scholarly journals Theoretical Disquisition on the Static and Dynamic Characteristics of an Adaptive Stepped Hydrostatic Thrust Bearing with a Displacement Compensator

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2949
Author(s):  
Vladimir Kodnyanko ◽  
Andrey Kurzakov ◽  
Olga Grigorieva ◽  
Maxim Brungardt ◽  
Svetlana Belyakova ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Metal Cutting ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Theoretical Research ◽  
Stable Operation ◽  
Adaptive Function ◽  
Main Bearing ◽  
Thrust Bearings ◽  
Wide Range

Stepped hydrostatic thrust bearings used in metal-cutting machines are characterized by high load capacity and damping, which ensure the stable operation of structures. However, in comparison with throttle thrust bearings, they have a high compliance. It is preferable that, in addition to the main bearing function, a modern hydrostatic bearing has the ability to provide low (including negative) compliance for the implementation of an adaptive function in order to actively compensate for the deformation of the machine resilient system, thereby increasing the accuracy of metalworking. This paper considers the design of a stepped hydrostatic thrust bearing, which, in order to reduce the compliance to negative values, features a technical improvement consisting of the use of an active displacement compensator on an elastic suspension. In this paper, the results of mathematical modeling and theoretical research of stationary and non-stationary modes of operation of the adaptive thrust bearing are presented. The possibility of a significant reduction in the static compliance of the structure, including the negative compliance values, is shown. It was found that negative compliance is provided in a wide range of loads, which can be up to 80% of the range of permissible bearing loads. The study of the dynamic characteristics showed that with a targeted selection of parameters that ensure optimal performance, the adaptive thrust bearing is able to operate stably in the entire range of permissible loads. It has been established that an adaptive stepped hydrostatic thrust bearing with a displacement compensator has a high stability margin, sufficient to ensure its operability when implementing the adaptive function.

The Static and Dynamic Characteristics of the Spiral-Grooved Thrust Bearing

1965 ◽  
Vol 87 (3) ◽  
pp. 547-555 ◽  
Author(s):  
S. B. Malanoski ◽  
C. H. T. Pan
Keyword(s):  
Phase Angle ◽  
Dynamic Characteristics ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Radius Ratio ◽  
Oscillatory Motion ◽  
Static And Dynamic Characteristics ◽  
Thrust Bearings ◽  
Rotor Bearing ◽  
Oscillating Motion

A generalized analysis for spiral-grooved thrust bearings is presented. The effects of local radius are considered. For the same grooving geometry and the same inside-to-outside radius ratio, the inflow design is shown to be superior in both stiffness and load capacity. The analysis also treats a relative, transverse, oscillatory motion of the bearing surfaces. Both the magnitude and phase angle (in the temporal sense) of the bearing reaction are dependent on the frequency of the motion. The results for the oscillating motion reveal the possibility of a self-excited, rotor-bearing instability. The criterion for determining the onset of this type of instability is given.

Identification of Dynamic Characteristics of Gas Foil Thrust Bearings Using Base Excitation

2016 ◽  
Author(s):  
Tae Ho Kim ◽  
Moon Sung Park ◽  
Jongsung Lee ◽  
Young Min Kim ◽  
Kyoung-Ku Ha ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Loss Factor ◽  
Load Capacity ◽  
Excitation Frequency ◽  
Vibrational Amplitude ◽  
Test Rig ◽  
Thrust Bearings ◽  
Bearing Plate ◽  
Bearing Stiffness

Gas foil bearings (GFBs) have clear advantages over oil-lubricated and rolling element bearings, by virtue of low power loss, oil-free operation in compact units, and rotordynamic stability at high speeds. However, because of the inherent low gas viscosity, GFBs have lower load capacity than the other bearings. In particular, accurate measurement of load capacity and dynamic characteristics of gas foil thrust bearings (GFTBs) is utmost important to widening their applications to high performance turbomachinery. In this study, a series of excitation tests were performed on a small oil-free turbomachinery with base excitations in the rotor axial direction to measure the dynamic load characteristics of a pair of six-pad, bump-type GFTBs, which support the thrust collar. An electromagnetic shaker provided dynamic sine sweep loads to the test bench (shaking table), which held rigidly the turbomachinery test rig for increasing excitation frequency from 10 Hz to 200 Hz. The magnitude of the shaker dynamic load, represented as an acceleration measured on the test rig, was increased up to 9 G (gravity). An eddy current sensor installed on the test rig housing measured the axial displacement (or vibrational amplitude) of the rotor thrust collar during the excitation tests. The axial acceleration of the rotor relative to the test rig was calculated using the measured displacement. A single degree-of-freedom base excitation model identified the frequency-dependent dynamic load capacity, stiffness, damping, and loss factor of the test GFTB for increasing shaker dynamic loads and increasing bearing clearances. The test results show that, for a constant shaker force and the test GFTB with a clearance of 155 μm, an increasing excitation frequency increases the dynamic load carried by the test GFTB, i.e., bearing reaction force, until a certain value of the frequency where it jumps down suddenly because of the influence from Duffing’s vibrations of the rotor. The bearing stiffness increases and the damping decreases dramatically as the excitation frequency increases. Generally, the bearing loss factor ranges from 0.5 to 1.5 independent of the frequency. As the shaker force increases, the bearing dynamic load, stiffness, damping, and loss factor increase depending on the excitation frequency. Interestingly, the agreements between the measured GFTB dynamic load versus the thrust runner displacement, the measured GFTB static load versus the structural deflection, and the predicted static load versus the thrust runner displacement are remarkable. Further tests with increasing GFTB clearances of 155, 180, 205, and 225 μm revealed that the vibrational amplitude increases and the jump-down frequency decreases with increasing clearances. The bearing load increases, but the bearing stiffness, damping, and loss factor decrease slightly as the clearance increases. The test results after a modification of the GFTB by rotating one side bearing plate by 30° relative to the other side bearing plate revealed insignificant changes in the dynamic characteristics. The present dynamic performance measurements provide a useful database of GFTBs for use in microturbomachinery.

An Accurate Solution of the Gas Lubricated, Flat Sector Thrust Bearing

1977 ◽  
Vol 99 (1) ◽  
pp. 82-88 ◽  
Author(s):  
I. Etsion ◽  
D. P. Fleming
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Thickness Distribution ◽  
Maximum Load ◽  
Accurate Solution ◽  
Operating Conditions ◽  
Thrust Bearings ◽  
Practical Design ◽  
Minimum Film Thickness

A flat sector shaped pad geometry for gas lubricated thrust bearings is analyzed considering both pitch and roll angles of the pad and the true film thickness distribution. Maximum load capacity is achieved when the pad is tilted so as to create a uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves. A comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

Static and Dynamic Characteristics of Aerostatic Circular Porous Thrust Bearings (Effect of the Shape of the Air Supply Area)

2000 ◽  
Vol 123 (3) ◽  
pp. 501-508 ◽  
Author(s):  
S. Yoshimoto ◽  
K. Kohno
Keyword(s):  
Porous Material ◽  
Dynamic Characteristics ◽  
Thrust Bearing ◽  
Aerostatic Bearing ◽  
Bearing Surface ◽  
Static And Dynamic Characteristics ◽  
Thrust Bearings ◽  
Porous Bearing ◽  
Air Supply ◽  
Bearing Design

Recently, graphite porous material has been used successfully in an aerostatic bearing. In actual bearing design, it is often necessary to reduce the thickness of porous material to make the bearing smaller. However, a reduction in thickness results in a reduction in the strength of the porous material. In particular, when the diameter of porous material is large, it is difficult to supply the air through the full pad area of porous material because it deforms. Therefore, in this paper, two types of air supply method (the annular groove supply and the hole supply) in a circular aerostatic porous thrust bearing are proposed to avoid the deflection of the bearing surface. The static and dynamic characteristics of aerostatic porous bearing with these air supply methods are investigated theoretically and experimentally. In addition, the effects of a surface restricted layer on the characteristics are clarified.

On the performance of foil thrust bearing with misaligned bearing runner

2017 ◽  
Vol 69 (2) ◽  
pp. 105-115 ◽  
Author(s):  
Abdelrasoul M. Gad
Keyword(s):  
High Speed ◽  
Thrust Bearing ◽  
Approximation Technique ◽  
Hydrodynamic Effect ◽  
Stable Operation ◽  
Content Type ◽  
Thrust Bearings ◽  
Load Carrying ◽  
Foil Thrust Bearing ◽  
Stiffness And Damping

Purpose Compliant foil thrust bearings are promising bearings for high-speed oil-free turbomachinery. However, most previous experimental and numerical approaches to investigate the performance of these bearings have ignored the effect of bearing runner misalignment. Therefore, this paper aims to evaluate the effects of static and dynamic angular misalignments of the bearing runner on the performance of a gas-lubricated foil thrust bearing. Design/methodology/approach The bearing runner is allowed a maximum angular misalignment that produces a minimum gas film thickness as low as 20 per cent of the nominal clearance. Then, the variations of bearing load carrying capacity, viscous power loss and stiffness and damping coefficients of the gas film with runner misalignment are thoroughly analyzed. The flow in the gas film is modeled with compressible Reynolds equation along with the Couette approximation technique, and the deformation of the compliant bearing is calculated with a robust analytical model. Small perturbations method is used to calculate the force and moment dynamic coefficients of the gas film. Findings The results show that misaligned foil thrust bearings are capable of developing a restoring moment sufficient enough to withstand the imposed misalignments. Furthermore, the enhanced hydrodynamic effect ensures a stable operation of the misaligned bearing, and the results highlighted the role of the compliant bearing structure to maintain foil bearing prominent features even at misaligned conditions. Originality/value The value of this study is the evaluation of the effects of runner angular misalignments on the static and dynamic characteristics of Generation II bump-type foil thrust bearing.

Stability Analysis of Finite Difference Model of Orthogonal Metal Cutting in Presence of Random Noises

1999 ◽  
Author(s):  
Alexandra Rodkina ◽  
Marian Wiercigroch
Keyword(s):  
Metal Cutting ◽  
Necessary Conditions ◽  
Random Noise ◽  
Resistance Force ◽  
Stable Operation ◽  
Difference Model ◽  
Single Degree Of Freedom ◽  
Wide Range ◽  
Orthogonal Metal Cutting ◽  
Cutting Processes

Abstract The dynamics of a nonlinear cutting process in the presence of random noise is defined and investigated. This approach is adequate for a wide range of models describing the orthogonal metal cutting processes by a single-degree-of-freedom oscillator, where the nonlinearity comes from the cutting force in form of a variable resistance force. The method of Lyapunov–Krasovskii functional was adopted to analyze the necessary conditions for a stable operation. The conditions ensuring an asymptotic stability in the presence of random noises are established.

Theoretical Study on Static Performance of Double-Bump Foil Bearings

2021 ◽  
Author(s):  
Fangcheng Xu ◽  
Jianhua Chu ◽  
Wenlin Luan ◽  
Guang Zhao
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Static Characteristics ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Static Performance ◽  
Initial Clearance

Abstract In this paper, single-bump foil models with different thickness and double-bump foil models with different initial clearances are established. The structural stiffness and equivalent viscous damping of double-bump foil and single-bump foil are analyzed by finite element simulation. The results show that the double-layer bump foil has variable stiffness and the displacement of the upper bump is greater than the initial gap when the two-layer bumps contact. A model for obtaining static characteristics of aerodynamic compliant foil thrust bearing is established on the basis of the stiffness characteristics of the double-bump foil. This paper solves gas Reynolds equation, the gas film thickness equation and the foil stiffness characteristic equation via the finite element method and the finite difference method. The static characteristics of the thrust bearings including the bearing pressure distribution, the gas film thickness and the friction power consumption have been obtained. The static characteristics of two kinds of foils have been compared and analyzed, and the effect of initial clearance on the static performance of double-bump foil bearings is studied. The results show that the double-bump foil structure can effectively improve the load capacity of thrust bearing. In addition, the static performance of double-bump foil thrust bearings is between the performance of the single-bump foil bearing and the double-bump foil bearing whose foil’s clearance is zero. The smaller the initial clearance is, the easier it will be to form a stable double-bump foil supporting structure.

Modeling and Experimental Investigation of Micro-Hydrostatic Gas Thrust Bearings for Micro-Turbomachines

2005 ◽  
Author(s):  
C. J. Teo ◽  
Z. S. Spakovszky
Keyword(s):  
Dynamic Stability ◽  
High Speed ◽  
Thrust Bearing ◽  
Dynamic Instability ◽  
Axial Stiffness ◽  
Stable Operation ◽  
Essential Information ◽  
Flow Choking ◽  
Thrust Bearings

One of the major challenges for the successful operation of high-power-density micro-devices lies in the stable operation of the bearings supporting the high-speed rotating turbomachinery. Previous modeling efforts by Piekos [1], Liu et al. [2] and Spakovszky and Liu [3] have mainly focused on the operation and stability of journal bearings. However, since thrust bearings play the vital role of providing axial support and stiffness, there is a need to gain a fuller understanding of their behavior. In this work, a rigorous theory is presented to analyze the effects of compressibility in micro-flows (characterized by low Reynolds numbers and high Mach numbers) through hydrostatic thrust bearings for application to microturbomachines. The analytical model, which combines a 1-D compressible flow model with Finite-Element Analysis, serves as a useful tool for establishing operating protocols and assessing the stability characteristics of hydrostatic thrust bearings. The model is capable of predicting key steady-state performance indicators, such as bearing mass flow, axial stiffness and natural frequency as a function of the hydrostatic supply pressure and thrust bearing geometry. The model has been applied to investigate the static stability of hydrostatic thrust bearings in micro-turbine-generators, where the electrostatic attraction between the stator and rotor gives rise to a negative axial stiffness contribution and may lead to device failure. Thrust bearing operating protocols have been established for a micro-turbopump, where the bearings also serve as an annular seal preventing the leakage of pressurized liquid from the pump to the gaseous flow in the turbine. The dual role of the annular pad poses challenges in the operation of both the device and the thrust bearing. The operating protocols provide essential information for the required thrust bearing supply pressures and axial gaps required to prevent the leakage of water into the thrust bearings for various pump outlet pressures. Good agreement is observed between the model predictions and experimental results. In addition, a dynamic stability analysis is also performed, which indicates the occurrence of unstable axial oscillations due to flow choking effects in both forward and aft thrust bearings. These a-priori dynamic stability predictions were subsequently verified experimentally on a micro-turbocharger. The frequencies of unstable axial oscillations predicted using the model compare favorably to those determined experimentally, thus vindicating the validity of the model. A simple and useful dynamic stability criterion is established, where the occurrence of flow choking in both thrust bearings give rise to dynamic instability.

The Influence of Ambient Pressure on the Measured Load Capacity of Bump-Foil and Spiral-Groove Gas Thrust Bearings at Ambient Pressures up to 69 Bar on a Novel High-Pressure Gas Bearing Test Rig

2019 ◽  
Author(s):  
Jason Wilkes ◽  
Ryan Cater ◽  
Erik Swanson ◽  
Kevin Passmore ◽  
Jerry Brady
Keyword(s):  
Power Loss ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Ambient Pressure ◽  
Spiral Groove ◽  
Test Rig ◽  
Thrust Bearings ◽  
Order Of Magnitude ◽  
Foil Thrust Bearing ◽  
Thrust Load

Abstract This paper will show the influence of ambient pressure on the thrust capacity of bump-foil and spiral-groove gas thrust bearings. The bearings were operating in nitrogen at various pressures up to 69 bar, and were tested to failure. Failure was detected at various pressures by incrementally increasing the thrust load applied to the thrust bearing until the bearing was no longer thermally stable, or until contact was observed by a temperature spike measured by thermocouples within the bearing. These tests were performed on a novel thrust bearing test rig that was developed to allow thrust testing at pressures up to 207 bar cavity pressure at 260°C while rotating at speeds up to 120,000 rpm. The test rig floats on hydrostatic air bearings to allow for the direct measurement of applied thrust load through linkages that connect the stationary thrust loader to the rotor housing. Test results on a 65 mm (2.56 in) bump-foil thrust bearing at 100 krpm show a marked increase in load capacity with gas density, which has not previously been shown experimentally. Results also show that the load capacity of a similarly sized spiral-groove thrust bearing are relatively insensitive to pressure, and supported an order-of-magnitude less load than that observed for the bump-foil thrust bearing. These results are compared with analytical predictions, which agree reasonably with the experimental results. Predicted power loss is also presented for the bump-foil bearing; however, measured power loss was substantially higher.

Development of Foil Thrust Bearings with Simple Structure for Micro Turbines

2011 ◽  
Vol 368-373 ◽  
pp. 1392-1395 ◽  
Author(s):  
Quan Zhou ◽  
Yu Hou ◽  
Ru Gang Chen
Keyword(s):  
High Speed ◽  
Simple Structure ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Complicated Structure ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Rotational Systems ◽  
Micro Turbine ◽  
Foil Thrust Bearing

Because of the low power loss and high stability, foil bearings are suitable lubrication components for high speed rotational systems. At present, the foil bearings used in actual applications almost have complicated structure and are hard to manufacture. In this paper, two kinds of foil thrust bearings with simple structure are presented. Configurations of these two foil thrust bearings are introduced; meanwhile, the load capacity and running stability are also tested in a high speed micro turbine. It is shown that viscoelastic supported foil thrust bearing has higher load capacity and hemisphere convex dots supported foil thrust bearing is more stable in high speed operational condition.

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