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Squeeze film dampers (SFDs) with low levels of external pressurization and poor end sealing are prone to air entrapment, thus reducing the damping capability. Furthermore, existing predictive models are too restrictive. Single frequency, unidirectional load and centered circular orbit experiments were conducted on a revamped SFD test rig. The damper journal is 1" in length and 5" in diameter, with nominal clearance of 5 mils (0.127 mm). The SFD feed end is flooded with oil, while the discharge end contains a recirculation groove and four orifice discharge ports to prevent air ingestion. The discharge end is fully sealed with a wave-spring that pushes a seal ring into contact with the SFD journal. 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 amplitude of motion dependent, albeit decreasing rapidly as the motion parameters increase. Identified force coefficients, damping and added mass, for the squeeze film damper alone agree very well with predictions based on the full film, short length SFD model.

Acoustic liners employing the Helmholtz resonator concept are commonly used in the intake duct of modern jet engines to reduce radiated noise. In response to reports of core failures, the possibility of acoustic loading as the source of these liner failures is investigated. Experimental data are used as input to a model for non-rigid cavity walls and the induced stresses analysed. An alternative, more robust, liner design utilizing viscous damping is proposed, and an analytical model developed and numerically validated against published data. A study of the key parameters leads to an improved configuration, the attenuating properties of which are compared to a typical liner.

A numerical method is used to predict flow fields and forces for squeeze film dampers (SFDs). A two dimensional SFD is modeled with different amplitudes and frequencies of the journal orbiting inside the wall. In addition to the typical circular centered orbit (CCO) motion prescribed in most studies, orbits can vary greatly from circular to linear. The study is divided into two distinctive models including single phase flow model and two phase flow model. The single phase flow model cases including three amplitudes, i.e. 0.002, 0.001, and 0.0005 inches, and three frequencies, i.e. 10, 50, and 200 Hz, of journal motions are conducted to portray flow fields and forces and ultimately determine their relationships. The numerical prediction shows that the journal amplitude and frequency affect flow and consequently force in the SFD. The force is directly proportional to frequency and motion amplitude. Owing to the presence of cavitation in the practical SFD, the two phase flow model is also presented with the journal amplitude of 0.0002 and three frequencies of 10, 50, and 100 Hz, respectively. The ambient pressure condition was set up for numerical processing ranging from 0.001 Mpa to 100 Mpa. The results indicate that the operating pressure has an integral role in suppressing the presence of the cavitation. The caviation disappears if the operating pressure is high enough above the vapor pressure of the lubricant.

Squeeze film dampers (SFDs) provide viscous damping to attenuate excessive vibrations and enhance system stability in turbomachinery. SFDs are of special importance in aircraft engines which use rolling element support bearings that, by themselves, do not provide enough damping to ensure safe operation. A modular test rig capable of simulating actual operating conditions in aircraft jet engines is used to test two centrally grooved, end sealed, SFDs. Both SFDs have diameter D and nominal radial clearance c and consist of two parallel squeeze film lands separated by a deep circumferential groove of length LG and depth dG. A short length damper with film land lengths L and a long damper with land lengths 2L are tested. Piston rings seal the damper lands. An ISO VG2 lubricant is supplied to the SFD via three radial holes that discharge lubricant into the central groove. The lubricant passes through the damper lands and across the piston ring seals to finally exit the damper at ambient pressure. Circular orbit tests of amplitude ~0.5c and for static eccentricities varying from 0 to ~0.36c are conducted on the two sealed dampers. The instrumental variable filter method (IVFM) serves to identify the SFD dynamic force coefficients. The parameter identification range is 50Hz to 210Hz for the short damper and 110Hz to 250Hz for the long damper. Large amplitude dynamic pressures measured in the central groove demonstrate that the central groove does not divide the damper in two separate film lands, but the lubricant in the groove interacts with the squeeze film lands, hence contributing significantly to the SFD forced response. Dynamic pressures in the film lands and in the central groove reveal that both dampers operate free of air ingestion or cavitation for the tested static eccentricities and amplitudes of motion. Comparisons to test results for the same SFD configurations but with open ends demonstrate the effectiveness of the end seals on increasing the direct damping coefficients. For the sealed ends short length damper, the added mass coefficients are ~2 times larger and the damping coefficients are ~3.8 times larger than the respective coefficients of the open ends long damper. For the sealed ends long damper, the damping coefficients are ~2.8 times, and the added mass coefficients are ~3.1 times larger than coefficients from the open ends configuration. The identified SFD direct stiffness coefficients are nearly zero except at the maximum static eccentricity for the long damper. Predictions from a novel computational model that include the effects of the central groove, the lubricant feed holes and the end seals are in excellent agreement with results from the short length damper. For the long damper, the predicted damping coefficients are in good agreement with the test results, while the added mass coefficients are under predicted by ~25 percent. Experimental results from the two sealed SFD configurations lead to a better understanding of the effects of end seals as well as central feed groves on the SFD forced performance. The results presented in this thesis will help improve the effectiveness of SFDs aircraft jet engines.

Fluid damping arising from squeeze film flow of air or some inert gas trapped between an oscillating micro mechanical structure, such as a beam or a plate, and a fixed substrate often dominates the other energy dissipation mechanisms in silicon based MEM devices. As a consequence, it has maximum effect on the resonant response or dynamic response of the device. Unfortunately, modelling of the squeeze film flow in most MEMS devices is quite complex because of several factors unique to MEMS structures. In this thesis, we set out to study the effect of these factors on squeeze film flow. First we list these factors and study each of them in the context of a particular application, using experimental measurements, extensive numerical simulations, and analytical modelling for all chosen factors. We consider five important factors. The most important factor perhaps is the effect of rarefaction that is dominant when a device is vacuum packed with low to moderate vacuum, typical for MEMS packaging. The second problem is to investigate and model the effect of perforations which are usually provided for efficient etching of the sacrificial layer during fabrication of the suspended structures. The third problem is to consider the effect of non-uniform deflection of the structure such as those in MEMS cantilever beams and model its effect on the squeeze film. The fourth effect studied is the influence of different boundary conditions such as simple, fully open and partially closed boundaries around the vibrating structure on the characteristics of the squeeze film flow. The fifth problem undertaken is to analyze the effect of high operating frequencies on the squeeze film damping. In the first problem, the rarefaction effect is studied by performing experiments under varying pressures. Depending on the ambient pressure or the size of the gap between the vibrating and the fixed structure, the fluid flow may fall in any of the flow regimes, ranging from continuum flow to molecular flow, and giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number, which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. Here, we study the effect of fluid pressure on the squeeze film damping by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 torr to 0.001 torr. The variation of this pressure over six orders of magnitude ensures the required rarefaction to range over all flow conditions. Finally, we get the variation of the quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q P-r, with different values of the exponent r in different flow regimes. To numerically model the effect of rarefaction, we propose the use of effective viscosity in Navier-Stokes equation. This concept is validated with analytical results for a simple case. It is then compared with the experimental results presented in this thesis. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h0/L < 0.01). However, as this ratio increases, the range of validity decreases. Next, a semianalytical approach is presented to model the rarefaction effect in double-gimballed MEMS torsion mirror. In this device, the air gap thickness is 80 µm which is comparable to the lateral dimension 400 µm of the oscillating plate and thus giving the air-gap to length ratio of 0.2. As the ratio 0.2 is much greater than 0.01, the conventional Reynolds equation cannot be used to compute the squeeze film damping. Consequently, we find the effective length of an equivalent simple mirror corresponding to the motion about the two axes of the mirror such that the Reynolds equation still holds. After finding the effective length, we model the rarefaction effect by incorporating effective viscosity which is based on different models including the one proposed in this paper. Then we compare the analytical solution with the experimental result and find that the proposed model not only captures the rarefaction effect in the slip, transition and molecular regimes but also couples well with the non-fluid damping in the intrinsic regime. For the second problem, several analytical models exist for evaluating squeeze film damping in rigid rectangular perforated MEMS structures. These models vary in their treatment of losses through perforations and squeezed film, in their assumptions of compressibility, rarefaction and inertia, and their treatment of various second order corrections. We present a model that improves upon previously reported models by incorporating more accurate losses through holes proposed by Veijola and treating boundary cells and interior cells differently as proposed by Mohite et al. The proposed model is governed by a modified Reynolds equation that includes compressibility and rarefaction effect. This equation is linearized and transformed to the standard two-dimensional diffusion equation using a simple mapping function. The analytical solution is then obtained using Green’s function. The solution thus obtained adds an additional term Γ to the damping and spring force expressions derived by Blech for compressible squeeze flow through non-perforated plates. This additional term contains several parameters related to perforations and rarefaction. Setting Γ = 0, one recovers Blech’s formulas. We benchmark all the models against experimental results obtained for a typical perforated MEMS structure with geometric parameters (e.g., perforation geometry, air gap, plate thickness) that fall well within the acceptable range of parameters for these models (with the sole exception of Blech’s model that does not include perforations but is included for historical reasons). We compare the results and discuss the sources of errors. We show that the proposed model gives the best result by predicting the damping constant within 10% of the experimental value. The approximate limit of maximum frequencies under which the formulas give reasonable results is also discussed. In the third problem, we study the effect of elastic modeshape during vibration on the squeeze film flow. We present an analytical model that gives the values of squeeze film damping and spring coefficients for MEMS cantilever resonators taking into account the effect of flexural modes of the resonator. We use the exact modeshapes of a 2D cantilever plate to solve for pressure in the squeeze film and then derive the equivalent damping and spring coefficient relations from the back force calculations. The relations thus obtained can be used for any flexural mode of vibration of the resonators. We validate the analytical formulas by comparing the results with numerical simulations carried out using coupled finite element analysis in ANSYS, as well as experimentally measured values from MEMS cantilever resonators of various sizes and vibrating in different modes. The analytically predicted values of damping are, in the worst case, within less than 10% of the values obtained experimentally or numerically. We also compare the results with previously reported analytical formulas based on approximate flexural modeshapes and show that the proposed model gives much better estimates of the squeeze film damping. From the analytical model presented here, we find that the squeeze film damping drops by 84% from the first mode to the second mode in a cantilever resonator, thus improving the quality factor by a factor of six to seven. This result has significant implications in using cantilever resonators for mass detection where a significant increase in quality factor is obtained only by using vacuum. In the fourth and fifth problem, the effects of partially blocked boundary condition and high operating frequencies on squeeze films are studied in a MEMS torsion mirror with different boundary conditions. For the structures with narrow air-gap, Reynolds equation is used for calculating squeeze film damping, generally with zero pressure boundary conditions on the side walls. This procedure, however, fails to give satisfactory results for structures under two important conditions: (a) for an air-gap thickness comparable to the lateral dimensions of the micro structure, and (b) for non-trivial pressure boundary conditions such as fully open boundaries on an extended substrate or partially blocked boundaries that provide side clearance to the fluid flow. Several formulas exist to account for simple boundary conditions. In practice, however, there are many micromechanical structures, such as torsional MEMS structures, that have non-trivial boundary conditions arising from partially blocked boundaries. The most common example is the double-gimballed MEMS torsion mirror of rectangular, circular, or hexagonal shape. Such boundaries usually have clearance parameters that can vary due to fabrication. These parameters, however, can also be used as design parameters if we understand their role on the dynamics of the structure. We take a MEMS torsion mirror as an example device that has large air-gap and partially blocked boundaries due to static frames. Next we model the same structure in ANSYS and carry out CFD (computational fluid dynamics) analysis to evaluate the stiffness constant K, the damping constant C, as well as the quality factor Q due to the squeeze film. We compare the computational results with experimental results and show that without taking care of the partially blocked boundaries properly in the computational model, we get unacceptably large errors. Subsequently, we use the CFD calculations to study the effect of two important boundary parameters, the side clearance c, and the flow length s, that specify the partial blocking. We show the sensitivity of K and C on these boundary design parameters. The results clearly show that the effect of these parameters on K and C is substantial, especially when the frequency of excitation becomes close to resonant frequency of the oscillating fluid and high enough for inertial and compressibility effects to be significant. Later, we present a compact model to capture the effect of side boundaries on the squeeze film damping in a simple rectangular torsional structure with two sides open and two sides closed. The analytical model matches well with the numerical results. However, the proposed analytical model is limited to low operating frequencies such that the inertial effect is negligible. The emphasis of this work has been towards developing a comprehensive understanding of different significant factors on the squeeze film damping in MEMS devices. We have proposed various ways of modelling these effects, both numerically as well as analytically, and shown the efficacy of these models by comparing their predictive results with experimental results. In particular, we think that the proposed analytical models can help MEMS device designers by providing quick estimates of damping while incorporating complex effects in the squeeze film flow. The contents of the thesis may also be of interest to researchers working in the area of microfluidics and nanofluidics.

No description available.

The aim of this work was to use experimental, analytical and computational Computational Fluid Dynamic - CFD methodologies to investigate so-called highly transient axi-symmetric squeeze flows. These flows occur between two co-axial and parallel discs which are subjected to an impact, arising from a falling mass, which induces a constant energy squeezing system, as distinct from the traditionally investigated constant force or constant velocity squeezing systems. Experiments were conducted using a test cell comprising two parallel discs of diameter 120 mm with a flexible bladder used to contain fluid. This test cell was bolted onto the base of a drop-weight tester used to induce constant energy squeeze flows. Glycerine was used as the working fluid, the temperature of which was appropriately monitored. Disc separation, together with pressures at three radial positions, were measured throughout the experimental stroke typically less than 10 ms duration. Two additional pressure transducers at the same radial position as the outermost transducer were also used to monitor and subsequently correct for minor non-axi-symmetries that arose in the system. Approximately 150 tests were conducted, embracing combinations of drop height from 0.1 to 1 m, drop mass from 10 to 55 kg and initial disc separation from 3 to 10 mm. Three elementary features were typically observed: a distinct preliminary pressure spike 1 immediately after impact corresponding to very large accelerations exceeding over 6 km/s2 in some experiments, a secondary major pressure spike 2 towards the termination of the stroke corresponding to diminishing disc separations and a bridging region 3 joining the two spikes corresponding to somewhat reduced pressures. While pressure distributions were observed to be closely parabolic during the major pressure spike, some uncertainty was present during the preliminary pressure spike, ascribed to sensitivities to deviations from axi-symmetry, and the likelihood of inertially generated pressures at the edge of the disc. The former feature appears not to have been reported on in the formal literature. iii Four analytical models were considered, invoking the parallel flow assumption in conjunction with the Navier Stokes equations: an inviscid/inertial model, a viscous model the lubrication approximation, a quasi-steady linear QSL model and a quasi-steady corrected linear QSCL model. The first two of these models, on incorporation of measured disc separations, and the derived velocities and accelerations, achieved acceptable correlations with pressure measurements largely within uncertainty bounds during the initial impact and towards the end of the stroke, respectively. The QSL model agreed satisfactorily with measurements throughout the entire duration of the experiment, while the QSCL model, by incorporating non-linear effects in an approximate linear way, yielded somewhat better correlations. By invoking the parallel flow assumption, all four models predict a parabolic radial pressure distribution. Utilizing a hypothetical case in which variations of disc separation, velocity and acceleration were considered employing similar magnitudes and timescales to those that were measured, outputs of the QSL model yielded results that correlated closely with CFD predictions, while the QSCL data were somewhat better. On the basis of the CFD data it was also inferred that, within practical uncertainty bounds, the parallel flow assumption was valid for the range of disc separation to radius ratios embraced in the current investigation.

This paper is going to emphasize on the air squeeze film damping effect on micro-mechanical resonant beam in MEMS. In general, the low energy density of electrode force will cause high-voltage power supply to drive the electro- micro resonators; reducing the distance between the electrode and resonant beam can be the most efficient way to solve this problem. But bringing different exciting frequency of system and environmental pressure to the air squeeze film effect might cause it changes form similarly to the damping qualities, and this will also change the dynamic characteristics of micro resonator. The dynamic model for double clamped micro-mechanical resonant beam is proposed by using Lagrange¡¦s equation in this study. The corresponding eigenvalue problems of resonant beam are formulated and solved by employing the hypothetical mode method. Under the presumption of viscous damping model, we may obtain a damping factor which includes the parameters of size, temperature and air pressure when energy transfer model is employed to simulate the squeeze film damping effect of two immediate objects. Eventually, the damping ratio and the dynamic characteristics of resonant microbeam are derived by means of exploring the frequency response function of system. Besides, the frequency change of micro-mechanical resonant beam due to an axial force is also considered in the thesis.

Taiwan PC OEM industry has developed almost 20 years. In these years, Taiwan PC OEM industry made large output volume and had a huge market share during these 20 years but the profit kept falling oppositely. Facing this repeating situation, the research use system thinking approach to construct the system structure which focus on the relationships between OEM firms and brand firms in notebook industry in order to find out the reason why OEM firms' profits squeeze continuously. First of all, this research analyze the interaction between key factors in the systems then depict structure of the issue. Furthermore, according to the system structure of the notebook industry, the research described how the main schemas changed time by time, and analyze the different forces that squeeze OEM firms¡¦ profits. Finally, the research provided some opinions on improving this profits squeezed situation.