Unsteady Flow and Dynamic Behavior of Ultrashort Lomakin Gas Bearings

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
C. J. Teo ◽  
Z. S. Spakovszky ◽  
S. A. Jacobson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Frequency Parameter ◽  
Singular Behavior ◽  
Gas Bearings ◽  
Reduced Frequency ◽  
Flow Through ◽  
Gas Bearing

Ultrashort microscale high-speed gas bearings exhibit a whirl instability limit and dynamic behavior much different from conventional hydrostatic gas bearings. In particular, the design space for a stable high-speed operation is confined to a narrow region and involves a singular behavior. The previously developed ultrashort gas bearing theory (Liu et al. (2005, “Hydrostatic Gas Journal Bearings for Micro-Turbomachinery,” ASME J. Vibr. Acoust., 127(2), pp. 157–164)) assumed fully developed flow in the journal bearing gap. There is experimental evidence that this assumption might not be fully applicable for the relatively short flow-through times in such bearings. This has an impact on the estimation of whirl instability onset, bearing operability and power requirements. In this paper, unsteady flow effects in the bearing gap are investigated with the goal to quantify their impact on the bearing dynamic behavior. It is shown that although three-dimensional flow calculations in the ultrashort journal bearing are necessary to quantify the onset of whirl instability, the underlying mechanisms can be qualitatively described by the impulsive starting of a Couette flow. Using this description, two time scales are identified that govern the journal bearing dynamic behavior: the viscous diffusion time and the axial flow-through time. Based on this, a reduced frequency parameter is introduced that determines the development of the flow field in the journal bearing and, together with bearing force models, yields a criterion for whirl instability onset. Detailed three-dimensional computational fluid dynamics calculations of the journal bearing flow have been conducted to assess the criterion. A singular behavior in whirl ratio as a function of the reduced frequency parameter is observed, verifying the refined stability criterion. Using high-fidelity flow calculations, the effects of unsteady journal bearing flow on whirl instability limit and bearing power loss are quantified, and design guidelines and implications on gas bearing modeling are discussed. The stability criterion is experimentally validated demonstrating repeatable, stable high-speed operation of a novel microbearing test device at whirl ratios of 35.

Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro Gas Journal Bearing Dynamic Behavior

2005 ◽  
Author(s):  
L. X. Liu ◽  
Z. S. Spakovszky
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
High Speed ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Stiffness Anisotropy ◽  
Bearing Stiffness ◽  
Gas Bearing ◽  
Gas Journal Bearing ◽  
Fabrication Tolerance

The high-speed micro hydrostatic gas journal bearings used in the high-power density MIT micro-engines are of very low aspect ratio with an L/D of less than 0.1 and are running at surface speeds of order 500 m/s. These ultra-short high-speed bearings exhibit whirl instability limits and a dynamic behavior much different from conventional hydrostatic gas bearings. The design space for stable high-speed operation is confined to a narrow region and involves singular behavior (Spakovszky and Liu (2003)). This together with the limits on achievable fabrication tolerance that can be achieved in the silicon chip manufacturing technology severely affects bearing operability and limits the maximum achievable speeds of the micro turbomachinery. This paper introduces a novel variation of the axial-flow hydrostatic micro-gas journal bearing concept which yields anisotropy in bearing stiffness. By departing from axial symmetry and introducing biaxial symmetry in hydrostatic stiffness, the bearing’s top speed is increased and fabrication tolerance requirements are substantially relieved making more feasible extended stable high-speed bearing operation. The objectives of this work are: (1) to characterize the underlying physical mechanisms and the dynamic behavior of this novel bearing concept, and (2) to report on the design, implementation and test of this new micro-bearing technology. The technical approach involves the combination of numerical simulations, experiment, and simple, first principles based modeling of the gas bearing flow field and the rotordynamics. A simple description of the whirl instability threshold with stiffness anisotropy is derived explaining the instability mechanisms and linking the governing parameters to the whirl ratio and stability limit. An existing analytical hydrostatic gas bearing model is extended and modified to guide the bearing design with stiffness anisotropy. Numerical simulations of the full non-linear governing equations are conducted to validate the theory and the novel bearing concept. Experimental results obtained from a micro-bearing test device are presented and show good agreement between the theory and the measurements. The theoretical increase in achievable bearing top speed and the relief in fabrication tolerance requirements due to stiffness anisotropy are quantified and important design implications and guidelines for micro gas journal bearings are discussed.

Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro Gas Journal Bearing Dynamic Behavior

2004 ◽  
Vol 129 (1) ◽  
pp. 177-184 ◽  
Author(s):  
L. X. Liu ◽  
Z. S. Spakovszky
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
High Speed ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Stiffness Anisotropy ◽  
Bearing Stiffness ◽  
Gas Bearing ◽  
Gas Journal Bearing ◽  
Fabrication Tolerance

The high-speed microhydrostatic gas journal bearings used in the high-power density MIT microengines are of very low aspect ratio with an L∕D of less than 0.1 and are running at surface speeds of order 500m∕s. These ultra-short high-speed bearings exhibit whirl instability limits and a dynamic behavior much different from conventional hydrostatic gas bearings. The design space for stable high-speed operation is confined to a narrow region and involves singular behavior (Spakovszky and Liu, 2005, “Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings,” ASME J. Vibr. Acoust., 127(3), pp. 254–261). This together with the limits on achievable fabrication tolerance, which can be achieved in the silicon chip manufacturing technology, severely affects bearing operability and limits the maximum achievable speeds of the microturbomachinery. This paper introduces a novel variation of the axial-flow hydrostatic micro gas journal bearing concept, which yields anisotropy in bearing stiffness. By departing from axial symmetry and introducing biaxial symmetry in hydrostatic stiffness, the bearing's top speed is increased and fabrication tolerance requirements are substantially relieved making more feasible extended stable high-speed bearing operation. The objectives of this work are: (i) to characterize the underlying physical mechanisms and the dynamic behavior of this novel bearing concept and (ii) to report on the design, implementation, and test of this new microbearing technology. The technical approach involves the combination of numerical simulations, experiment, and simple, first-principles-based modeling of the gas bearing flow field and the rotordynamics. A simple description of the whirl instability threshold with stiffness anisotropy is derived explaining the instability mechanisms and linking the governing parameters to the whirl ratio and stability limit. An existing analytical hydrostatic gas bearing model is extended and modified to guide the bearing design with stiffness anisotropy. Numerical simulations of the full nonlinear governing equations are conducted to validate the theory and the novel bearing concept. Experimental results obtained from a microbearing test device are presented and show good agreement between the theory and the measurements. The theoretical increase in achievable bearing top speed and the relief in fabrication tolerance requirements due to stiffness anisotropy are quantified and important design implications and guidelines for micro gas journal bearings are discussed.

Influence of geometric parameters and operating conditions on the thermohydrodynamic behaviour of plain journal bearings

2000 ◽  
Vol 214 (5) ◽  
pp. 445-457 ◽  
Author(s):  
I Pierre ◽  
M Fillon
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Thermal Dissipation ◽  
Radial Clearance ◽  
Geometric Factors ◽  
Essential Components ◽  
Mass Flowrate

Hydrodynamic journal bearings are essential components of high-speed machinery. In severe operating conditions, the thermal dissipation is not a negligible phenomenon. Therefore, a three-dimensional thermohydrodynamic (THD) analysis has been developed that includes lubricant rupture and re-formation phenomena by conserving the mass flowrate. Then, the predictions obtained with the proposed numerical model are validated by comparison with the measurements reported in the literature. The effects of various geometric factors (length, diameter and radial clearance) and operating conditions (rotational speed, applied load and lubricant) on the journal bearing behaviour are analysed and discussed in order to inform bearing designers. Thus, it can be predicted that the bearing performance obtained highly depends on operating conditions and geometric configuration.

Three-Dimensional Dynamic Model of TEHD Tilting-Pad Journal Bearing—Part I: Theoretical Modeling

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Junho Suh ◽  
Alan Palazzolo
Keyword(s):  
Heat Conduction ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Tilting Pad ◽  
Fluid Film Thickness ◽  
Three Dimensional Finite Element ◽  
Tilting Pad Journal Bearing

This paper is focused on a new modeling method of three-dimensional (3D) thermo-elasto-hydro-dynamic (TEHD) cylindrical pivot tilting-pad journal bearing (TPJB). Varying viscosity Reynolds equation and 3D energy equation are coupled via lubricant temperature and viscosity relationship. Three-dimensional finite element method (FEM) is adopted for the analysis of: (1) heat conduction in shaft and bearing pad, (2) thermal deformation of shaft and pad, (3) flexible bearing pad dynamic behavior, and (4) heat conduction, convection, and viscous shearing in thin lubricant film. For the computational efficiency, modal coordinate transformation is utilized in the flexible pad dynamic model, and pad dynamic behavior is represented only by means of modal coordinate. Fluid film thickness is calculated by a newly developed node based method, where pad arbitrary thermal and elastic deformation and journal thermal expansion are taken into account simultaneously. The main goal of this research is to provide more accurate numerical TPJB model than developed before so that the designers of rotating machinery are able to understand the bearing dynamic behavior and avoid unpredicted problem by selection of physical parameters.

High-Speed Operation of a Gas-Bearing Supported MEMS-Air Turbine

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
C. J. Teo ◽  
L. X. Liu ◽  
H. Q. Li ◽  
L. C. Ho ◽  
S. A. Jacobson ◽  
...  
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Journal Bearing ◽  
Operating Conditions ◽  
Feed System ◽  
Coupling Effects ◽  
Leakage Flows ◽  
Aspect Ratios ◽  
Air Turbine ◽  
Gas Bearing

Silicon based power micro-electro-mechanical system (MEMS) applications require high-speed microrotating machinery operating stably over a large range of operating conditions. The technical barriers to achieving stable high-speed operation with micro-gas-bearings are governed by (1) stringent fabrication tolerance requirements and manufacturing repeatability, (2) structural integrity of the silicon rotors, (3) rotordynamic coupling effects due to leakage flows, (4) bearing losses and power requirements, and (5) transcritical operation and whirl instability issues. To enable high-power density the micro-turbomachinery must be run at tip speeds comparable to conventional scale turbomachinery. The rotors of the micro-gas turbines are supported by hydrostatic gas journal and hydrostatic gas thrust bearings. Dictated by fabrication constraints the location of the gas journal bearings is at the outer periphery of the rotor. The high bearing surface speeds (target nearly 10×106 mm rpm), the very low bearing aspect ratios (L/D<0.1), and the laminar flow regime in the bearing gap (Re<500) place these micro-bearing designs into unexplored regimes in the parameter space. A gas-bearing supported micro-air turbine was developed with the objectives of demonstrating repeatable, stable high-speed gas-bearing operation and verifying the previously developed micro-gas-bearing analytical models. The paper synthesizes and integrates the established micro-gas-bearing theories and insight gained from extensive experimental work. The characteristics of the new micro-air turbine include a four-chamber journal bearing feed system to introduce stiffness anisotropy, labyrinth seals to avoid rotordynamic coupling effects of leakage flows, a reinforced thrust bearing structural design, a redesigned turbine rotor to increase power, a symmetric feed system to avoid flow and force nonuniformity, and a new rotor micro-fabrication methodology for reduced rotor imbalance. A large number of test devices were successfully manufactured demonstrating repeatable bearing geometry. More specifically, three sets of devices with different journal bearing clearances were produced to investigate the dynamic behavior as a function of bearing geometry. Experiments were conducted to characterize the “as-fabricated” bearing geometry, the damping ratio, and the natural frequencies. Repeatable high-speed bearing operation was demonstrated using isotropic and anisotropic bearing settings reaching whirl-ratios between 20 and 40. A rotor speed of 1.7×106 rpm (equivalent to 370 m/s blade tip speed or a bearing DN number of 7×106 mm rpm) was achieved demonstrating the feasibility of MEMS-based micro-scale rotating machinery and validating key aspects of the micro-gas-bearing theory.

The Comparison of Four Pressure-Thermal Models of Oil Film Bearing With the Non-Newtonian and Temperature-Viscosity Effects

2016 ◽  
Author(s):  
Feng Liang ◽  
Quanyong Xu ◽  
Xudong Lan ◽  
Ming Zhou
Keyword(s):  
Temperature Field ◽  
Numerical Model ◽  
High Speed ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Oil Film ◽  
Viscosity Effects

The thermohydrodynamic analysis of oil film bearing is essential for high speed oil film bearing. The temperature field is coupled with the pressure field. The numerical model can be built or chosen according to the complexity of the objects and requirement of the accuracy. In this paper, four pressure-thermal (P-T) models are proposed, which are zero-dimensional temperature field coupled with Reynolds equation (0D P-T model), two-dimensional temperature field coupled with Reynolds equation (2D P-T model), two-dimensional temperature with third dimensional correction coupled with Dawson equation (2sD P-T model), three-dimensional temperature field coupled with Dawson equation (3D P-T model). The non-Newtonian and temperature-viscosity effects of the lubrication oil are considered in all the four models. Two types of cylindrical journal bearing, the bearing with/without axial grooves, are applied for the simulation. All the simulated cases are compared with the solutions of the CFX. The results show that the 0D P-T model fails to predict the behavior of high speed bearing; The 2D and 2sD P-T model have an acceptable accuracy to predict the performance of the bearing without grooves, but are not able to simulate the P-T field of the bearing with grooves because of the under-developed thermal boundary layer; The 2sD P-T model shows a great improvement when calculating the pressure field compared with the 2D P-T model; the 3D P-T model coincides well with the CFX at any condition. The comparison of these four models provides a reference to help designer choose a proper numerical model for a certain project.

Estimation of the Rotordynamic Coefficients of a Compressor Mounted on Gas Bearings Using the Phase Diagram and the Unbalance Response

2015 ◽  
Author(s):  
Claudia Aide González ◽  
Juan Carlos Jáuregui ◽  
Oscar De Santiago ◽  
Víctor Solórzano
Keyword(s):  
Phase Diagram ◽  
Three Dimensional ◽  
Dynamic Parameters ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Rotordynamic Coefficients ◽  
Dynamic Coefficients ◽  
Unidentified Source ◽  
Spring System ◽  
Gas Bearing

This paper presents a novel method for identifying the dynamic parameters of a gas bearing, whose force coefficients are strong functions of frequency. The method is based on the analysis of the phase diagram with the model assuming a mass-damper-spring system with time-dependent force coefficients. Usually, it is necessary a controlled mechanism to find the transfer function, this condition limits the application of the method. On the other hand, estimation of the damping and stiffness parameters under real loading is very cumbersome and requires a special care on identifying the excitation forces. One of the main difficulties is the isolation of noise and those vibration signals with an unidentified source. In this work, the excitation force was taken from the unbalance loading of a rotor test. Therefore, there is no need for a special test rig. The dynamic parameters can be estimated analyzing data from the actual rotor mounted on the gas bearings. Identifying the parameters that cause gas bearing instabilities is a big challenge. The gas properties are very sensitive to temperature and pressure changes, and, as a consequence the bearing rotor-dynamic coefficients change drastically and the rotor behaves chaotically, which means that the dynamic parameters are nonlinear. In this research a methodology based on the phase diagram construction to identify nonlinear instabilities of gas bearings is presented. The results show the method capability to estimate the dynamic coefficients by the analysis of the energy variation. Among nonparametric methods, the phase diagram or phase space is in use to identify nonlinearities in dynamic systems. The identification is conducted through the analysis of the energy variations. The energy variations can be represented as a three dimensional function E(x,v,t). In this way the phase diagram can be related to the frequency and the dynamic parameters of the system. According to Taken’s theorem, a dynamic system can be obtained by reconstructing the phase diagram. Then, using this method, the damping and stiffness coefficients are estimated.

Theoretical Solution as a Boundary Value Problem for Externally Pressurized Porous Gas-Bearings

1965 ◽  
Vol 87 (3) ◽  
pp. 622-630 ◽  
Author(s):  
H. Mori ◽  
H. Yabe ◽  
T. Shibayama
Keyword(s):  
Porous Media ◽  
Boundary Value ◽  
Three Dimensional ◽  
Flow In Porous Media ◽  
Gas Bearings ◽  
Bearing Clearance ◽  
Reasonable Prediction ◽  
Gas Bearing ◽  
Theoretical Results ◽  
Theoretical Standpoint

In this paper, an analytical solution is obtained and discussed for externally pressurized porous gas-bearings from a theoretical standpoint in which the flowing condition in bearing clearance is taken into consideration as a boundary value of the three-dimensional flow in porous media. This approach makes it possible to investigate the characteristics of various bearing configurations with consideration of anisotropy of porous material. And it is assumed that the flow in bearing clearance is laminar and fully viscous while the flow in porous media is characterized by Darcy’s law. The theoretical results are found to give more reasonable prediction of porous gas-bearing performance than those in the previous paper [1].

Calculation of Stiffness and Damping Properties of Gas Bearings

1968 ◽  
Vol 90 (4) ◽  
pp. 793-803 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Static Load ◽  
Journal Bearing ◽  
Computational Method ◽  
Gas Bearings ◽  
Rotating Speed ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing ◽  
Gas Bearing

The dynamic characteristics of a gas bearing can be represented by a set of spring and damping coefficients (impedances) which are functions of the static load on the bearing, the rotating speed and the whirl frequency of the journal. For a rotor supported in gas bearings, these coefficients can be used directly in a critical speed calculation or an unbalance response calculation. In addition, the coefficients can be employed in a stability investigation. The paper gives the computational method for obtaining the spring and damping coefficients and, also, describes how they are used in rotor calculations and stability studies. Numerical results are given in graphical and tabular form for a tilting pad journal bearing and a three-lobe journal bearing.

Development of a High Speed Gas Bearing Test Rig to Measure Rotordynamic Force Coefficients

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
J. Jeffrey Moore ◽  
Andrew Lerche ◽  
Timothy Allison ◽  
David L. Ransom ◽  
Daniel Lubell
Keyword(s):  
High Speed ◽  
High Amplitude ◽  
Fluid Film ◽  
Test Rig ◽  
Force Coefficient ◽  
Gas Bearings ◽  
Foil Bearings ◽  
Fluid Film Bearings ◽  
Wide Range ◽  
Gas Bearing

The use of gas bearings has increased over the past several decades to include microturbines, air cycle machines, and hermetically sealed compressors and turbines. Gas bearings have many advantages over traditional bearings, such as rolling element or oil lubricated fluid film bearings, including longer life, ability to use the process fluid, no contamination of the process with lubricants, accommodating high shaft speeds, and operation over a wide range of temperatures. Unlike fluid film bearings that utilize oil, gas lubricated bearings generate very little damping from the gas itself. Therefore, successful bearing designs such as foil bearings utilize damping features on the bearing to improve the damping generated. Similar to oil bearings, gas bearing designers strive to develop gas bearings with good rotordynamic stability. Gas bearings are challenging to design, requiring a fully coupled thermo-elastic, hydrodynamic analysis including complex nonlinear mechanisms such as Coulomb friction. There is a surprisingly low amount of rotordynamic force coefficient measurement in the literature despite the need to verify the model predictions and the stability of the bearing. This paper describes the development and testing of a 60,000 rpm gas bearing test rig and presents measured stiffness and damping coefficients for a 57 mm foil type bearing. The design of the rig overcomes many challenges in making this measurement by developing a patented, high-frequency, high-amplitude shaker system, resulting in excitation over most of the subsynchronous range.

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