Theoretical Analysis and Numerical Simulation of Oil Lubricated Foil Bearing With Elastic Supported Bump Foil Structure

2016 ◽  
Author(s):  
Guanghui Zhang ◽  
Qiang Chen ◽  
Jiajia Yan ◽  
Xianghe Wang ◽  
Zhansheng Liu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Reynolds Equations ◽  
Rotating Speed ◽  
Flexibility Matrix ◽  
Cavitation Effect ◽  
Foil Bearing ◽  
Deformation Equation ◽  
Bearing Load ◽  
The Stability

The oil lubricated multi-leaf foil bearing is developed to meet the demand of high rotating speed for hydraulic turbo-pump, where the lubricated oil is easy to obtain. For the stability of this kind oil lubricated foil bearing needs to be guaranteed, the bearing with elastic supported bump foil structure is proposed to improve the performance of foil bearing. Theoretical analysis and numerical simulation is carried out in this paper. The film thickness expression of multi-leaf foil bearing is established for the cases with and without top foil deformation. The total flexibility matrix considering elastic supported bump foil structure is developed based on Castigliano’s theorem. By employing the Reynolds boundary condition, the oil cavitation effect is presented. The established flexibility matrix is substituting into classical incompressible Reynolds equation, then the deformation equation of the foil and Reynolds equations are solved coupling by successive over relaxation method. The static characteristics such as pressure distribution, bearing load and static equilibrium position are obtained. By employing the perturbation method to Reynolds equations and foil deformation equation, the dynamic characteristics of multi-leaf foil bearing with elastic supported bump foil structure are acquired. The stability of the bearing is analyzed and compared with other type bearings by Routh-Hurwitz method. The effects of bearing load and sommerfeld parameter on the stiffness and damping coefficients are studied. The results indicate that the performance of foil bearing with elastic supported bump foil structure is improved and this kind bearing is suitable for high rotating speed application.

Performance Analysis of Oil Lubricated Foil Bearing With Flexible Supported Back Spring Structure—Part I: Model Development and Numerical Investigation

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Guanghui Zhang ◽  
Xie Liang ◽  
Yu Wang ◽  
Zhansheng Liu
Keyword(s):  
Reynolds Equation ◽  
Load Capacity ◽  
Model Development ◽  
Foil Thickness ◽  
Film Rupture ◽  
Finite Element Software ◽  
Flexibility Matrix ◽  
Foil Bearing ◽  
Deformation Equation ◽  
The Stability

A new type of multileaf oil lubricated foil bearing with flexible supported back spring structure was proposed to satisfy the requirement of high rotating velocity for turbo pump, where the rotor was submerged in the hydraulic oil. The numerical analysis was carried out in this paper. Based on the structure of oil foil bearing, the film thickness model was established without foil deformation. By employing Castigliano's theorem, the total flexibility matrix including the elastic back spring and cantilevered curved beam was calculated, and then compared with commercial finite element software to verify the accuracy of the proposed model. The obtained flexibility matrix was brought into the static and dynamic oil lubricated Reynolds equation. The Reynolds boundary condition was considered to simulate the oil film rupture effect. The deformation equation for the structure and the Reynolds equation were solved coupled by the successive over relaxation method. The static and dynamic characteristics of the oil lubricated multileaf foil bearing with supported back spring were acquired. The effect of the foil thickness on the load capacity was discussed. The variation of the dynamic coefficients with bearing load was acquired. By employing Routh–Hurwitz method, the stability of the bearing was analyzed. The results indicated that the load capacity of the foil bearing with back supported spring was bigger than that of the foil bearing without back supported spring. The stability characteristics of the foil bearing with back supported structure was better than traditional rigid self-acting bearing, particular for the high rotating speed case.

scholarly journals Theoretical Research and Numerical Simulation on Water Resistance Mechanism of Textile Bag in Water Passage

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Ang Li ◽  
Yuxuan Yang ◽  
Mingcheng Zhu ◽  
Wenzhong Zhang ◽  
Bingnan Ji ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Water Resistance ◽  
Simulation Analysis ◽  
Water Pressure ◽  
Water Inrush ◽  
Deformation Characteristics ◽  
Water Blocking ◽  
The Stability ◽  
Water Passage

It is an important problem in the mine water disaster prevention and control to control the large passage moving water. Traditional grouting technology is to put coarse aggregate and fine aggregate downward first and then grouting treatment. But the aggregate and cement flow distance is long, consumption is large, cost is high, and easy to appear secondary water inrush. Centering on the technical difficulties in the rapid construction of the blocking body of the moving water passage, a water-blocking textile bag was invented. The purpose of blocking the tunnel water inrush was achieved by grouting inside the bag body, which fundamentally realized the rapid blocking of the large passage through water under the condition of moving water. However, the mechanism, water plugging law, and design parameters of water blocking roadway with textile bag are still unclear. In this paper, the slip law and stability of the textile bag in the moving water and the deformation characteristics caused by the dynamic water pressure are theoretically analyzed and simulated. Through theoretical analysis, the ultimate antihydraulic stress value of a textile bag of a certain specification is calculated, and the parameters of the textile bag that affect the stability of the bag body are also determined. Xflow was used for numerical simulation analysis to study the deformation characteristics of the textile bag under water and the law of water barrier. The simulation analysis focuses on the water resistance effect and flow field distribution characteristics of the textile bag in the water passage under the condition of low flow rate and low pressure, as well as the stability and self-deformation characteristics of the textile bag under the condition of high flow rate and high pressure. The accuracy of the limit resistance to water pressure of the textile bag obtained from theoretical analysis is verified. The results show that the theoretical analysis is consistent with the simulation results. The textile bag can realize the fast controllable plugging of the large water passage of moving water within the limit of the antihydraulic stress.

scholarly journals MIXED JACOBI-FOURIER SPECTRAL METHOD FOR FISHER EQUATION

2018 ◽  
Vol 23 (2) ◽  
pp. 240-261 ◽  
Author(s):  
Yujian Jiao ◽  
Tianjun Wang ◽  
Xiandong Shi ◽  
Wenjie Liu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Spectral Method ◽  
Stability And Convergence ◽  
Fisher Equation ◽  
Fourier Spectral Method ◽  
Fourier Approximation ◽  
Regional Center ◽  
Sparse System ◽  
The Stability

In this paper, we propose a mixed Jacobi-Fourier spectral method for solving the Fisher equation in a disc. Some mixed Jacobi-Fourier approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. We use the generalized Jacobi approximation to simulate the singularity of solution at the regional center. This also simplifies the theoretical analysis and provides a sparse system. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this new algorithm and coincide well with the theoretical analysis.

A New Coupled Map Car-Following Model Considering the Synergy Effect of Ahead-Backward Vehicles

2014 ◽  
Vol 1061-1062 ◽  
pp. 1059-1063
Author(s):  
Tong Zhou ◽  
Yu Xuan Li ◽  
Xiu Yun Li ◽  
Cheng Zeng
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Control Theory ◽  
Traffic Flow ◽  
Stability Condition ◽  
Synergy Effect ◽  
Car Following ◽  
Theoretical Scheme ◽  
Car Following Model ◽  
The Stability

Based on the pioneer work of Konishi et al., with consideration of the influence of the synergy effect of ahead-backward vehicles on the traffic flow, we develop a new coupled map car-following model on single road. By applying the control theory, the stability condition of our model is derived. To check the validity of the present theoretical scheme, the numerical simulation is carried out for our model, and it confirms the correctness of the theoretical analysis.

scholarly journals Failure Analysis of Deep Composite Roof Roadway and Support Optimization of Anchor Cable Parameters

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Chen Li ◽  
Wenlong Zhang ◽  
Tianhong Huo ◽  
Rui Yu ◽  
Xidong Zhao ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Underground Mining ◽  
Field Monitoring ◽  
Simulation Software ◽  
Surrounding Rock ◽  
Economic Damage ◽  
Anchor Cable ◽  
Stress Diffusion ◽  
The Stability

The stability of the roadway surrounding rock is the key factor of underground mining. Roof subsidence occurred during roadway excavation in the Menkeqing Coal Mine. For the sake of safety, it was decided to stop tunneling project and strengthen roadway support, which resulted in a delay of the construction period and economic damage. To maintain the stability of the surrounding rock, we carried out a systematic study through field monitoring, theoretical analysis, and numerical simulation. The deformation and failure law of the surrounding rock, roof structure characteristics, and mechanical properties of the surrounding rock were obtained by field monitoring. The failure characteristics and forms of deep composite roof roadway are further analyzed. The key points of stability of the roadway surrounding rock of soft rock composite laminated roof are obtained by theoretical analysis, i.e., improving the effective stress diffusion efficiency of the anchor cable through the reasonable arrangement of the anchor cable. We use FLAC numerical simulation software to study the influence of different supporting parameters of anchor cable on the stress diffusion in the surrounding rock and put forward the optimal parameters. The optimized support parameters have been applied in the field, and the ideal results have been obtained.

Performance Analysis of Oil Lubricated Foil Bearing With Flexible Supported Back Spring Structure—Part II: Comparison of Predictions and Measured Test Data

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Guanghui Zhang ◽  
Xie Liang ◽  
Yu Wang ◽  
Zhansheng Liu
Keyword(s):  
Numerical Simulation ◽  
Performance Analysis ◽  
Theoretical Analysis ◽  
Gas Turbines ◽  
Load Capacity ◽  
Identification Algorithm ◽  
Theoretical Simulation ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Foil Bearing

As described in Part I (Zhang et al., “Performance Analysis of Oil Lubricated Foil Bearing With Flexible Supported Back Spring Structure—Part I: Model Development and Numerical Investigation”, ASME J. Eng. Gas Turbines Power, 136(11), p. 112501), a new type of multileaf oil lubricated foil bearing with flexible supported back spring structure was proposed and the characteristics were obtained by theoretical analysis and numerical simulation. Until now, nearly no paper about the modeling method and experimental verification for this type foil bearing published. So it is necessary to study the performance of this kind bearing by experiments. The experimental rig for the static and dynamic characteristics of the bearing was installed and the experiments were carried out. The stiffness of the back supported spring was measured. By employing the dynamic coefficients identification algorithm for oil foil bearing, the data acquisition delay was compensated. The load capacity, stiffness coefficients and damping coefficients were obtained. The load capacity resulting from the experiment was coincided with the theoretical simulation well. The stiffness and damping coefficients from the experiments had the similar tendency with those from the theoretical analysis. The stiffness coefficients obtained from experiments were coincided well with the numerical simulation results, and the difference of damping coefficients was a little bigger.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

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