Squeeze Film Air Research Articles

Effects of air damping on quality factors of different probes in tapping mode atomic force microscopy

Abstract The AFM probe in tapping mode is a continuous process of energy dissipation, from moving away from to intermittent contact with the sample surfaces. At present, studies regarding the energy dissipation mechanism of this continuous process have only been reported sporadically, and there are no systematic explanations or experimental verifications of the energy dissipation mechanism in each stage of the continuous process. The quality factors can be used to characterize the energy dissipation in TM-AFM systems. In this study, the vibration model of the microcantilever beam was established, coupling the vibration and damping effects of the microcantilever beam. The quality factor of the vibrating microcantilever beam under damping was derived, and the air viscous damping when the probe is away from the sample and the air squeeze film damping when the probe is close to the sample were calculated. In addition, the mechanism of the damping effects of different shapes of probes at different tip–sample distances was analyzed. The accuracy of the theoretical simplified model was verified using both experimental and simulation methods. A clearer understanding of the kinetic characteristics and damping mechanism of the TM-AFM was achieved by examining the air damping dissipation mechanism of AFM probes in the tapping mode, which was very important for improving both the quality factor and the imaging quality of the TM-AFM system. This study’s research findings also provided theoretical references and experimental methods for the future study of the energy dissipation mechanism of micro-nano-electromechanical systems.

High-Speed Near-Surface Tracking for Fast Atomic Force Microscope Scan Switching Based on the Squeeze Film Damping Effect

Atomic force microscope (AFM) is a crucial metrology tool in the semiconductor industry. However, the bottleneck of the AFM technique is its low efficiency, primarily owing to the time-consuming scanning point switching. The traditional method takes approximately one minute for a single switching. To shield the probe and sample, the switching should first lift the probe a considerable distance, move it to the next point, and finally engage the probe slowly to the sample surface. We propose a near-surface tracking method for use in fast scanning point switching. The probe-sample distance was sensed by the squeeze air film damping effect, and the probe was kept at a small constant height during the switching via feedback control. The method can decrease the lift and engage distance from approximately 1 mm to 5 μm, which was two order of reduction; thereby shortening the single switching time from 45 s to 6.1 s, which is an 87% reduction. Generally, the fast switching method can improve the measurement efficiency of the existing AFM working in the air, but it can not be used in liquid and vacuum. Furthermore, the proposed squeeze film damping effect based distance sensing method can be applied in various fields, such as vibration sensing and temperature drift measurement.

Experimental Verification of the CFD Model of the Squeeze Film Lifting Effect

The presented study shows the results of the research into the squeeze film levitation phenomena. The system introduced in the investigation is composed of a vibrating surface, air squeeze film, and the surface of the body freely suspended over the film. The use of the CFD (Computational Fluid Dynamics) model used in the system allows us to determine the steady state, periodic behavior of the air film (described by Navier–Stokes, continuity equations, and ideal gas law), and the lifted object dynamics. The model allows us to determine multiple factors, among others, mean film thickness and pressure distribution inside the fluid film. The influence of factors, such as vibration amplitude, frequency, and load on the lifting conditions, was presented. A series of calculations show the levitations height in the range of 5.61 up to 58.12 microns, obtained for masses of samples between 5–20 g, vibration frequency of 5–25 kHz, and the motions amplitude of 0.5–1.5 µm. A series of CFD multivariable calculations for a standing wave inducer were not previously published. The CFD model was validated with the use of experiments on a specially developed test rig. The authors experimentally obtained the height of levitation up to 200 microns.

Research on load characteristics of squeeze-film air bearings based on fluid–solid coupling

In order to obtain the loading capacity and its variation of the squeeze-film air bearing, taking an air bearing as the research object, the structure model and the equivalent disk model of the squeeze-film air bearing are established. The modal analysis of the designed structure is carried out, and the mode of the bearing structure in the ultrasonic frequency range and the working squeeze frequency of the bearing are obtained. At the same time, the influence of air film thickness on the load characteristics of squeeze-film air bearing is analyzed by the fluid–solid coupling method. The relationship between air film thickness and loading capacity, and the relationship between contact area and loading capacity are obtained, respectively, by the above method. The results show that reducing the gap between the bearing bush and the rotor, increasing the amplitude of the bearing bush, and increasing the contact area between the bearing bush and the rotor can improve the loading capacity of the squeeze-film air bearing.

Squeeze film air bearing for controlling the shaft positions based on a radial basis function neural network

This study presents a squeeze film air bearing (SFAB) with flexure pivot-tilting pads that can be used to control the shaft positions. As the vibration characteristics and coupling relationship of three pads in the bearings, which determine the position control accuracy, are highly complicated, an intelligence algorithm based on a radial basis function neural network is proposed to forecast the desired pad amplitudes for the shaft reaching target positions. The database of the intelligence algorithm established on the basis of the air lubrication theory model is verified via an experimental test. Different target shaft positions that construct various trajectories are then used as the inputs of the intelligence algorithm. The desired pad amplitudes can be directly outputted from the intelligence algorithm and reused as the initial parameters of the air lubrication theory model to recalculate the shaft positions. The recalculated and target positions are compared and found to be in excellent agreement. This finding proves that the presented SFABs can precisely control the shaft to reach the target positions or move at the intended trajectories with the assistance of an intelligence algorithm.

Recent Progress on Mechanical Optimization of MEMS Electret-Based Electrostatic Vibration Energy Harvesters

In recent years, self-powered energy harvesting technology has been widely studied, which may provide supplementary power for wireless sensing networks with low power consumptions. The energy harvester could reduce the use of conventional power supply of batteries, and even eliminate the challenge of battery replacement for large scale networks. In this review, the fundamentals and theories of energy conversion from mechanical vibration to electrical current via variable capacitor are introduced, followed by the discussion of frequency bandwidth broadening, structural parameters, such as surface potential, initial air gap, and stopper heights, as the aspects for controlling squeeze-film air damping force and the output power. Representative examples of the design optimizations of vacuum operating pressure and perforated holes on bottom electrode are presented. Also, special electret processing and built-in corona needles for enhanced space charge stability and self-recharging capability are briefed. This review can provide the research community with a better understanding of the MEMS-compatible electrostatic vibration energy harvester, and further facilitate its development for future potential applications.

Study on the Dynamic Characteristics of a SiC-Based Capacitive Micro-Accelerometer in Rarefied Air.

In this study, we investigated the viscosity, squeeze-film damping, and a SiC-based capacitive micro-accelerometer in rarefied air. A specific expression for the effective viscosity coefficient of the air was derived, and when the air pressure drops from the standard atmospheric pressure, the viscosity of the air will decrease accordingly. Decreases in the air pressure and the viscosity of the air lead to the change in the squeeze-film air damping in the micro-accelerometer, and both the viscous damping force and the elastic damping force of the air film between the moving electrode plate and the fixed electrode plate will also decrease. The damping coefficient and relative damping ratio of the micro-accelerometer in rarefied air were calculated, which was also confirmed by simulations. The changes of the damping coefficient and the relative damping ratio of the system will directly affect the dynamic characteristics of the micro-accelerometer. When the air pressure in the working environment is below the standard atmospheric pressure, the micro-accelerometer will be in an underdamping state. With the decrease in the air pressure, the working bandwidth of the micro-accelerometer will decrease significantly, and the resonant phenomenon may appear. However, the decrease in the air pressure will not have a notable impact on the response time of the micro-accelerometer. Therefore, this work provides a theoretical basis for the study of the performance characteristics of a SiC-based capacitive accelerometer in rarefied air.

Accurate mechanical-optical theoretical model of cross-axis sensitivity of an interferometric micro-optomechanical accelerometer.

An interferometric micro-optomechanical accelerometer usually has ultrahigh sensitivity and accuracy. However, cross-axis interference inevitably degrades the performance, including its detection accuracy and output signal contrast. To accurately clarify the influence of cross-axis interference, a modified mechanical-optical theoretical model is established. The rotation of the proof mass and the detected light intensity are quantitatively investigated with a load of cross-axis acceleration. A simulation and experiment are performed to verify the correctness of the theoretical model when the cross-axis acceleration is from 0 to 0.175 g. The results demonstrate that this model has a more than fivefold accuracy increase compared with conventional theoretical models when the cross-axis acceleration is from 0.06 to 0.175 g. In addition, we provide a suppression method to diminish the rotation of the proof mass based on squeeze film air damping, which significantly suppresses the contrast reduction caused by cross-axis interference.

Correlated Theory of Cross-Axis Interference of MEMS Devices Based on Parallel Plate and Squeeze Film Air Damping Induced Suppression

Owing to inevitable errors of the material and fabrication process, the cross-axis sensitivity commonly exists in a large number of MEMS devices based on parallel plate structures. Such cross-axis interference results in the non-negligible rotation of the plate that deteriorates the performance of MEMS devices. Therefore, suppressing the cross-axis sensitivity is extremely critical in the device design. This paper proposes a novel theory to identify the interplay between the cross-axis interference and squeeze film air damping, and further develops a correlated theory of the damping induced suppression. The model of tilting plate with a tiny amplitude is set up by exploiting the Reynolds equation coupled with the equations of the mass deflection, and the analytical expressions of corresponding properties are derived to elucidate the suppression mechanism and its characterization. The analytical calculation and numerical simulation analysis demonstrate that the damping induced improvement effect exists objectively and is remarkable in the condition of a large mass and a small air film thickness. The cross-axis sensitivity rendered by the tilt angle quantitatively declines 80% in terms of the air damping. The theoretical underpinning can be utilized to elaborate the ubiquitous interplay between squeeze film air damping and cross-axis interference in non-vacuum MEMS devices, which is of paramount importance for achieving high performance and stability. More importantly, it is not an exclusive method that can be combined with other methods to minimize the cross-axis interference fully.

Extending the Validity of Squeeze Film Damping Models with Lower Aspect Ratios.

Squeeze film air damping is a significant factor in the design of MEMS devices owing to its great impact on the dynamic performance of vibrating structures. However, the traditional theoretical results of squeeze film air damping are derived from the Reynolds equation, wherein there exists a deviation from the true results, especially in low aspect ratios. While expensive efforts have been undertaken to prove that this deviation is caused by the neglect of pressure change across the film, a quantitative study has remained elusive. This paper focuses on the investigation of the finite size effect of squeeze film air damping and conducts numerical research using a set of simulations. A modified expression is extended to lower aspect ratio conditions from the original model of squeeze film air damping. The new quick-calculating formulas based on the simulation results reproduce the squeeze film air damping with a finite size effect accurately with a maximum error of less than 1% in the model without a border effect and 10.185% in the compact model with a border effect. The high consistency between the new formulas and simulation results shows that the finite size effect was adequately considered, which offers a previously unattainable precise damping design guide for MEMS devices.

Effect of air squeeze film damping in multi-mode atomic force microscopy

Effect of air squeeze film damping in multi-mode atomic force microscopy

A TRT-LBM model of squeeze film air damping of micro-beam in the transition regime

A TRT-LBM model of squeeze film air damping of micro-beam in the transition regime

Theoretical analysis on the static and dynamic performances of a squeeze film air journal bearing with three separate pads structure

Owing to their distinct non-contact and oil-free characteristics, squeeze film air bearings have been introduced to satisfy ultra-precision, low wear, and ultra-clean requirements. This paper proposes an analytical model of a three-pad squeeze film bearing to study its static and dynamic performance. The bearing force is calculated by integrating the pressure distribution over the bearing surface, which is governed by the Reynolds equation. The stable equilibrium position of the rotor is obtained by the Newton-Raphson method. A numerical method to acquire the bearing dynamic coefficients is originally proposed by considering the vibration of its pad. These dynamic coefficients are determined by solving the perturbation equations derived from the combination of the Reynolds equation and the modified film thickness and pressure. The predicted static and dynamic results show good agreement with experimental results. The parameter study shows that the variation in eccentricity with respect to the rotational speed can be controlled by reasonably adjusting the vibration amplitude or the nominal clearance of the bearing. In addition, the results indicate that the direct stiffness and damping coefficients are increased by decreasing the rotation speed or increasing the vibration amplitude of the bearing pad.

Optimization of MEMS Vibration Energy Harvester With Perforated Electrode

In this paper, electret based vibration energy harvesters are designed and fabricated with perforated electrode based on MEMS technology. Through-holes are distributed onthe fixed electrode in the device to optimize the energy harvesting process. The effect of the holes on the output power of the device are analyzed and discussed both in the finite element method (FEM) simulation and the experiments. It can be noticed that the through-holes can effectively lower the squeeze-film air damping force on the moveable proof mass at the atmosphere. Therefore, the energy loss due to the air damping could be reduced, and the output power of the device increases. Theeffects of the hole diameter and numbers on the output power of our device are also investigated in detail. By optimizing the configuration of the holes, the perforated device with the hole diameter of 400μm and depth of 100μm exhibits the highest power output at the low acceleration of 1.84 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ,which proves promising application for self-powered electronics in the future.

Intermodal Brillouin scattering in solid-core photonic crystal fibers

We investigate intermodal forward Brillouin scattering in a solid-core photonic crystal fiber (PCF), demonstrating efficient power conversion between the HE11 and HE21 modes, with a maximum gain coefficient of 21.4 W−1 km−1. By exploring mechanical modes of different symmetries, we observe both polarization-dependent and polarization-independent intermodal Brillouin interaction. Finally, we discuss the role of squeeze film air damping and leakage mechanisms, ultimately critical to the engineering of PCF structures with enhanced interaction between high-order optical modes through flexural mechanical modes.

Models for analyzing squeeze film air damping depending on oscillation modes of micro/nano beam resonators

Models for analyzing squeeze film air damping depending on the oscillation mode of cantilever and double-clamped micro/nanobeam resonators are presented. The models are obtained from the damping theory of a rigid rectangular plate moving parallelly to a nearby object in viscous and molecular flow regime and electrostatic theory. The analysis results based on the models show that the influence of oscillation mode on squeeze film air damping in viscous regime is remarkably large compared to that in molecular flow regime. The damping in the first-order mode is larger than that in the high-order modes, while there is little deference in damping among the high-order modes. The damping of oscillation modes depends strongly on the oscillation amplitude and electrostatic spring softening. The obtained damping analysis models are useful for the optimal design of micro/nanobeam resonators and verifying the discrepancy between the theoretically calculated results and experiment data.

Simulation study on squeeze film air damping

Simulation study on squeeze film air damping

Analytical investigation of air squeeze film damping for bi‐axial micro‐scanner using eigenfunction expansion method

Squeeze film damping is an important factor in the dynamic stability of the bi‐axial microelectromechanic systems. The purpose of this article is to provide an analytical solution for calculating the air squeeze film damping in bi‐axial torsional micro‐mirrors, considering the changes of pressure distribution in rotation around different axes. This is the first time that has been done for a circular micro‐mirror. One of the advantages of bi‐axis micro‐scanners compared to single‐axis types is the larger space covered by the scan in different axes. To calculate the pressure distribution in different rotation of micro‐mirror and also to achieve the squeeze film damping torque, Reynolds nonlinear equations have been used in polar coordinates, which have been solved by Taylor series expansion and also by eigenfunction expansion method. The results are verified with previous research in single‐axis mode. The results also show that with increasing gap between the micro‐mirror and the scanner substrate, the coefficient squeeze film damping will be less, but if the air gap is not changed, increasing the micro‐mirror radius will increase the damping coefficient. When the radius of micro‐mirror decrease, in order for the damping coefficient to be higher, the angle of rotation of the micro‐mirror must be greater too. The results of this article can be used for accurate modeling of squeeze film damping in micro‐scanners, control of dual‐axis torsion micro‐mirrors, and improvement of their efficiency.

Running Performance of a Squeeze Film Air Bearing with Flexure Pivot Tilting Pad

A novel flexure pivot tilting pad squeeze film air bearing (FPTP-SFAB) based on near-field acoustic levitation (NFAL) for a rotor is proposed in this article. The most important advantage of this structure is the suitability of the bearing for high-speed and light load conditions because the FPTP can adapt well to squeeze action during operation. The rotating orbit of the rotor can be adjusted according to the machining conditions. A theoretical model is employed to analyze the running characteristics of the rotor by using the coupled NFAL and FPTP model. Experiments were conducted to investigate the running performance of the rotor–bearing system. Moreover, the effects of input voltage, rotational speed, eccentricity ratio, radial clearance, vibration amplitude, and installation method on bearing performance were analyzed. Numerical and experimental results show that a rotor supported by the FPTP-SFAB with a reasonable input excitation magnitude can effectively adjust the rotating orbit of the rotor and inhibit the divergence of the rotor vibration amplitude, thus improving the stability of the rotor–bearing system under complicated and alternating machining conditions.

Electrical equivalent modeling of MEMS differential capacitive accelerometer

The paper presents an electrical equivalent model of Micro-Electro-Mechanical Systems (MEMS) differential capacitive accelerometer. The accelerometer structure is symmetrically suspended using folded beam springs. An electrical equivalent circuit is proposed for the mechanical structure using Force-Current analogy. Electrical circuit model of squeeze air film damping is also taken into account. The simulation results of temperature and pressure variations on the accelerometer for both mechanical and electrical domains are analyzed and compared using MATLAB®, and the results for both the domains are found to be closely matching. The results are compared with the analytical mechanical model of MEMS differential capacitive accelerometer recently reported by Mukhiya et al. (2019) [23]; and are found to be closely matching. The optimum pressure range for operation is found to be 200 ​Pa–300 ​Pa. Settling time is found to be less than 10 ​ms, which also verifies a bandwidth of 100 ​Hz. The proposed model has reasonably good accuracy and requires less computational time in comparison to FEM-based numerical models.