Enhanced Groove Geometry for Herringbone Grooved Journal Bearings

2013 ◽  
Author(s):  
J. Schiffmann
Keyword(s):  
Cross Section ◽  
Mass Parameter ◽  
Critical Mass ◽  
Stability Margin ◽  
Design Guidelines ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
Width Ratio ◽  
Constant Pitch ◽  
Order Of Magnitude

Although gas lubricated Herringbone Grooved Journal Bearings (HGJB) are known for high rotordynamic stability thresholds, small clearance to diameter ratios are required for stable rotor operation. Tight clearances not only increase bearing losses but also yield challenging manufacturing and assembly tolerances, which ultimately translate into cost. Traditionally, the grooves of HGJB are of helical nature with constant cross-section and pitch. The current paper aims at increasing the clearance to diameter ratio and the stability threshold of grooved bearings by introducing enhanced groove geometries. The axial evolution of groove width, depth and local pitch are described by individual 3rd order polynomials with four interpolation points. The expression for the smooth pressure distribution resulting from the narrow groove theory is modified to enable the calculation of bearing properties with modified groove patterns. The reduced order bearing model is coupled to a linear rigid body rotordynamic model for predicting the whirl speed map and the corresponding stability. By introducing a critical mass parameter as a measure for stability, a criterion for the instability onset is proposed. The optimum groove geometry is found by coupling the gas bearing supported rotor model with a multi-objective optimizer. By maximizing both the clearance to diameter ratio and the rotordynamic stability it is shown that with optimal groove geometry, which deviates from helicoids with constant pitch and cross-section, the critical mass parameter can be improved by more than one order of magnitude compared to traditional HGJB geometries. The clearance to diameter ratio can be increased by up to 80% while keeping the same stability margin, thus reducing both losses and manufacturing constraints. The optimum groove pattern distributions (width ratio, angle and depth) are summarized for a variety of L/D ratios and for different compressibility numbers in a first attempt to set up general design guidelines for enhanced gas lubricated HGJB.

Enhanced Groove Geometry for Herringbone Grooved Journal Bearings

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
J. Schiffmann
Keyword(s):  
Cross Section ◽  
Mass Parameter ◽  
Critical Mass ◽  
Stability Margin ◽  
Design Guidelines ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
Width Ratio ◽  
Constant Pitch ◽  
Order Of Magnitude

Although gas-lubricated herringbone grooved journal bearings (HGJB) are known for high rotordynamic stability thresholds, small clearance to diameter ratios are required for stable rotor operation. Tight clearances not only increase bearing losses but also yield challenging manufacturing and assembly tolerances, which ultimately translate into cost. Traditionally, the grooves of HGJB are of helical nature with constant cross section and pitch. The current paper aims at increasing the clearance to diameter ratio and the stability threshold of grooved bearings by introducing enhanced groove geometries. The axial evolution of groove width, depth, and local pitch are described by individual third order polynomials with four interpolation points. The expression for the smooth pressure distribution resulting from the narrow groove theory is modified to enable the calculation of bearing properties with modified groove patterns. The reduced order bearing model is coupled to a linear rigid body rotordynamic model for predicting the whirl speed map and the corresponding stability. By introducing a critical mass parameter as a measure for stability, a criterion for the instability onset is proposed. The optimum groove geometry is found by coupling the gas bearing supported rotor model with a multiobjective optimizer. By maximizing both the clearance to diameter ratio and the rotordynamic stability it is shown that with optimal groove geometry, which deviates from helicoids with constant pitch and cross section, the critical mass parameter can be improved by more than one order of magnitude compared to traditional HGJB geometries. The clearance to diameter ratio can be increased by up to 80% while keeping the same stability margin, thus reducing both losses and manufacturing constraints. The optimum groove pattern distributions (width ratio, angle, and depth) are summarized for a variety of L/D ratios and for different compressibility numbers in a first attempt to set up general design guidelines for enhanced gas-lubricated HGJB.

Stability of Flexibly Supported Oil Journal Bearings Using Non-Newtonian Lubricants: Linear Perturbation Analysis

2000 ◽  
Vol 123 (3) ◽  
pp. 651-654 ◽  
Author(s):  
K. Raghunandana ◽  
B. C. Majumdar, and ◽  
R. Maiti
Keyword(s):  
Power Law ◽  
Perturbation Analysis ◽  
Perturbation Technique ◽  
Stability Margin ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
Linear Perturbation ◽  
Flexible Support ◽  
The Stability ◽  
Power Law Index

The purpose of this paper is to study the effect of non-Newtonian lubricant on the stability of oil film journal bearings mounted on flexible support using linear perturbation technique. The model of non-Newtonian lubricant developed by Dien and Elrod is taken into consideration. The dynamic co-coefficients are calculated for different values of power law index and length to diameter ratio. These are then used to find stability margin for different support parameters to study the effect of the non-Newtonian lubricant.

Linear stability analysis of double-layered porous journal bearings under coupled-stress lubrication with slip flow and percolation effect of additives

2019 ◽  
Vol 71 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Shitendu Some ◽  
Sisir Kumar Guha
Keyword(s):  
Linear Stability ◽  
Mass Parameter ◽  
Critical Mass ◽  
Slip Flow ◽  
Tangential Velocity ◽  
Journal Bearings ◽  
Content Type ◽  
Percolation Effect ◽  
The Stability ◽  
Coupled Stress

Purpose In the application of hydrostatic double-layered porous journal bearings, instability of bearing systems is a major problem. On the other hand, the use of non-Newtonian fluid as a lubricant is more practical in the present days. Furthermore, in case of porous bearing, neglecting slip effect and percolation effect of additives into the pores may lead to erroneous result. Hence, this paper aims to present the linear stability analysis of finite hydrostatic double-layered porous journal bearings lubricated with coupled-stress lubricant with tangential velocity slip and percolation effect. Design/methodology/approach First, considering the tangential velocity slip, the most general modified Reynolds-type equation has been derived for the film region and the governing equations for flow in the coarse and fine layers of porous medium incorporating the percolation effect. A linearized first-order perturbation method has been applied to obtain the threshold of stability in terms of critical mass parameter. The effect of various parameters on the stability is investigated and represented in the form of graphs. Furthermore, a comparison between the stability of double- and single-layered porous journal bearings has been exhibited. Findings In this paper, threshold of stability has been obtained in terms of critical mass parameter. The effect of slip coefficient, percolation factor, coupled-stress parameter, eccentricity ratio and bearing feeding parameter on the stability has been found. Originality/value There is no literature available so far that addresses the analysis of the linear stability of externally pressurized double-layered porous journal bearings with slip flow, including the percolation effect under coupled-stress lubrication. But in this paper, all these points are included which made this paper valuable in design purpose.

scholarly journals Foil Bearing Design Guidelines for Improved Stability

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
J. Schiffmann ◽  
Z. S. Spakovszky
Keyword(s):  
Pressure Distribution ◽  
Mass Parameter ◽  
Critical Mass ◽  
Design Guidelines ◽  
Fluid Film ◽  
Structural Damping ◽  
Foil Bearing ◽  
Improved Stability ◽  
Bearing Design ◽  
The Impact

Experimental evidence in the literature suggests that foil bearing-supported rotors can suffer from subsynchronous vibration. While dry friction between top foil and bump foil is thought to provide structural damping, subsynchronous vibration is still an unresolved issue. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing-supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear, rotordynamic model. A sensitivity analysis suggests that structural damping has limited effect on stability. Further, it is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore, selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multiobjective optimization using the foil bearing-supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that, with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2), the optimum shim patterns vary little with bearing geometry; thus, a generalized shim pattern is proposed for low compressibility numbers.

scholarly journals Foil Bearing Design Guidelines for Improved Stability

2012 ◽  
Author(s):  
J. Schiffmann ◽  
Z. S. Spakovszky
Keyword(s):  
Pressure Distribution ◽  
Mass Parameter ◽  
Critical Mass ◽  
Design Guidelines ◽  
Fluid Film ◽  
Structural Damping ◽  
Foil Bearing ◽  
Improved Stability ◽  
Bearing Design ◽  
The Impact

Experimental evidence in the literature suggests that foil bearing supported rotors can suffer from sub-synchronous vibration. While dry-friction between top foil and bump foil is thought to provide structural damping, sub-synchronous vibration is still an unresolved issue and has been recently attributed to the non-linearity of the bump-foil support stiffness. A non-linear rotordynamic model corroborates this hypothesis, however a forcing is required to excite the system. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear rotordynamic model. Using this model it is shown that the excitation source inducing sub-synchronous vibration is a classical aerodynamic instability resulting from bearing fluid film forces. A sensitivity analysis suggests that structural damping has limited effect on stability. It is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis further indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multi-objective optimization using the foil bearing supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2) the optimum shim patterns vary little with bearing geometry, thus a generalized shim pattern is proposed for low compressibility numbers.

Linear and nonlinear analysis of mount angle effects on the dynamic stability of micropolar lubricated hydrodynamic lobed journal bearings

2019 ◽  
Vol 234 (1) ◽  
pp. 104-125 ◽  
Author(s):  
M Zare Mehrjardi ◽  
AD Rahmatabadi ◽  
R Rashidi Meybodi
Keyword(s):  
Nonlinear Analysis ◽  
Dynamic Stability ◽  
High Speed ◽  
Mass Parameter ◽  
Critical Mass ◽  
Journal Bearings ◽  
Nonlinear Method ◽  
Load Carrying ◽  
Linear And Nonlinear ◽  
Generalized Differential

Journal bearings are one of the most widely used types of supporting devices for industrial machinery, especially for high-speed rotary systems. Considering the importance of mechanical systems ability to control vibrations and motion disturbances, the design of noncircular journal bearings has been one of the appropriate techniques used in recent years. In the present work, the effects of mount angle as a noncircularity unique feature on the dynamic stability of lobed journal bearings with micropolar lubricant are studied. For this purpose, modified Reynolds equation based on the linear and nonlinear methods is solved by generalized differential quadrature (GDQ) method. Then the static and dynamic characteristics of two-, three- and four-lobe bearings including load carrying capacity, whirl frequency ratio, critical mass parameter and rotor perturbation in terms of bifurcation diagram and Poincare map are presented for different values of mount angle. Nonlinear analysis results indicate that variation of mount angle can change the rotor response from limit cycle oscillations to convergent perturbation to static equilibrium point. Further, against plain circular journal bearings, choosing an appropriate orientation or mounting angle provides the optimal stability of noncircular lobed journal bearings. Also, the linear analysis results for the range of dynamic stability are more cautious than the nonlinear method in most of investigated cases.

Control of self-excited rotor disturbances in three-lobe journal bearing space using a couple stress lubricant

2021 ◽  
pp. 135065012110195
Author(s):  
Mahdi Zare Mehrjardi ◽  
Asghar Dashti Rahmatabadi
Keyword(s):  
Couple Stress ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Mass Parameter ◽  
Critical Mass ◽  
Journal Bearings ◽  
Polymer Chains ◽  
Couple Stress Fluid ◽  
Analysis Model ◽  
Stability Range

In this study, the dynamic behavior of three-lobe noncircular hydrodynamic journal bearings lubricated with couple stress fluid is presented. Currently, application of journal bearings with different geometries such as lobed bearings and using non-Newtonian lubricants, including various additives, are the common suggested solutions by tribology researchers to improve the performance of rotor-journal bearing systems. Due to the incompatibility of new lubricant behaviors including polymer chains or other types of suspended particles with considerable size from the classic Navier–Stokes equations, different models such as couple stress fluid theory have been proposed to evaluate their performance. To investigate the self-excited rotor disturbances caused by various factors, like operating in critical speeds, simultaneous solution of governing Reynolds equation of oil lubricant and the rotor motion equations has been done. The result of dynamic analyses using linear and nonlinear approaches indicates the possibility of enhancing the stiffness and damping ability of the three-lobe bearings by strengthening the couple stress properties of lubricant. It is seen from the results that by increasing the couple stress parameter of oil, the type of rotor perturbations in the bearing clearance space changes from divergent oscillations, as a leading cause of collision between the rotor surface and the bearing shell, to limit cycle motion around the rotor stable position or convergent fluctuations to the static equilibrium point. This improvement in the stability range of three-lobe journal bearings using a couple stress lubricant appears in the results of a linear analysis model in terms of increasing the critical mass parameter and decreasing the whirl frequency ratio. In addition, bifurcation diagram results show that using noncircular three-lobe bearings instead of circular types and replacing the Newtonian lubricant with the couple stress fluid improve the dynamic stability of rotor- bearing supports.

ISOSPIN DECOMPOSITION OF pp → NNππ CROSS SECTIONS — DO WE SEE A SIGN OF Δ(1600) EXCITATION IN THE nnπ+π+ CHANNEL?

2009 ◽  
Vol 24 (02n03) ◽  
pp. 450-453
Author(s):  
◽  
T. SKORODKO ◽  
M. BASHKANOV ◽  
D. BOGOSLOWSKY ◽  
H. CALÉN ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Pion Production ◽  
Significant Contribution ◽  
Differential Cross Sections ◽  
Pp Collisions ◽  
Theoretical Predictions ◽  
Order Of Magnitude ◽  
The Cross

The two-pion production in pp-collisions has been investigated in exclusive measurements from threshold up to Tp = 1.36 GeV . Total and differential cross sections have been obtained for the channels pnπ+π0, ppπ+π-, ppπ0π0 and also nnπ+π+. For intermediate incident energies Tp > 1 GeV , i.e. in the region, which is beyond the Roper excitation but at the onset of ΔΔ excitation the total ppπ0π0 cross section falls behind theoretical predictions by as much as an order of magnitude near 1.2 GeV, whereas the nnπ+π+ cross section is a factor of five larger than predicted. A model-unconstrained isospin decompostion of the cross section points to a significant contribution of an isospin 3/2 resonance other than the Δ(1232). As a possible candidate the Δ(1600) is discussed.

Analysis of Pneumatic Instability of Externally Pressurized Porous Gas Journal Bearings

1979 ◽  
Vol 101 (1) ◽  
pp. 48-53 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Theoretical Analysis ◽  
Mass Parameter ◽  
Journal Bearings ◽  
Order Perturbation ◽  
Rigid Rotor ◽  
Eccentricity Ratio ◽  
Dynamic Displacement ◽  
First Order ◽  
Supply Pressure ◽  
First Order Perturbation

A theoretical analysis is presented for the study of pneumatic instability for a rigid rotor supported in externally pressurized porous gas journal bearings. The analysis is based on a first-order perturbation with respect to the amplitude of dynamic displacement of rotor. The variation of threshold mass parameter with feeding parameter is shown. In addition, the effects of supply pressure, eccentricity ratio, L/D ratio, and porosity parameter are investigated and presented in the form of graphs.

On the Optimum Groove Geometry for Herringbone Grooved Journal Bearings

2006 ◽  
Vol 128 (3) ◽  
pp. 585-593 ◽  
Author(s):  
A. M. Gad ◽  
M. M. Nemat-Alla ◽  
A. A. Khalil ◽  
A. M. Nasr
Keyword(s):  
Groove Depth ◽  
Radial Force ◽  
Journal Bearings ◽  
Friction Torque ◽  
Performance Characteristics ◽  
Width Ratio ◽  
Geometrical Parameters ◽  
Thrust Bearings ◽  
Circular Groove ◽  
Groove Profile

Recently, herringbone-grooved journal bearings have had important applications in miniature rotating machines. The scribed grooves, on either the rotating or stationary member of the bearing, can pump the lubricant inward, which generates supporting stiffness and improves the dynamic stability, especially for concentric operation. Most of the previous investigations that dealt with herringbone grooved journal bearings and grooved thrust bearings were theoretical. Few experimental attempts for the investigation of the performance characteristics of herringbone grooved journal bearings (HGJBs) and grooved thrust bearings have been done. All these investigations concentrated on rectangular and circular groove profiles of HGJBs. In order to improve the performance characteristics of HGJBs, a new design of the groove profile, the beveled-step groove profile, is introduced. The introduced groove profile is capable of increasing the pressure recovery at the divergence of the flow over the step. In addition, it increases the amount of oil pumped inward over the circular groove profile. Optimization processes were carried out experimentally, in order to obtain the optimal geometry of the introduced groove profile. The optimum geometrical parameters of the groove (groove angle α, groove width ratio β, and groove depth ratio Γ) are 29deg, 0.5, and 2.0, respectively, which give maximum radial force and maximum radial stiffness of the beveled-step HGJB. In order to check the effectiveness of the introduced beveled-step groove profile, the obtained results were compared with that for rectangular groove profile. The comparison shows that the introduced beveled-step HGJBs have higher radial force, higher load carrying capacity, and lower friction torque than the rectangular HGJBs.

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