On the Dynamics of Elastohydrodynamic Mixed Lubricated Ball Bearings. Part I: Formulation of Stiffness and Damping Coefficients

2005 ◽  
Vol 219 (6) ◽  
pp. 411-421 ◽  
Author(s):  
M Sarangi ◽  
B. C. Majumdar ◽  
A. S. Sekhar
Keyword(s):  
Surface Roughness ◽  
Steady State ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Design Parameters ◽  
Asperity Contact ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Stiffness And Damping

The problems of stiffness and damping characteristics of isothermal elastohydrodynamic mixed lubricated point contact are evaluated numerically considering surface roughness effect including asperity contact load. A set of equations under steady-state and dynamic conditions is derived from the classical Reynolds equation, using linear perturbation method. The elasticity equation and steady-state Reynolds equation are solved simultaneously for finding the steady-state pressure distribution, using finite difference method. Then, the set of perturbed equations is solved for the dynamic pressure distribution in the contact. A Gaussian surface roughness is adopted to model both surface roughness and mixed lubrication. Total load capacity of the contact is calculated from the lubricant film pressure and contact pressure distribution. Results are compared with those of smooth isothermal cases. The stiffness and damping coefficients of the contact are determined using the dynamic pressures. The asperity contact stiffness is calculated separately. Effect of various design parameters on stiffness and damping characteristics of a ball bearing is investigated.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearing: Part 4 — Fitted Type of Bearings

Tribology ◽  
2006 ◽  
Author(s):  
A. W. Yacout ◽  
A. S. Ismaeel ◽  
S. Z. Kassab
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Major Effect ◽  
Design Parameters ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Spherical Bearing ◽  
Stiffness And Damping ◽  
Fluid Compressibility

Analytical solutions are not available for spherical bearing problems except for very specialized cases. However, this study offers a theoretical analysis, using the first order perturbations, to evaluate the frequency dependent stiffness and damping characteristics of compensated hydrostatic thrust spherical bearing including the surface roughness, the shaft rotation and the recess volume fluid compressibility effects. The dynamic stiffness and damping coefficients are presented for capillary tube and/or office compensated bearing. Results are obtained for various vibration frequencies or squeeze parameters (frequency parameters) and recess volume fluid compressibility parameters in addition to the other usual bearing design parameters. The study shows that both of the surface roughness and the centripetal inertia have slight effect on the stiffness and the damping coefficients while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearings: Part 5 of 5 — Clearance Type of Bearings

2007 ◽  
Author(s):  
Ahmad W. Yacout
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Major Effect ◽  
Design Parameters ◽  
Compressibility Effect ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Fluid Compressibility

This study has theoretically analyzed the surface roughness, centripetal inertia and recess volume fluid compressibility effects on the dynamic behavior of a restrictor compensated hydrostatic thrust spherical clearance type of bearing. The stochastic Reynolds equation, with centripetal inertia effect, and the recess flow continuity equation with recess volume fluid compressibility effect have been derived to take into account the presence of roughness on the bearing surfaces. On the basis of a small perturbations method, the dynamic stiffness and damping coefficients have been evaluated. In addition to the usual bearing design parameters the results for the dynamic stiffness and damping coefficients have been calculated for various frequencies of vibrations or squeeze parameter (frequency parameter) and recess volume fluid compressibility parameter. The study shows that both of the surface roughness and the centripetal inertia have slight effects on the stiffness coefficient and remarkable effects on the damping coefficient while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics. The cross dynamic stiffness showed the bearing self-aligning property and the ability to oppose whirl movements. The orifice restrictor showed better dynamic performance than that of the capillary tube.

Steady-State and Dynamic Behaviour of Multi-Recess Hybrid Oil Journal Bearings

1979 ◽  
Vol 21 (5) ◽  
pp. 345-351 ◽  
Author(s):  
M. K. Ghosh ◽  
B. C. Majumdar ◽  
J. S. Rao
Keyword(s):  
Perturbation Theory ◽  
Steady State ◽  
Theoretical Analysis ◽  
Dynamic Behaviour ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Time Dependent ◽  
Damping Coefficients ◽  
Stiffness And Damping

A theoretical analysis of the steady-state and dynamic characteristics of multi-recess hybrid oil journal bearings is presented. A perturbation theory for small vibrations is used to solve an incompressible, finite journal bearing with a time-dependent term. Load capacity, attitude angle, friction parameter, stiffness and damping coefficients are evaluated for a capillary-compensated bearing.

scholarly journals Multi-Objective Optimisation of an Aerostatic Pad: Design of Position, Number and Diameter of the Supply Holes

2020 ◽  
Vol 36 (3) ◽  
pp. 347-360
Author(s):  
F. Colombo ◽  
F. Della Santa ◽  
S. Pieraccini
Keyword(s):  
Genetic Algorithm ◽  
Load Capacity ◽  
Design Parameters ◽  
Objective Functions ◽  
Aerostatic Bearing ◽  
Multiobjective Optimisation ◽  
Damping Coefficients ◽  
Supply Pressure ◽  
Design Variables ◽  
Stiffness And Damping

ABSTRACTIn this paper, a rectangular aerostatic bearing with multiple supply holes is optimised with a multiobjective optimisation approach. The design variables taken into account are the supply holes position, their number and diameter, the supply pressure, while the objective functions are the load capacity, the air consumption and the stiffness and damping coefficients. A genetic algorithm is applied in order to find the Pareto set of solutions. The novelty with respect to other optimisations which can be found in literature is that number and location of the supply holes is completely free and not associated to a pre-defined scheme. A vector x associated with the supply holes location is introduced in the design parameters and given in input to the optimizer.

Limiting Stiffness and Damping Coefficients of Foil Bearing

2005 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
T. V. V. L. N. Rao
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Necessary Conditions ◽  
Load Capacity ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Infinitesimal Perturbation ◽  
Stiffness And Damping ◽  
Limiting Values ◽  
Gas Journal Bearing

The limiting values of load capacity, stiffness and damping coefficients for a foil bearing are presented. The necessary conditions for high bearing numbers (journal operating at high speed) are obtained by simplifying the compressible Reynolds equation. Linearized stiffness and damping coefficients are obtained using infinitesimal perturbation method. Results of load capacity, stiffness and damping coefficients, for foil bearing are compared with those obtained for a rigid gas journal bearing. The limiting values of dynamic characteristics for a foil bearing are constant for all eccentricity ratios.

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

2006 ◽  
Vol 129 (3) ◽  
pp. 850-857 ◽  
Author(s):  
Luis San Andrés ◽  
Dario Rubio ◽  
Tae Ho Kim
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Load Capacity ◽  
Test System ◽  
Foil Bearings ◽  
Rotor Imbalance ◽  
Synchronous Motion ◽  
Damping Characteristics ◽  
Rotor Surface ◽  
Stiffness And Damping

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10mm. Coast down rotor responses from 25krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5krpm to 15krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

Numerical study on the dynamic characteristics of water-lubricated rubber bearing under asperity contact

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Guo Xiang ◽  
Yijia Wang ◽  
Cheng Wang ◽  
Zhongliang Lv
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Water Film ◽  
Radial Clearance ◽  
Asperity Contact ◽  
Stiffness Coefficient ◽  
Content Type ◽  
Damping Coefficients ◽  
Rubber Bearing ◽  
Stiffness And Damping

Purpose In this study, the dynamic characteristics of the water-lubricated rubber bearing considering asperity contact are numerically studied, including water-film stiffness and damping coefficients and plastic-elastic contact stiffness coefficient. Design/methodology/approach The Kogut-Etsion elastic-plastic contact model is applied to calculate the contact stiffness coefficient at the bearing-bush interface and the perturbed method is used to calculate the stiffness and damping coefficients of water-film. In addition, the rubber deformation is determined by the finite element method (FEM) during the simulation. Parametric studies are conducted to assess the effects of the radial clearance, rubber thickness and elastic modulus on the dynamic characteristic of water-lubricated rubber bearing. Findings Numerical results indicate that stiffness and damping coefficients of water film and the contact stiffness of asperity are increased with the decreasing of the radial clearance and the dynamic coefficients are less sensitive to the rubber thickness compared with the elastic modulus of rubber. Furthermore, due to the existed groove, a sudden change of the water film direct stiffness and damping coefficients is observed when the eccentricity ratio ranges from 0.6 to 1.0. Originality/value It is expected this study can provide more information to establish a dynamic equation of water-lubricated rubber bearings exposed to mixed lubrication conditions.

Plain and Full Floating Bearing Simulations With Rigid Shaft Dynamics

2007 ◽  
Author(s):  
Ian McLuckie ◽  
Scott Barrett
Keyword(s):  
System Development ◽  
Equations Of Motion ◽  
Time Integration ◽  
Forced Response ◽  
Design Parameters ◽  
Integration Scheme ◽  
Damping Coefficients ◽  
Time Integration Scheme ◽  
Combined Solution ◽  
Stiffness And Damping

This paper shows a promising predictive bearing model that can be used to reduce turbocharger bearing system development times. Turbocharger development is normally done by varying design parameters such as bearing geometry in a very time consuming experimentation process. Full Floating Bearings (FFB) are used in most automotive turbochargers and, due to emissions regulations, there has been a push towards downsizing engines and applying turbo charging to generate optimized engine solutions for both gasoline and diesel applications. In this paper the turbocharger rotor is regarded as being rigid, and the equations of motion are solved using the Bulirsch Stoer time integration scheme. These equations are solved simultaneously with the bearing model which is used also to determine nonlinear stiffness and damping coefficients. The bearings are solved using a Rigid Hydro Dynamic (RHD) Finite Difference Successive Over Relaxation (SOR) scheme of Reynolds equation that includes both rotational and squeeze velocity terms. However the solver can also consider bearing and rotor elasticity in a Multi-Body Dynamic (MBD) and Elasto-Hydro Dynamic (EHD) combined solution. Two bearing types have been studied, a plain grooved (PGB) and a full floating bearing (FFB) for comparative purposes. The mathematical models used are generic and suitable for whole engine bearing studies. The results in this paper show they are suitable for determining the onset of turbocharger bearing instability, and also the means by which bearing instability may be suppressed. The current study has investigated forced response with the combined effects of gravity and unbalance. It is worth noting that the effects of both housing excitation and aerodynamic excitation from the compressor and turbine can be easily accommodated, and will be the subject of a future paper. Other topics introduced here that will be explored further in the future include the effect of bearing and rotor flexibility in the MBD and EHD solution and the use of automatically generated stiffness and damping coefficients for any bearing geometry.

Dynamic Reynolds equation for micropolar fluids and the analysis of plane inclined slider bearings with squeezing effect

2007 ◽  
Vol 221 (7) ◽  
pp. 823-829 ◽  
Author(s):  
N. B. Naduvinamani ◽  
G. B. Marali
Keyword(s):  
Reynolds Equation ◽  
Coupling Parameter ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Form Solution ◽  
Squeezing Effect ◽  
Micropolar Fluids ◽  
Slider Bearings ◽  
Damping Characteristics ◽  
Stiffness And Damping

The general dynamic Reynolds equation of sliding-squeezing surfaces with micro-polar fluids is derived for the assessment of dynamic characteristics of bearings with general film thickness. The detailed analysis is presented for the plane inclined slider bearings by using perturbation method. Two Reynolds-type equations corresponding to steady performance and perturbed characteristics are obtained. The closed form solution of these equations is obtained. The numerical computations of the results show that, the micropolar fluids provide an improved characteristics for both steady-state and the dynamic stiffness and damping characteristics. It is found that the maximum steady-load-carrying capacity is function of coupling parameter and is achieved at smaller values of profile parameter for larger values of the coupling parameter.

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