Luis San Andrés

Bump-Type Foil Bearing Structural Stiffness: Experiments and Predictions

Gas foil bearings (FB) satisfy many of the requirements noted for novel oil-free turbomachinery. However, FB design remains largely empirical, in spite of successful commercial applications. The mechanical structural characteristics of foil bearings, namely stiffness and damping, have been largely ignored in the archival literature. Four commercial bump-type foil bearings were acquired to measure their load capacity under conditions of no shaft rotation. The test bearings contain a single Teflon-coated foil supported on 25 bumps. The nominal radial clearance is 0.036mm for a 38mm journal. A simple test setup was assembled to measure the FB deflections resulting from static loads. The tests were conducted with three shafts of increasing diameter to induce a degree of preload into the FB structure. Static measurements show nonlinear FB deflections, varying with the orientation of the load relative to the foil spot weld. Loading and unloading tests evidence hysteresis. The FB structural stiffness increases as the bumps-foil radial deflection increases (hardening effect). The assembly preload results in notable stiffness changes, in particular for small radial loads. A simple analytical model assembles individual bump stiffnesses and renders predictions for the FB structural stiffness as a function of the bump geometry and material, dry-friction coefficient, load orientation, clearance and preload. The model predicts well the test data, including the hardening effect. The uncertainty in the actual clearance (gap) upon assembly of a shaft into a FB affects most of the predictions.

Finite Element Analysis of Herringbone Groove Journal Bearings: A Parametric Study

Currently, the herringbone groove journal bearing (HGJB) has important applications in miniature rotating machines such as those found in the computer information storage industry. Grooves scribed on either the rotating or stationary member of the bearing pump the lubricating fluid inward thus generating support stiffness and improving its dynamic stability when operating concentrically. The narrow groove theory (NGT), traditionally adopted to model the concentric operation of these bearings, is limited to bearings with a large number of grooves. A finite element analysis is introduced for prediction of the static and rotordynamic forced response in HGJBs with finite numbers of grooves. Results from this analysis are then compared to available experimental data as well as to estimates from the NGT. A bearing geometry parametric study is then conducted to determine optimum rotordynamic force coefficients. A discussion on the temporal variation of the bearing reaction forces and force coefficients for a rotating journal with a small number of grooves is also presented. These changes can be significant at high operating eccentricities, possibly inducing a parametric excitation in rotating systems employing this type of bearing.

On the Numerical Modeling of High-Speed Hydrodynamic Gas Bearings

A numerical study of high-speed hydrodynamic gas bearing performance is presented using both finite element and finite difference methods. Efficient numerical procedures are developed to analyze diffusive-convective thin film gas flows in some simple geometries. A novel direct finite element formulation employing a new class of shape functions is specially devised to solve the Reynolds equation for compressible fluids, The formulation is as computationally efficient as the classical upwind finite element schemes without introducing artificial diffusion into the solution. Bearing load-capacity, static stiffness coefficients and frequency-dependent force coefficients are calculated for gas-lubricated plane and Rayleigh step slider bearings.

Hybrid flexure pivot-tilting pad gas bearings : Analysis and experimental validation

Gas film bearings offer unique advantages enabling successful deployment of high-speed micro-turbomachinery. Current applications encompass micro power generators, air cycle machines and turbo expanders. Mechanically complex gas foil bearings are in use; however, their excessive cost and lack of calibrated predictive tools deter their application to mass-produced oil-free turbochargers, for example. The present investigation advances the analysis and experimental validation of hybrid gas bearings with static and dynamic force characteristics desirable in high-speed turbomachinery. These characteristics are adequate load support, good stiffness and damping coefficients, low friction and wear during rotor startup and shutdown, and most importantly, enhanced rotordynamic stability at the operating speed. Hybrid (hydrostatic/hydrodynamic) flexure pivot-tilting pad bearings (FPTPBs) demonstrate superior static and dynamic forced performance than other geometries as evidenced in a high speed rotor-bearing test rig. A computational model including the effects of external pressurization predicts the rotordynamic coefficients of the test bearings and shows good correlation with measured force coefficients, thus lending credence to the predictive model. In general, direct stiffnesses increase with operating speed and external pressurization; while damping coefficients show an opposite behavior. Predicted mass flow rates validate the inherent restrictor type orifice flow model for external pressurization. Measured coast down rotor speeds demonstrate very low-friction operation with large system time constants. Estimated drag torques from the gas bearings validate indirectly the recorded system time constant.Copyright

Experimental Versus Theoretical Characteristics of a High-Speed Hybrid (Combination Hydrostatic and Hydrodynamic) Bearing

The high-speed test facility designed and installed at Texas A&M to study water lubricated journal bearings has been successfully used to test statically an orifice compensated five-recess-hybrid (combination hydrostatic and hydrodynamic) bearing for two radial clearance configurations. Measurements of relative-bearing position, torque, recess pressure, flow rate, and temperature were made at speeds from 10,000 to 25,000 rpm and supply pressures of 6.89 MPa (1,000 psi), 5.52 MPa (800 psi), and 4.14 MPa (600 psi)

Rotordynamics of Small Turbochargers Supported on Floating Ring Bearings—Highlights in Bearing Analysis and Experimental Validation

Turbochargers (TCs) improve performance in internal combustion engines. Due to low production costs, TC assemblies are supported on floating ring bearings (FRBs). TCs show subsynchronous motions of significant amplitudes over a wide speed range. However, the subsynchronous whirl motions generally reach a limit cycle enabling continuous operation. The paper advances progress on the validation against measurements of linear and nonlinear rotordynamic models for predicting shaft motions of automotive TCs. A comprehensive thermohydrodynamic model predicts the floating ring speeds, inner and outer film temperatures and lubricant viscosity changes, clearances thermal growth, operating eccentricities for the floating ring and journal, and linearized force coefficients. A nonlinear rotordynamics program integrates the FRB lubrication model for prediction of system time responses under actual operating conditions. Measurements of shaft motion in a TC unit driven by pressurized air demonstrate typical oil-whirl induced instabilities and, due to poor lubricant conditions, locking of the floating rings at high shaft speeds. Nonlinear predictions are in good agreement with the measured total amplitude and subsynchronous frequencies when implementing the measured ring speeds into the computational model. The computational tools aid to accelerate TC prototype development and product troubleshooting.

Structural Stiffness, Dry Friction Coefficient, and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to its mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1 mm in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from 25 to 75°C. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e., null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not significantly affect the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.

A Model for Squeeze Film Dampers Operating With Air Entrainment and Validation With Experiments

Squeeze film dampers (SFDs) reduce vibrations and aid in suppressing instabilities in high performance rotor-bearing systems. However, air ingestion and entrapment, pervasive in open-ended dampers with low supply pressures, leads to a bubbly lubricant that severely reduces the dynamic film forces and the overall damping capability. Analyses based on conventional film rupture models, vapor or gaseous lubricant cavitation, fail to predict the actual performance of SFDs, and thus lack credibility in engineering practice. A modified Reynolds equation for prediction of the pressure in a homogeneous bubbly mixture flow is advanced along with an empirical formula for estimation of the amount of air entrained in an open-ended damper. Careful experimentation in a test SFD operating with controlled bubbly mixtures and freely entrained air evidenced similar physical behavior, guided the analytical developments, and provided the basis for validation of the model forwarded, Comparisons of predictions and test results show a fair correlation. A simple equation to predict the amount of air ingestion is also advanced in terms of the damper geometry, supplied flow and operating conditions. The criterion may lack practical implementation since the persistence of air entrainment increases with the frequency and amplitude of journal motions, unless enough lubricant is supplied at all operating conditions.

Effect of Fluid Inertia on Squeeze-Film Damper Forces for Small-Amplitude Circular-Centered Motions

Fluid-film forces generated by squeeze-film dampers (SFD) in response to small-amplitude centered motions are of special interest for stability analyses of rotating machinery employing SFDs with strong centering springs. They form the basis for calculation of linearized damping and inertia force coefficients obtained by subjecting the journal center to very small perturbations in velocity and acceleration. The analysis considers the fluid flow in an open-ends SFD due to small-amplitude circular-centered motions. Simplified governing equations are derived; and regarding the flow to be stable and laminar, the linear flow equations are solved exactly for arbitrary values of the Reynolds number. Exact damping and inertia force coefficient are then derived for open ends SFDs with arbitrary L/D ratios. Presented at the 41st Annual Meeting in Toronto, Ontario, Canada May 12–15, 1986

Measurement of Structural Stiffness and Damping Coefficients in a Metal Mesh Foil Bearing

Engineered Metal Mesh Foil Bearings (MMFB) are a promising low cost bearing technology for oil-free microturbomachinery. In a MMFB, a ring shaped metal mesh (MM) provides a soft elastic support to a smooth arcuate foil wrapped around a rotating shaft. The paper details the construction of a MMFB and the static and dynamic load tests conducted on the bearing for estimation of its structural stiffness and equivalent viscous damping. The 28.00 mm diameter, 28.05 mm long bearing, with a metal mesh ring made of 0.3 mm Copper wire and compactness of 20%, is installed on a test shaft with a slight preload. Static load versus bearing deflection measurements display a cubic nonlinearity with large hysteresis. The bearing deflection varies linearly during loading, but nonlinearly during the unloading process. An electromagnetic shaker applies on the test bearing loads of controlled amplitude over a frequency range. In the frequency domain, the ratio of applied force to bearing deflection gives the bearing mechanical impedance, whose real part and imaginary part give the structural stiffness and damping coefficients, respectively. As with prior art published in the literature, the bearing stiffness decreases significantly with the amplitude of motion and shows a gradual increasing trend with frequency. The bearing equivalent viscous damping is inversely proportional to the excitation frequency and motion amplitude. Hence, it is best to describe the mechanical energy dissipation characteristics of the MMFB with a structural loss factor (material damping). The experimental results show a loss factor as high as 0.7 though dependent on the amplitude of motion. Empirically based formulas, originally developed for metal mesh rings, predict bearing structural stiffness and damping coefficients agreeing well with the experimentally estimated parameters. Note, however, that the metal mesh ring, after continuous operation and various dismantling and reassembly processes, showed significant creep or sag that resulted in a gradual decrease of its structural force coefficients.Copyright