Semi-Analytical Dynamic Analysis of Spiral-Grooved Mechanical Gas Face Seals

2003 ◽  
Vol 125 (2) ◽  
pp. 403-413 ◽  
Author(s):  
Brad A. Miller ◽  
Itzhak Green
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Prony Series ◽  
Closed Form Solutions ◽  
Face Seals ◽  
Mechanical Face Seal ◽  
Natural Response ◽  
Nonlinear Numerical Simulation ◽  
The Stability

A novel semi-analytical formulation is presented for the linearized dynamic analysis of spiral-grooved mechanical gas face seals. The linearized rotordynamic properties of the gas film are numerically computed and then represented analytically by a constitutive model consisting of a cosine modified Prony series. The cosine modification enables the Prony series to characterize the gas film properties of face seals in applications with large compressibility numbers. The gas film correspondence principle is then employed to couple the constitutive model to the dynamics of the mechanical face seal. Closed-form solutions are presented for the transient natural response to initial velocity conditions, the steady-state response to rotor runout and initial stator misalignment, the transmissibility ratios, and the stability threshold. Results from the closed-form solutions are all within a few percent of the results from a full nonlinear numerical simulation.

scholarly journals Thermodynamic compatibility conditions of a new class of hysteretic materials

2021 ◽  
Author(s):  
Salvatore Sessa
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Iterative Procedure ◽  
Displacement Amplitude ◽  
Compatibility Conditions ◽  
Algebraic Functions ◽  
New Class ◽  
Thermodynamic Compatibility ◽  
Constitutive Parameters

AbstractThe thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

A New Constitutive Model in the Theory of Plasticity—Part II: Examples

1995 ◽  
Vol 117 (4) ◽  
pp. 371-377 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Closed Form ◽  
Hardening Model ◽  
Closed Form Solutions ◽  
Loading Paths ◽  
Theory Of Plasticity ◽  
Thin Walled Tube ◽  
Thin Walled

This part of the paper presents several examples to further demonstrate the hardening model proposed in the first part of the paper. Closed-form solutions are achieved for a thin-walled tube subjected to linear, rectangular, and circular loading paths, and the corresponding yield center loci and plastic strain trajectories are illustrated. The features of this model are further discussed.

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.

Nonlinear Spatial Equilibria and Stability of Cables Under Uni-axial Torque and Thrust

1994 ◽  
Vol 61 (4) ◽  
pp. 879-886 ◽  
Author(s):  
C.-L. Lu ◽  
N. C. Perkins
Keyword(s):  
Closed Form ◽  
Elliptic Integral ◽  
Broad Class ◽  
Local Equilibrium ◽  
Three Dimensional ◽  
Equilibrium States ◽  
Form Complex ◽  
Closed Form Solutions ◽  
The Stability ◽  
Low Tension

Low tension cables subject to torque may form complex three-dimensional (spatial) equilibria. The resulting nonlinear static deformations, which are dominated by cable flexure and torsion, may produce interior loops or kinks that can seriously degrade the performance of the cable. Using Kirchhoffrod assumptions, a theoretical model governing cable flexure and torsion is derived herein and used to analyze (1) globally large equilibrium states, and (2) local equilibrium stability. For the broad class of problems described by pure boundary loading, the equilibrium boundary value problem is integrable and admits closed-form elliptic integral solutions. Attention is focused on the example problem of a cable subject to uni-axial torque and thrust. Closed-form solutions are presented for the complex three-dimensional equilibrium states which, heretofore, were analyzed using purely numerical methods. Moreover, the stability of these equilibrium states is assessed and new and important stability conclusions are drawn.

Stability of biped robotic walking with frictional constraints

Robotica ◽  
2012 ◽  
Vol 31 (4) ◽  
pp. 573-588 ◽  
Author(s):  
Xuefeng Zhou ◽  
Yisheng Guan ◽  
Li Jiang ◽  
Haifei Zhu ◽  
Chuanwu Cai ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Closed Form ◽  
Contact Area ◽  
Frictional Force ◽  
Biped Robot ◽  
Biped Locomotion ◽  
Stability Criteria ◽  
Closed Form Solutions ◽  
Zero Moment ◽  
The Stability

SUMMARYTipping-over and slipping, which are related to zero moment point (ZMP) and frictional constraint respectively, are the two most common instability forms of biped robotic walking. Conventional criterion of stability is not sufficient in some cases, since it neglects frictional constraint or considers translational friction only. The goal of this paper is to fully address frictional constraints in biped walking and develop corresponding stability criteria. Frictional constraints for biped locomotion are first analyzed and then the method to obtain the closed-form solutions of the frictional force and moment for a biped robot with rectangular and circular feet is presented. The maximum frictional force and moment are calculated in the case of ZMP at the center of contact area. Experiments with a 6-degree of freedom active walking biped robot are conducted to verify the effectiveness of the stability analysis.

scholarly journals Impact-Angle and Terminal-Maneuvering-Acceleration Constrained Guidance against Maneuvering Target

Aerospace ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 22
Author(s):  
Wanqing Zhang ◽  
Wanchun Chen ◽  
Wenbin Yu
Keyword(s):  
Closed Form ◽  
Linear Time ◽  
Stability Domain ◽  
Impact Angle ◽  
Generalized Solutions ◽  
Time Varying ◽  
Closed Form Solutions ◽  
Maneuvering Target ◽  
The Stability ◽  
The Impact

A new, highly constrained guidance law is proposed against a maneuvering target while satisfying both impact angle and terminal acceleration constraints. Here, the impact angle constraint is addressed by solving an optimal guidance problem in which the target’s maneuvering acceleration is time-varying. To deal with the terminal acceleration constraint, the closed-form solutions of the new guidance are needed. Thus, a novel engagement system based on the guidance considering the target maneuvers is put forward by choosing two angles associated with the relative velocity vector and line of sight (LOS) as the state variables, and then the system is linearized using small angle assumptions, which yields a special linear time-varying (LTV) system that can be solved analytically by the spectral-decomposition-based method. For the general case where the closing speed, which is the speed of approach of the missile and target, is allowed to change with time arbitrarily, the solutions obtained are semi-analytical. In particular, when the closing speed changes linearly with time, the completely closed-form solutions are derived successfully. By analyzing the generalized solutions, the stability domain of the guidance coefficients is obtained, in which the maneuvering acceleration of the missile can converge to zero finally. Here, the key to investigating the stability domain is to find the limits of some complicated integral terms of the generalized solutions by skillfully using the squeeze theorem. The advantages of the proposed guidance are demonstrated by conducting trajectory simulations.

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