The Stability Analysis of Hydrodynamic Journal Bearings Allowing for Manufacturing Tolerances. Part II: Stability Analysis Model with Consideration of Tolerances

2009 ◽  
Author(s):  
Peter J. Ogrodnik ◽  
Mike J. Goodwin ◽  
Gordon A. Bancroft ◽  
Wubin Xu
Keyword(s):  
Stability Analysis ◽  
Journal Bearings ◽  
Analysis Model ◽  
Manufacturing Tolerances ◽  
The Stability

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Journal Bearings With Rectangular Dimples

2015 ◽  
Author(s):  
Ram Turaga
Keyword(s):  
Stability Analysis ◽  
Surface Texture ◽  
Transient Stability ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Pressure Curve ◽  
Rigid Rotor ◽  
Non Linear ◽  
The Stability ◽  
Transient Stability Analysis

The influence of deterministic surface texture on the sub-synchronous whirl stability of a rigid rotor has been studied. Non-linear transient stability analysis has been performed to study the stability of a rigid rotor supported on two symmetric journal bearings with a rectangular dimple of large aspect ratio. The surface texture parameters considered are dimple depth to minimum film thickness ratio and the location of the dimple on the bearing surface. Journal bearings of different Length to diameter ratios have been studied. The governing Reynolds equation for finite journal bearings with incompressible fluid has been solved using the Finite Element Method under isothermal conditions. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. When the dimple is located in the raising part of the pressure curve the positive rectangular dimple is seen to decrease the stability whereas the negative rectangular dimple is seen to improve the stability of the rigid rotor.

Nonlinear Simulation Analysis and Experiment of Fluid Plain Journal Bearing With Incompressible Fluid

2003 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Koji Yoshioka ◽  
Kouhei Okuno ◽  
Hiroaki Tanaka ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Journal Bearing ◽  
Simulation Analysis ◽  
Journal Bearings ◽  
Stable Region ◽  
Flexible Rotor ◽  
Nonlinear Simulation ◽  
Fluid Forces ◽  
The Stability

Recently, in many areas such as computers and information equipments etc., the fluid journal bearings are required to rotate at higher speed. To satisfy this requirement, the strictly stability analysis of the journal is indispensable. In this paper, we investigate the stability analysis of the dynamic behavior of the fluid plain journal bearing with an incompressible fluid considering the nonlinear terms of fluid forces. The stability analysis is examined by the numerical simulations on each model of a rigid rotor and a flexible rotor. The stable regions by nonlinear analysis are compared with the regions by classical linear analysis. Performing the nonlinear simulation analysis, it becomes clear that there is rather a stable region which amplitude does not grow up abruptly, and this phenomenon can not only be pointed out, but also is judged to be unstable by linear stable analysis. Finally, the experiment using actual bearings is performed and compared with the numerical results.

Stability Bearing Capacity of Dendritic Arms in Tainter Gate

2015 ◽  
Vol 733 ◽  
pp. 464-467
Author(s):  
Yong Kang Shen ◽  
Zheng Zhong Wang ◽  
Chun Long Zhao
Keyword(s):  
Stability Analysis ◽  
Bearing Capacity ◽  
Effective Length ◽  
Analysis Method ◽  
Analysis Model ◽  
Minimum Potential Energy ◽  
Stability Bearing Capacity ◽  
Minimum Potential ◽  
The Stability ◽  
Radial Gate

The new arms form of radial gate—dendritic arms is introduced for the proper mechanical mechanism, however the stability design is very difficult. According to the stability theory of structure, the stability analysis model of step column with lateral restraints was proposed for dendritic arms, some equations was derived from the principle of minimum potential energy, the practical formulas of buckling bearing capacity and effective length coefficient were provided. According to an example, the accuracy on formulas was verified by finite analysis method.

Stability Analysis of a Complex Geared Rotor-Bearing System in a Turbine Reduction Gearbox

2013 ◽  
Author(s):  
Yuanhong Guan ◽  
Edward W. Sieveking ◽  
Varad Sampathkumar
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
Low Frequency ◽  
Stability Margin ◽  
Journal Bearings ◽  
Root Cause ◽  
Rotor Bearing ◽  
Noise Vibration ◽  
The Stability ◽  
Load Conditions

It is well known that the rotor system will meet several critical speeds or unstable regions as its rotation speed increases, especially when the rotor system is supported by journal bearings, since there exists a strong fluid-structure coupling which is rather prone to stability issues. Stability analysis of rotor-bearing systems (such as turbine-compressor) has been extensively studied in the literatures over the past 50 years. However, few studies have been performed on geared rotor-bearing systems, especially for complex multi-stage gear train systems. In this paper, the abnormal noise/vibration problem on a high speed 2 stage epicyclic reduction gearbox of a turbine-generator system is studied. This gearbox showed abnormal low frequency vibrations at low speed cranking and high speed partial load conditions. Further detailed probe testing showed that the gear bodies which were supported by 6 journal bearings had quite large sub-synchronized vibrations and shaft whirls were developed when the abnormal noise was present. In order to better understand the root cause and to fully eliminate such low frequency noise/vibration, a detailed finite element model for the whole turbine-gearbox-generator was developed under different speed / load conditions. The linearized journal bearing stiffness and damping matrix were calculated using a separate tool and then plugged into the above FE model. The gears are modeled as rigid bodies and connected by gear mesh stiffness. Gyroscopic force terms have also been included in the model. The stability of the whole system was evaluated by a complex eigenvalue analysis and the stability margin evaluated by the corresponding damping factor (or log decrement). The model predicts a range of instability regions and has good correlation with testing data. The root cause of this abnormal noise/vibration is due to the strong torsional-lateral coupling of gear systems, and further coupling with the fluid dynamics of the journal bearings under certain speed/load conditions. Some sensitivity studies are also performed in order to increase the stability margin and eliminate the sub-synchronized vibrations.

scholarly journals Stability analysis of long hydrodynamic journal bearings based on the journal center trajectory

Friction ◽  
2020 ◽  
Author(s):  
Yu Huang ◽  
Haiyin Cao ◽  
Zhuxin Tian
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Journal Bearing ◽  
Stability Boundary ◽  
Initial Point ◽  
Journal Bearings ◽  
Bearing Surface ◽  
Rotating Speed ◽  
Stability Threshold ◽  
The Stability

AbstractIn this study, we observe that there are two threshold speeds (stability threshold speed and second threshold speed) for the long journal bearing, which is different for the short bearing. When the rotating speed is below the stability threshold speed, the stability boundary nearly coincides with the clearance circle, and the journal center gradually returns to the equilibrium point after being released at an initial point. If the rotating speed is between the stability threshold speed and the second threshold speed, after being released at an initial point, the journal center converges to a contour containing the equilibrium point. In this situation, for a higher rotating speed, the corresponding contour is also larger. When the rotating speed exceeds the second threshold speed, the journal gradually moves towards the bearing surface after being released at an initial point.

Stability Analysis Model of Eco Economic System based on Discrete Selection

2021 ◽  
Vol 7 (6) ◽  
pp. 6375-6387
Author(s):  
Yijing Wang
Keyword(s):  
Stability Analysis ◽  
Economic System ◽  
Resource Utilization ◽  
Evaluation System ◽  
System Analysis ◽  
Selection Model ◽  
Net Income ◽  
Analysis Model ◽  
Comprehensive Development ◽  
The Stability

The internal structure of eco-economic system is relatively complex, and its stability is easily affected by external environmental factors such as region, which results in poor accuracy of die results of its analysis. Based on this, the stability analysis model of eco-economic system based on discrete selection is proposed. In order to improve the accuracy of eco-economic system analysis, the characteristics of discrete selection model are analyzed. Based on the principles of scientificity, practicability, regionality, operability and dynamic, and the comprehensive development of four sub-systems of economy, land, environment and society, the indexes of economy, land, environment and society are selected to build the stability evaluation of eco-economic system Price index system: through adjusting the structure of resource utilization, the indexes are selected hierarchically to truly reflect the structure of resource utilization. The weight of each index is obtained by AHP, and the component of each index in the evaluation system is reasonably divided. According to the theory of stochastic utility, the elements of discrete selection model are analyzed, and then the discrete selection model is constructed. By studying the close degree of each evaluation object and ideal solution, the stability analysis of ecological economic system is realized. The experimental results show that the influence of the proposed model on net income per unit is relatively stable at the positive and negative balance points, which is consistent with the actual situation., and the shortest analysis time is 1.2 min, which is feasible.

Stability Analysis Model of a Quadruped Walking Machine at Walking up a Step

2013 ◽  
Vol 284-287 ◽  
pp. 950-957
Author(s):  
Yu Gang Chen ◽  
Jo Peng Tsai
Keyword(s):  
Stability Analysis ◽  
Analysis Model ◽  
Ancient China ◽  
Walking Machine ◽  
Walking Gait ◽  
Uneven Terrain ◽  
The Stability

According to the documents, an ancient Chinese carpenter named Lu Ban invented a four-legged wooden horse carriage in the Chou Dynasty in ancient China, around 480 B.C. This wooden horse carriage could simulate the walking gait of a horse very well but it needed a carriage to keep balance while walking. This paper proposes a method of stability analysis model for the locomotion of a quadruped wooden horse without the support of a carriage. First of all, four most unstable conditions are constructed based on the gait theory of the quadruped wooden horse. The stability areas are obtained by taking the intersections of supporting boundaries that are constructed under various unstable conditions for walking on even and uneven terrain. These results of the stability analysis model are useful for supervising the stability of locomotion of a quadruped.

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