scholarly journals Numerical estimation of linear and nonlinear stiffness and damping coefficients of journal hydrodynamic bearings

Mechanik ◽  
2016 ◽  
pp. 648-649
Author(s):  
Łukasz Breńkacz ◽  
Grzegorz Żywica
Keyword(s):  
Nonlinear Stiffness ◽  
Numerical Estimation ◽  
Hydrodynamic Bearings ◽  
Damping Coefficients ◽  
Linear And Nonlinear ◽  
Stiffness And Damping

scholarly journals The Experimental Identification of the Dynamic Coefficients of two Hydrodynamic Journal Bearings Operating at Constant Rotational Speed and Under Nonlinear Conditions

2017 ◽  
Vol 24 (4) ◽  
pp. 108-115 ◽  
Author(s):  
Łukasz Breńkacz
Keyword(s):  
Least Squares Method ◽  
Propulsion Systems ◽  
Hydrodynamic Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Experimental Identification ◽  
Research Procedure ◽  
Stiffness And Damping ◽  
Rotor Mass

AbstractHydrodynamic bearings are commonly used in ship propulsion systems. Typically, they are calculated using numerical or experimental methods. This paper presents an experimental study through which it has been possible to estimate 24 dynamic coefficients of two hydrodynamic slide bearings operating under nonlinear conditions. During the investigation, bearing mass coefficients are identified by means of a newly developed algorithm. An impact hammer was used to excite vibration of the shaft. The approximation by means of the least squares method was applied to determine bearing dynamic coefficients. Based on the performed research, the four (i.e. two main and two crosscoupled) coefficients of stiffness, damping and mass for each bearing were obtained. The mass coefficients add up to the complex shaft weight. These values are not required for modeling dynamics of the machine because the rotor mass is usually known, however, they may serve as a good indicator to validate the correctness of the stiffness and damping coefficients determined. Additionally, the experimental research procedure was described. The signals of displacements in the bearings and the excitation forces used for determination of the bearing dynamic coefficients were shown. The study discussed in this article is about a rotor supported by two hydrodynamic bearings operating in a nonlinear manner. On the basis of computations, the results of bearing dynamic coefficients were presented for a selected speed.

The Effect of Thermal Distortion on the Characteristics of Large Hydrodynamic Bearings

1988 ◽  
Vol 202 (3) ◽  
pp. 219-225 ◽  
Author(s):  
P G Morton ◽  
J H Johnson ◽  
G D Wale
Keyword(s):  
Experimental Investigation ◽  
Steady State ◽  
Journal Bearing ◽  
Thermal Distortion ◽  
Hydrodynamic Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Oil Whirl ◽  
Stabilizing Effect ◽  
Stiffness And Damping

An experimental investigation has been carried out on a 350 mm partial arc journal bearing to determine the steady state characteristics and the stiffness and damping coefficients. The bearing was found to distort due to thermal influences and the pressure distribution and dynamic coefficients consequently differed markedly from those obtained using standard theoretical techniques. Calculations of the speed at which resonant oil whirl develops in a rotor supported by bearings of this type show that the threshold speed is far higher using experimental coefficients than theoretical coefficients. It is concluded that thermal distortion has a significant stabilizing effect on large hydrodynamic bearings.

A Nonlinear Dynamic Model With Confidence Bounds for Hydrodynamic Bearings

1998 ◽  
Vol 120 (3) ◽  
pp. 595-604 ◽  
Author(s):  
Chin S. Chu ◽  
Kristin L. Wood ◽  
Ilene J. Busch-Vishniac
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Small Amplitude ◽  
Taylor Series Expansion ◽  
Higher Order ◽  
Slider Bearing ◽  
Nonlinear Dynamic Model ◽  
Hydrodynamic Bearings ◽  
Damping Coefficients ◽  
Stiffness And Damping

In conventional rotordynamic modeling, hydrodynamic bearings are often characterized by a set of linear stiffness and damping coefficients obtained from a first-order Taylor series expansion of bearing reactions. Theoretically, these coefficients are only valid for small amplitude motion about an equilibrium position. In this paper, a nonlinear dynamic model that overcomes the small amplitude assumption in the conventional linear analysis is described. By including higher-order terms in the bearing reaction expansion, nonlinearity in the oil film forces for large amplitude motion can be captured and represented by a set of nonlinear stiffness and damping coefficients. These coefficients are functions of static bearing displacement. A finite difference approach is described and is used to solve for these coefficients. The stated model is applied to a conventional slider bearing and a mechanical smart slider bearing that experiences large variations in load. Error assessment is performed numerically on the higher-order solutions to determine an acceptable displacement bound for the higher order coefficients.

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.

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.

Calculation and Measurement of the Stiffness and Damping Coefficients for a Low Impedance Hydrodynamic Bearing

1997 ◽  
Vol 119 (1) ◽  
pp. 57-63 ◽  
Author(s):  
M. J. Goodwin ◽  
P. J. Ogrodnik ◽  
M. P. Roach ◽  
Y. Fang
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Perturbation Technique ◽  
The Novel ◽  
Oil Film ◽  
Hydrodynamic Bearing ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Novel Design

This paper describes a combined theoretical and experimental investigation of the eight oil film stiffness and damping coefficients for a novel low impedance hydrodynamic bearing. The novel design incorporates a recess in the bearing surface which is connected to a standard commercial gas bag accumulator; this arrangement reduces the oil film dynamic stiffness and leads to improved machine response and stability. A finite difference method was used to solve Reynolds equation and yield the pressure distribution in the bearing oil film. Integration of the pressure profile then enabled the fluid film forces to be evaluated. A perturbation technique was used to determine the dynamic pressure components, and hence to determine the eight oil film stiffness and damping coefficients. Experimental data was obtained from a laboratory test rig in which a test bearing, floating on a rotating shaft, was excited by a multi-frequency force signal. Measurements of the resulting relative movement between bearing and journal enabled the oil film coefficients to be measured. The results of the work show good agreement between theoretical and experimental data, and indicate that the oil film impedance of the novel design is considerably lower than that of a conventional bearing.

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

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.

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