Sinusoidal Three-Lobe Bearings—Optimization and Stability Charts

1980 ◽  
Vol 102 (4) ◽  
pp. 416-424 ◽  
Author(s):  
W. E. ten Napel ◽  
R. Bosma
Keyword(s):  
Film Thickness ◽  
Stability Parameters ◽  
Stability Regions ◽  
Damping Coefficients ◽  
Optimum Position ◽  
Minimum Film Thickness ◽  
Stiffness And Damping

In contradistinction to the commonly used segmented three-lobe bearing, another type of bearing, i.e., the sinusoidal three-lobe bearing has been investigated in this paper. The main advantage of this bearing is that it can very easily be manufactured. Special attention has been paid to problems of optimization with regard to minimum film thickness and friction, respectively. Stiffness and damping coefficients have been calculated as well as stability regions and stability parameters. Additionally, the optimum position of the oil grooves has been investigated.

Improvements to the Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models

2007 ◽  
Author(s):  
Luis San Andre´s ◽  
Tae Ho Kim
Keyword(s):  
Film Thickness ◽  
Gas Turbines ◽  
Load Capacity ◽  
Structural Models ◽  
Underlying Structure ◽  
Fe Model ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Minimum Film Thickness ◽  
Stiffness And Damping

Gas foil bearings (GFBs) find widespread usage in oil-free turbo expanders, APUs and micro gas turbines for distributed power due to their low drag friction and ability to tolerate high level vibrations, including transient rubs and shaft misalignment, static and dynamic. The static load capacity and dynamic forced performance of GFBs depends largely on the material properties of the support elastic structure, i.e. a smooth foil on top of bump strips. Conventional models include only the bumps as an equivalent stiffness uniformly distributed around the bearing circumference. More complex models couple directly the elastic deformations of the top foil to the bump underlying structure as well as to the hydrodynamics of the gas film. This paper details two FE models for the top foil supported on bump strips, one considers a 2D shell anisotropic structure and the other a 1D beam-like structure. The Cholesky decomposition of the stiffness matrix representing the top foil and bump strips is performed off-line prior to computations coupling it to the gas film analysis governed by Reynolds equation. The procedure greatly enhances the computational efficiency of the numerical scheme. Predictions of journal attitude angle and minimum film thickness for increasing static loads and two journal speeds are obtained for a GFB tested decades ago. 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, while underestimating it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data; reproducing closely the experimental circumferential wavy-like minimum film thickness profile. The 1D top foil model is recommended due to its low computational cost. Predicted stiffness and damping coefficients versus excitation frequency show that the two FE top foil structural models result in slightly lower direct stiffness and damping coefficients than those from the simple elastic foundation model.

Influence of dissimilar radial clearances on the performance of hydrodynamic rotor-bearing systems considering misalignment effects

2017 ◽  
Vol 232 (3) ◽  
pp. 231-243 ◽  
Author(s):  
Jian Li ◽  
Haiyin Cao ◽  
Lei Lv ◽  
Hong Yang ◽  
Lianxin Zhang
Keyword(s):  
Finite Difference Method ◽  
Film Thickness ◽  
Type Equation ◽  
External Loading ◽  
Solution Technique ◽  
Damping Coefficients ◽  
Minimum Film Thickness ◽  
Rotor Bearing ◽  
Unbalanced Load ◽  
Stiffness And Damping

Influence of dissimilar radial clearances of the two end bearings on the performance of hydrodynamic rotor-bearing systems is investigated in the present paper. The rotor misalignment effects are considered. A parameter ξ is introduced to measure the dissimilar level and three typical applied points ( Case Left, Case Center, and Case Right) of external load are also investigated during the analysis. Finite difference method is adopted to solve the Reynolds-type equation and verification of the solution technique is conducted by comparison with previous work. The rotor equilibrium postures are solved at different dissimilar parameters ( ξ) for the three external loading situations. Results show that dissimilar radial clearances have significant effects on rotor postures, minimum film thickness, stiffness and damping coefficients. Under unbalanced load situations ( Case Right, Case Left), small values of ξ (<1.0) will alleviate and large one ξ (>1.0) will aggravate the misaligned effects. Meanwhile, the minimum film thickness increases with ξ (<1.0) and decreases with ξ (>1.0). For stiffness and damping coefficients, the variations with ξ have no obvious rules. During the design and analysis of hydrodynamic rotor-bearing systems, the dissimilarity should be considered intensively for reaching appropriate results.

Gas-Expanded Lubricant Performance and Effects on Rotor Stability in Turbomachinery

2014 ◽  
Author(s):  
Brian K. Weaver ◽  
Timothy W. Dimond ◽  
Jason A. Kaplan ◽  
Alexandrina Untaroiu ◽  
Andres F. Clarens
Keyword(s):  
Film Thickness ◽  
Power Loss ◽  
High Speed ◽  
Turbine Generator ◽  
Generator System ◽  
Polyol Ester ◽  
Damping Coefficients ◽  
Wide Range ◽  
Bearing Stiffness ◽  
Stiffness And Damping

Gas-expanded lubricants (GELs) are tunable mixtures of synthetic oil and carbon dioxide that enable dynamic control of lubricant viscosity during bearing operation. This control can help reduce bearing power loss and operating temperatures while also providing direct control over bearing stiffness and damping, which can enhance rotordynamic performance. In this work, the bearing and rotordynamic performance of two representative high-speed machines was evaluated when different lubricants, including GELs, were supplied to the machine bearings. The machines chosen for this analysis, an 8-stage centrifugal compressor and a steam turbine-generator system, represent a wide range of speed and loading conditions encountered in modern turbomachinery. The fluids compared for machine performance were standard petroleum-based lubricants, polyol ester synthetic oils, and polyol ester based-GELs. The performance simulations were carried out using a thermoelastohydrodynamic bearing model, which provided bearing stiffness and damping coefficients as inputs to finite element rotordynamic models. Several bearing performance metrics were evaluated including power loss, operating temperature, film thickness, eccentricity, and stiffness and damping coefficients. The rotordynamic analysis included an evaluation of rotor critical speeds, unbalance response, and stability. Bearing performance results for the compressor showed a 40% reduction in power loss at operating speed when comparing the GEL to the petroleum-based lubricant. The GEL-lubricated compressor also exhibited lower operating temperatures with minimal effects on film thickness. GELs were also predicted to produce lower bearing stiffness when compared to standard fluids in the compressor. Rotordynamic results for the compressor showed that the fluid properties had only minor effects on the unbalance response, while GELs were found to increase the stability margin by 43% when compared with standard fluids. The results from the turbine-generator system also demonstrated increases in low-speed bearing efficiency with the use of GELs, though at higher speeds the onset of turbulent flow in the GEL case offset these efficiency gains. Rotordynamic results for this system showed a contrast with the compressor results, with the GELs producing lower stability margins for a majority of the modes predicted due to increased bearing stiffness in the high-speed turbine bearings and negative stiffness in the lightly loaded, low-speed pinion bearings. These results suggest that GELs could be beneficial in providing control over a wide range of machine designs and operating conditions and that some machines are especially well suited for the tunability that these fluids impart.

Gas-Expanded Lubricant Performance and Effects on Rotor Stability in Turbomachinery

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Brian K. Weaver ◽  
Timothy W. Dimond ◽  
Jason A. Kaplan ◽  
Alexandrina Untaroiu ◽  
Andres F. Clarens
Keyword(s):  
Film Thickness ◽  
Power Loss ◽  
High Speed ◽  
Turbine Generator ◽  
Generator System ◽  
Low Speed ◽  
Damping Coefficients ◽  
Wide Range ◽  
Bearing Stiffness ◽  
Stiffness And Damping

Gas-expanded lubricants (GELs) are tunable mixtures of synthetic oil and carbon dioxide that enable dynamic control of lubricant viscosity during bearing operation. This control can help reduce bearing power loss and operating temperatures while also providing direct control over bearing stiffness and damping, which can enhance rotordynamic performance. In this work, the bearing and rotordynamic performance of two representative high-speed machines was evaluated when different lubricants, including GELs, were supplied to the machine bearings. The machines chosen for this analysis, an eight-stage centrifugal compressor and a steam turbine-generator system, represent a wide range of speed and loading conditions encountered in modern turbomachinery. The fluids compared for machine performance were standard petroleum-based lubricants, polyol ester (POE) synthetic oils, and POE-based GELs. The performance simulations were carried out using a thermoelastohydrodynamic bearing model, which provided bearing stiffness and damping coefficients as inputs to finite element rotordynamic models. Several bearing performance metrics were evaluated including power loss, operating temperature, film thickness, eccentricity, and stiffness and damping coefficients. The rotordynamic analysis included an evaluation of rotor critical speeds, unbalance response, and stability. Bearing performance results for the compressor showed a 40% reduction in power loss at operating speed when comparing the GEL to the petroleum-based lubricant. The GEL-lubricated compressor also exhibited lower operating temperatures with minimal effects on film thickness. GELs were also predicted to produce lower bearing stiffness when compared to standard fluids in the compressor. Rotordynamic results for the compressor showed that the fluid properties had only minor effects on the unbalance response, while GELs were found to increase the stability margin by 43% when compared with standard fluids. The results from the turbine-generator system also demonstrated increases in low-speed bearing efficiency with the use of GELs, though at higher speeds the onset of turbulent flow in the GEL case offset these efficiency gains. Rotordynamic results for this system showed a contrast with the compressor results, with the GELs producing lower stability margins for a majority of the modes predicted due to increased bearing stiffness in the high-speed turbine bearings and negative stiffness in the lightly loaded, low-speed pinion bearings. These results suggest that GELs could be beneficial in providing control over a wide range of machine designs and operating conditions and that some machines are especially well suited for the tunability that these fluids impart.

Theoretical and Experimental Study on Dynamic Coefficients and Stability for a Hydrostatic/Hydrodynamic Conical Bearing

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Guo Hong ◽  
Lai Xinmin ◽  
Cen Shaoqi
Keyword(s):  
Dynamic Performance ◽  
Flow Equation ◽  
Operating Conditions ◽  
Fluid Film ◽  
Radial Clearance ◽  
Stability Parameters ◽  
Damping Coefficients ◽  
Conical Bearing ◽  
The Stability ◽  
Stiffness And Damping

This paper presents a theoretical study and experimental method to recognize the dynamic performance (stiffness and damping coefficients) of an externally pressurized deep/shallow pockets hybrid conical bearing compensated by flat capillary restrictors. The equations governing the flow of fluid film in the conical bearing together with the pressure boundary condition and the restrictor flow equation are solved by using the finite element method. A delicate test rig is constructed and bearings having a big end diameter of 97 mm, a length of 90 mm, and a radial clearance of 0.02–0.025 mm are analyzed. It is assumed that the fluid film force of the hydrostatic/hydrodynamic conical bearing is characterized by a set of linear stiffness and damping coefficients. The experiment used the impulse excitation method to recognize these coefficients and established their characteristics under different operating conditions. Numerical results are compared with the experimental results. The stability parameters of hybrid conical, hydrodynamic, and hydrostatic bearings are compared. The results show that the hybrid conical bearing has the advantages of high load carrying capability and high stability under small eccentricity.

Static and dynamic characteristics of a Rayleigh-steps mechanical seal with reverse steps

2021 ◽  
pp. 135065012110658
Author(s):  
Yunlei Wang ◽  
Jiu Hui Wu ◽  
Lushuai Xu ◽  
Hongjun Liu
Keyword(s):  
Film Thickness ◽  
Optimization Design ◽  
Frictional Torque ◽  
Stable Operation ◽  
Mechanical Seal ◽  
Mechanical Seals ◽  
Angular Misalignment ◽  
Damping Coefficients ◽  
Cavitation Phenomenon ◽  
Stiffness And Damping

This paper presents a Rayleigh-steps mechanical seal with reverse steps (RS-MS), and the governing equation was solved by the finite difference method (FDM). The effects of angular misalignment, working condition parameters, and film thickness on sealing performance were discussed, including the opening force, cavitation ratio, leakage rate, frictional torque, stiffness and damping coefficients. The results indicate that the cavitation phenomenon in the reverse step groove can restrain the leakage, while it also affects the stability of the seal. The angular misalignment makes the seal have greater stiffness and damping coefficients. The stiffness and damping coefficients decrease rapidly with the increase of the film thickness, and the dynamic stability of the mechanical seal decreases with the increase of the film thickness, which is not conducive to the stable operation of the seal. The research results can guide the optimization design of mechanical seals.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

Predictive tool for frictional performance of piston ring-pack/liner conjunction

2019 ◽  
Vol 13 (3) ◽  
pp. 5513-5527
Author(s):  
J. W. Tee ◽  
S. H. Hamdan ◽  
W. W. F. Chong
Keyword(s):  
Film Thickness ◽  
Mathematical Models ◽  
Piston Ring ◽  
Published Data ◽  
Predictive Tool ◽  
Frictional Losses ◽  
Fundamental Understanding ◽  
Minimum Film Thickness ◽  
Piston Ring Pack ◽  
Ring Pack

Fundamental understanding of piston ring-pack lubrication is essential in reducing engine friction. This is because a substantial portion of engine frictional losses come from piston-ring assembly. Hence, this study investigates the tribological impact of different piston ring profiles towards engine in-cylinder friction. Mathematical models are derived from Reynolds equation by using Reynolds’ boundary conditions to generate the contact pressure distribution along the complete piston ring-pack/liner conjunction. The predicted minimum film thickness is then used to predict the friction generated between the piston ring-pack and the engine cylinder liner. The engine in-cylinder friction is predicted using Greenwood and Williamson’s rough surface contact model. The model considers both the boundary friction and the viscous friction components. These mathematical models are integrated to simulate the total engine in-cylinder friction originating from the studied piston ring-pack for a complete engine cycle. The predicted minimum film thickness and frictional properties from the current models are shown to correlate reasonably with the published data. Hence, the proposed mathematical approach prepares a simplistic platform in predicting frictional losses of piston ring-pack/liner conjunction, allowing for an improved fundamental understanding of the parasitic losses in an internal combustion engine.

Dynamic Analysis of Tilting-Pad Journal Bearing—Influence of Pad Deformations

1994 ◽  
Vol 116 (3) ◽  
pp. 621-627 ◽  
Author(s):  
H. Desbordes ◽  
M. Fillon ◽  
C. Chan Hew Wai ◽  
J. Frene
Keyword(s):  
Film Thickness ◽  
Pressure Field ◽  
Journal Bearing ◽  
Maximum Pressure ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Dimensional Finite Element ◽  
The One ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

A theoretical nonlinear analysis of tilting-pad journal bearings is presented for small and large unbalance loads under isothermal conditions. The radial displacements of internal pad surface due to pressure field are determined by a two-dimensional finite element method in order to define the actual film thickness. The influence of pad deformations on the journal orbit, on the minimum film thickness and on the maximum pressure is studied. The effects of pad displacements are to decrease the minimum film thickness and to increase the maximum pressure. The orbit amplitude is also increased by 20 percent for the large unbalance load compared to the one obtained for rigid pad.

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