scholarly journals Estimated Fluid Force and Damping Characteristics of a Thin Film Damper Comparison Between Closed-Form Solutions and Numerical Analysis

2019 ◽  
Author(s):  
Jason T. Cook
Keyword(s):  
Thin Film ◽  
Closed Form ◽  
Closed Form Solution ◽  
Fluid Film ◽  
Dynamics Simulation ◽  
Radial Clearance ◽  
Fluid Viscosity ◽  
Fluid Force ◽  
Reynolds Equations ◽  
Closed Form Solutions

Abstract Analytical solutions of thin film dampers are useful for determining critical speeds and stability of rotor systems. Most thin film dampers in use are of short axial length, and closed-form solutions to the Reynolds equations exist for estimating pressure, forces, and damping for these types of dampers. This article compares the fluid film forces and damping estimated by the short film bearing model form of the Reynolds equations to the calculated forces and damping of a transient computational fluid dynamic simulation. For this comparison, the fluid was assumed to be incompressible, laminar, and isoviscous. The fluid film forces and damping are calculated from integrating the pressure distribution over the surface of the damper due to small amplitude motions about a steady state static off-center circular orbit. In this case, no cavitation is assumed, and the journal has no angular velocity, so direct stiffness cannot be calculated from the closed-form solution. Radial clearance, journal length, and journal eccentricity have a significant effect on fluid force and damping within a thin film damper. Fluid density does not affect fluid force or damping substantially, while fluid viscosity does. Both the closed-form solutions and computational fluid dynamics simulation compare well with each other and reflect these trends.

scholarly journals A Theoretical Study on an Elastic Polymer Thin Film-Based Capacitive Wind-Pressure Sensor

Polymers ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2133
Author(s):  
Xue Li ◽  
Jun-Yi Sun ◽  
Bin-Bin Shi ◽  
Zhi-Hang Zhao ◽  
Xiao-Ting He
Keyword(s):  
Thin Film ◽  
Closed Form ◽  
Pressure Sensor ◽  
Closed Form Solution ◽  
Form Solution ◽  
Wind Pressure ◽  
Polymer Thin Film ◽  
Movable Electrode ◽  
Elastic Polymer ◽  
Electrode Plate

This study is devoted to the design of an elastic polymer thin film-based capacitive wind-pressure sensor to meet the anticipated use for real-time monitoring of structural wind pressure in civil engineering. This sensor is composed of four basic units: lateral elastic deflection unit of a wind-driven circular polymer thin film, parallel plate capacitor with a movable circular electrode plate, spring-driven return unit of the movable electrode plate, and dielectric materials between electrode plates. The capacitance of the capacitor varies with the parallel move of the movable electrode plate which is first driven by the lateral elastic deflection of the wind-driven film and then is, after the wind pressure is reduced or eliminated, returned quickly by the drive springs. The closed-form solution for the contact problem between the wind-driven thin film and the spring-driven movable electrode plate is presented, and its reliability is proved by the experiment conducted. The numerical examples conducted show that it is workable that by using the numerical calibration based on the presented closed-form solution the proposed sensor is designed into a nonlinear sensor with larger pressure-monitoring range and faster response speed than the linear sensor usually based on experimental calibration.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

scholarly journals A New Closed-Form Solution of the Side Abutment Pressure Distribution of Roadway

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liang Cheng ◽  
Yidong Zhang
Keyword(s):  
Plastic Zone ◽  
Pressure Distribution ◽  
Closed Form ◽  
Abutment Pressure ◽  
Closed Form Solution ◽  
Evaluation Process ◽  
Friction Angle ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Roadway Stability

Instability of coal wall is one of the hot-button and difficult issues in the study of coal mine ground control. The shallow side coal of roadway in the coal measures is usually weak and consequently easy to bring about failure. Hence, the side abutment pressure redistributes and dramatically influences the roadway stability. Since the previous closed-form solutions of the side abutment pressure do not take into account all the necessary parameters which include the properties of the coal and the interface between coal and roof/floor, the roadway height, and the support strength, a mechanical model is established based on the equilibrium of the plastic zone, and a new closed-form solution is derived in this paper. Moreover, a numerical investigation is conducted to validate the accuracy of the closed-form solution. The numerical results of the side abutment pressure distribution are in good agreement with the closed-form solution. Afterwards, a parametric analysis of the width of the plastic zone is carried out, and the results show that the width of the plastic zone is nearly negatively linearly correlated with the friction angle and the cohesion of the coal, the interfacial cohesion, and the support strength. By contrast, it is positively linearly correlated with the roadway height and negatively exponentially correlated with the interfacial friction angle. The results obtained in the present study could be useful for the evaluation process of roadway stability.

Use of Resultants and the Bernshtein Formula in the Dimensional Synthesis of Linkage Components

1994 ◽  
Vol 116 (4) ◽  
pp. 1171-1172 ◽  
Author(s):  
Chuen-Sen Lin ◽  
Bao-Ping Jia
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Polynomial Equations ◽  
Dimensional Synthesis ◽  
Fourth Degree ◽  
Finite Precision ◽  
Closed Form Solutions ◽  
System Of Polynomial Equations ◽  
Resultant Theory

The applications of resultants and the Bernshtein formula for the dimensional synthesis of linkage components for finite precision positions are discussed. The closed-form solutions, which are derived from systems of polynomials in multiple unknowns by applying resultant theory, are in forms of polynomial equations of a single unknown. For the case of two compatibility equations, the closed form solution is a sixth degree solution polynomial. For the case of three compatibility equations, the solution is a fifty-fourth degree solution polynomial. For each case, the Bernshtein formula is applied to calculate the number of solutions of the system of polynomial equations. The calculated numbers of solutions match the degrees of the solution polynomials for both cases.

The Rheological Properties of Nanoscale Fluid

2009 ◽  
Author(s):  
JiaPeng Li ◽  
Yunfei Chen ◽  
Min Chen ◽  
Changzheng Xiang ◽  
Zan Wang
Keyword(s):  
Shear Rate ◽  
Charge Density ◽  
Surface Charge ◽  
Rheological Properties ◽  
Shear Viscosity ◽  
Surface Density ◽  
Surface Charge Density ◽  
Fluid Film ◽  
Dynamics Simulation ◽  
Fluid Viscosity

Nonequilibrium molecular dynamics simulation is used to simulate the rheological properties of the nanoscale fluid. A physical model of the “bulk – nanochannel – bulk” that resembles a fluid film confined between two solid walls was simulated. The simulation is performed at variable wall speeds, nanochannel heights and surface charge densities. Simulation results indicate that the effective densities of water decrease with the size as the channel size below 1 nm when the surface charge density is −0.30 C/m2. And it is also demonstrated that the water density increases with the surface charge density. The fluid viscosity keeps at around 1.78 cp when the thickness of the film more than 1.5 nm, the −0.30 C/m2 surface charge density and the 5×1010 S−1 shear rate, which is quite close to the bulk value. The fluid viscosity keeps at around 1.69 cp when the surface charge density is −0.15 C/m2, and 1.28 cp when the surface density is 0 C/m2. In addition, the shear rate shows strong influence on the nanoscale fluid film. Compare to the surface density −0.30 C/m2 and −0.15 C/m2, the fluid density of the 0 C/m2 has different properties when the shear rate varied from 0.1×011 S−1 to 1.0×1011 S−1. Especially, when the nanochannel height is 0.8 nm, the shear viscosity begins to increase and reach the peak when the shear rate is 0.2×1011 S−1, then the shear viscosity decreases with the shear rate increase. The shear viscosity of the height of 2.5 nm and 3.0 nm show a constant value which is quite close to the bulk value, and shear viscosity of 1.5 nm height increases and reaches plateau when the shear rate exceeds 0.2×1011 S−1.

scholarly journals Comparison of closed-form solutions to experimental magnetic force between two cylindrical magnets

2021 ◽  
pp. 141-146
Author(s):  
Sampart Cheedket ◽  
Chitnarong Sirisathitkul
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Magnetic Force ◽  
Permanent Magnets ◽  
Magnetic Levitation ◽  
Closed Form Solution ◽  
Vertical Tube ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Set Up

The force between permanent magnets implemented in many engineering devices remains an intriguing problem in basic physics. The variation of magnetic force with the distance x between a pair of magnets cannot usually be approximated as x-4 because of the dipole nature and geometry of magnets. In this work, the force between two identical cylindrical magnets is accurately described by a closed-form solution. The analytical model assumes that the magnets are uniformly magnetized along their length. The calculation, based on the magnetic field exerted by one magnet on the other along the direction of their orientation, shows a reduction in the magnetic force with the distance x and a dependence on the size parameters of magnets. To verify the equation, the experiment was set up by placing two cylindrical neodymium iron boron type magnets in a vertical tube. The repulsive force between the identical upper and lower magnets of 2.5 cm in diameter and 7.5 cm in length was measured from the weight on the top of the upper magnet. The resulting separation between the magnets was recorded as x. The forces measured at x=0.004-0.037 m differ from the values calculated using the analytic solution by -0.55 % to -13.60 %. The calculation also gives rise to a practical remnant magnetic field of 1.206 T. When x is much large than the equation of force is approximated as a simple form proportional to 1/x-4. The finding can be directly used in magnetic levitation as well as applied in calculating magnetic fields and forces in other systems incorporating permanent magnets.

scholarly journals Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1770
Author(s):  
Jun-Yi Sun ◽  
Qi Zhang ◽  
Xue Li ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Circular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Circular Ring ◽  
Form Solution ◽  
Elastic Response ◽  
Geometrically Nonlinear ◽  
Closed Form Solutions ◽  
Annular Membrane

The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

Quasi-Steady Axisymmetric Bingham-Plastic Model of Magnetorheological Flow Damper Behavior

Aerospace ◽  
2005 ◽  
Author(s):  
Jin-Hyeong Yoo ◽  
Norman M. Wereley
Keyword(s):  
Closed Form ◽  
Yield Stress ◽  
Dynamic Range ◽  
Closed Form Solution ◽  
Form Solution ◽  
Damping Capacity ◽  
Stress Profile ◽  
Mr Fluid ◽  
Bingham Plastic ◽  
Closed Form Solutions

A typical magnetorheological (MR) flow mode damper consists of a piston attached to a shaft that travels in a tightly fitting hydraulic cylinder. The piston motion makes fluid flow through an annular valve in the MR damper. An electro-magnet applies magnetic field to the MR fluid as it flows through the MR valve, and changes its yield stress. An MR fluid, modeled as a Bingham-plastic material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Although the analysis of such an annular MR valve is well understood, a closed form solution for the damping capacity of a damper using such an MR valve has proven to be elusive. Closed form solutions for the velocity and shear stress profile across the annular gap are well known. However, the location of the plug must be computed numerically. As a result, closed form solutions for the dynamic range (ratio of field on to field off damper force) cannot be derived. Instead of this conventional theoretic procedure, an approximated closed form solution for a dampers dynamic range, damping capacity and other key performance metrics is derived. And the approximated solution is used to validate a rectangular duct simplified analysis of MR valves for small gap condition. These approximated equations are derived, and the approximation error is also provided.

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