Analysis on Dynamic Performance of Hydrodynamic Tilting-Pad Gas Bearings Using Partial Derivative Method

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Yang Lihua ◽  
Qi Shemiao ◽  
Yu Lie
Keyword(s):  
Analytical Method ◽  
Gas Turbines ◽  
High Speed ◽  
Dynamic Performance ◽  
Gas Bearings ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Dynamic Performances ◽  
Perturbation Frequency ◽  
San Andres

Tilting-pad gas bearings are widely used in high-speed rotating machines due to their inherent stability characteristics. This paper advances the analytical method for prediction of the dynamic performances of tilting-pad gas bearings. The main advantage of the analytical method is that the complete set of dynamic coefficients of tilting-pad gas bearings can be obtained. The predictions show that the perturbation frequency has the strong effects on the dynamic coefficients of gas bearings. In general, at lower perturbation frequency, the equivalent direct stiffness coefficients increase with frequency, whereas equivalent direct damping coefficients dramatically reduce. For higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the equivalent dynamic coefficients of four-pad tilting-pad gas bearing obtained by the method in this paper are in good agreement with those obtained by Zhu and San Andres [(2007), “Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,” ASME J. Eng. Gas Turbines Power, 129(4), pp. 1020–1027] in the published paper. The results validate the feasibility of the method presented in this paper in calculating the dynamic coefficients of gas-lubricated tilting-pad bearings.

Frequency Effects on Dynamic Characteristics of Tilting-Pad Journal Bearings due to Pivot Flexibility

2017 ◽  
Author(s):  
Tian Jiale ◽  
Yu Lie ◽  
Zhou Jian
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Dynamic Coefficients ◽  
Stability Performance ◽  
Limit Value ◽  
Tilting Pad ◽  
Perturbation Frequency ◽  
Tilting Pad Journal Bearings

The stable working condition of high speed, heavy loaded rotating machinery depends strongly on the stability provided by the journal bearing. Tilting pad journal bearings (TPJB) are widely used under such situation due to their inherent stability performance. However, because of the complexity of the TPJB structure, obtaining a reliable prediction of the journal bearing’s dynamic characteristics has always been a challenging task. In this paper, a theoretical analysis has been done to investigate the dynamic performance of a 4 pad TPJB with ball-in-socket pivot, emphasizing on the frequency dependency due to pivot flexibility. The analytical model containing the complete set of dynamic coefficients of the TPJB is built and the pivot stiffness is calculated and used to evaluate the equivalent dynamic coefficients of the bearing. In general, at lower perturbation frequency, the equivalent stiffness and damping increase with frequency. While for higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the results also show the limit value of the dynamic characteristics of the TPJB when the perturbation frequency is set to 0+ and ∞.

The Influence of Pad Pivot Elastic Deformation on Static and Dynamic Coefficients for Fixed-Tilting Pad Journal Bearing

2017 ◽  
Author(s):  
Tian Jiale ◽  
Yang Baisong ◽  
Sun Yanhua ◽  
Yu Lie ◽  
Zhou Jian
Keyword(s):  
Elastic Deformation ◽  
High Speed ◽  
Journal Bearing ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Oil Film ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Two Factors ◽  
Tilting Pad Journal Bearing

High-speed and heavy-loaded rotating machinery require accurate prediction of rotor’s response and stability, which can be characterized by the static and dynamic coefficients of the bearing support. In this paper, a theoretical study has been done to investigate the performance of a fixed-tilting pad journal bearing with ball-in-socket pivot. The analytical model is established with the flexibility of the pad pivot and turbulent effect of the oil film both taken consideration. Under such situation, the pad pivot elastic deformation and its stiffness are calculated using Hertz Contact Theory for various operating points of the rotor-bearing system. The finite element method is adopted to simulate the static coefficients of the fixed-tilting pad bearing, obtaining its oil film pressure distribution varied with the bearing eccentricity ratio. The corresponding dynamic stiffness and damping of the oil film are solved using partial derivative method. In addition, a special interest is put in investigating the effect of the series complex stiffness of the oil film and pad pivot, according to which, the equivalent dynamic characteristics are obtained. The results show that the relation between these two factors are complex and interactive, both of which have a significant influence on the static and dynamic performance of the bearing.

Dynamic Performance Analysis on High-Speed Railway Continuous Girder Bridge

2011 ◽  
Vol 280 ◽  
pp. 186-190
Author(s):  
Shou Tan Song ◽  
Ji Wen Zhang ◽  
Xin Yuan
Keyword(s):  
High Speed ◽  
Moving Load ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Wheel Load ◽  
Dynamic Coefficients ◽  
Bridge Structures ◽  
Continuous Girder Bridge ◽  
Girder Bridge ◽  
Dynamic Performance Analysis

The dynamic performance of continuous girder under the train in a series of speed is studied through examples, and the main conclusions are given in the following. The resonance mechanism of continuous girder is similar to simply supported beam. The vehicle wheel load forms regular moving load series, which induces periodical action and resonance of the bridge. The damping ratio of bridge itself has less effect on the amplitude at the loading stage, but significant effects appear when the load departs from the bridge. The count of continuous spans also has less impact on the dynamic coefficients, so three continuous spans can be adopted for calculation and analysis. Span and fundamental frequency have significant influence on dynamic coefficients of bridge structures. To extend the span of the bridge structure can reduce the dynamic coefficient while keeping its frequency invariant. The fundamental frequencies of different bridges are corresponding to certain resonant speeds, which calls for the attention in the design.

Analysis on the Dynamic Performance of Vehicles

2021 ◽  
Vol 42 ◽  
pp. 71-78
Author(s):  
Oana Victoria Oțăt ◽  
Ilie Dumitru ◽  
Laurenţiu Racilă ◽  
Dragoș Tutunea ◽  
Lucian Matei
Keyword(s):  
Initial Data ◽  
Analytical Method ◽  
Dynamic Performance ◽  
Automotive Sector ◽  
Vehicle Dynamic ◽  
Car Model ◽  
Dynamic Performances

The current accelerated developments within the automotive sector have triggered a series of performance, comfort, safety and design-related issues. Hence, oftentimes manufacturers are challenged to combine various elements so as to achieve an attractive design, without diminishing the vehicle’s dynamic performance. In order to determine the vehicle dynamic performances we carried out an analysis by two methods. In the first part of the paper, we have used the analytical method to establish the dynamic performances of a vehicle. The second part of our study addresses another method to determine the star performances of the vehicle by means of computerized simulations. The first test aimed to determine vehicle starting performances for two vehicle models, with similar technical configuration, but with the same initial data. In the second test, we aimed at determining the start performance for the same car model, with the same initial data, but for different adhesion coefficients

scholarly journals Influence of Temperature Effect on the Static and Dynamic Performance of Gas-Lubricated Microbearings

Micromachines ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 716
Author(s):  
Liangliang Li ◽  
Zhufeng Liu ◽  
Chongyu Wang ◽  
Yonghui Xie
Keyword(s):  
High Speed ◽  
Load Capacity ◽  
Dynamic Performance ◽  
Operating Environment ◽  
Low Friction ◽  
Operating Stability ◽  
Comprehensive Performance ◽  
Different Temperatures ◽  
Dynamic Performances ◽  
The Difference

Gas-lubricated microbearings are widely applied in multiple fields due to their advantages of high-speed, low friction level and other features. The operating environment of microbearings is complex, and the difference of temperature has an important influence on their comprehensive performance. In this investigation, FEM (finite element method) is employed to investigate the static, dynamic and limit characteristics of microbearings lubricated by different kinds of gas at different temperatures. The results show that the rise of temperature leads to the decline of equivalent viscosity of gas, which weakens the load capacity of microbearings, and furthermore, affects the operating stability of microbearings. The dynamic performances of microbearings at different temperatures are very different, and the two dynamic limit characteristics are more sensitive to temperature when it changes.

Analytical Method for Hydrodynamic Force in Finite-Length Tilting-Pad Journal Bearing Including Turbulence Effect

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Yingze Jin ◽  
Xiaoyang Yuan
Keyword(s):  
Finite Length ◽  
Analytical Method ◽  
Nonlinear Dynamic ◽  
Separation Of Variables ◽  
Dynamic Performance ◽  
Published Data ◽  
Hydrodynamic Bearing ◽  
Low Viscosity ◽  
Tilting Pad ◽  
Turbulence Effect

Abstract To improve the efficiency in nonlinear dynamic calculation of finite-length tilting-pad journal bearings (TPJBs) under dynamic loads, an analytical method for hydrodynamic bearing forces, which considers the turbulence effect, is proposed using the method of separation of variables under the dynamic Gümbel boundary condition. No thermal effects are considered because this method is designed for the low viscosity case. The infinitely long bearing pressure is introduced as the circumferential pressure, and a general solution of the nonhomogeneous Reynolds equation is derived as the axial pressure. The turbulence model of Ng and Pan is characterized by a linear function of film thicknesses. A complete analytical expression of hydrodynamic bearing forces is derived. The analytical simulation shows slight differences and extremely low time expense in lubricating and dynamic performance compared to published data and finite difference method (FDM) simulation. The analytical method could be used to fast evaluate the nonlinear dynamic performance of a TPJB-rotor system in the low viscosity environment, supporting the nonlinear dynamic design of the system.

scholarly journals Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui-Hui Feng ◽  
Chun-Dong Xu ◽  
Jie Wan
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Eccentricity Ratio ◽  
Dynamic Coefficients ◽  
Pressure Fields ◽  
Dynamic Performances ◽  
Rotary Speed

The water-lubricated bearings have been paid attention for their advantages to reduce the power loss and temperature rise and increase load capacity at high speed. To fully study the complete dynamic coefficients of two water-lubricated, hydrostatic journal bearings used to support a rigid rotor, a four-degree-of-freedom model considering the translational and tilting motion is presented. The effects of tilting ratio, rotary speed, and eccentricity ratio on the static and dynamic performances of the bearings are investigated. The bulk turbulent Reynolds equation is adopted. The finite difference method and a linear perturbation method are used to calculate the zeroth- and first-order pressure fields to obtain the static and dynamic coefficients. The results suggest that when the tilting ratio is smaller than 0.4 or the eccentricity ratio is smaller than 0.1, the static and dynamic characteristics are relatively insensitive to the tilting and eccentricity ratios; however, for larger tilting or eccentricity ratios, the tilting and eccentric effects should be fully considered. Meanwhile, the rotary speed significantly affects the performance of the hydrostatic, water-lubricated bearings.

Material Considerations for High Temperature Tilting Pad Gas Bearings

1968 ◽  
Vol 90 (4) ◽  
pp. 818-828 ◽  
Author(s):  
S. F. Murray ◽  
M. B. Peterson
Keyword(s):  
High Temperature ◽  
Contact Area ◽  
High Speed ◽  
Contact Problems ◽  
Sliding Contact ◽  
Gas Bearings ◽  
Hydrodynamic Bearing ◽  
Tilting Pad ◽  
Short Time

This paper is concerned with the sliding contact problems encountered in tilting pad gas bearings operating at temperatures up to 1400 deg F. Both the pivots and the bearing surfaces are considered. Short time experimental evaluations of pivot damage are summarized. The results of start-stop and high-speed rub tests on a single tilting pad hydrodynamic bearing are also described. Based on the results obtained to date, damage-resistant coatings are available for use on the bearing surfaces at high temperature. There are also suitable pivot materials, but the pivot must be properly designed to minimize slip in the contact area.

Rotordynamic Performance of Flexure Pivot Tilting Pad Gas Bearings With Vibration Damper

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Aaron Rimpel ◽  
Daejong Kim
Keyword(s):  
Gas Turbines ◽  
Dynamic Models ◽  
Natural Frequencies ◽  
Clean Energy ◽  
Design Guidelines ◽  
Vibration Damper ◽  
Shell Mass ◽  
Gas Bearings ◽  
Tilting Pad ◽  
Rotor Bearing

Recently, gas-lubricated bearings have drawn enormous attention for clean energy conversion/process systems such as fuel cells, micro-gas-turbines, gas compressors, etc. Among many different types of gas bearings, tilting pad gas bearings have many attractive features such as high rotor-bearing stability and less severe thermal issues (due to multipad configurations) than foil gas bearings. However, extension of the application of the tilting pad gas bearings to flexible rotors and harsh environments with external vibrations/impacts poses significant design challenges. The design problem addressed in this paper is the vibration damper to be integrated with the flexure pivot tilting pad gas bearing (FPTPGB) with and without pad radial compliance. Linear and nonlinear dynamic models of the FPTPGB with vibration damper were developed, and rotordynamic performance was evaluated to prescribe design guidelines for the selection of bearing shell mass and damper properties. Direct numerical integration (time-domain orbit simulations) and linear analyses were employed to predict rotordynamic responses and other interesting behaviors relevant of rotor-bearing systems with the vibration damper. Rotor-bearing systems showed better performance with larger damper stiffness for both with and without radial compliance. However, bearing shell mass showed different tendencies; lower bearing shell mass was shown to be ideal for bearings with radial compliance, while the opposite trend was observed for bearings without radial compliance. Although increasing the degrees of freedom of the system by allowing the bearing shell to move introduces additional natural frequencies, careful design considerations could allow the placement of the natural frequencies outside of the operating range.

Experimental Studies on Flexure Pivot Tilting Pad Gas Bearings With Pad Radial Compliance

2007 ◽  
Author(s):  
Kyuho Sim ◽  
Aaron Rimpel ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Experimental Studies ◽  
Experimental Results ◽  
Frequency Dependent ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Operation Frequency ◽  
Large Rotor ◽  
Good Agreement

This paper presents experimental studies on imbalance responses of a rotor supported by two flexure pivot tilting pad gas bearings with radial compliance. The radial compliance was aimed to accommodate large rotor centrifugal growth inherent with high speed operation. Frequency-dependent rotordynamic force coefficients calculated from developed software were used to predict critical speeds and onset speed of instability and compared with experimental results. Two results show very good agreement.

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