Lloyd E. Barrett

Frequency Effects in Tilting-Pad Journal Bearing Dynamic Coefficients

This paper examines the effects of damped vibrational frequencies on the linear reduced dynamical stiffness and damping coefficients of tilting-pad journal bearings. The frequency ratio (damped frequency/running speed) can be used to judge the accuracy of employing synchronously reduced linear coefficients in rotordynamic stability analyses. The use of these coefficients can result in simpler formulations of the system dynamical equations of motion and solution techniques as well as reduced computational and analysis time. Results presented here indicate that synchronously reduced bearing dynamical coefficients are generally adequate for stability analyses with positively preloaded tilting-pad bearings. Plots of dynamic coefficients are included for a five-pad bearing. Presented at the 37th Annual Meeting in Cincinnati, Ohio, May 10–13, 1982

The Effect of Bearing Support Flexibility on Critical Speed Prediction

Some vendors and many users of rotating machinery are arbitrarily reducing the bearing damping by as much as 75 percent in order to accurately predict the location of the first and second lateral critical speeds. This paper shows that if the bearing support flexibility is considered, accurate critical speed predictions are possible without reducing the bearing damping. The equations for the equivalent support stiffness and damping are given for a flexible support spring, mass, and damper in series with the fluid film stiffness and damping properties of a tilting-pad bearing. These equations can easily be incorporated with any synchronous response and/or stability computer program. Examples of test stand results for four production rotors are shown illustrating the accuracy of this method. Presented at the 40th Annual Meeting in Las Vegas, Nevada May 6–9, 1985

The Eigenvalue Dependence of Reduced Tilting Pad Bearing Stiffness and Damping Coefficients

A method is presented for calculating reduced tilting pad bearing stiffness and damping coefficients eliminating the explicit dependence of the pad degrees of freedom. Previous analyses are extended to include the real part of the system eigenvalues, so the present analysis is applicable to general free damped vibratory motion as well as synchronous and nonsynchronous steady state response previously considered. The number of coefficients is reduced from a total of 2(5n + 4), when the pad rotational degrees of freedom are retained, to eight, the number required to describe the translational dynamics of a rotor in fixed pad hydrodynamic bearings. The eight coefficients are especially suited for we in bearing optimization schemes for optimizing the stability of rotor-bearing system. Calculations are presented for five pad bearings with the static load directed between pads and with negligible pad inertia for a range of bearing preload and operating Sommerfeld number. Presented as a Society of Tribologists a...

Measured Performance of a Highly Preloaded Three-Lobe Journal Bearing–-Part I: Static Characteristics

The static characteristics of a three-lobe bearing with a preload factor of 0.75 were studied. Operating eccentricity within the clearance space, circumferential film thickness profiles, and temperatures were measured. In addition, circumferential pressure profiles were measured at three axial locations. Three operating speeds were tested and, for each speed, the load was varied so that the Sommerfeld number ranged from 0.23 to 2.87. Data indicated that the maximum pressure occurred circumferentially near the point of minimum oil film. Eccentricity measurements were presented and verified through independent film thickness measurements. Detailed data was provided to facilitate analytical comparisons. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Lahaina, Hawaii, October 16–20, 1994

Thermoelastohydrodynamic analysis of fixed geometry thrust bearings including runner deformation

A thermoelastohydrodynamic theory for the analysis of sector thrust bearings is presented. The analysis includes the generalized Reynolds equation and a fully elliptic three-dimensional energy equation in the film. In addition, full three-dimensional heat transfer is allowed in the pad while axisymmetric conduction is allowed in the runner. Three-dimensional elastic deformation due to mechanical and thermal loading is allowed in the pad while axisymmetric mechanical elasticity is allowed in the runner. The performance of a parallel tapered-land thrust bearing including runner deformation effects is analyzed as a function of different models. It is seen that mechanical deformation of the pad affects the operating characteristics only slightly while thermal deformation of the pad can cause large increases in operating temperature. The runner deformation effects can include a reduction of the maximum film temperature at slight deformation or a large increase in film temperature at the inner radius of the pad...

Measured performance of tilting-pad journal bearings over a range of preloads. Part I: Static operating conditions

This article presents the measured static characteristics for five tilting-pad journal bearings with a range of preload factors. The bearings had five shoes with static forces applied both on the pad and between pads. The journal diameter was 70 mm, with a length-to-diameter ratio of 0.75, a pivot offset ratio of 0.50, and a nominal assembled radial clearance of 81.3 μm. The rocker-backed pads have nominal radial machined clearances of 176.8, 114.3, 91.4, 73.7, and 61.0 μm. These clearances constitute a range of preloads from −0.333 to 0.540. Most tilting pad bearings are intentionally designed with positive preloads, although with pivot wear and/or pad and pivot distortion or machining tolerances, bearings can operate with zero or negative preloads. Measured results for bearings with negative preload factors have not previously been available. Measurements reported here were made for a variety of speed-load conditions encompassing a Sommerfeld number of 0.1 to 4.5. The measured parameters are eccentricity magnitude, attitude angle, film thickness, and temperatures sufficient to define thermal boundary conditions. Also measured are oil supply pressure, flow rate, and on-shaft pressure profiles. The focus of the work presented herein is to quantify the influence of preload on film thickness, maximum pad temperature, and eccentricity magnitude and attitude angle. Measurements showed preload had a moderate influence on operating eccentricity but not on attitude angle. Negative preloads resulted in the greatest temperature rise, although all temperature rises were relatively small.

Analysis of Axially Grooved Journal Bearings with Heat Transfer Effects

An approximate solution technique for axially grooved fluid film journal bearings is presented. The method makes use of earlier approximations for the axial pressure distribution and the circumferential temperature variation and extends the theory to include heat transfer between the film and the bearing and journal. A second-order profile is assumed to represent the temperature distribution across the film. The classical Reynolds equation is applied, using the viscosity determined by the cross-film average of temperature. The conduction of heat through the bearing is modeled in two dimensions by using a series expansion for the temperature in the sleeve, and the journal surface temperature is given by a circumferential average of film temperatures. Results are compared with those of another theory by Lund and with experimental results. The predicted temperatures agree with experiment over the loaded part of a two-axial-groove bearing but not as well in the unloaded part. They agree closely with those giv...

A Flexible Rotor on Flexible Bearing Supports: Stability and Unbalance Response

An experimental study of the effects of bearing support flexibility on rotor stability and unbalance response is presented. A flexible rotor supported by fluid film bearings on flexible supports was used with fifteen support configurations. The horizontal support stiffness was varied systematically while the vertical stiffness was kept constant. The support characteristics were determined experimentally by measuring the frequency response functions of the support structure at the bearing locations. These frequency response functions were used to calculate polynomial transfer functions that represented the support structure. Stability predictions were compared with measured stability thresholds. The predicted stability thresholds agree with the experimental data within a confidence bound for the logarithmic decrement of ±0.01. For unbalance response, the second critical speed of the rotor varied from 3690 rpm to 5200 rpm, depending on the support configuration. The predicted first critical speeds agree with the experimental data within -1.7 percent. The predicted second critical speeds agree with the experimental data within 3.4 percent. Predictions for the rotor on rigid supports are included for comparison.

Influence of Pad Pivot Friction on Tilting-Pad Journal Bearing Measurements—Part I: Steady Operating Position©

This paper presents measured results for the eccentricity ratios for two tilting-pad journal bearing. Comparison between a bearing with spherical seated ball and socket pad pivots and one with line contact rocker-back pad pivots is made. The bearings have a length to diameter ratio of 0.75, offset ratios of 0.50, preloads of about 0.320, a journal diameter of 70 mm and a radial machined pad clearance of 113.0 μm. Measurements were made for a range of speed-load conditions encompassing a Sommerfeld number range of 0.1 to 2.0. Comparison of the eccentricity magnitude for the two bearing agreed within uncertainty levels. For the bearing with rocker-back pad pivots, the journal attitude angle with respect to the applied load direction is nearly zero. Attitude angles range from 13° to 33° for the bearing with spherical seated ball and socket pad pivots. The deviation from zero attitude angle for this bearing increased with increasing speed. A hypothesis for larger pad pivot friction in the ball and socket pivo...

Influence of Pad Pivot Friction on Tilting-Pad Journal Bearing Measurements—Part II: Dynamic Coefficients©

This paper presents measured results for the dynamic stiffness and damping force coefficients for two tilting-pad journal bearings. Comparison between a bearing with spherical seated ball and socket pad pivots and one with line contact rocker-back pad pivots is made. The bearings tested were preloaded five pad designs with load directed on the pivots. The bearings have length to diameter ratios of 0.75, offset ratios of 0.50, preloads of about 0.320, a journal diameter of 70 mm, and radial machined pad clearances of 113.0 μm. Measurements were made for a range of speedload conditions encompassing a Sommerfeld number range of 0.1 to 2.0. Comparison of the principal stiffness and damping coefficients for the two bearings show the same trends. Nearly zero cross-coupled stiffness coefficients were measured for the bearing with rocker-back pad pivots. For the bearing with spherical seated pad pivots, non-dimensional cross-coupled stiffness coefficients for Kxy ranged from -1.2 to -0.9 and for Kyx ranged from -...