Low-Order Models for Very Short Hybrid Gas Bearings

2000 ◽  
Vol 123 (2) ◽  
pp. 368-375 ◽  
Author(s):  
N. Savoulides ◽  
K. S. Breuer ◽  
S. Jacobson ◽  
F. F. Ehrich
Keyword(s):  
Small Scale ◽  
Stable Operation ◽  
Order Model ◽  
High Speeds ◽  
Standard Operating ◽  
Operating Space ◽  
Pressurization System ◽  
Stiffness And Damping ◽  
Gas Bearing ◽  
Low Order

A low-order model was created to analyze a small-scale gas bearing with a diameter of 4.1 mm, designed to spin at 2.4 million rpm. Due to microfabrication constraints, the bearing lies outside the standard operating space and stable operation is a challenge. The model is constructed by reference to Newton’s second law for the rotor and employs stiffness and damping coefficients predicted by other models. At any operating point it is able to predict (1) whether the journal can sustain stable operation, and (2) the whirling frequency of the journal. Analysis shows that the best way to operate the bearing is in a hybrid mode where the bearing relies on hydrostatics at low speeds and hydrodynamics at high speeds. However, in transitioning from hydrostatic to hydrodynamic operation, the model shows that the bearing is prone to instability problems and great care must be taken in scheduling the bearing pressurization system in the course of accelerating through low and intermediate rotational speeds.

Compliant Gas Foil Bearings and Analysis Tools

2015 ◽  
Vol 138 (5) ◽  
Author(s):  
Michael Branagan ◽  
David Griffin ◽  
Christopher Goyne ◽  
Alexandrina Untaroiu
Keyword(s):  
Load Capacity ◽  
Current Status ◽  
Stable Operation ◽  
Foil Bearings ◽  
High Speeds ◽  
Analysis Tools ◽  
Low Load ◽  
Bearing Stiffness ◽  
Stiffness And Damping ◽  
Analytical Tools

Compliant gas foil bearings are composed of two layers of thin metallic foil and a thin film of gas to support the journal. The bottom foil creates an elastic structure which supports the top foil. This support structure can take a variety of shapes that range from a series of bumps around the circumference to a series of overlapping leaves. The top foil and the rotation of the rotor create a wedge of air that supports the rotor. The complaint foil structure deforms in response to the pressure developed within the gas film. These bearings have several advantages over conventional fluid film bearings. These advantages include reduced weight due to the elimination of the oil system, stable operation at higher speeds and temperatures, low power loss at high speeds and long life with little maintenance. Some disadvantages of gas foil bearings are low load capacities at low speed and modest stiffness and damping values. Due to these properties, compliant gas foil bearings are commonly used in specialized applications such as compressors for aircraft pressurization, engines for turboshaft propulsion, air cycle machines (ACMs), turboexpanders, and small microturbines. The ability to predict the behavior of these bearings and design them to meet the needs of the application is invaluable to the design process. This behavior can include things such as bearing stiffness, damping, and load capacity. Currently most foil bearing analysis tools involve some sort of coupling between hydrodynamics and structural analyses. These analysis tools can often have convergence issues and can require the use of empirically derived characteristics. This paper reviews the current status of the compliant gas foil bearings research, focusing mainly on the journal bump-type gas foil bearings and the development of the analysis tools for these bearings. This paper contributes to the field by making recommendations of the future developments of the analytical tools of journal bump-type gas foil bearings.

Measurements of Static and Dynamic Load Performance of a 102 MM Carbon-Graphite Porous Surface Tilting-Pad Gas Journal Bearing

2021 ◽  
Author(s):  
Luis San Andres ◽  
Jing Yang ◽  
Ryan McGowan
Keyword(s):  
Dynamic Load ◽  
Load Capacity ◽  
Stable Operation ◽  
Specific Load ◽  
Damping Coefficients ◽  
Supply Pressure ◽  
Air Supply ◽  
Frequency Independent ◽  
Stiffness And Damping ◽  
Gas Bearing

Abstract Aerostatic journal bearings with porous tilting pads enable shaft support with minute drag power losses. To date archival information on the static and dynamic load performance of this bearing type is scant. Thus, the paper presents measurements conducted with an air bearing with diameter 102 mm and comprising four tilting pads made of porous carbon-graphite, each with length = 76 mm. At ambient temperature of 21°C, as the air supply pressure into the bearing pads increases, so does the bearing aerostatic specific load that reaches 58% of the pressure difference. With a supply pressure of 7.8 bar(a), the test bearing static stiffness = 13.1 MN/m, is independent of both shaft speed and static load. While operating with shaft speeds = 6 krpm and 9 krpm and under specific loads to 115 kPa and 101 kPa respectively, dynamic load experiments with excitation frequencies up to 342 Hz show the test bearing supplied with air at 7.8 bar(a) has frequency independent stiffness and damping coefficients. For rotor speeds equaling 0, 6 and 9 krpm, the bearing direct stiffnesses range from 13.6 MN/m to 32.7 MN/m as the specific load increases from 0 kPa to 115 kPa. The direct damping coefficients are as large as 5.8 kN·s/m. The test porous gas bearing reached its intended load capacity, demonstrated a dynamically stable operation and produced force coefficients mainly affected by the pads' pivot supports and the magnitude of air supply pressurization.

Synchronous Response to Rotor Imbalance Using a Damped Gas Bearing

2009 ◽  
Author(s):  
Bugra H. Ertas ◽  
Massimo Camatti ◽  
Gabriele Mariotti
Keyword(s):  
High Speed ◽  
Experimental Tests ◽  
Rotor System ◽  
Rotor Imbalance ◽  
High Speeds ◽  
Speed Range ◽  
Speed Stability ◽  
Stiffness And Damping ◽  
Gas Bearing ◽  
Large Rotor

One type of test performed for evaluating bearings for application into turbomachinery is the synchronous bearing response to rotor imbalance. This paper presents rotordynamic tests on a rotor system using a 70mm diameter damped gas bearing reaching ultra-high speeds of 50,000 rpm. The main objective of the study was to experimentally evaluate the ability of the damped gas bearing to withstand large rotor excursions and provide adequate damping through critical speed transitions. Two critical speeds were excited through varying amounts and configurations of rotor imbalance, while measuring synchronous rotordynamic response at two different axial locations. The results indicated a well-damped rotor system and demonstrated the ability of the gas bearing to safely withstand rotor vibration levels while subjected to severe imbalance loading. Also, a waterfall plot was used to verify ultra high-speed stability of the rotor system throughout the speed range of the test vehicle. In addition to the experimental tests, a rotordynamic computer model was developed for the rotor-bearing system. Using the amplitude/frequency dependent stiffness and damping coefficients for the ball bearing support and the damped gas-bearing support, a pseudo-nonlinear rotordynamic response to imbalance was performed and compared to the experiments.

Synchronous Response to Rotor Imbalance Using a Damped Gas Bearing

2009 ◽  
Vol 132 (3) ◽  
Author(s):  
Bugra H. Ertas ◽  
Massimo Camatti ◽  
Gabriele Mariotti
Keyword(s):  
High Speed ◽  
Experimental Tests ◽  
Rotor System ◽  
Rotor Imbalance ◽  
High Speeds ◽  
Speed Range ◽  
Speed Stability ◽  
Stiffness And Damping ◽  
Gas Bearing ◽  
Large Rotor

One type of test performed for evaluating bearings for application into turbomachinery is the synchronous bearing response to rotor imbalance. This paper presents rotordynamic tests on a rotor system using a 70 mm diameter damped gas bearing reaching ultra-high speeds of 50,000 rpm. The main objective of the study was to experimentally evaluate the ability of the damped gas bearing to withstand large rotor excursions and provide adequate damping through critical speed transitions. Two critical speeds were excited through varying amounts and configurations of rotor imbalance while measuring the synchronous rotordynamic response at two different axial locations. The results indicated a well-damped rotor system and demonstrated the ability of the gas bearing to safely withstand rotor vibration levels while subjected to severe imbalance loading. Also, a waterfall plot was used to verify ultra-high-speed stability of the rotor system throughout the speed range of the test vehicle. In addition to the experimental tests, a rotordynamic computer model was developed for the rotor-bearing system. Using the amplitude/frequency dependent stiffness and damping coefficients for the ball bearing support and the damped gas-bearing support, a pseudononlinear rotordynamic response to imbalance was performed and compared with the experiments.

Compliant Gas Foil Bearings and Analysis Tools

2015 ◽  
Author(s):  
Michael Branagan ◽  
David Griffin ◽  
Christopher Goyne ◽  
Alexandrina Untaroiu
Keyword(s):  
Load Capacity ◽  
Current Status ◽  
Stable Operation ◽  
Foil Bearings ◽  
High Speeds ◽  
Analysis Tools ◽  
Low Load ◽  
Bearing Stiffness ◽  
Stiffness And Damping ◽  
Analytical Tools

Compliant gas foil bearings are composed of two layers of thin metallic foil and a thin film of gas to support the journal. The bottom foil creates an elastic structure which supports the top foil. This support structure can take a variety of shapes that range from a series of bumps around the circumference to a series of overlapping leaves. The top foil and the rotation of the rotor create a wedge of air that supports the rotor. The complaint foil structure deforms in response to the pressure developed within the gas film. These bearings have several advantages over conventional fluid film bearings. These advantages include reduced weight due to the elimination of the oil system, stable operation at higher speeds and temperatures, low power loss at high speeds and long life with little maintenance. Some disadvantages of gas foil bearings are low load capacities at low speed and modest stiffness and damping values. Due to these properties, compliant gas foil bearings are commonly used in specialized applications such as compressors for aircraft pressurization, engines for turboshaft propulsion, air cycle machines, turboexpanders, and small micro turbines. The ability to predict the behavior of these bearings and design them to meet the needs of the application is invaluable to the design process. This behavior can include things such as bearing stiffness, damping, and load capacity. Currently most foil bearing analysis tools involve some sort of coupling between hydrodynamics and structural analyses. These analysis tools can often have convergence issues and can require the use of empirically derived characteristics. This paper reviews the current status of the compliant gas foil bearings research, focusing mainly on the journal bump-type gas foil bearings and the development of the analysis tools for these bearings. This paper contributes to the field by making recommendations of the future developments of the analytical tools of journal bump-type gas foil bearings.

Hybrid Reduced Model of Rotor

2013 ◽  
Vol 60 (3) ◽  
pp. 319-333
Author(s):  
Rafał Hein ◽  
Cezary Orlikowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hybrid Model ◽  
Rotor System ◽  
Reduced Model ◽  
Order Model ◽  
Gyroscopic Effect ◽  
Reduced Models ◽  
Rigid Finite Element Method ◽  
Low Order

Abstract In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

On-line thermal regulation of a capillary pumped loop via state feedback control using a low order model

2016 ◽  
Vol 108 ◽  
pp. 614-627 ◽  
Author(s):  
Etienne Videcoq ◽  
Manuel Girault ◽  
Vincent Ayel ◽  
Cyril Romestant ◽  
Yves Bertin
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Thermal Regulation ◽  
Order Model ◽  
Capillary Pumped Loop ◽  
On Line ◽  
Low Order

A Reduced-Order Model for the Preliminary Design of Small-Scale Radial Inflow Turbines

2021 ◽  
Author(s):  
Marco Manfredi ◽  
Marco Alberio ◽  
Marco Astolfi ◽  
Andrea Spinelli
Keyword(s):  
Heat Recovery ◽  
Internal Combustion Engines ◽  
Reduced Order Model ◽  
Pollutant Emissions ◽  
Small Scale ◽  
Preliminary Design ◽  
Order Model ◽  
Reduced Order ◽  
Wide Range ◽  
Loss Models

Abstract Power production from waste heat recovery represents an attractive and viable solution to contribute to the reduction of pollutant emissions generated by industrial plants and automotive sector. For transport applications, a promising technology can be identified in bottoming mini-organic Rankine cycles (ORCs), devoted to heat recovery from internal combustion engines (ICE). While commercial ORCs exploiting turbo-expanders in the power range of hundreds kW to several MW are a mature technology, well-established design guidelines are not yet available for turbines targeting small power outputs (below 50 kW). The present work develops a reduced-order model for the preliminary design of mini-ORC radial inflow turbines (RITs) for high-pressure ratio applications, suitable to be integrated in a comprehensive cycle optimization. An exhaustive review of existing loss models, whose development pattern is retraced up to the original approaches, is proposed. This investigation is finalized in a loss models effectiveness analysis performed by testing several correlations over six existing geometries. These test case turbines, operating with different fluids and covering a wide range of target expansion ratio, size, and gross power output, are then employed to carry out the validation procedure, whose results prove the robustness and prediction capability of the proposed reduced-order model.

Gradient-Free Optimization in Thermoacoustics: Application to A Low-Order Model

2021 ◽  
Author(s):  
Johann Moritz Reumschüssel ◽  
Jakob G. R. von Saldern ◽  
Yiqing Li ◽  
Christian Oliver Paschereit ◽  
Alessandro Orchini
Keyword(s):  
Optimization Algorithms ◽  
Optimization Methods ◽  
Theoretical Studies ◽  
Order Model ◽  
Output Data ◽  
Fuel Injectors ◽  
Solution Strategies ◽  
The Past ◽  
Downhill Simplex ◽  
Low Order

Abstract Machine learning and automatized routines for parameter optimization have experienced a surge in development in the past years, mostly caused by the increasing availability of computing capacity. Gradient-free optimization can avoid cumbersome theoretical studies as input parameters are purely adapted based on output data. As no knowledge about the objective function is provided to the algorithms, this approach might reveal unconventional solutions to complex problems that were out of scope of classical solution strategies. In this study, the potential of these optimization methods on thermoacoustic problems is examined. The optimization algorithms are applied to a generic low-order thermoacoustic can-combustor model with several fuel injectors at different locations. We use three optimization algorithms — the well established Downhill Simplex Method, the recently proposed Explorative Gradient Method, and an evolutionary algorithm — to find optimal fuel distributions across the fuel lines while maintaining the amount of consumed fuel constant. The objective is to have minimal pulsation amplitudes. We compare the results and efficiency of the gradient-free algorithms. Additionally, we employ model-based linear stability analysis to calculate the growth rates of the dominant thermoacoustic modes. This allows us to highlight general and thermoacoustic-specific features of the optimization methods and results. The findings of this study show the potential of gradient-free optimization methods on combustor design for tackling thermoacoustic problems, and motivate further research in this direction.

Sign in / Sign up

Export Citation Format

Share Document