Damper Geometry Research Articles

A Model and Experimental Validation for a Piston Rings—Squeeze Film Damper: A Step Toward Quantifying Air Ingestion

Abstract Rotor-bearing systems often rely on squeeze film dampers (SFDs) to increase the dynamic stability and reduce rotor motion amplitudes while traversing critical speeds. In aircraft engines, to increase the damping capacity within a limited physical space, piston rings (PRs) seal the axial ends of a squeeze film land. However, lubricant still leaks through the slit in the PR abutted ends, and air enters into the film to make a bubbly oil mixture with a much reduced damping capability. This paper presents a volume of fluid (VOF) model for a PR sealed ends SFD facing ambient air (not submerged in lubricant and prone to air entrainment) and delivers predictions benchmarked against experimental results obtained in a dedicated test rig. A lubricant feeds pressure and flows large enough to prevent air ingestion vary with the damper geometry, the lubricant inlet and outlet conditions, and the kinematics of the journal. A parametric study for a typical SFD shows the period-averaged gas volume fraction (GVF) increases as the journal squeeze film velocity (vs) increases and as the film clearance decreases. Most importantly, the location of the PR slit relative to the feedhole affects the amount of air drawn into the film. When the PR slit faces a feedhole, the film land is mostly filled with a pure lubricant. The GVF increases as the arc distance from the PR slit to the feedhole increases. The physical model, anchored by the test data, effectively addresses a fundamental challenge in SFD design and operation; namely, quantifying the amount of air ingested and its effect on the damper forced performance.

On the Efficiency of a Conical Underplatform Damper for Turbines

Abstract Underplatform dampers (UPDs) are commonly used in aircraft engines to limit the risk of high-cycle fatigue of turbine blades. The latter is located in a groove between two consecutive blades. The dry friction contact interface between the damper and the blades dissipates energy and so reduces the vibration amplitudes. Two common geometries of dampers are used nowadays, namely wedge and cylindrical dampers, but their efficiency is limited when the blades have an in-phase motion (or a motion close to it), since the damper tends to have a pure rolling motion. The objective of this study is to analyze a new damper geometry, based on a conical shape, which prevents from this pure rolling motion of the damper and ensures a high kinematic slip. The objective of this study is to demonstrate the damping efficiency of this geometry. Hence, in a first part, the kinematic slip is approximated with analytical considerations. Then, a nonlinear dynamic analysis is performed, and the damping efficiency of this new geometry is compared to the wedge and the cylindrical geometries. The results demonstrate that the conical damper has a high damping capacity and is more efficient and more robust than the two others.

Robust design optimisation of underplatform dampers for turbine applications using a surrogate model

Underplatform dampers (UPD) represent an effective way to limit blade vibration in turbomachinery via frictional energy dissipation, leading to a wide range of applications. The design of an effective and reliable UPD is highly challenging, due to the inherently nonlinear nature of the contact forces, the associated computational cost for high fidelity simulation, and the manufacturing uncertainties in damper geometry. This paper presents a novel UPD optimisation approach that combines high-order, detailed nonlinear modelling of the damper interfaces with a surrogate model optimisation technique. The nonlinear dynamic behaviour of the UPD is predicted using the existing explicit damper model in combination with an ‘in-house’ multi-harmonic balance solvers, which enables capture of the damper kinematics and local contact conditions. A radial basis function based surrogate model will be used to address the computational requirement of the high fidelity simulations for alternative designs. The objective function takes into account the damping performance, resonance frequency stability and robustness due to possible uncertain variations of design parameters with manufacture tolerance. The feasibility of the proposed approach is demonstrated on a cottage roof UPD by comparing the proposed optimisation method with conventional parametric simulation method. A significantly improved solution with considerable reduction in computational effort is achieved by the current method.

Linear Stability Analysis and Dynamic Response of Shimmy Dampers for Main Landing Gears

This paper presents the analysis and study of common shimmy dampers used today for main landing gears with the use of analytical and numerical tools. The shimmy phenomenon is studied by using the tire stretched string theory model and by developing linear approximations of the dynamics of a single tire landing gear. The dynamics of commonly used shimmy dampers are then incorporated into the model. The objectives of this paper are to study already developed shimmy damper designs and to develop tools to design a new innovative and better shimmy damper for main landing gears, those which have nonsteerable wheels. Two shimmy damper designs are studied in this paper, one developed by Boeing and another by UTC Aerospace Systems (UTAS). A linear approximation of the dynamics of these dampers is obtained, omitting the freeplay, saturation, and nonlinear dynamics. Stability plots are then created by changing the system's parameters, such as the velocity, caster length, and the shimmy damper stiffness and damping coefficients. These plots show the comparison of using a UTC two-arm design against the Boeing damper, for which the former spans larger zones of stability but requires higher damping coefficients due to the UTC damper's geometry which is very impractical. In addition, a multibody model is developed in MSC adams (from MSC Software Corporation) to study the dynamic response of these systems and to create a modeling tool that can be used to design a new and improved shimmy damper for main landing gears. The simulation results from the model show the disadvantages of using the UTC two-arm damper, which include an asymmetrical vibration response. Further recommendations are given to design an improved shimmy damper.

Viscoplastic flow in an extrusion damper

Numerical simulations of the flow in an extrusion damper are performed using a finite volume method. The damper is assumed to consist of a shaft, with or without a spherical bulge, oscillating axially in a containing cylinder filled with a viscoplastic material of Bingham type. The response of the damper to a forced sinusoidal displacement is studied. In the bulgeless case the configuration is the annular analogue of the well-known lid-driven cavity problem, but with a sinusoidal rather than constant lid velocity. Navier slip is applied to the shaft surface in order to bound the reaction force to finite values. Starting from a base case, several problem parameters are varied in turn in order to study the effects of viscoplasticity, slip, damper geometry and oscillation frequency to the damper response. The results show that, compared to Newtonian flow, viscoplasticity causes the damper force to be less sensitive to the shaft velocity; this is often a desirable damper property. The bulge increases the required force on the damper mainly by generating a pressure difference across itself; the latter is larger the smaller the gap between the bulge and the casing is. At high yield stresses or slip coefficients the amount of energy dissipation that occurs due to sliding friction at the shaft-fluid interface is seen to increase significantly. At low frequencies the flow is in quasi steady state, dominated by viscoplastic forces, while at higher frequencies the fluid kinetic energy storage and release also come into the energy balance, introducing hysteresis effects.

Linear viscoelastic fluid characterization of ultra-high-viscosity fluids for high-frequency damper design

This paper presents the use of a state of the art damper for high-precision motion stages as a sliding plate rheometer for measuring linear viscoelastic properties in the frequency range of 10 Hz–10 kHz. This device is relatively cheap and enables to obtain linear viscoelastic (LVE) fluid models for practical use in precision mechanics applications. This is an example of reversed engineering, i.e., turning a machine part into a material characterization device. Results are shown for a high-viscosity fluid. The first part of this paper describes the damper design that is based on a high-viscosity fluid. This design is flexure-based to minimize parasitic nonlinear forces such as hysteresis and stick-slip. In the second part of the paper, LVE fluid characterization by means of the damper setup is presented. Measurements are performed and model parameters are fitted by a non-convex optimization algorithm in order to obtain the frequency-dependent behavior of the fluid. The resulting fluid model is validated by comparison with a second measurement with a different damper geometry. This paper shows that LVE fluid characterization between 10 Hz and 10 kHz for elastic high-viscosity fluids is possible with a motion stage damper for which the undamped behavior is known.

Influence of partial constrained layer damping on the bending wave propagation in an impacted viscoelastic sandwich

This paper presents a parametric model to study the transient bending wave propagation in a viscoelastic sandwich plate due to impact loading. The effect of partial constrained layer damping (PCLD) geometry on wave propagation is investigated by comparing with propagation in single layer elastic plate. Several boundary conditions are also considered, and their effect on wave propagation is highlighted.The equation of motion is obtained from Lagrange’s equations. For the single layer plate, the governing equation is solved in time domain using Newman and Wilson method. For the plate with PCLD, the frequency dependant viscoelastic behavior of the core is represented by Prony series; the equation of motion is converted into frequency domain using Fourier transform the displacement is obtained in the frequency domain and is converted into time domain with the Inverse Fast Fourier Transform.The model was validated in our previous paper (Khalfi and Ross (2013)) with experimental results, additional validation is carried in this paper with literature, and good agreement is recorded. The results show that the plate covered with PCLD remains a dispersive medium. The shape of the wave is mainly related to the sandwich stiffness while the viscoelastic layer contributes in reducing the amplitude and speed of propagation. The particularity of this transient model lies in its ability to follow the shape of the bending wave at all times to observe formation, propagation and disappearance. With this model, the influence of any structural input parameters on the bending wave can be studied. The findings presented will also serve as a research base for more advanced horizons.

The Use of Perforated Damping Liners in Aero Gas Turbine Combustion Systems

This paper considers the use of perforated porous liners for the absorption of acoustic energy within aero style gas turbine combustion systems. The overall combustion system pressure drop means that the porous liner (or “damping skin”) is typically combined with a metering skin. This enables most of the mean pressure drop, across the flame tube, to occur across the metering skin with the porous liner being exposed to a much smaller pressure drop. In this way porous liners can potentially be designed to provide significant levels of acoustic damping, but other requirements (e.g., cooling, available space envelope, etc) must also be considered as part of this design process. A passive damper assembly was incorporated within an experimental isothermal facility that simulated an aero-engine style flame tube geometry. The damper was therefore exposed to the complex flow field present within an engine environment (e.g., swirling efflux from a fuel injector, coolant film passing across the damper surface, etc.). In addition, plane acoustic waves were generated using loudspeakers so that the flow field was subjected to unsteady pressure fluctuations. This enabled the performance of the damper, in terms of its ability to absorb acoustic energy, to be evaluated. To complement the experimental investigation a simplified one-dimensional (1D) analytical model was also developed and validated against the experimental results. In this way not only was the performance of the acoustic damper evaluated, but also the fundamental processes responsible for this measured performance could be identified. Furthermore, the validated analytical model also enabled a wide range of damping geometry to be assessed for a range of operating conditions. In this way damper geometry can be optimized (e.g., for a given space envelope) while the onset of nonlinear absorption (and hence the potential to ingest hot gas) can also be identified.

Modeling underplatform dampers for turbine blades: a refined approach in the frequency domain

Friction damping is one of the most exploited systems of passive control of the vibration of mechanical systems. In order to mitigate vibration of turbine blades, friction dampers are commonly included in the bladed disk design. A common type of blade-to-blade friction dampers are the so-called underplatform dampers (UPDs); these are metal devices placed under the blade platforms and held in contact with them by the centrifugal force acting during rotation. The effectiveness of UPDs to dissipate energy by friction and reduce vibration amplitude depends mostly on the damper geometry and material and on the static loads pressing the damper against the blade platforms. The common procedure used to estimate the static loads acting on UPDs consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to compute the static pressure distribution over the damper/blade interfaces, assuming that it does not change when vibration occurs. In this paper a coupled approach is proposed. The static and the dynamic displacements of blade and UPD are coupled together during the forced response calculation. Both the primary structure (the bladed disk) and the secondary structure (the damper) are modeled by finite elements and linked together by contact elements, allowing for stick, slip and lift off states, placed between each pair of contact nodes, by using a refined version of the state-of-the-art friction contact model. In order to model accurately the blade/damper contact with a large number of contact nodes without increasing proportionally the size of the set of nonlinear equations to be solved, damper and blade dynamics are modeled by linear superposition of a truncated series of normal modes. The proposed method is applied to a bladed disk under cyclic symmetric boundary conditions in order to show the capabilities of the method compared to the classical decoupled approaches.

Research on Blade with Particle Dampers

The performance of particle damper is highly nonlinear whose energy dissipation is derived from a combination of mechanisms including plastic collisions, friction, and momentum transfer between particles. Particle damper can be applied in extreme temperature environments. In this paper, an investigation on particle damper is performed analytically and experimentally. A simulation algorithm and results of simulative studies aimed at understanding the effects of parameters of particle damper are presented. Parameters considered include damper geometry, particle material and particle size.

Nonlinear Analysis of Squeeze Film Damper with Entrained Air in Rotordynamic Systems

Squeeze film dampers are widely used in aircraft engines, land-based gas turbines, and other rotating machines to improve system damping. They often have entrained air within the oil film, which is usually not taken into account in rotordynamics analysis due to lack of good formulations of the effects involved. The effects on the damping force calculation can be significant. This work presents a new formulation of the nonlinear Reynolds equation pressure evaluation within the squeeze film damper, including the effects of entrained air, with resulting changes in effective lubricant density and viscosity. Viscosity and density expressions are developed as a function of the air/oil volume fraction. The density of the bubbly oil is a function of the air bubble diameter, which changes due to surface tension effects during lubricant motion in the bubbly oil film. The lubricant viscosity decreases due to the entrained volume of air but increases due to the surface tension effects taken from experimental tests. Pressure supply and bubbly oil film cavitation effects are included in the analysis and end seal effects are evaluated. The nonlinear time-transient forces in the squeeze film damper are evaluated as functions of (1) lubricant and air properties; (2) damper geometry including diameter, length, clearance; (3) end seal properties; and (4) shaft position and velocity. Example cases of pressure calculations and radial and tangential forces are shown. Example nonlinear transient motions are presented for a rigid, symmetrical rotor and for a nonsymmetrical rotor representing a gas turbine–type fan rotor.

Adaptive Snubber-Type Magnetorheological Fluid-Elastomeric Helicopter Lag Damper

A snubber-type magnetorheological fluid-elastomeric lag damper is developed to provide adaptive lead-lag damping augmentation for a hingeless helicopter rotor. The magnetorheological fluid-elastomeric lag damper consists of a flow valve, a flexible snubber body, and a flexible center wall separating the body into two fluid chambers. Magnetorheological fluid enclosed in the snubber body can flow through two magnetorheological valves and be activated by a magnetic field in the valves. Consistent with the loading conditions for a helicopter lag damper, the magnetorheological fluid-elastomeric damper is tested under single and dual frequency excitations. The complex modulus method was used to compare the magnetorheological fluid-elastomeric device damping performance with the baseline passive Fluidlastic damper. A significant controllable damping range is observed as current is applied to the magnetorheological valve in the magnetorheological fluid-elastomeric damper. Furthermore, to account for the nonlinear hysteresis behavior ofthe magnetorheological fluid-elastomeric damper and estimate the damping force, a time-domain hydromechanical model is formulated based on lumped parameters. Model parameters are established using damper geometry, material properties, and experimental data. The model is then applied to simulate the force vs displacement response and force time history under both single and dual frequency excitations.

Shear‐thinning effects in annular‐orifice viscous fluid dampers

The number of construction projects using viscous fluid dampers for the purpose of seismic energy dissipation has been increasing in recent years. Usually, resisting forces provided by a viscous fluid damper are nonlinearly related to the damper operation velocity. In the current study, the mechanism of the nonlinear behavior is studied. It is found that the fluid shear rate in the orifices of a damper is high enough to cause shear thinning of the fluid, that is, the non‐Newtonian behavior of the fluid must be considered to capture the viscous damper's non‐linearity. Carreau's equation giving the shear‐thinning relationship between fluid viscosity and shear rate is employed in a finite element model. The model is used to calculate the fluid dynamics in viscous dampers and the calculated results successfully explain the nonlinear behavior. Effects of the damper geometry and the fluid viscosity on the damper non‐linearity are also tested and discussed. Again, the trend shown in experimental results can be fully explained by the shear‐thinning concept. In addition, the behavior of a damper operated at ultra high velocity is addressed.

Chebyshev Polynomials Fits for Efficient Analysis of Finite Length Squeeze Film Damped Rotors

The nonlinear behavior of the hydrodynamic forces generated by squeeze film dampers makes dynamical analyses of rotor-bearing systems incorporating such devices a complex and often long task. When steady-state orbits are to be sought, approximate methods (e.g., harmonic balance method, trigonometric collocation method) can be used in order to save computation cost. However, numerical integration in the time domain cannot be avoided if one wishes to calculate transient responses, or to carry out more meticulous analyses concerning the effects of the damper nonlinear nature on the motion of the system. For finite length squeeze film dampers, neither the short nor the long bearing approximations can be suitably applied, and the fluid pressure field has to be estimated numerically, thus rendering rotordynamics predictions even longer and, for engineering purposes computationally prohibitive. To surmount this problem, the present paper proposes a straightforward procedure to derive polynomial expressions for the squeeze film damper (SFD) forces, for given damper geometry and boundary conditions. This is achieved by applying Chebyshev orthogonal polynomial fits over force data generated by numerically solving the two-dimensional pressure field governing equation. For both transient and steady-state calculations, the use of the SFD forces polynomial expressions is seen to be very efficient and precise.

Pressure Measurements and Flow Visualization in a Squeeze Film Damper Operating With a Bubbly Mixture

Squeeze film dampers (SFDs) reduce rotor vibrations and control dynamic instabilities in turbomachinery. Depending on damper geometry and operating conditions, the kinematics of journal motion can induce air ingestion and entrapment, produce lubricant vapor cavitation, or both. Air ingestion is the most common condition found in open ended dampers due to the low levels of external pressurization used in practice. The degrading effect of air entrapment on damper performance not only defies predictive models but also constrains the design of SFDs to a costly trial and error process based on prior experience. The present measurements correlate for the first time dynamic squeeze film pressures and pictures of the flow field with the air volume content in the lubricant mixture of a damper performing circular centered motion. The photographs of the flow field at key instances of journal motion show the development of a non-homogeneous flow with large striated cavities of air that persist even in the regions of positive (above ambient) dynamic pressures.

Response of Impact Dampers with Granular Materials in a Vertically Vibrating System.

The damping effect of an impact damper with granular materials in a vertically vibrating system is studied both experimentally and analytically. The motion of the damper is solved by Discrete Element Method (DEM), which is often used in the investigation of soil mechanics and powder technology. Mechanical elements like springs, dashpots and frictional sliders are used to express the contact force. It is shown that the performance depends on the particle radius and the damper geometry as well as various physical parameters. The validity of the numerical method is examined by comparison with experimental results.

Damping of wind induced oscillations through liquid sloshing

Energy dissipation due to sloshing liquid in torus-shaped nutation dampers is studied using the simple potential flow procedure in conjunction with the first order boundary layer correction. This is followed by an extensive test program to assess effectiveness of the dampers in arresting relatively low frequency oscillations frequently encountered in industrial aerodynamics problems. Results suggest damping characteristics to be particularly sensitive to the liquid height in the torus, damper geometry, and dynamical parameters representing amplitude and frequency. Tests on two and three dimensional structural models in smooth flow and boundary layer wind tunnels, with the models undergoing vortex-induced resonance and galloping instability, show that nutation dampers can effectively suppress both forms of instabilities over a wide range of wind speed.

On the Control of Instabilities in Fluid-Structure Interaction Problems

Energy dissipation due to sloshing liquid in torus-shaped nutation dampers is studied using the simple potential flow procedure in conjunction with the first order boundary layer correction. This is followed by an extensive test program to assess effectiveness of the dampers in arresting relatively low frequency oscillations frequently encountered in industrial aerodynamics problems. results suggest damping characteristics to be particularly sensitive to physical properties of the liquid used, its height in the torus, damper geometry, and dynamical parameters representing amplitude and frequency. Tests on two and three dimensional structural models in smooth flow and boundary layer wind tunnels, with the models undergoing vortex-induced resonance and galloping instability, suggest that nutation dampers can effectively suppress both forms of instabilities over a wide range of wind speed. The concept is likely to prove effective in tackling industrial aerodynamics, earthquake and ocean engineering problems

Experimental and Analytical Investigation of Squeeze Film Bearing Damper Forces Induced by Offset Circular Whirl Orbits

A basic research program was conducted to investigate the hydrodynamic forces of a squeeze film bearing damper. These forces were induced by controlled offset circular whirl orbits of the damper journal. The orbits were mechanically produced by eccentric damper rings and cams in a specially designed, end sealed test rig. Aircraft engine damper geometry and operating conditions were simulated. The instantaneous circumferential pressure profiles, for specific orbits, were measured by eight high response pressure transducers. From these data, twelve composite pressure plots were developed; each was numerically integrated to determine the damper forces corresponding to every 30 deg position of the damper center, i.e., 0–360 deg. The variations in oil film thickness data were monitored via two proximity probes. A numerical method which uses the proximity test data and the damper geometry to calculate the instantaneous values of damper center eccentricity (e), phase angle (φ), radial velocity (e˙), and whirl velocity (φ˙) is presented. These test values are required to compare theory with test. Since the data reduction for offset orbits is extremely complicated, this simple method was found to be very useful in analyzing the test results. Test results for pressure profiles as well as damper forces were compared with theoretical predictions. Agreement was good. The analysis is based on “long bearing” solution of Reynolds equation and includes the effect of inlet and cavitation pressures. For the cavitated oil film, inlet pressure was shown to have important effect on damper forces.

Investigation of Squeeze Film Damper Forces Produced by Circular Centered Orbits

This paper presents the results of an experimental and analytical investigation of the dynamic forces generated by a squeeze film bearing damper constrained to move in circular centered orbits. These orbits were mechanically produced in a specially designed, end sealed, test rig. Aircraft engine damper geometry and operating conditions were simulated. The effect of journal speed, oil viscosity, inlet pressure, and eccentricity ratio on the damper performance was studied. The pressure distributions about the journal were measured for each test condition by high-response diaphragm-type pressure transducers. These pressure profiles were numerically integrated to determine the force components of the squeeze film. Experimental results were compared to an analysis which is summarized in this paper and included the effects of inlet and cavitation pressures. The “long bearing theory” was found to be reasonably accurate in predicting the shape and magnitude of the pressure distribution. Considerable emphasis was directed to the study of the circumferential pressure distributions between 180 deg and 360 deg since aircraft engine dampers generally operate in this region. For the cavitated film (i.e., pressure distributions less than 360 deg), accurate prediction of the damper forces was found to be critically dependent on the effect of inlet and cavitation pressures.