Dynamic Stability Prediction of Spherical Spiral Groove Hybrid Gas Bearings Rotor System

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Chenhui Jia ◽  
Huanjie Pang ◽  
Wensuo Ma ◽  
Ming Qiu
Keyword(s):  
Dynamic Stiffness ◽  
Three Dimensional ◽  
Pressure Control ◽  
Spiral Groove ◽  
Gas Bearings ◽  
Hurwitz Stability ◽  
Damping Coefficients ◽  
Control Equation ◽  
Perturbation Pressure ◽  
Stiffness And Damping

Taking the hemisphere spiral groove hybrid gas bearings (HSGHGB) as the research object, the nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established with the axis instantaneous position and instantaneous displacement speed as the parameters. The perturbation pressure control equation is solved by means of the finite difference method in generalized coordinate system. The calculation program is prepared based on VC++6.0, and the transient perturbation pressure distribution of three-dimensional (3D) gas film, nonlinear gas film force, and dynamic stiffness and damping coefficients are numerically calculated. The influences of different speeds, eccentricity ratios, and gas supply pressures on the dynamic characteristic coefficients of gas film are studied. The results show that the influence of bearing's supply pressure, speed, and eccentricity on the dynamic characteristics of gas film is significant. The dynamic equations of rotor-bearing system containing the gas film dynamic stiffness and the damping coefficients are established, and the stability of the gas film is predicted based on the Routh–Hurwitz stability criterion. The research provides the theoretical foundation for actively controlling the bearing running stiffness and damping and stemming the instability of gas film.

Analysis of dynamic characteristics and stability prediction of gas bearings

2017 ◽  
Vol 69 (2) ◽  
pp. 123-130 ◽  
Author(s):  
Chenhui Jia ◽  
Huanji Pang ◽  
Wensuo Ma ◽  
Ming Qiu
Keyword(s):  
Dynamic Stiffness ◽  
Content Type ◽  
Gas Bearings ◽  
Hurwitz Stability ◽  
Damping Coefficients ◽  
Supply Pressure ◽  
The Stability ◽  
Control Equation ◽  
Perturbation Pressure ◽  
Stiffness And Damping

Purpose The prediction model to estimate the stability of a rotor-bearing system is established, which can predict the stability of gas bearings by applying Routh–Hurwitz stability criterion. This paper aims to provide the theoretical foundation for controlling actively the bearing running stiffness and damping and stemming the instability of a gas film. Design/methodology/approach The nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established. Perturbation control equation is derived by the partial derivative method. The finite difference method is used to discrete the perturbation control equation in generalized coordinate system, and the difference expression of perturbation pressure is derived. The relational expression which involves the relationship between the dynamic characteristic coefficients of HSGHGB systems and perturbation pressure is deduced. So, the transient perturbation pressure distribution of a three-dimensional micro gas film, nonlinear gas film force, dynamic stiffness and dynamic damping coefficients of bearings are numerically computed using VC++6.0 programs. Findings The results show that the influence of supply pressure, speed and eccentricity on the dynamic characteristics of bearings is significant. Originality/value The influence law of supply pressure, speed and eccentricity ratio on the dynamic stiffness and damping coefficients of HSGHGB systems is researched. The prediction model to estimate the stability of rotor-bearing system is established, which can predict the stability of gas bearings by applying the Routh–Hurwitz stability criterion.

Numerical Analysis of Dynamic Coefficients for Gas Film Face Seals

2002 ◽  
Vol 124 (4) ◽  
pp. 743-754 ◽  
Author(s):  
Yuchuan Liu ◽  
Xinmin Shen ◽  
Wanfu Xu
Keyword(s):  
Numerical Analysis ◽  
Degrees Of Freedom ◽  
Axial Direction ◽  
Spiral Groove ◽  
Gas Bearings ◽  
Damping Coefficients ◽  
Face Seals ◽  
Stiffness And Damping ◽  
Three Degrees Of Freedom ◽  
Perturbation Approximation

A numerical analysis of stiffness and damping coefficients for gas film face seals in three degrees of freedom is presented in this paper. By applying small perturbation approximation, the steady and perturbed Reynolds equations, taking account of both hydrodynamic and hydrostatic effects, are obtained and solved by finite element method. Several numerical samples, including externally pressurized annular thrust gas bearings and spiral groove thrust gas bearings, validate the model and numerical algorithm. The results show that the interactions between axial and angular perturbation are negligible. Hence, in the dynamic analysis of gas film face seals, the perturbation in three degrees of freedom can be simplified as two independent ones, an axial movement and an angular wobble around two orthogonal axes perpendicular to axial direction.

Calculation and Measurement of the Stiffness and Damping Coefficients for a Low Impedance Hydrodynamic Bearing

1997 ◽  
Vol 119 (1) ◽  
pp. 57-63 ◽  
Author(s):  
M. J. Goodwin ◽  
P. J. Ogrodnik ◽  
M. P. Roach ◽  
Y. Fang
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Perturbation Technique ◽  
The Novel ◽  
Oil Film ◽  
Hydrodynamic Bearing ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Novel Design

This paper describes a combined theoretical and experimental investigation of the eight oil film stiffness and damping coefficients for a novel low impedance hydrodynamic bearing. The novel design incorporates a recess in the bearing surface which is connected to a standard commercial gas bag accumulator; this arrangement reduces the oil film dynamic stiffness and leads to improved machine response and stability. A finite difference method was used to solve Reynolds equation and yield the pressure distribution in the bearing oil film. Integration of the pressure profile then enabled the fluid film forces to be evaluated. A perturbation technique was used to determine the dynamic pressure components, and hence to determine the eight oil film stiffness and damping coefficients. Experimental data was obtained from a laboratory test rig in which a test bearing, floating on a rotating shaft, was excited by a multi-frequency force signal. Measurements of the resulting relative movement between bearing and journal enabled the oil film coefficients to be measured. The results of the work show good agreement between theoretical and experimental data, and indicate that the oil film impedance of the novel design is considerably lower than that of a conventional bearing.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearings: Part 5 of 5 — Clearance Type of Bearings

2007 ◽  
Author(s):  
Ahmad W. Yacout
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Major Effect ◽  
Design Parameters ◽  
Compressibility Effect ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Fluid Compressibility

This study has theoretically analyzed the surface roughness, centripetal inertia and recess volume fluid compressibility effects on the dynamic behavior of a restrictor compensated hydrostatic thrust spherical clearance type of bearing. The stochastic Reynolds equation, with centripetal inertia effect, and the recess flow continuity equation with recess volume fluid compressibility effect have been derived to take into account the presence of roughness on the bearing surfaces. On the basis of a small perturbations method, the dynamic stiffness and damping coefficients have been evaluated. In addition to the usual bearing design parameters the results for the dynamic stiffness and damping coefficients have been calculated for various frequencies of vibrations or squeeze parameter (frequency parameter) and recess volume fluid compressibility parameter. The study shows that both of the surface roughness and the centripetal inertia have slight effects on the stiffness coefficient and remarkable effects on the damping coefficient while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics. The cross dynamic stiffness showed the bearing self-aligning property and the ability to oppose whirl movements. The orifice restrictor showed better dynamic performance than that of the capillary tube.

scholarly journals Study on dynamic characteristics of gas films of spherical spiral groove hybrid gas bearings

2019 ◽  
Vol 233 (8) ◽  
pp. 1169-1181
Author(s):  
Chenhui Jia ◽  
Haijiang Zhang ◽  
Shijun Guo ◽  
Ming Qiu ◽  
Wensuo Ma ◽  
...  
Keyword(s):  
Pressure Effect ◽  
Dynamic Pressure ◽  
Iteration Algorithm ◽  
Unstable State ◽  
Gas Bearings ◽  
Damping Coefficients ◽  
The Stability ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Gas Bearing

According to the gas film force variation law, when the bearing axis is slightly displaced from the static equilibrium position, displacement and velocity disturbance relation expressions for the gas film force increment are constructed. Moreover, combined with the bearing rotor system motion equation, calculation model equations for the gas film stiffness and damping coefficients are established. The axial and radial vibration and velocity of the gas bearings during operation are collected. The instantaneous stiffness and damping coefficients of the gas film are calculated by the rolling iteration algorithm using MATLAB. The dynamic changes in the gas film stiffness and damping under different motion states are analyzed, and the mechanism of the gas film vortex and oscillation is studied. The results demonstrate the following: (1) When the gas bearing is running in the linear steady state in cycle 1, the dynamic pressure effect is enhanced and the stability is improved by increasing the eccentricity; when the gas supply pressure is increased, the static pressure effect is enhanced and the gas film vortex is reduced, but the oscillation is strengthened. (2) With the increase in rotational speed, the gas film vortex force gradually exceeds the gas film damping force, and the stability gradually worsens, causing a fluctuation in the gas film stiffness and damping, following which singularity occurs and a half-speed vortex is formed. Meanwhile, the gas film oscillation is intensified, and the rotor enters the nonlinear stable cycle 2 state operation. (3) As the fluctuation of the film force increases, the instantaneous stiffness and damping oscillation of the film intensifies, most of the stiffness and damping coefficients exhibit distortion, and the rotor operation will enter a chaotic or unstable state. Therefore, the gas bearing stiffness and damping variation characteristics can be used to study and predict the gas bearing operating state. Finally, measures for reducing the vortex and oscillation of the gas film and improving the stability of the gas bearing operation are proposed.

Three-Dimensional Thermo-Elasto-Hydrodynamic Computational Fluid Dynamics Model of a Tilting Pad Journal Bearing—Part II: Dynamic Response

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Jongin Yang ◽  
Alan Palazzolo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Dynamic Response ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Static Response ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Part II presents a novel approach for predicting dynamic coefficients for a tilting pad journal bearing (TPJB) using computational fluid dynamics (CFD) and finite element method (FEM), including fully coupled elastic deflection, heat transfer, and fluid dynamics. Part I presented a similarly novel, high fidelity approach for TPJB static response prediction which is a prerequisite for the dynamic characteristic determination. The static response establishes the equilibrium operating point values for eccentricity, attitude angle, deflections, temperatures, pressures, etc. The stiffness and damping coefficients are obtained by perturbing the pad and journal motions about this operating point to determine changes in forces and moments. The stiffness and damping coefficients are presented in “synchronously reduced form” as required by American Petroleum Institute (API) vibration standards. Similar to Part I, an advanced three-dimensional thermal—Reynolds equation code validates the CFD code for the special case when flow Between Pad (BP) regions is ignored, and the CFD and Reynolds pad boundary conditions are made identical. The results show excellent agreement for this validation case. Similar to the static response case, the dynamic characteristics from the Reynolds model show large discrepancies compared with the CFD results, depending on the Reynolds mixing coefficient (MC). The discrepancies are a concern given the key role that stiffness and damping coefficients serve instability and response predictions in rotordynamics software. The uncertainty of the MC and its significant influence on static and dynamic response predictions emphasizes a need to utilize the CFD approach for TPJB simulation in critical machines.

Simple Method for Dynamic Interaction between Two Rigid Foundations

2011 ◽  
Vol 250-253 ◽  
pp. 2225-2228
Author(s):  
Bin Yan ◽  
Ying Hui Lv ◽  
Ping Hu
Keyword(s):  
Dynamic Stiffness ◽  
Dynamic Interaction ◽  
Foundation Soil ◽  
Simple Method ◽  
Damping Coefficients ◽  
The Past ◽  
Calculating Method ◽  
Interaction Factors ◽  
Two Parameters ◽  
Stiffness And Damping

In the past many researchers studied dynamic stiffness and damping coefficients of surface and embedded rigid foundations of arbitrary shapes in the elastic homogenous half space. Dynamic stiffness and damping coefficients were obtained by using regularly shaped foundations instead of arbitrarily shaped ones. Obviously, the calculating methods were not perfect. In addition, the two parameters mentioned above were calculated only in the case of a single foundation. But the cases of two or more foundations were not presented because the interactions between foundations were not considered in all present papers. This paper eliminates two faults named above by using the assumption of the plane strain and of dynamic foundation-soil interaction factors. The calculating method of dynamic impedances presented by the paper proved to be accurate and practical.

Technical Note: Rolling dynamic stiffness and damping characteristics of small-sized pneumatic tyres

2000 ◽  
Vol 214 (3) ◽  
pp. 243-248 ◽  
Author(s):  
V. H. Saran ◽  
V. K. Goel
Keyword(s):  
Normal Load ◽  
Dynamic Stiffness ◽  
Technical Note ◽  
Inflation Pressure ◽  
Laboratory Technique ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Stiffness And Damping

In this paper, a laboratory technique for determination of rolling dynamic stiffness and damping coefficients of small-sized, bias-ply tyres has been discussed. The effect of normal load, inflation pressure and speed on four different tyres has been reported. The results show similar trends to those reported by other investigators.

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