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.

Effect of fluid inertia on the dynamic coefficients and stability of journal bearings

2000 ◽  
Vol 214 (3) ◽  
pp. 229-240 ◽  
Author(s):  
S. K. Kakoty ◽  
B. C. Majumdar
Keyword(s):  
Reynolds Number ◽  
Journal Bearing ◽  
Perturbation Technique ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Fluid Inertia ◽  
Viscous Forces ◽  
A Value ◽  
The Stability ◽  
Negligible Contribution

In the analysis of hydrodynamic journal bearings the effect of fluid inertia is generally neglected in view of its negligible contribution compared with viscous forces. However, there is a necessity to evaluate its effect at moderate values of the modified Reynolds number. An attempt is made to study the effect of fluid inertia on the stability of journal bearing for a flow in the laminar regime, i.e. for a value of the modified Reynolds number of the order of one. A linear perturbation technique is used to find the dynamic characteristics and stability of a finite journal bearing.

Heat Transfer Enhancement in Annular Shear-Thinning Flows Over a Sudden Pipe Expansion

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Power Law ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Transfer Enhancement ◽  
Heat Transfer Augmentation ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
The Impact

Heat transfer enhancement in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers, Nu, higher than the fully developed value, in the downstream pipe, is observed only for Pr = 10 and 100. Higher Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane. Heat transfer augmentation for Pr = 10 and 100, is more dramatic for suddenly expanding annular flows, in comparison with suddenly expanding pipe flow. For a given annular diameter ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, for both Newtonian and shear-thinning non-Newtonian flows.

Vibration and Dynamic Stability of Pre-Twisted Thick Cantilever Beam Made of Functionally Graded Material

2015 ◽  
Vol 15 (04) ◽  
pp. 1450058 ◽  
Author(s):  
Sukesh Chandra Mohanty ◽  
Rati Ranjan Dash ◽  
Trilochan Rout
Keyword(s):  
Dynamic Stability ◽  
Power Law ◽  
Twist Angle ◽  
Stability Boundary ◽  
Parametric Instability ◽  
Functionally Graded ◽  
Load Factor ◽  
Graded Material ◽  
The Stability ◽  
Power Law Index

In the present work, the vibration and dynamic stability of functionally graded ordinary (FGO) pre-twisted cantilever Timoshenko beam has been investigated. Finite element shape functions are established from differential equations of static equilibrium. Expressions for element stiffness and mass matrices are obtained from energy considerations. Floquet's theory is used to establish the stability boundary. The material properties along the thickness of the beam are assumed to vary according to the power law. The effects of power law index and pre-twist angle on the natural frequencies and dynamic stability of the beam have been investigated. Increase in pre-twist angle enhances the stability of the beam for first mode whereas it makes the beam more prone to parametric instability for the second mode. The increase in power law index is found to have a detrimental effect on the stability of the beam. The chance of parametric instability is enhanced with the increase in static load factor.

scholarly journals Generalized Newtonian flow analysis in the microchannel manufactured by SLA considering nano-scale stair effect

2022 ◽  
Vol 14 (1) ◽  
pp. 168781402110704
Author(s):  
Jianhua Sun ◽  
Hai Gu ◽  
Jie Zhang ◽  
Yuanyuan Xu ◽  
Guoqing Wu ◽  
...  
Keyword(s):  
Power Law ◽  
Flow Analysis ◽  
Surface Force ◽  
Layer By Layer ◽  
Large Power ◽  
Manufacturing Method ◽  
Nano Scale ◽  
The Stability ◽  
Boltzmann Method ◽  
Power Law Index

SLA (stereolithography), as a rapid and accurate additive manufacturing method, can be used to mold the microchannel. The stair effect is inevitable when the part is printed layer by layer, which has an important influence on the printing performance. In the current work, the power-law flow in the microchannel with nano-scale stairs manufactured by SLA is simulated and investigated. To improve the stability caused by the non-Newtonian behavior, a modified lattice Boltzmann method (LBM) is proposed and validated. Then, a series of simulations are conducted and analyzed, the results show that both the stair effect and power-law index are important factors. The stairs on the surface force the streamlines to be curved and increase the outlet velocity. In addition, different power-law indexes result in completely different flows. The small power-law index leads to a much larger velocity than other cases, while the large power-law index makes the outlet velocity unstable at the middle position.

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.

Inflow Conditions and Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Inflow Velocity ◽  
Flow Recirculation ◽  
Shear Thinning Fluids ◽  
Power Law Index ◽  
The Impact ◽  
Inflow Conditions

The impact of inflow conditions on the flow structure and evolution characteristics of annular flows of Newtonian and shear-thinning fluids through a sudden pipe expansion are studied. Numerical solutions to the elliptic form of the governing equations along with the power-law constitutive equation were obtained using a finite-difference scheme. A parametric study is performed to reveal the influence of inflow velocity profiles, annular diameter ratio, k, and power-law index, n, over the following range of parameters: inflow velocity profile = {fully-developed, uniform}, k = {0, 0.5, 0.7} and n = {1, 0.8, 0.6}. Flow separation and entrainment, downstream of the expansion plane, creates central and a much larger outer recirculation regions. The results demonstrate the influence of inflow conditions, annular diameter ratio, and rheology on the extent and intensity of both flow recirculation regions, the wall shear stress distribution, and the evolution and redevelopment characteristics of the flow downstream the expansion plane. Fully-developed inflows result in larger reattachment and redevelopment lengths as well as more intense recirculation, within the central and corner regions, in comparison with uniform inflow conditions.

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 Analysis of a Complex Geared Rotor-Bearing System in a Turbine Reduction Gearbox

2013 ◽  
Author(s):  
Yuanhong Guan ◽  
Edward W. Sieveking ◽  
Varad Sampathkumar
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
Low Frequency ◽  
Stability Margin ◽  
Journal Bearings ◽  
Root Cause ◽  
Rotor Bearing ◽  
Noise Vibration ◽  
The Stability ◽  
Load Conditions

It is well known that the rotor system will meet several critical speeds or unstable regions as its rotation speed increases, especially when the rotor system is supported by journal bearings, since there exists a strong fluid-structure coupling which is rather prone to stability issues. Stability analysis of rotor-bearing systems (such as turbine-compressor) has been extensively studied in the literatures over the past 50 years. However, few studies have been performed on geared rotor-bearing systems, especially for complex multi-stage gear train systems. In this paper, the abnormal noise/vibration problem on a high speed 2 stage epicyclic reduction gearbox of a turbine-generator system is studied. This gearbox showed abnormal low frequency vibrations at low speed cranking and high speed partial load conditions. Further detailed probe testing showed that the gear bodies which were supported by 6 journal bearings had quite large sub-synchronized vibrations and shaft whirls were developed when the abnormal noise was present. In order to better understand the root cause and to fully eliminate such low frequency noise/vibration, a detailed finite element model for the whole turbine-gearbox-generator was developed under different speed / load conditions. The linearized journal bearing stiffness and damping matrix were calculated using a separate tool and then plugged into the above FE model. The gears are modeled as rigid bodies and connected by gear mesh stiffness. Gyroscopic force terms have also been included in the model. The stability of the whole system was evaluated by a complex eigenvalue analysis and the stability margin evaluated by the corresponding damping factor (or log decrement). The model predicts a range of instability regions and has good correlation with testing data. The root cause of this abnormal noise/vibration is due to the strong torsional-lateral coupling of gear systems, and further coupling with the fluid dynamics of the journal bearings under certain speed/load conditions. Some sensitivity studies are also performed in order to increase the stability margin and eliminate the sub-synchronized vibrations.

Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane

2003 ◽  
Vol 70 (6) ◽  
pp. 915-923 ◽  
Author(s):  
R. Usha ◽  
B. Uma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Nonlinear Stability ◽  
Flow System ◽  
Nonlinear Stability Analysis ◽  
Power Law Fluid ◽  
Inclined Plane ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Power Law Index

Weakly nonlinear stability analysis of thin power-law liquid film flowing down an inclined plane including the phase change effects at the interface has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear stability solution and the nonlinear stability solution for the film flow system. The results show that both the supercritical stability and subcritical instability are possible for condensate, evaporating and isothermal power-law liquid film down an inclined plane. The stability characteristics of the power-law liquid film show that isothermal and evaporating films are unstable for any value of power-law index ‘n’ while there exists a critical value of power-law index ‘n’ for the case of condensate film above which condensate film flow system is always stable. Thus, the results of the present analysis show that the mass transfer effects play a significant role in modifying the stability characteristics of the non-Newtonian power-law fluid flow system. The condensate (evaporating) power-law fluid film is more stable (unstable) than the isothermal power-law fluid film flowing down an inclined plane.

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