaviour of brush seals operating at conditions more realistic to real engine operation environment in order to complete the understanding of the seal dynamics in real operation condition.

A Journal Bearing With Variable Geometry for the Reduction of the Maximum Amplitude During Passage Through Resonance

A concept for a journal bearing with variable stiffness and damping properties is developed in order to decrease the vibration amplitude of a rotor-journal bearing system during passage through resonance. The introduction of an additional fluid film thickness in the bearing is proposed in this work in order to alter the dynamic properties in the bearing. The bearing ring is divided into two parts with the upper part being fixed with the housing and the lower part being flexibly mounted by a preloaded spring in parallel with a viscous damper. This allows relative motion between the two parts of the bearing ring. The relative motion introduces an additional fluid film zone in the bearing under the passive displacement of the lower part due to increased impedance forces that are developed in the lubricant film at resonance operation. The general concept is to change the system’s damping and stiffness coefficients using this extra fluid film thickness only when the system passes through its critical speed in order to quench the vibration amplitude. For rotational speeds outside of the resonant regions, the bearing is considered to be fixed in order to behave as it was designed under the nominal loading operational conditions. [DOI: 10.1115/1.4007242]

Enhancing stability of industrial turbines using adjustable partial arc bearings

The paper presents the principal of operation, the simulation and the characteristics of two partial-arc journal bearings of variable geometry and adjustable/controllable stiffness and damping properties. The proposed journals are supposed to consist of a scheme that enables the periodical variation of bearing properties. Recent achievements of suppressing rotor vibrations using plain circular journal bearings of variable geometry motivate the further extension of the principle to bearings of applicable geometry for industrial turbines. The paper describes the application of a partial-arc journal bearing to enhance stability of high speed industrial turbines. The proposed partial-arc bearings with adjustable/controllable properties enhance stability and they introduce stable margins in speeds much higher than the 1st critical.

Modal interaction and vibration suppression in industrial turbines using adjustable journal bearings

The vibration suppression by deliberately introducing a parametric excitation in the fluid-film bearings is investigated for an industrial turbine rotor system. A journal bearing with variable adjustable geometry is operated in such a way that the effective stiffness and damping properties vary periodically in time. The proposed bearing is designed for having the ability of changing the bearing fluid film thickness in a semi-active manner. Such an adjustment of the journal bearing properties introduces in the system a time-periodic variation of the effective stiffness and damping properties of the fluid-film. If the time-periodicity is tuned properly to match a parametric anti-resonance, vibration suppression is achieved in the overall system. The paper presents the principle of operation of the recently developed bearings. The simulation of an industrial turbine rotor-bearing shaft line at induced parametric excitation motivates the further development and application of such bearings since the vibration amplitudes are considerably decreased in critical speeds.