Squeeze Film Damper Research Articles

Measurement of Steam-Generator-Tube Vibration Damping Caused by Anti-Vibration-Bar Supports

Abstract In 2013, Atomic Energy of Canada Limited (now Canadian Nuclear Laboratories) experimentally measured the damping of a straight tube with a variety of tube supports to examine low-frequency damping. These tests were motivated by the discovery of severe tube damage caused by in-plane fluidelastic instability (FEI) in the U-bend regions of new replacement recirculating steam generators (SG). The measurements were intended to assess the applicability of existing design guidelines for estimating the support-related damping of a tube. In the tests, the damping ratios of a single steam generator tube were measured using both log-decrement and power-based methods. Noncontacting excitation and position-sensing techniques were employed to improve accuracy. Initial baseline tests explored configurations with no support and drilled-hole supports of different hole sizes, and these results were compared with previously published work. Subsequent tests were performed to measure damping of tube vibration parallel to flat-bar supports. Most of the tests were performed with the tube fully submerged in still water. The tests examined the effects of fluid (water or air), natural frequency, gap width, preload, and vibration normal to the bars. This paper describes the test apparatus, methods, and analysis techniques. A summary of the results is presented. The initial baseline results showed that the damping ratios measured without any supports and with a drilled-hole support were consistent with previously published data. However, the subsequent measurements showed that, contrary to a published design guideline, the anti-vibration bars resulted in no significant additional viscous or squeeze-film damping when the vibration was parallel to the bars. On the other hand, the results did show that anti-vibration bars could introduce significant in-plane Coulomb-type damping if there was sufficient tube-to-support preload or impacting.

Dynamic modeling and response analysis of misaligned rotor system with squeeze film dampers under maneuver loads

Dynamic modeling and response analysis of misaligned rotor system with squeeze film dampers under maneuver loads

Bifurcation and dynamics of periodic solutions of MEMS model with squeeze film damping

In this paper, we study the oscillations of an idealized mass–spring model of micro-electro-mechanical system (MEMS) with squeeze film damping. The model consists of two parallel electrodes separated by a gap d: one of them is fixed, and another one is movable and attached to a linear spring with stiffness coefficient k>0. The oscillation, under the influence of AC–DC voltage V(t)=vdc+vaccos2πTt, is ruled by the following singular differential equation my′′+[A(d−y)3+Ad−y]y′+ky=θ0A2V2(t)(d−y)2.Here, y is the vertical displacement of the moving plate (y is always assumed to be less than d), m>0 is its mass, A>0 is the electrode area, and θ0>0 is the absolute dielectric constant of vacuum. Taking d as the parameter, we show the existence of saddle–node bifurcation of T-periodic solutions to the equation in the parameter space. This answers, from certain point of view, the open problem proposed by Torres in his monograph, see Torres (2015, Open Problem 2.1, p. 18). Further, we prove that the equation has exactly two classes of T-periodic solutions: as d tends to +∞, one of them uniformly tends to +∞ at the rate of d, while the minimum values of the second class tend to, or cross, 0.

Analytical model of curvic coupling and application in nonlinear vibration analysis of a squeeze film damper - rolling bearing - rotor system

The curvic coupling has been extensively employed in the rotor system of aero-engine. Effects of the radical slip of the teeth and damping are usually neglected in the traditional models of the curvic coupling. Additionally, there are only a few researches on the vibration characteristics of the rotor system with curvic coupling, squeeze film damper (SFD) and rolling bearing. In this paper, an analytical model of the curvic coupling is proposed. The nonlinear vibration analysis of a SFD - rolling bearing - rotor system with curvic coupling is furtherly carried out. The Jenkins element is adopted to simulate the dynamic behaviors of the curvic coupling in the model. The hysteresis curves of the analytical model show good agreement with the results of the three-dimensional (3D) finite element (FE) simulation. After that, the dynamic equation of a SFD - rolling bearing - rotor system with curvic coupling is formulated. Subsequently, detailed parametric analyses, including preload, number of teeth and pressure angle, are conducted to investigate the vibration characteristics of the rotor system. Results show that the curvic coupling mainly produces stiffness loss and damping at the interface of the curvic coupling. The motion stability of the rotor system can be enhanced by increasing the preload, number of teeth at multiple curvic couplings and pressure angle. Moreover, the vibration level of the rotor system initially decreases and then increases as the number of the teeth and pressure angle increase. Finally, the numerical results are validated to be reasonable by an experimental study.

Monolithic finite element modeling of compressible fluid‐structure‐electrostatics interactions in MEMS devices

AbstractThis work presents a monolithic finite element strategy for the accurate solution of strongly‐coupled fluid‐structure‐electrostatics interaction problems involving a compressible fluid. The complete set of equations for a compressible fluid is employed within the framework of the arbitrary Lagrangian–Eulerian (ALE) fluid formulation on the reference configuration. The proposed numerical approach incorporates geometric nonlinearities of both the structural and fluid domains, and can thus be used for investigating dynamic pull‐in phenomena and squeeze film damping in high aspect‐ratio micro‐electro‐mechanical systems (MEMS) structures immersed in a compressible fluid. Through various illustrative examples, we demonstrate the significant influence of fluid compressibility on the dynamics of MEMS devices subjected to constrained geometry and/or high‐frequency electrostatic actuation. Moreover, we compare the proposed formulation with the nonlinear compressible Reynolds equation and highlight that, particularly at low pressures and high fluid viscosity, the Reynolds equation fails to provide a reliable approximation to the complete set of equations utilized in our proposed formulation.

Experimental Study on Vibration and Noise Reduction of Gear Transmission System Based on ISFD

Gear transmission systems are widely used in ship propulsion systems, but, during operations, they produce serious vibration and noise problems, reducing the fatigue life of gears and affecting the performance of ships and the comfort of operators. Taking into account the complex frequencies and vibration components of gear transmission systems, this study conducted wide-band vibration suppression and noise reduction research on a gear transmission system using an integral squeeze film damper (ISFD), providing a novel approach for reducing vibration and noise in gear transmission systems. By conducting a simulation analysis and numerical calculations, the ISFD was analyzed via a static analysis and a dynamic analysis. We developed an experimental platform for reducing vibration and noise in gear transmission systems using sliding bearings, and the experiments were conducted under different speed and load conditions to study the vibration suppression and noise reduction of gears based on the ISFD. The experimental results show that the ISFD has good vibration suppression capabilities for gears at different speeds, with a horizontal vibration reduction of 75.44% and a vertical vibration reduction of 68.48% at 2400 r/min. The ISFD has wide-band vibration suppression capabilities, especially for mesh frequency and twice-mesh frequency, with a vibration reduction of 86.96% or more. Moreover, the ISFD has good vibration suppression capabilities for gears at different load torques, with a reduction of more than 35% in all directions. In addition, the ISFD also has noise reduction capabilities, reducing the gears’ noise by 1.92 dB at different speeds.

Influence of Squeeze Film Damper on the Rub-Impact Response of a Dual-Rotor Model

Influence of Squeeze Film Damper on the Rub-Impact Response of a Dual-Rotor Model

Tilt effect on squeeze-film damping in electrostatic micro-actuators

In this study, we theoretically explore the impact of tilt on the switching dynamics of a MEMS device operated by a pair of electrostatic actuators and subject to pronounced squeeze-film damping in the transition and free molecular flow regimes. Our investigation reveals that inducing tilt, achieved through the application of uneven voltages on the electrodes, introduces additional source terms in the modified Reynolds equation governing the pressure distribution in the squeeze-film gap. These added terms result in an accelerated decay of the squeeze film force, facilitating faster device switching between the initial and target configurations.To analyze the device dynamics, we develop a coupled numerical model and employ evolutionary multi-objective optimization to determine an optimal actuation scheme. This optimization is carried out for scenarios where initially different voltages are applied to the electrodes during a certain pre-defined time interval before transitioning to the steady voltage corresponding to the target gap size at equilibrium. Our findings highlight that the suggested actuation strategy leads to substantial improvements in the switching time of the device. Furthermore, we provide insights into the conditions favoring tilt actuation over parallel-motion actuation where the initially applied voltages are equal.

Exploiting Nonlinearities of Electrostatic MEMS Resonators for Tunable Low Pressure Sensing

In this paper, we demonstrate the potential functionalization of inherent nonlinearities associated with electrostatic MEMS resonators for low air pressure applications, with operating ranges as low as 0.65-295 mbar. The proposed pressure sensor is made of a polysilicon microplate subject to electrostatic actuation via an underneath electrode and attached to two cantilever microbeams. The pressure sensing mechanism relies on the motion-induced current method, a transduction mechanism that converts the dynamic alteration of the microplate due to pressure variations into an electrical signal detected via a lock-in amplifier. The experimental study showed evidence of the possible tunability of the pressure sensor via the deployment of different detection mechanisms to achieve superior performance in terms of sensitivity and low pressure operating range. These mechanisms rely on nonlinear dynamic features that result from the strong coupling between the microplate and the surrounding fluid along with the electrostatic actuation. These include dynamic pull-in instability, bifurcation and softening behavior associated with the elastic effect of the squeeze-film damping. The experimental results revealed that tracking the bifurcation frequency allows for the detection of low pressure levels, in the range of a few millibars. This capability is not provided by the resonance frequency shift method, which, while offering higher sensitivity, does not achieve the same low-pressure detection.

A MEMS resonant vacuum gauge for high vacuum measurement

In this paper, a MEMS resonant vacuum gauge (MRVG) based on the squeezed film damping is proposed and its theoretical measurement model is established. The sensitive structure and electrodes of the MRVG were fabricated on SOI wafers and were wafer level packaged including intake hole. An resonance excitation and capacitive detection circuit consists of capacitive voltage converter (C/V) module, PLL and modulation and demodulation module was designed. Experimental tests were carried out in a standard vacuum calibration chamber, and the measurement results verified the theoretical model. The indication accuracy of the MRVG is less than ±20% in the vacuum range of 9×10−5 Pa ∼ 1 Pa. Moreover, the output voltage is still not saturated at the highest vacuum level (9×10−5 Pa), which lays the foundation for subsequent measurement of higher vacuum levels.

Vibration stability and bifurcation analysis of two-stage spur gear systems supported by squeeze film dampers

Vibration stability and bifurcation analysis of two-stage spur gear systems supported by squeeze film dampers

Simulation Analysis of Non-concentric Squeeze Film Damper

Squeeze film dampers are components that provide additional damping for rotating motors. In general, in order to achieve the best results of the squeeze film damper, it is necessary to appropriately increase the damping value, reduce the stiffness and set a reasonable eccentricity. In the process of designing the squeeze film damper, we can apply the rotor dynamics module of COMSOL software to model and simulate it, so as to achieve better simulation results and lay a foundation for the subsequent development and design of the product. In COMSOL software, in order to simplify the modeling of rotor components, we usually model squeeze film dampers based on the damping coefficient. The model calculates the damping coefficient for a short squeeze film damper and compares the results with the analytically calculated values. In addition, the damping coefficient depends on the position of the journal in the damper, i.e., the magnitude of the eccentricity. In this paper, by analyzing the dimensionless damping coefficient, bearing stiffness, journal displacement, and fluid load at different eccentricity, and plotting the fluid pressure distribution and the average oil film flow rate of the squeeze film damper, we can find the most suitable range of eccentricity and the damage-prone part of the damper, which can provide an important reference for the actual design of the squeeze film damper.

Numerical Simulations and Experimental Validation of Squeeze Film Dampers for Aircraft Jet Engines

Squeeze film dampers are used to reduce vibration in aircraft jet engines supported by rolling element bearings. The underlying physics of the squeeze film dampers has been studied extensively over the past 50 years. However, the research on the SFDs is still ongoing due to the complexity of modeling of several effects such as fluid inertia and the modeling of the piston rings, which are often used to seal SFDs. In this work, a special experimental setup has been designed to validate the numerical models of SFDs. This experimental setup can be used with various SFD geometries (including piston ring seals) and simulate almost all conditions that may occur in an aircraft jet engine. This work also focuses on the inertia forces of the fluid. The hydrodynamic pressure distribution of a detailed 3D-CFD model is compared with the solution of the Reynolds equation including inertia effects. Finally, the simulation results are compared with experimental data and good agreement is observed.

Influence of width of squeeze film damper on the transient response of rotor systems

Influence of width of squeeze film damper on the transient response of rotor systems

Vibration characteristics of dual-rotor system with staggered-type double elastic ring squeeze film dampers under maneuvering flight

The vibration of the rotor system is significantly intensified during maneuvering flight, rendering traditional elastic ring squeeze film dampers (ERSFDs) insufficient or unstable. To improve the applicability of dampers, a novel structure of staggered-type double elastic ring squeeze film dampers (SDERSFD) is proposed in this paper. Through the synergistic effect of double elastic rings, the damping effect is significantly enhanced, and the circumferential stiffness anisotropy of the damper is improved, which is more suitable for vibration reduction requirements under complex working conditions. Utilizing the Reynolds equation, the internal and external pressure field control equations of the double elastic rings are established. The finite difference method is then employed to solve the dynamic characteristics of the damper. Additionally, a finite element model of the dual-rotor system with SDERSFDs considering complex dynamic factors such as unbalanced force, oil film force, gravity, and additional inertial force caused by maneuvering flight is established for the study of nonlinear rotor dynamic characteristics and the analysis of SDERSFDs vibration reduction effect. Based on the model, the influence of various factors such as maneuvering speed, maneuvering radius, rotor speed and unbalance on the transient response of dive-pull up condition is analyzed. The results reveal that during dive-pull up, the vibration of the rotor system intensifies significantly. When compared with the ERSFDs, the SDERSFDs effectively reduce the vibration amplitudes of the rotor system under maneuvering flight condition, achieving the maximum vibration reduction ratio of 48.9%. Furthermore, the SDERSFD exhibits robustness against large maneuvering loads, enhancing the stability of the rotor system under extreme conditions.

Quantifying squeeze film damping in four-leaf clover-coupled micro-resonators: A comprehensive study under variable vacuum degrees

The squeeze film effect has a significant impact on the performance of micro-resonators when utilizing the electrostatic excitation and capacitive detection technique, due to the narrow air gaps present. It becomes the most critical damping effect that needs to be addressed. However, when micro-resonators are encapsulated in vacuum or rarefied air, squeeze film damping analysis can become considerably complex due to high-quality factors. In this study, we systematically investigate the squeeze film damping of a widely-used four-leaf clover-coupled micro-resonator under different vacuum degrees. The characteristic frequencies of micro-resonators are determined by applying the principle of mode superposition. Subsequently, the energy transfer theory is utilized to derive the theoretical formula for the quality factor caused by squeeze film damping, for varying levels of vacuum. Finite element analysis is then conducted to simulate the characteristic behavior and squeeze film damping of the resonator, confirming the accuracy of the proposed theory. In the experiment, a novel four-leaf silicon micro-resonator is fabricated using bulk anisotropic wet etching and other micromachining technologies. An experimental platform is established to study the squeeze film damping of the micro-resonator under various vacuum degrees, where the micro-resonator is excited electrostatically and detected capacitively. The frequency response and quality factor of the resonator under different vacuum degrees are measured using a house-made modal test circuit board. The experimental results demonstrate excellent agreement with the theoretical and simulated results, indicating that the proposed method can be a reliable and precise guide for understanding the squeeze film damping effect in advance, once the primary model of a micro-resonator has been designed.

Theoretical and Experimental Study on the Performance of Hermetic Diaphragm Squeeze Film Dampers for Gas-Lubricated Bearings

Low damping characteristics have always been a key sticking points in the development of gas bearings. The application of squeeze film dampers can significantly improve the damping performance of gas lubricated bearings. This paper proposed a novel hermetic diaphragm squeeze film damper (HDSFD) for oil-free turbomachinery supported by gas lubricated bearings. Several types of HDSFDs with symmetrical structure were proposed for good damping performance. By considering the compressibility of the damper fluid, based on hydraulic fluid mechanics theory, a dynamic model of HDSFDs under medium is proposed, which successfully reflects the frequency dependence of force coefficients. Based on the dynamic model, the effects of damper fluid viscosity, bulk modulus of damper fluid, thickness of damper fluid film and plunger thickness on the dynamic stiffness and damping of HDSFDs were analyzed. An experimental test rig was assembled and series of experimental studies on HDSFDs were conducted. The damper fluid transverse flow is added to the existing HDSFD concept, which aims to make the dynamic force coefficients independent of frequency. Although the force coefficient is still frequency dependent, the damping coefficient at high frequency excitation with damper fluid supply twice as that without damper fluid supply. The results serve as a benchmark for the calibration of analytical tools under development.

Nonlinear Dynamic Properties of Rigid–Elastic–Liquid Coupled Ball Bearings Considering External Load Excitation

In this study, a novel dynamic model of a ball bearing based on rigid–elastic–liquid (REL) coupling structure considering external load excitation is established, and the dynamic response of its outer ring under external load excitation is examined. First, the differential equation of the journal motion (i.e. the outer ring) is derived based on Newton’s law, and the oil film force induced by the REL coupling structure is determined by using the central finite difference method, planar bending theory of thin ring, and Simpson’s rule. Further, the fourth and fifth-order variable step length Runge–Kutta method is used to solve the kinematic differential equation. Second, the dynamic characteristics of the outer ring of the bearing under different speeds and elastic support structural parameters are examined. Finally, the feasibility of the theoretical model is verified through experiments. The results show that compared with the traditional squeeze film damper (SFD) system, the ball bearing with REL coupling structure is more stable, and the vibration damping effect is better under higher bearing speed, lower squirrel cage stiffness, and smaller elastic ring flexibility coefficient. The above findings provide useful insights into the dynamic characteristics of REL coupled ball bearings under unbalanced excitation, which can serve as a reference for the optimization design of such ball bearings.

Optimization design of rotor system with squeeze film damper

For the rotor system with squeeze film damper (SFD), an optimization design method based on eccentricity iteration was proposed. In this method, ANSYS is used to calculate the dynamic characteristics of the rotor, and Isight is used to solve the optimization design problem. The position of bearing, the position of disks and the support stiffness of SFD was selected as design variables. The optimization design of a double-disk flexible rotor system with SFD was performed, and a series of comparative experiments were carried out. The experimental results show that: after optimization, the amplitude response of the two disks is only 0.052 mm and 0.08 mm respectively when the rotor system passes through the critical speed, and the reaction response of the two supports is only 35 N and 34.2 N respectively. The experimental results demonstrate the effectiveness of the method. It can be used as a general method to deal with the engineering problems of optimal design of complex rotor system with SFD. The optimal design result of the rotor system is that the stiffness of the elastic support is reduced to the minimum, and the position of the two disks is close to the support on the premise that the critical speed satisfies the constraint.

Research on Load Control Of Main Bearing Based on Isfd Principle

The main bearing load of the internal combustion engine is one of the main excitation sources that cause the vibration and radiation noise of the body structure. By reducing the main bearing load transmitted from the main bearing cap to the body, the vibration and noise of the internal combustion engine can be effectively reduced. In this paper, the main bearing cap damper is designed based on the principle of integral squeeze film damper (ISFD), and the load is controlled on the transmission path of the main bearing load. The main bearing load measurement scheme is designed. The load changes of the main bearing cap before and after the installation of the main bearing cap damper are measured experimentally. The load control effect of the main bearing cap damper is analyzed and verified.