Viscous Damping Coefficients Research Articles

Identification of Force Coefficients in a Squeeze Film Damper With a Mechanical End Seal—Part I: Unidirectional Load Tests

Squeeze film dampers (SFDs) with low levels of external pressurization and poor end sealing are prone to air entrapment, thus not generating enough damping capability. Single frequency, unidirectional load tests were conducted on a SFD test rig replicating a commercial jet-engine configuration. The damper journal is 2.54cm in length and 12.7cm in diameter, with nominal clearance of 0.127mm. The SFD feed end is flooded with oil, while the discharge end contains a recirculation groove and four orifice ports, and a mechanical seal ring in contact with the damper journal. A wave spring pushes the ring ensuring tight sealing to prevent gas ingestion. The mechanical seal also serves to contain the lubricant within the squeeze film land for extended periods of time and; while in operation, to prevent contamination of the ball bearing cartridge. The measurements conducted without and with lubricant in the squeeze film lands, along with a frequency domain identification procedure, render the mechanical seal dry-friction force and viscous damping force coefficients as functions of frequency and motion amplitude. The end seal arrangement is quite effective in eliminating side leakage and preventing air entrainment into the film lands. Importantly enough, the dry friction force, arising from the contact forces in relative motion, increases significantly the test element equivalent viscous damping coefficients. The identified system damping coefficients are thus frequency and motion amplitude dependent, albeit decreasing rapidly as the motion parameters increase. Identified squeeze film force coefficients, damping and added mass, agree well with predictions based on the full film, short length damper model.

Forced linear oscillations of microbubbles in blood capillaries.

A theoretical investigation of the forced linear oscillations of a gas microbubble in a blood capillary, whose radius is comparable in size to the bubble radius is presented. The natural frequency of oscillation, the thermal and viscous damping coefficients, the amplitude resonance, the energy resonance, as well as the average energy absorbed by the system, bubble plus vessel, have been computed for different kinds of gas microbubbles, containing air, octafluropropane, and perflurobutane as a function of the bubble radius and applied frequency. It has been found that the bubble behavior is isothermal at low frequencies and for small bubbles and between isothermal and adiabatic for larger bubbles and higher frequencies, with the viscous damping dominating over the thermal damping. Furthermore, the width of the energy resonance is strongly dependent on the bubble size and the natural frequency of oscillation is affected by the presence of the vessel wall and position of the bubble in the vessel. Therefore, the presence of the blood vessel affects the way in which the bubble absorbs energy from the ultrasonic field. The motivation of this study lies in the possibility of using gas microbubbles as an aid to therapeutic focused ultrasound treatments.

Advancements in the Structural Stiffness and Damping of a Large Compliant Foil Journal Bearing: An Experimental Study

This paper presents the results of an experimental investigation into the dynamic structural stiffness and damping characteristics of a 21.6‐cm(8.5in.)-diameter compliant surface foil journal bearing. The goal of this development was to achieve high levels of damping without the use of oil, as is used in squeeze film dampers, while maintaining a nearly constant dynamic stiffness over a range of frequencies and amplitudes of motion. In the experimental work described herein, a full compliant foil bearing was designed, fabricated, and tested. The test facility included a non-rotating journal located inside the bearing. The journal was connected to an electrodynamic shaker so that dynamic forces simulating expected operating conditions could be applied to the structurally compliant bump foil elements. Excitation test frequencies to a maximum of 400Hz at amplitudes of motion between 25.4 and 102μm were applied to the damper assembly. During testing, both compressive preload and unidirectional static loads of up to 1335 and 445N, respectively, were applied to the damper assembly. The experimental data from these tests were analyzed using both a single degree of freedom model and an energy method. These methods of data analysis are reviewed here and results are compared. Excellent agreement in results obtained from the two methods was achieved. Equivalent viscous damping coefficients as high as 1050N.s∕cm(600lbf.s∕in) were obtained at low frequencies. Dynamic stiffness was shown to be fairly constant with frequency.

Forced linear oscillations of microbubbles in blood capillaries

A numerical investigation of the forced oscillations of ultrasound contrast agents in blood capillaries are investigated by means of a simplified model based on the assumption of small amplitude oscillations of the microbubbles acoustically driven. The natural frequencies of oscillations, the thermal and viscous damping coefficients, the amplitude resonances, as well as the average power absorbed by the system, bubble plus vessel, are computed for different kinds of contrast agent bubbles, containing air, octafluropropane, and perflurobutane. It is found that viscous damping is much larger than thermal damping and that the natural frequencies depend much more on the system parameters than the nature of the gas contained in the bubble. Our motivation for this study lies in the possibility of using bubbles as vectors for directed drug delivery and gene transfection into living cells.

Verification of damped cable system performance in the seismic rehabilitation of buildings

The performance capacities of the damped cable system are evaluated by the results of an experimental campaign developed on a full-scale three-story reinforced concrete structure retrofitted by this innovative protective technology. The experimental activity, carried out as part of a European Community funded Research Project, consisted of a repeated series of forced vibration tests, which offered a first realistic verification of the system response capabilities. This provided essential information on the on-site behaviour of the assembled system components, among which were cable connections with fluid viscous spring-dampers and story beams. The dynamic test results, elaborated in terms of equivalent transmissibility coefficients, energy dissipated by the spring-dampers and the entire structure, relevant energy ratios, and equivalent viscous damping coefficients, showed a significant improvement of structural performance in rehabilitated conditions, as well as a satisfactory correlation with design predictions. The analytical model of the structure, properly calibrated on the experimental data, was also used for a numerical seismic investigation, which confirmed the high degree of protection guaranteed by the examined technology.

MR유체를 이용한 다방향 제진형 마운트의 응답특성

This paper presents response property of the squeeze mode type mount using Magneto-Rheological fluid (MR fluid) . The MR mount for the isolation of multi-directional vibrations was constructed in this study. Both the mechanism and shape of the mount are the same as squeeze film dampers for a rotor system. In the present work, the performance of the mount was experimentally Investigated according to the magnetic field strength. The experimental results present that the MR mount can effectively reduce the vibration in a wide range of frequency by controlling the applied electromagnetic filed strength. Viscous damping and stiffness coefficients of the MR mount tend to be changed according to the variation of the applied currents In this study.

MR 유체를 이용한 스퀴즈모드형 마운트의 동특성

This paper presents investigation of damping characteristics of squeeze mode type MR (magneto-rheological) mount experimentally. Since damping property of the MR fluid is changed by variation of the applied magnetic field strength, squeeze mode type MR mount proposed in the study has variable damping characteristics according to the applied magnetic field strength. In the present work, the performance of the mount was experimentally Investigated according to the magnetic field strength and exciting frequencies. The experimental results present that the MR mount can effectively reduce the vibration in a wide range of frequency by controlling the applied electromagnetic field strength. Viscous damping and stiffness coefficients of the MR mount tend to be changed according to the variation of the applied currents in this study and MR effect is reduced by increasing exciting frequency.

Sliding Mode Semi-Active Base Isolation Using the Switching Hyperplane Designed by Disturbance-Accommodating Bilinear Control.

In vibration isolation control problem, semi-active control methods in which coefficient of viscous damping is varied effectively have been proposed and expected to realize a high performance. However, the semi-active system is classified into a bilinear system which belongs to a nonlinear system. In this study, the switching hyperplane of sliding mode control is designed by the disturbance-accommodating bilinear optimal control theory and it is applied to a semi-active vibration base isolation problem. The proposed method adopts the damping force in criteria function, and the controller takes into account the disturbance dynamics by difining an augemented bilinear system. This study deals with a ten-degree-of-freedom structural model with base isolation. And the computer simulation is carried out by taking account of the delay of switching the coefficient of dampers. As a result, the usefulness of the present method was demonstrated.

DAMPING ESTIMATES FROM EXPERIMENTAL NON-LINEAR TIME-SERIES

This paper seeks to illustrate the utility of the Lyapunov spectrum in estimating the damping of an experimental non-linear system. A mechanical model of Duffing's equation operating in the chaotic regime is used to generate a single observable. Using standard techniques from non-linear time-series analysis, the complete Lyapunov spectrum is estimated. The sum of these exponents may, via the divergence theorem, be related directly to the coefficient of viscous damping. Estimations are performed in this manner for both a three- and four-dimensional response and results are compared to estimates taken from two linear-based techniques. The indication is that use of the Lyapunov spectrum to obtain quantitative damping estimates is a comparable alternative to methods requiring transient data or detailed knowledge of the dynamics.

Bilinear Optimal Control Theory and its Application to Semi-Active Vibration Isolation Control.

In vibration isolation control problem, semi-active control methods in which coefficient of viscous damping or spring constant are varied effectively have been proposed and expected to realize a high performance with a little energy consumption. However, the semi-active system is classified into a bilinear system which belongs to a nonlinear system and its controller design is not easy. In this study, a bilinear optimal control theory is established by adopting the damping force in criteria function and it is applied to a semi-active base isolation problem. This study deals with 10 stories structure model corresponding to an actual building and the dynamics of an oil damper is taken into consideration by using the Maxwell model in the modelling. Moreover, the dynamics of disturbance is taken into account, and the controller is designed for the augmented bilinear system which includes both the control object and the disturbance. And the computer simulation is carried out by taking account of the delay to switch the coefficient of dampers in order to compare the performance on semi-active base isolation controls designed by the proposed method with skyhook control method and passive isolations. As a result, the usefulness of the present method was demonstrated.

Semi-active base isolation for a building structure

Recently semi-active control methods have been proposed and received much attention. In semi-active base isolation, the coefficient of viscous damping or the spring constant is changed effectively according to the state of the control object. The system using a semi-active damper is classified as a bilinear system which belongs to non-linear systems. In this paper, optimal control theory is applied to a bilinear system using feedforward information of disturbance, and the bilinear optimal control law is derived. Then the method is applied to an actual building which is modelled by a 10 degree-of-freedom structure model with base isolation using a semi-active oil damper. The numerical analysis shows that the method has high control performance in a wide frequency range, and it is effective for the vibration base isolation of building structures.

A simplified random vibration analysis on portable electronic products

A random vibration analysis on a portable electronic product is presented in this paper based on a simplified physical model. The analysis emphasizes the dynamic relative transverse deflection, or the stopping distance, of the liquid crystal display, which is taken to be a thin elastic plate element, under random acceleration excitations. The expressions of the mean value and the autocorrelation function of the relative transverse deflection of the plate element are derived for stationary stochastic process acceleration excitations, and some statistical quantities are discussed. As a numerical example, a portable computer product under an idealized white noise stationary random acceleration excitation is analyzed, and some numerical results of the statistical quantities, such as the autocorrelation function and the standard deviation, are presented. According to our analysis, to decrease the random dispersion of the relative transverse deflection (stopping distance) of the plate element, both the viscous damping coefficients of the plate and its support should be over designed, but with that of the plate being larger than that of the support. In practice, it is possible to select proper support materials and correctly design the mounting of the chassis to meet this requirement, because compared to the liquid crystal display, the mounting of the chassis is easier to design for. With a normal distribution assumption for the relative transverse deflection, the maximum possible relative transverse deflections (stopping distances) of the plate element are obtained, at chosen confidence levels, which can be used as a preliminary check for designing a similar portable computer product.

Imbalance Response of a Rotor Supported on Open-Ends Integral Squeeze Film Dampers

Rotor vibration attenuation and structural components isolation in jet engines are achieved with squeeze film dampers, many of them supported on long elastic squirrel cages. Integral squeeze film dampers (ISFDs) are comprised of arcuate pads and wire-EDM webs rendering a compact viscoelastic support. An experimental study is conducted to evaluate the effectiveness of ISFDs in attenuating the imbalance response of a massive test rotor. Measurements of the damper structural stiffness and rotor natural frequencies are detailed. Impact tests on the test rotor supported on its dampers reveal the supporting structure to be very flexible, thus requiring the experimental evaluation of an equivalent stiffness for the damper and supports system. System damping coefficients extracted from impact load excitations vary with the lubricant viscosity and include a significant structural damping from the bearing supports. Rotor coast-down tests demonstrate the ISFDs to damp well the rotor response with peak vibration amplitude proportional (linear) to the imbalance. Viscous damping coefficients estimated from the amplitude response at the critical speeds agree reasonably well with predictions from a full-film, finite element model.

IMPROVEMENT OF THE PERFORMANCE ON PNEUMATIC SERVO TYPE ACTIVE SUSPENSION USING SIMULTANEOUS OPTIMUM DESIGN METHOD OF STRUCTURAL AND CONTROL SYSTEMS

In this paper, we propose the simultaneous optimum design method of structural and control systems for an active suspension using a sensitivity analysis. We deal with an analytical half-car model based on the experimental equipment which has a pneumatic servo type active suspension. Control design variables for the optimum design are feedback gains of optimal control and structural design variables are spring constants, viscous damping coefficients, cylinder sectional areas, piston strokes and a wheelbase. We confirmed that the simultaneous optimum design method is useful for the pneumatic servo type active suspension from the numerical simulation results.

Viscoelastic tensile and shear properties of the 62 wt% Sn-36 wt% Pb-2 wt% Ag solder alloy

In this paper the results of the experimental determination of the viscoelastic tensile and shear properties of the eutectic 62 wt% Sn–36 wt% Pb–2 wt% Ag solder alloy in the temperature range between −20 and 100 °C are presented. The dynamic tensile and shear moduli and the viscous damping coefficients were measured using a phase-sensitive resonance technique. The results show that the temperature dependence of the dynamic Young's and shear moduli can be approximated by linear functions and a quadratic polynomial can be used to define a lower bound of the temperature dependence of the viscous damping coefficients of the material. For a temperature rise from 20 to 65 °C the dynamic Young's and shear moduli decrease by approximately 6% and the damping coefficient increases by approximately 80%.

The mode shape reversal with viscous damping

The conventional characteristic-value, characteristic-vector solution to the discrete, linear elastic vibration problem evolves from Newton's second law, while the recently discovered modal equations method is based upon the principle of conservation of energy. The conventional method begins with the dynamical equations for the system and always requires a solution to the characteristic polynomial, which is easily accomplished computationally in the forward sense. However, this same characteristic polynomial precludes any successful development and decomposition in its backward sense, so that the conventional solution always fails for the vibration problem reversal; this is one of the great enigmas of classical mechanics. Due to the energy based origin of the modal equations method for solving vibrations problems, both the dynamical equations and characteristic polynomial are eliminated and this procedure then encounters no restrictions to its backward solution. The published modal equations forward solution to the vibration problem already includes viscous damping, but its corresponding backward solution is presently restricted to the undamped case. The material presented here improves the mode shape reversal process so as to add viscous damping to the problem and it thereby results in a significantly greater computational accuracy. Beginning with any arbitrary set of mode shapes describing the deflections of a discrete, viscously damped, linear elastic system in free vibration, the required mass, viscous damping and stiffness coefficient values are developed by means of a converging iteration scheme in a digital computer program. Thus, the consumate theoretical solution to the vibration problem reversal is accomplished. A sample problem is investigated.

Damped oscillation analysis of natural and artificial periodontal membranes.

The mechanical mobility of human teeth was studied by using a wave data treatment system with an accelerometer attached to a personal computer. The healthy teeth in different generations of men and women, who ranged in age from their teens to their forties, showed similar damped oscillation patterns. The spring constant and coefficient of viscous damping were estimated by using a viscoelastic model of damped oscillation with 1 degree of freedom. The coefficient of viscous damping increased dramatically with increases in the damping factor, whereas the spring constant scarcely varied. Silicone membranes were used as model periodontal membranes. The coefficient of viscous damping decreased with increases in silicone membrane thickness. Collagen membranes, which are expected to function as artificial periodontal membranes, were adhered to the model tooth by drying collagen gel and fixed with apatite-collagen composites. The collagen membranes showed damped oscillation wave patterns similar to those of human periodontal membranes.

Three-Dimensional Viscous Flows Between Concentric Cylinders Executing Axially Variable Oscillations: A Hybrid Spectral/Finite Difference Solution

A hybrid spectral/finite difference method is developed in this paper for the analysis of three-dimensional unsteady viscous flows between concentric cylinders subjected to fully developed laminar flow and executing transverse oscillations. This method uses a partial spectral collocation approach, based on spectral expansions of the flow parameters in the transverse coordinates and time, in conjunction with a finite difference discretization of the axial derivatives. The finite difference discretization uses central differencing for the diffusion derivatives and a mixed central-upwind differencing for the convective derivatives, in terms of the local mesh Reynolds number. This mixed scheme can be used with coarser as well as finer axial mesh spacings, enhancing the computational efficiency. The hybrid spectral/finite difference method efficiently reduces the problem to a block-tridiagonal matrix inversion, avoiding the numerical difficulties otherwise encountered in a complete three-dimensional spectral-collocation approach. This method is used to compute the unsteady fluid-dynamic forces, the real and imaginary parts of which are related, respectively, to the added-mass and viscous-damping coefficients. A parametric investigation is conducted to determine the influence of the Reynolds and oscillatory Reynolds (or Stokes) numbers on the axial variation of the real and imaginary components of the unsteady forces. A semi-analytical method is also developed for the validation of the hybrid spectral method, in the absence of previous accurate solutions or experimental results for this problem. Good agreement is found between these very different methods, within the applicability domain of the semi-analytical method.

Identification of Single-Degree-of-Freedom Nonlinear Vibrating System by Piecewise Linear Approximation.

A new method for parameter identification of single-degree-of-freedom nonlinear vibrating systems is proposed in the time domain. The nonlinearity is approximated by piecewise linear characteristics. The nonlinear characteristics of restoring force and damping can be obtained from the linear spring constants and linear viscous damping coefficients identified on each piecewise linear section. Two experimental procedures, that is, the impact excitation method and the additional mass method without excitation, are performed. The response and excitation data for the impact excitation are required in the impact excitation method and the free vibration responses of the system with and without additional mass are required in the additional mass method. System parameters of the vibrating systems with various nonlinear characteristics, Duffing-type system and clearance system, can be accurately identified by both the procedures. It is shown that the additional mass method is valid for torsional nonlinear systems on which the measurement of excitation force is difficult.

Spectral Solutions For Unsteady Annular Flows Between Eccentric Cylinders Induced By Transverse Oscillations

A spectral collocation method is formulated in this paper for the analysis of unsteady annular flows between eccentric cylinders, induced by transverse oscillations of one of the cylinders. This method uses convenient spatial and temporal expansions for the unsteady flow parameters and a collocation approach to determine the a prioriunknown complex coefficients in these spectral expansions. The method is first used to solve the unsteady potential flow between long eccentric cylinders generated by small amplitude translational oscillations. For validation, the resulting solutions for the added mass coefficients are compared with the available ideal flow results for concentric and eccentric configurations. Spectral solutions are then obtained with this method for the more complex problem of unsteady viscous flows. Solutions for the unsteady pressure and fluid-dynamic forces are obtained for oscillations either in the plane of symmetry of the eccentric annular configuration or normal to it; they are compared to existing analytical and finite element viscous flow solutions, for concentric and eccentric cylinders, respectively. A parametric investigation is conducted to expose the influence of the relative eccentricity, outer to inner radius ratio and the oscillatory Reynolds number on the added mass and viscous damping coefficients.