Lateral Equilibrium Position Analysis Program With Applications to Electric Submersible Pumps

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Clay S. Norrbin ◽  
Dara W. Childs
Keyword(s):  
Equilibrium Position ◽  
Static Equilibrium ◽  
Analysis Program ◽  
Eccentricity Ratio ◽  
Vertical Orientation ◽  
Maximum Curvature ◽  
First Finding ◽  
Static Eccentricity ◽  
Lateral Equilibrium ◽  
Vertical Case

The long length of subsea electric submersible pumps (ESPs) requires a large amount of annular seals. Loading caused by gravity and housing curvature changes the static equilibrium position (SEP) of the rotor in these seals. This analysis predicts the SEP due to gravity and/or well curvature loading. The analysis also displays the rotordynamics around the SEP. A static and rotordynamic analysis is presented for a previously studied ESP model. This study differs by first finding the SEP and then performing a rotordynamic analysis about the SEP. Predictions are shown in a horizontal and a vertical orientation. In these two configurations, viscosities and clearances are varied through four cases: 1X 1cP, 3X 1cP, 1X 30cP, and 3X 30cP. In a horizontal, straight-housing position, the model includes gravity and buoyancy on the shaft. At 1cP-1X and 1cP-3X, the horizontal statics, show a moderate eccentricity ratio for the shaft with respect to the housing. With 30cP-1X, the predicted static eccentricity ratio is low at 0.08. With 30cP-3X, the predicted eccentricity ratio increases to 0.33. Predictions for a vertical case of the same model are also presented. The curvature of the housing is varied in the Y–Z plane until rub or close-to-wall rub is expected. The curvature needed for a rub with a 1X 1cP fluid is 7.5 deg of curvature. Curvature has little impact on stability. With both 1X 30cP and 3X 30cP, the maximum curvature for a static rub is over 25 deg of curvature. Both 1X 30cP and 3X 30cP remain unstable with increasing curvature.

Lateral Equilibrium Position Analysis Program With Applications to Electric Submersible Pumps

2017 ◽  
Author(s):  
Clay S. Norrbin ◽  
Dara W. Childs
Keyword(s):  
Equilibrium Position ◽  
Static Equilibrium ◽  
Analysis Program ◽  
Eccentricity Ratio ◽  
Vertical Orientation ◽  
Maximum Curvature ◽  
First Finding ◽  
Static Eccentricity ◽  
Lateral Equilibrium ◽  
Vertical Case

The long length of sub-sea Electric Submersible Pumps (ESPs) requires a large amount of annular seals. Loading caused by gravity and housing curvature changes the Static Equilibrium Position (SEP) of the rotor in these seals. This analysis predicts the SEP due to gravity and/or well curvature loading. The analysis also interfaces displays the rotordynamics around the SEP. A static and rotordynamic analysis is presented for a previously studied ESP model. This study differs by first finding the SEP and then performing a rotordynamic analysis about the SEP. Predictions are shown in a horizontal and a vertical orientation. In these two configurations, viscosities and clearances are varied through 4 cases: 1X 1cP, 3X 1cP, 1X 30cP, and 3X 30cP. In a horizontal, straight-housing position, the model includes gravity and buoyancy on the shaft. At 1cP-1X and 1cP-3X, the horizontal statics show a moderate eccentricity ratio for the shaft with respect to the housing. With 30cP-1X, the predicted static eccentricity ratio is low at 0.08. With 30cP-3X, the predicted eccentricity ratio increases to 0.33. Predictions for a vertical case of the same model are also presented. The curvature of the housing is varied in the Y-Z plane until rub or close-to-wall rub is expected. The curvature needed for a rub with a 1X 1cP fluid is 7.5 degrees of curvature. Curvature has little impact on stability. With both 1X 30cP and 3X 30cP, the maximum curvature for a static rub are over 25 degrees of curvature. Both 1X 30cP and 3X 30cP remain unstable with increasing curvature.

A new dynamic mesh algorithm for studying the 3D transient flow field of tilting pad journal bearings

2016 ◽  
Vol 230 (12) ◽  
pp. 1470-1482 ◽  
Author(s):  
Mengxuan Li ◽  
Chaohua Gu ◽  
Xiaohong Pan ◽  
Shuiying Zheng ◽  
Qiang Li
Keyword(s):  
Flow Field ◽  
Equilibrium Position ◽  
Transient Flow ◽  
Journal Bearings ◽  
Dynamic Mesh ◽  
Static Equilibrium ◽  
Time Step ◽  
Tilting Pad ◽  
Grid Nodes ◽  
Tilting Pad Journal Bearings

A new dynamic mesh algorithm is developed in this paper to realize the three-dimensional (3D) computational fluid dynamics (CFD) method for studying the small clearance transient flow field of tilting pad journal bearings (TPJBs). It is based on a structured grid, ensuring that the total number and the topology relationship of the grid nodes remain unchanged during the dynamic mesh updating process. The displacements of the grid nodes can be precisely recalculated at every time step. The updated mesh maintains high quality and is suitable for transient calculation of large journal displacement in FLUENT. The calculation results, such as the static equilibrium position and the dynamic characteristic coefficients, are consistent with the two-dimensional (2D) solution of the Reynolds equation. Furthermore, in the process of transient analysis, under conditions in which the journal is away from the static equilibrium position, evident differences appear between linearized and transient oil film forces, indicating that the nonlinear transient calculation is more suitable for studying the rotor-bearing system.

Modal and Stability Analysis of a Micro-Beam Structure Actuated by Electrostatic Force

2006 ◽  
Vol 505-507 ◽  
pp. 403-408 ◽  
Author(s):  
Hong Hee Yoo ◽  
Kang Sik Jung ◽  
Seung Jae Moon
Keyword(s):  
Stability Analysis ◽  
Equilibrium Position ◽  
Equilibrium Equation ◽  
Electrostatic Force ◽  
Static Equilibrium ◽  
Static Deflection ◽  
Beam Structure ◽  
Design Specification ◽  
Nonlinear Equilibrium ◽  
The Stability

For the design of a vibrating micro-beam structure, modal and stability analyses of the structure actuated by electrostatic force is performed in the present study. Static deflection of the micro-beam caused by the electrostatic force is first obtained by solving the nonlinear equilibrium equation and the modal and stability characteristics are calculated at the static equilibrium position. It is found that the amplitude and the frequency of the applied electrostatic voltage influence the stability of the structure significantly. A design specification of a vibrating micro-beam structure can be effectively determined from the modal and the stability analysis results.

Reliability Analysis of the Suspension Device in the Refit of a Tracked Vehicle

2014 ◽  
Vol 945-949 ◽  
pp. 1129-1134 ◽  
Author(s):  
Wei Sun ◽  
Bing Ma ◽  
Jin Ma ◽  
Yao Zhao
Keyword(s):  
Fatigue Life ◽  
Fatigue Strength ◽  
Stress State ◽  
Reliability Analysis ◽  
Equilibrium Position ◽  
Performance Testing ◽  
Static Equilibrium ◽  
Tracked Vehicles ◽  
And Performance ◽  
Torsion Bar

To improve the flexibility performance of tracked vehicles, lots of jobs has been done in the refit of driveline. Therefore, tough risks are transferred to the strength and fatigue life of suspension device. Through analyzing the effect of driveline refit to the performance of suspension device, a scheme that enhancing the stiffness of the torsion bar is proposed. By using the MSC.Patran/Nastran software, the model of suspension device is constructed, via the simulation of the stress state and fatigue strength that is loaded on the main suspension parts at the static equilibrium position and the maximum stroke position of equilibrium elbow, and performance testing on actual roads, this scheme is considered to be reliable.

Analytical Method for Determining the Static Equilibrium Position of the Rear Axles Guiding Mechanisms of the Motor Vehicles

2016 ◽  
Vol 841 ◽  
pp. 59-64 ◽  
Author(s):  
Cătălin Alexandru
Keyword(s):  
Equilibrium Position ◽  
Original Method ◽  
Static Equilibrium ◽  
Motor Vehicles ◽  
Car Body ◽  
Mathematical Algorithm ◽  
Positional Analysis ◽  
Reaction Forces ◽  
External Forces ◽  
Elastic Elements

The work deals with an analytical algorithm for determining the static equilibrium position of the multi-link guiding mechanisms used for the rear axles of the motor vehicles. The method is based on the virtual mechanical work principle, considering the external forces applied to the wheels, as well the reaction forces in the elastic elements of the suspension. The equilibrium position of the guiding mechanism is established relative to the car body, considering the static model of the suspension system, in which the car body is fixed connected to ground (in other words, the car body is the reference part of the system). For determining the reaction forces in the elastic elements of the suspension (springs, bumpers and rebound elements, bushings, anti-roll bar), an original method for the positional analysis of the axle guiding mechanisms was developed and integrated in the mathematical algorithm for establishing the equilibrium position.

scholarly journals A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position

2017 ◽  
Vol 4 (5) ◽  
pp. 161059 ◽  
Author(s):  
Wenjie Zhou ◽  
Xuesong Wei ◽  
Leqin Wang ◽  
Guangkuan Wu
Keyword(s):  
Finite Length ◽  
Carrying Capacity ◽  
Equilibrium Position ◽  
Journal Bearing ◽  
Secant Method ◽  
Static Equilibrium ◽  
Computational Time ◽  
Load Carrying Capacity ◽  
Dynamic Coefficients ◽  
Load Carrying

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method—twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

scholarly journals Stability Effects of Non-Circular Geometry in Floating Ring Bearings

Lubricants ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 99
Author(s):  
Giovanni Adiletta
Keyword(s):  
Equilibrium Position ◽  
Transient Analysis ◽  
Numerical Study ◽  
Theoretical Aspect ◽  
Static Equilibrium ◽  
Geometrical Parameters ◽  
Nonlinear Transient ◽  
Minor Part ◽  
The Stability ◽  
A Minor

The present study theoretically evaluates the stability potential of noncircular geometries when they are adopted in the outer bearing of floating ring bearings (FRB). A numerical study is carried out to evaluate the stability about the static equilibrium position of a balanced, symmetrical, rigid rotor, horizontally placed, and supported at both ends by identical FRBs. In the analysis, the outer bearing of these FRBs is alternatively shaped with common circular bore (CB), two lobe-wave bore (2LWB) or lemon bore (LB), assuming a linearization of the film forces. A minor part of the study consists of partially supporting the results of the above study by means of a nonlinear, transient analysis. Despite limiting to the theoretical aspect, dealt with under several simplifying hypotheses, the investigation highlights the influence of the examined non-circular geometries on the stability of the static equilibrium position, when these geometries are adopted for shaping the outer housing of the FRB. The paper shows that contrasting effects are obtained, depending on the chosen geometrical parameters. In the paper, the acronyms CB, 2LWB, and LB are used to indicate the FRB layouts respectively equipped with outer circular, wave, and lemon bearing.

scholarly journals Approximated Stiffness Coefficients in Rotor Systems Supported by Bearings with Clearance

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
Magnus Karlberg
Keyword(s):  
Equilibrium Position ◽  
Equation Of Motion ◽  
Rotating Machinery ◽  
Static Equilibrium ◽  
Rotor Systems ◽  
Supporting Structure ◽  
Stiffness Coefficients ◽  
Analytical Expressions

Many kinds of rotating machinery are supported by bearings with clearance, which are further clamped in a supporting structure. When designing such machinery it is important to be able to predict dynamics and hence valid models are needed. Due to gravity, the shaft often vibrates close to a static equilibrium position leading to a possibility to linearise the equation of motion. Although several studies on bearings with clearance exist, there are still no reports on how such clearances affects the stiffness coefficients close to a static equilibrium position. Therefore, analytical expressions for such approximated pedestal stiffness coefficients have been derived in this paper. By using such approximated pedestals in simple rotordynamical models, it was found that the eigenfrequencies decrease significantly with clearance. It is further shown that the approximated pedestal stiffness coefficients only will be valid for vibrations close to the static equilibrium position.

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