A Parametric Analysis of the Transient Forced Response of Noncontacting Coned-Face Gas Seals

2001 ◽  
Vol 124 (1) ◽  
pp. 151-157 ◽  
Author(s):  
Itzhak Green ◽  
Roger M. Barnsby
Keyword(s):  
Equations Of Motion ◽  
Forced Response ◽  
Coupled Analysis ◽  
Face Seal ◽  
Reference Case ◽  
Stable Mode ◽  
Pressure Drops ◽  
Stability Issue ◽  
Gas Seals ◽  
The Stability

A properly designed mechanical face seal must satisfy two requirements: (1) the seal must be stable, and (2) the seal forced response must be such that the stator tracks the misaligned rotor with the smallest clearance possible, with the smallest relative tilt, and with the largest minimum film thickness. The stability issue was investigated in a previous paper. Here a numerical solution is presented for the transient response of a noncontacting gas lubricated face seal that is subjected to stator and rotor forcing misalignments. The seal dynamic response is obtained in axial and angular modes of motion in a coupled analysis where the Reynolds equation and the equations of motion are solved simultaneously. The steady-state response is first identified for a reference case. Subsequently a parametric study is performed to gauge the influence of the various seal effects, such as speeds, inner to outer radii ratios, face coning heights, pressure drops, support stiffness and damping, and forcing misalignments. The transient responses to static stator misalignment and rotor runout are given, showing that properly designed coned face seals can operate in a stable mode with the stator tracking dynamically a misaligned rotor.

A Simultaneous Numerical Solution for the Lubrication and Dynamic Stability of Noncontacting Gas Face Seals

2000 ◽  
Vol 123 (2) ◽  
pp. 388-394 ◽  
Author(s):  
Itzhak Green ◽  
Roger M. Barnsby
Keyword(s):  
Numerical Solution ◽  
Equations Of Motion ◽  
Critical Value ◽  
Pressure Drops ◽  
Mode 2 ◽  
Face Seals ◽  
Natural Response ◽  
The Stability ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A numerical solution is presented for the dynamic analysis of gas lubricated noncontacting mechanical face seals having a single grounded flexibly mounted stator. Seal dynamics is solved in axial and angular modes of motion. Both the Reynolds equation and the equations of motion are arranged into a single state space form, allowing the fluid film lubrication and the dynamics to be solved simultaneously. The resulting set of equations is solved using a high-order multistep ordinary differential equation solver, yielding a complete simulation for the seal dynamic behavior. Examples of seal motion are given in detailed transient responses. The stability threshold is investigated to gauge the influence of seal parameters such as inertia, speed, coning, and the direction of sealed pressure drops. The results show two modes of instability: (1) When the inertia effect is larger than a critical value, the natural response of the seal grows monotonically in a half-frequency-whirl mode. (2) When the seal coning is less than some critical value in an outside pressurized seal, the minimum film thickness diminishes because of hydrostatic instability, and face contact occurs. Conversely, an inside pressurized seal is shown to be hydrostatically stable and have a superior dynamic response at any coning.

Dynamical Behavior of a Rotor Under Rotational Random Base Excitation

2007 ◽  
Author(s):  
Lucie Bachelet ◽  
Nicolas Driot ◽  
Guy Ferraris ◽  
Fabrice Poirion
Keyword(s):  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Gaussian White Noise ◽  
Forced Response ◽  
Power Spectrum Density ◽  
Largest Lyapunov Exponent ◽  
Base Excitation ◽  
Spectrum Density ◽  
The Stability ◽  
Truncated Gaussian

This paper investigates the dynamical behavior of a rotor under a random rotational base excitation, which is assumed to be a stationary and ergodic truncated Gaussian white noise. As the base motion is a rotation, the equations of motion present both internal and external random excitations. The stability of the rotor is then studied by computing the largest Lyapunov exponent with an iterative formula. Then, the power spectrum density of the stationary forced response is obtained from a Monte Carlo simulation. Finally, we perform a comparative analysis on the influence of the required number of modal shapes to describe accurately the response.

Armor-Like Passivated CsPbBr3 Quantum Dots: Boosted Stability with Hand-in-Hand Ligands and Enhanced Performance of Nuclear Battery

2021 ◽  
Author(s):  
Haibo Zeng ◽  
Dandan Yang ◽  
Zhiheng Xu ◽  
Chunhui Gong ◽  
Xiaoming Li ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Inorganic Perovskite ◽  
Surface Ligands ◽  
Perovskite Quantum Dots ◽  
Stability Issue ◽  
The Stability ◽  
Nuclear Battery ◽  
Cspbbr3 Quantum Dots

One of the main reasons for the stability issue of inorganic perovskite quantum dots (PQDs) is the fragile protection of surface ligands. Here, an armor-like passivation strategy is proposed to...

Stabilization of networked switched affine systems with event-triggered strategy

2021 ◽  
pp. 014233122110213
Author(s):  
Dandan Li ◽  
Zhiqiang Zuo ◽  
Yijing Wang
Keyword(s):  
Affine Systems ◽  
Switching Law ◽  
Event Time ◽  
Sliding Motion ◽  
State Dependent ◽  
Event Triggering ◽  
Stability Issue ◽  
The Stability ◽  
Event Based ◽  
Selection Of

Using an event-based switching law, we address the stability issue for continuous-time switched affine systems in the network environment. The state-dependent switching law in terms of the region function is firstly developed. We combine the region function with the event-triggering mechanism to construct the switching law. This can provide more candidates for the selection of the next activated subsystem at each switching instant. As a result, it is possible for us to activate the appropriate subsystem to avoid the sliding motion. The Zeno behavior for the switched affine system can be naturally ruled out by guaranteeing a positive minimum inter-event time between two consecutive executions of the event-triggering threshold. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

Hydro-Mechanical Coupled Analysis of the Stability of Surrounding Rock Mass of Underground Water-Sealed Oil Storage

2013 ◽  
Vol 405-408 ◽  
pp. 402-405 ◽  
Author(s):  
Yun Jie Zhang ◽  
Tao Xu ◽  
Qiang Xu ◽  
Lin Bu
Keyword(s):  
Rock Mass ◽  
Underground Water ◽  
Surrounding Rock ◽  
Comsol Multiphysics ◽  
Coupled Analysis ◽  
Coupling Theory ◽  
Oil Storage ◽  
Stability Of Surrounding Rock ◽  
Straight Wall ◽  
The Stability

Based on the fluid-solid coupling theory, we study the stability of surrounding rock mass around underground oil storage in Huangdao, Shandong province, analyze the stress of the surrounding rock mass around three chambers and the displacement change of several key monitoring points after excavation and evaluate the stability of surrounding rock mass using COMSOL Multiphysics software. Research results show that the stress at both sides of the straight wall of cavern increases, especially obvious stress concentration forms at the corners of the cavern, and the surrounding rock mass moves towards the cavern after excavation. The stress and displacement of the surrounding rock mass will increase accordingly after setting the water curtains, but the change does not have a substantive impact on the stability of surrounding rock mass.

scholarly journals Spectral optimization for the Stekloff–Laplacian: The stability issue

2012 ◽  
Vol 262 (11) ◽  
pp. 4675-4710 ◽  
Author(s):  
Lorenzo Brasco ◽  
Guido De Philippis ◽  
Berardo Ruffini
Keyword(s):  
Stability Issue ◽  
Spectral Optimization ◽  
The Stability

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Efficient Dynamic Computer Simulation of Simple-Closed Spatial Linkages

1990 ◽  
Author(s):  
L. T. Wang
Keyword(s):  
Computer Simulation ◽  
Computational Algorithm ◽  
Equations Of Motion ◽  
Joint Space ◽  
Kinematic Chains ◽  
Spatial Linkages ◽  
Dynamic Computer Simulation ◽  
The Stability ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Abstract A new method of formulating the generalized equations of motion for simple-closed (single loop) spatial linkages is presented in this paper. This method is based on the generalized principle of D’Alembert and the use of the transformation Jacobian matrices. The number of the differential equations of motion is minimized by performing the method of generalized coordinate partitioning in the joint space. Based on this formulation, a computational algorithm for computer simulation the dynamic motions of the linkage is developed, this algorithm is not only numerically stable but also fully exploits the efficient recursive computational schemes developed earlier for open kinematic chains. Two numerical examples are presented to demonstrate the stability and efficiency of the algorithm.

Experimental Validation of Forced Response Methods in a Multi-Stage Axial Turbine

2018 ◽  
Author(s):  
Thomas Hauptmann ◽  
Christopher E. Meinzer ◽  
Joerg R. Seume
Keyword(s):  
Experimental Data ◽  
Vibration Amplitude ◽  
Turbine Blades ◽  
Service Condition ◽  
Sensitivity Study ◽  
Forced Response ◽  
Tip Clearance ◽  
Computational Time ◽  
Reference Case ◽  
Axial Turbine

Depending on the in service condition of jet engines, turbine blades may have to be replaced, refurbished, or repaired in the course of an engine overhaul. Thus, significant changes of the turbine blade geometry can be introduced due to regeneration and overhaul processes. Such geometric variances can affect the aerodynamic and aeroelastic behavior of turbine blades. One goal in the development of the regeneration process is to estimate the aerodynamic excitation of turbine blades depending on these geometric variances caused during the regeneration. Therefore, this study presents an experimentally validated comparison of two methods for the prediction of forced response in a multistage axial turbine. Two unidirectional fluid structure interaction (FSI) methods, a time-linearized and a time-accurate with a subsequent linear harmonic analysis, are employed and the results validated against experimental data. The results show that the vibration amplitude of the time-linearized method is in good agreement with the experimental data and, also requires lower computational time than the time-accurate FSI. Based on this result, the time-linearized method is used to perform a sensitivity study of the tip clearance size of the last rotor blade row of the five stage axial turbine. The results show that an increasing tip clearances size causes an up to 1.35 higher vibration amplitude compared to the reference case, due to increased forcing and decreased damping work.

Nonlinear Analysis of a Rigid Rotor on Magnetic Bearings

1995 ◽  
Author(s):  
C. Nataraj
Keyword(s):  
Nonlinear Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Magnetic Bearings ◽  
Rigid Rotor ◽  
Stability Criteria ◽  
Safe Operation ◽  
Qualitative And Quantitative ◽  
Quantitative Results ◽  
Nonlinear Equations Of Motion

A simple model of a rigid rotor supported on magnetic bearings is considered. A proportional control architecture is assumed, the nonlinear equations of motion are derived and some essential nondimensional parameters are identified. The free and forced response of the system is analyzed using techniques of nonlinear analysis. Both qualitative and quantitative results are obtained and stability criteria are derived for safe operation of the system.

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