Design Approach for Large Foil Bearings Considering Rotordynamics

2017 ◽  
Author(s):  
Srikanth Honavara Prasad ◽  
Daejong Kim
Keyword(s):  
Scaling Laws ◽  
Load Capacity ◽  
Scale Up ◽  
Design Guidelines ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Support Structure ◽  
Foil Bearings ◽  
Systems Research ◽  
Scale Down

In recent years, gas foil bearings have gained increased attention due to potential applications in aerospace systems. Research and development efforts have been focused towards simplifying design and analysis methods or experimentally demonstrating stable bearing performance under various operating conditions. Many researchers have proposed design guidelines for parameters such as load capacity, stiffness, and damping etc., for extending the state of the art based on experimental data available in existing literature. The authors previously presented scaling laws for radial clearance and support structure stiffness of radial foil bearings. In that study, the criteria for selecting radial clearance and support structure stiffness for scale up or scale down of an existing bearing design was presented. In addition, the results from that paper showed that a hydrodynamic film could be sustained for large bearings (up to 300 mm diameter) demonstrating that the bearings would have adequate load capacity. However, the rotordynamic effects for the various bearing sizes were not considered in that study. This paper serves as an extension of the paper on scaling laws by the same authors. The subject of this paper is a four degree of freedom (4-DOF) rotordynamic analysis performed for turbomachinery systems that employ bearings designed using the scaling laws for radial clearance and support structure stiffness. Further, case studies to show feasibility of foil bearings for applications in Mega Watt range turbo blowers and turbo compressors is presented.

Scaling Laws for Radial Clearance and Support Structure Stiffness of Radial Foil Bearings

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Srikanth Honavara Prasad ◽  
Daejong Kim
Keyword(s):  
Scaling Laws ◽  
Heating Temperature ◽  
Frictional Heating ◽  
Fluid Pressure ◽  
Design Guidelines ◽  
Structural Deformation ◽  
Radial Clearance ◽  
Support Structure ◽  
Foil Bearings ◽  
Highly Nonlinear

Design and analysis of foil bearings involve consideration to various physical aspects such as fluid pressure, structural deformation, and heat generation due to viscous effects within the bearing. These complex physical interactions are mathematically governed by highly nonlinear partial differential equations. Therefore, foil bearing design involves detailed calculations of flow fields (velocities, pressures), support structure deflections (structural compliance), and heat transfer phenomena (viscous dissipation in the fluid, frictional heating, temperature profile, etc.). The computational effort in terms of time and hardware requirements make high level engineering analyses tedious which presents an opportunity for development of rule of thumb laws for design guidelines. Scaling laws for bearing clearance and support structure stiffness of radial foil bearings of various sizes are presented in this paper. The scaling laws are developed from first principles using the scale invariant Reynolds equation and support structure deflection equation. Power law relationships are established between the (1) radial clearance and bearing radius and (2) support structure stiffness and bearing radius. Simulation results of static and dynamic performance of various bearing sizes following the proposed scaling laws are presented.

Scaling Laws of Radial Clearance and Bump Stiffness of Radial Foil Bearings

2016 ◽  
Author(s):  
Srikanth Honavara Prasad ◽  
Daejong Kim
Keyword(s):  
Scaling Laws ◽  
Heating Temperature ◽  
Frictional Heating ◽  
Fluid Pressure ◽  
Design Guidelines ◽  
Structural Deformation ◽  
Radial Clearance ◽  
Viscous Effects ◽  
Foil Bearings ◽  
Highly Nonlinear

Design and analysis of foil bearings involve consideration to various physical aspects such as fluid pressure, structural deformation and heat generation due to viscous effects within the bearing. These complex physical interactions are mathematically governed by highly nonlinear partial differential equations. Therefore, foil bearing design involves detailed calculations of flow fields (velocities, pressures), bump deflections (structural compliance) and heat transfer phenomena (viscous dissipation in the fluid, frictional heating, temperature profile etc.). The computational effort in terms of time and hardware requirements make high level engineering analyses tedious which presents an opportunity for development of rule of thumb laws for design guidelines. Scaling laws for bearing clearance and bump stiffness of radial foil bearings of various sizes are presented in this paper. The scaling laws are developed from first principles using the scale invariant Reynolds equation and bump deflection equation. Power law relationships are established between the 1) radial clearance and bearing radius and 2) bump stiffness and bearing radius. Simulation results of static and dynamic performance of various bearing sizes following the proposed scaling laws are presented.

Influence of geometric parameters on the bump foil bearing performance

2019 ◽  
Vol 234 (7) ◽  
pp. 1017-1026
Author(s):  
Sadanand Kulkarni ◽  
Soumendu Jana
Keyword(s):  
Carrying Capacity ◽  
High Speed ◽  
System Development ◽  
Load Capacity ◽  
Radial Clearance ◽  
Load Carrying Capacity ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Load Carrying ◽  
Lift Off

High-speed rotating system development has drawn considerable attention of the researchers, in the recent past. Foil bearings are one of the major contenders for such applications, particularly for high speed and low load rotating systems. In foil bearings, process fluid or air is used as the working medium and no additional lubricant is required. It is known from the published literature that the load capacity of foil bearings depend on the operating speed, viscosity of the medium, clearance, and stiffness of the foil apart from the geometric dimensions of the bearing. In case of foil bearing with given dimensions, clearance governs the magnitude of pressure developed, whereas stiffness dictates the change in radial clearance under the generated pressure. This article deals with the effect of stiffness, clearance, and its interaction on the bump foil bearings load-carrying capacity. For this study, four sets of foil bearings of the same geometry with two levels of stiffness and clearance values are fabricated. Experiments are carried out following two factor-two level factorial design approach under constant load and in each case, the lift-off speed is measured. The experimental output is analyzed using statistical techniques to evaluate the influence of parameters under consideration. The results indicate that clearance has the maximum influence on the lift-off speed/ load-carrying capacity, followed by interaction effect and stiffness. A regression model is developed based on the experimental values and model is validated using error analysis technique.

Investigation of Structural Conformity in a Three-Pad Adaptive Air Foil Bearing With Regard to Active Control of Radial Clearance

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Hossein Sadri ◽  
Henning Schlums ◽  
Michael Sinapius
Keyword(s):  
Shape Control ◽  
Degrees Of Freedom ◽  
Load Capacity ◽  
Radial Clearance ◽  
Foil Bearings ◽  
Compliant Structure ◽  
Foil Bearing ◽  
Points Of View ◽  
Lift Off ◽  
Structural Conformity

Abstract Various solutions for the design of oil-free bearings are discussed in the literature. Adding hydrodynamic preload to the foil bearings by profiling the inner bore of the bearing is one of the most frequently investigated methods for improving the bearing stability and damping character of the entire system. However, this approach leads to a reduced load capacity and thus to an increased lift-off speed of the foil bearings. Observations of this kind lead to the presentation of various solutions for active bearing contour adjustment, which benefits from different profiles of the lubricant film. Most of these concepts use piezoelectric stack actuators to generate the required alternating force, although the influence of the stiffness of adaptive elements on bearing performance is not fully discussed in the literature. The focus of this study is on the investigation of structural conformity, i.e., the harmonization of stiffness with respect to the requirements for shape control and load capacity of an adaptive air foil bearing (AAFB). The result may be a basis for the consideration of additional degrees of freedom in any concept with shape control as the main design framework in interaction between the lubricant and compliant structure in an air foil bearing from both static and dynamic points of view.

Hybrid Air Foil Bearings With External Pressurization

Tribology ◽  
2006 ◽  
Author(s):  
Daejong Kim ◽  
Soonkuk Park
Keyword(s):  
Load Capacity ◽  
Experimental Studies ◽  
Axial Flow ◽  
Steel Tube ◽  
Operating Conditions ◽  
Drag Torque ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Hybrid Operation ◽  
Lift Off

Foil bearings are widely used for oil-free microturbomachinery. One of the critical technical issues related to reliability of the foil bearings is a coating wear on the top foil and rotor during start/stops. Especially for heavily loaded foil bearings, large start torque requires a large drive motor. Bearing cooling is also mandatory for certain applications because the foil bearings can generate significant amount of heat depending on operating conditions. Usually axial flow is used through the space between the top foil and bearing sleeve. In this paper, a hybrid air foil bearing with external pressurization is introduced. A flexible steel tube is attached to the backside of the top foil with orifice holes, and externally pressurized air is directly supplied to the bearing clearance to lift off the rotor before rotor spins. The hybrid operation eliminates the coating wear during start/stop cycles, reduces drag torque during starts, and eliminates axial flow cooling. The hybrid foil gas bearing was constructed using a multiple compression springs to demonstrate a feasibility of the concept. A simple analytical model to calculate top foil deflection under hydrostatic pressurization has been developed. Predictions via orbit simulations indicate the hybrid air foil bearings can have much higher critical speed and onset speed of instability than hydrodynamic counter part. Measured load capacity was slightly higher than hydrodynamic bearing even under smaller amount of air flow. In addition, the hybrid operation was very effective for bearing cooling even if the cooling flow rate was lower than hydrodynamic counterpart. The measured very small drag torque during the start/stop demonstrates the hybrid foil bearing can have near-infinite life time without wear of the bearing and rotor surface. The experimental studies show high potential of the hybrid air foil bearings for various oil-free turbomachinery, especially for heavily loaded high temperature applications.

scholarly journals Compliant Foil Journal Bearing Performance at Alternate Pressures and Temperatures

2008 ◽  
Author(s):  
Robert J. Bruckner ◽  
Bernadette J. Puleo
Keyword(s):  
Journal Bearing ◽  
Load Capacity ◽  
Ambient Pressure ◽  
Operating Conditions ◽  
Test Program ◽  
Foil Bearings ◽  
Current Test ◽  
Foil Bearing ◽  
Development Risk ◽  
Highly Loaded

An experimental test program has been conducted to determine the highly loaded performance of current generation gas foil bearings at alternate pressures and temperature. Typically foil bearing performance has been reported at temperatures relevant to turbomachinery applications but only at an ambient pressure of one atmosphere. This dearth of data at alternate pressures has motivated the current test program. Two facilities were used in the test program, the ambient pressure rig and the high pressure rig. The test program utilized a 35 mm diameter by 27 mm long foil journal bearing having an uncoated Inconel X-750 top foil running against a shaft with a PS304 coated journal. Load capacity tests were conducted at 3, 6, 9, 12, 15, 18, and 21 krpm at temperatures from 25°C to 500°C and at pressures from 0.1 to 2.5 atmospheres. Results show an increase in load capacity with increased ambient pressure and a reduction in load capacity with increased ambient temperature. Below one-half atmosphere of ambient pressure a dramatic loss of load capacity is experienced. Additional lightly loaded foil bearing performance in nitrogen at 25°C and up to 48 atmospheres of ambient pressure has also been reported. In the lightly loaded region of operation the power loss increases for increasing pressure at a fixed load. Knowledge of foil bearing performance at operating conditions found within potential machine applications will reduce program development risk of future foil bearing supported turbomachines.

Link-Spring Model of Bump-Type Foil Bearings

2009 ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Wide Spectrum ◽  
Load Capacity ◽  
Ambient Air ◽  
Radial Clearance ◽  
Interaction Forces ◽  
Friction Forces ◽  
Foil Bearings ◽  
Foil Bearing

The field experiences of gas foil bearings (GFBs) from the 1960s prove that GFBs offer several advantages over traditional oil bearings and rolling element bearings. They have the potential to be applied in a wide spectrum of turbomachinery. Bump-type foil bearings, which are considered as the best structure for GFBs, can be simply described as a hydrodynamic bearing utilizing the ambient air as the lubricant and a smooth shell supported by a corrugated bump foil as the bearing surface. However, the performance predictions of bump-type foil bearings are difficult due to mechanical complexity of the support elastic structure, especially for the effects of four factors, elasticity of bump foil, interaction forces between bumps, friction forces at contact surfaces, and local deflection of top foil. In this investigation, an analytical model of bump-type foil bearings considering the effects of all above factors is presented. In this model, each bump of the bump strip is simplified to two rigid links and a horizontally spaced spring, whose stiffness is determined from Castigliano’ theorem. Then, interaction forces and friction forces can be coupled with the bump flexibility though the horizontal elementary spring. The local deflection of top foil is described using a Finite Element model and added to the film thickness for the pressure prediction with the Reynolds’ equation. The bump deflections of a strip with ten bumps under different load distributions are calculated with the presented model and the predictions show consistency with published results. Moreover, the predicted bearing load and film thickness of a full bump-type foil bearing using this model are very close to the experimental data. Also, radial clearance and friction force variations in the foil bearing are noted to change the stiffness of bump significantly. And the predictions from the calculation with a proper selection of radial clearance and friction coefficients show extremely good agreement with the experimental data. The assumption of minimum reachable film thickness is based on experimental data to determine the load capacity of bearing. The results demonstrate that the radial clearance of foil bearing has an optimum value for the maximum load capacity.

Effect of Operating Conditions on the Elastohydrodynamic Performance of Foil Thrust Bearings for Supercritical CO2 Cycles

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Kan Qin ◽  
Ingo H. Jahn ◽  
Peter A. Jacobs
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Supercritical Co2 ◽  
Load Capacity ◽  
Fluid Phase ◽  
Operating Conditions ◽  
Inertia Force ◽  
Fluid Structure ◽  
Thrust Bearings ◽  
Foil Bearings

In this paper, a quasi-three-dimensional fluid–structure model using computational fluid dynamics for the fluid phase is presented to study the elastohydrodynamic performance of foil thrust bearings for supercritical CO2 cycles. For the simulation of the gas flows within the thin gap, the computational fluid dynamics solver Eilmer is extended, and a new solver is developed to simulate the bump and top foil within foil thrust bearings. These two solvers are linked using a coupling algorithm that maps pressure and deflection at the fluid structure interface. Results are presented for ambient CO2 conditions varying between 0.1 and 4.0 MPa and 300 and 400 K. It is found that the centrifugal inertia force can play a significant impact on the performance of foil thrust bearings with the highly dense CO2 and that the centrifugal inertia forces create unusual radial velocity profiles. In the ramp region of the foil thrust bearings, they generate an additional inflow close to the rotor inner edge, resulting in a higher peak pressure. Contrary to the flat region, the inertia force creates a rapid mass loss through the bearing outer edge, which reduces pressure in this region. This different flow fields alter bearing performance compared to conventional air foil bearings. In addition, the effect of turbulence in load capacity and torque is investigated. This study provides new insight into the flow physics within foil bearings operating with dense gases and for the selection of optimal operating condition to suit CO2 foil bearings.

A Thermohydrodynamic Sparse Mesh Model of Bump-Type Foil Bearings

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko
Keyword(s):  
Load Capacity ◽  
Computational Effort ◽  
Radial Clearance ◽  
Foil Bearings ◽  
Mesh Model ◽  
Thermal Growth ◽  
Bearing Load ◽  
Cooling Air ◽  
Air Film ◽  
Generalized Reynolds Equation

A numerical model for 3D thermohydrodynamic analysis of bump-type foil bearings with a sparse mesh across the air film is described. The model accounts for heat convection into cooling air, thermal expansion of the bearing components, and material property variations due to temperature rise. Deflection of the compliant foil strip, described as a link-spring structure, is coupled to the solution of the generalized Reynolds equation and the energy equation to account for the effect of foil deformation on the film thickness. The variation in bump stiffness with the thermal growth of bumps is also considered in the model. The unique airflow in foil bearings created by the top foil detachment in the subambient region is analyzed for use in modifying the thermal boundary condition. The Lobatto point quadrature algorithm is used to represent the model on a sparse mesh and thereby reduce the computational effort. The calculated bearing temperatures are in remarkable agreement with both the published test data with the use of cooling air and that without the use of cooling air. The change of bearing radial clearance due to thermal growth of the bearing components was found to significantly affect the bearing load and to be a likely cause of the obvious drop in load capacity with a rise in ambient temperature.

Design Characteristics of an Aerodynamic Foil Bearing With Adaptable Bore Clearance

2018 ◽  
Author(s):  
Hossein Sadri ◽  
Henning Schlums ◽  
Michael Sinapius
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Load Capacity ◽  
Functional Model ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Static Properties ◽  
Advantages And Disadvantages ◽  
Aerodynamic Pressure ◽  
Foil Bearing

Aerodynamic foil bearings are suitable to support light, high-speed rotors under extreme operating conditions such as very low or very high temperatures, e.g. in cooling turbines, small gas turbines or exhaust gas turbochargers. The required bearing load capacity is generated by an aerodynamic pressure build-up in the corresponding lubrication gap. Due to the high dependence of the bearing performance on the bore geometry, the rotordynamic behavior (e.g. bearing stability) and static properties (e.g. load capacity) as a function of radial clearance and hydrodynamic preload are one of the main points of interest in recent studies. The outcome of both the experimental and the numerical investigations show the advantages and disadvantages of the various configurations of the bearing bore in different operating conditions. These observations lead to the basic idea of an adaptive air foil bearing (AAFB) in which, depending on the operating conditions, the bearing bore contour is changed by means of piezoelectric actuators applied to the compliant supporting shell. Similar to other shape morphing approaches, optimization with regard to various components of the mechanism is the next step in the design process after targeting the design pattern. This paper concentrates on an AAFB as an efficient approach to actively shape the contour of the bore clearance in a 3-pad bearing. Numerous FEM analyses of a functional model for an AAFB in addition to the experimental efforts reveal the main concerns of the design. Finally, the result of this study is a working graph for the AAFB under various loading conditions while operating with different input voltages of the actuators.

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