Flexure Pivot Tilting Pad Research Articles

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Flexure Pivot Tilting Pad Journal Bearing in Comparison to a Fixed Profile Journal Bearing With Experimental Verification

Abstract In this paper, an efficient numerical method consisting of the real mode component mode synthesis (CMS) model reduction, shooting method with parallel computing, and Floquet analysis was developed for nonlinear rotordynamics analysis of a flexible rotor supported by a four-lobe flexure pivot tilting pad journal bearing (FPTPJB) in load-on-pad (LOP) and load-between-pad (LBP) orientations in comparison to a fixed profile journal bearing (JB) of the same pad geometry. The method used the rotor's finite elements and bearing forces obtained from directly solving the Reynolds equation to determine the limit cycles and Hopf bifurcation types. For the investigated rotor and bearing parameters, the numerical results indicated that the onset speed of instability (OSI) of FPTPJB is considerably higher than that of JB of the same orientation. Also, FPTPJB in LOP orientation yielded substantially higher OSI than the LBP one, whereas the OSI of JB in LOBP orientation was higher than the LOP counterpart. Nonlinear calculation results indicated that all bearing types and orientations gave subcritical Hopf bifurcation. The FPTPJB in LOP orientation produced the largest stable operating region, whereas the JB in LBP configuration yielded the smallest one. The experiment showed subcritical Hopf bifurcation occurred at speed close to the calculated OSI in all cases except FPTPJB in LOP orientation that the OSI is higher than the maximum test rig speed. The whirling orbit had the same frequency as the first critical speed and was precessed in the shaft rotation direction.

Running Performance of a Squeeze Film Air Bearing with Flexure Pivot Tilting Pad

A novel flexure pivot tilting pad squeeze film air bearing (FPTP-SFAB) based on near-field acoustic levitation (NFAL) for a rotor is proposed in this article. The most important advantage of this structure is the suitability of the bearing for high-speed and light load conditions because the FPTP can adapt well to squeeze action during operation. The rotating orbit of the rotor can be adjusted according to the machining conditions. A theoretical model is employed to analyze the running characteristics of the rotor by using the coupled NFAL and FPTP model. Experiments were conducted to investigate the running performance of the rotor–bearing system. Moreover, the effects of input voltage, rotational speed, eccentricity ratio, radial clearance, vibration amplitude, and installation method on bearing performance were analyzed. Numerical and experimental results show that a rotor supported by the FPTP-SFAB with a reasonable input excitation magnitude can effectively adjust the rotating orbit of the rotor and inhibit the divergence of the rotor vibration amplitude, thus improving the stability of the rotor–bearing system under complicated and alternating machining conditions.

Numerical and experimental study on the influence of material characteristics on the levitation performance of squeeze-film air bearing

Abstract This research investigated the effects of material characteristics on the load-carrying capacity of squeeze-film air bearings (SFABs). Bearings with the same size and structure but are made of different materials, namely, aluminum (AL 2024), brass (CuSn35), and spring steel (60Si2Mn), were manufactured and tested. A theoretical analysis model was established to investigate the levitation performance of SFABs by coupling the near-field acoustic levitation (NFAL) and flexure pivot-tilting pad models. A test apparatus with the facility of measuring the floating performance of a shaft was designed and fabricated. Studies have shown that material characteristics are extremely important for the levitation performance of SFABs, and aluminium (AL 2024) was identified as the most suitable materials among the three materials.

Bump-Type Foil Bearings and Flexure Pivot Tilting Pad Bearings for Oil-Free Automotive Turbochargers: Highlights in Rotordynamic Performance

Oil-free turbochargers (TCs) require gas bearings in compact units of enhanced rotordynamic stability, mechanical efficiency, and improved reliability with reduced maintenance costs compared with oil-lubricated bearings. Implementation of gas bearings into automotive TCs requires careful thermal management with accurate measurements verifying model predictions. Gas foil bearings (GFBs) are customarily used in oil-free microturbomachinery because of their distinct advantages including tolerance to shaft misalignment and centrifugal/thermal growth, and large damping and load capacity compared with rigid surface gas bearings. Flexure pivot tilting pad bearings (FPTPBs) are widely used in high-performance turbomachinery since they offer little or no cross-coupled stiffnesses with enhanced rotordynamic stability. The paper details the rotordynamic performance and temperature characteristics of two prototype oil-free TCs; one supported on foil journal and thrust bearings and the other one is supported on FPTP journal bearings and foil thrust bearings of identical sizes (outer diameter (OD) and inner diameter (ID)) with the same aerodynamic components. The tests of the oil-free TCs, each consisting of a hollow rotor (∼0.4 kg and ∼23 mm in OD at the bearing locations), are performed for various imbalances in noise, vibration, and harshness (NVH; i.e., cold air driven rotordynamics rig) and gas stand test facilities up to 130 krpm. No forced cooling air flow streams are supplied to the test bearings and rotor. The measurements demonstrate the stable performance of the rotor–gas bearing systems in an ambient NVH test cell with cold forced air into the turbine inlet. Post-test inspection of the test FPTPGBs after the hot gas stand tests evidences seizure of the hottest bearing, thereby revealing a notable reduction in bearing clearance as the rotor temperature increases. The compliant FPTPGBs offer a sound solution for stable rotor support only at an ambient temperature condition while demonstrating less tolerance for shaft growth, centrifugal, and thermal, beyond its clearance. The current measurements give confidence in the present GFB technology for ready application into automotive TCs for passenger car and commercial vehicle applications with increased reliability.

Experimental and Analytical Studies on Flexure Pivot Tilting Pad Gas Bearings With Dampers Applied to Radially Compliant Pads

Hydrodynamic flexure pivot tilting pad gas bearings (FPTPGBs) can enable successful operation of oil-free microturbomachinery and FPTPGBs with radially compliant pads permit rotor centrifugal and/or thermal growth to exceed original bearing clearances and achieve higher speeds. This work presents the experimental and analytical study of such bearings and the application of dampers behind the pad radial compliance structure. A time domain orbit simulation method was implemented as the primary analysis tool to predict the rotor-bearing response to imbalance, the presence and location of critical speeds, etc., and to compare with test results. Experiments demonstrate the stable hydrodynamic operation of FPTPGBs with an ∼28.6 mm, 0.8 kg rotor above 120 krpm, for the first time. The rotor-bearing system was intentionally destabilized in tests by increasing bearing clearances and the viscoelastic dampers added behind the FPTPGB pads delayed the onset of subsynchronous vibrations (from 43 krpm without damper to above 50 krpm with damper). Midrange subsynchronous vibrations of the destabilized system initiated at ∼20 krpm were suppressed by ∼25 krpm due to the stabilizing effect of rotor centrifugal growth. The viscoelastic dampers had a negligible effect on suppressing these midrange subsynchronous vibrations in experiments, but this was not demonstrated in simulations, presumed to be due to much lower stiffness contribution of the damper at lower frequencies.

Flexure Pivot Tilting Pad Hybrid Gas Bearings: Operation With Worn Clearances and Two Load-Pad Configurations

Abstract Gas film bearings enable the successful deployment of high-speed microturbomachinery. Foil bearings are in use; however, cost and lack of calibrated predictive tools prevent their widespread application. Other types of bearing configurations, simpler to manufacture and fully engineered, are favored by commercial turbomachinery manufacturers. Externally pressurized tilting pad bearings offer a sound solution for stable rotor support. This paper reports measurements of the rotordynamic response of a rigid rotor, 0.825kg and 28.6mm in diameter, supported on flexure pivot tilting pad hybrid gas bearings. The tests are performed for various imbalances, increasing supply pressures, and under load-on-pad (LOP) and load-between-pad (LBP) configurations. Presently, the initial condition of the test bearings shows sustained wear and dissimilar pad clearances after extensive testing reported earlier, (Zhu, X., and San Andrés, L., 2007, “Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,” ASME J. Eng. Gas Turbines Power, 129, pp. 1020–1027). In the current measurements, there are no noticeable differences in rotor responses for both LOP and LBP configurations due to the light-weight rotor, i.e., small static load acting on each bearing. External pressurization into the bearings increases their direct stiffnesses and reduces their damping, while raising the system critical speeds with a notable reduction in modal damping ratios. The rotor supported on the worn bearings shows an ∼10% drop in first critical speeds and roughly similar modal damping than when tested with pristine bearings. Pressurization into the bearings leads to large times for rotor deceleration, thus demonstrating the little viscous drag typical of gas bearings. Rotor deceleration tests with manually controlled supply pressures eliminate the passage through critical speeds, thus paving a path for rotordynamic performance without large amplitude motions over extended regions of shaft speed. The rotordynamic analysis shows critical speeds and peak amplitudes of motion agreeing very well with the measurements. The synchronous rotor responses for increasing imbalances demonstrate the test system linearity. Superior stability and predictable performance of pressurized flexure pivot gas bearings can further their implementation in high performance oil-free microturbomachinery. More importantly, the measurements show the reliable performance of the worn bearings even when operating with enlarged and uneven clearances.

Design of Flexure Pivot Tilting Pads Gas Bearings for High-speed Oil-Free Microturbomachinery

This paper introduces flexure pivot tilting pad gas bearings with pad radial compliance for high-speed oil-free microturbomachinery. The pad radial compliance was for accommodation of rotor centrifugal growth at high speeds. Analytical equation for the rotor centrifugal growth based on plane stress model agreed very well with finite element method results. Parametric studies on pivot offset, preload, and tilting stiffness were performed using nonlinear orbit simulations and coast-down simulations. Higher preload and pivot offset increased both critical speeds of the rotor-bearing system and onset speeds of instability due to the increased wedge effect. Pad radial stiffness and nominal bearing clearance were very important design parameters for high-speed applications due to the physically existing rotor centrifugal growth. From the series of parametric studies, the maximum achievable rotor speed was limited by the minimum clearance at the pad pivot calculated from the rotor growth and radial deflection of pads due to hydrodynamic pressure. Pad radial stiffness also affects the rotor instability significantly. Small radial stiffness could accommodate rotor growth more effectively but deteriorated rotor instability. From parametric studies on a bearing with 28.5mm in diameter and 33.2mm in length, optimum pad radial stiffness and bearing clearance are 1-2×107N∕m and 35μm, respectively, and the maximum achievable speed appears 180krpm. The final design with suggested optimum design variables could be also stable under relatively large destabilizing forces.

Hybrid Flexure Pivot-Tilting Pad Gas Bearings: Analysis and Experimental Validation

Gas film bearings offer unique advantages enabling successful deployment of high-speed microturbomachinery. 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 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, whereas 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 indirectly validate the recorded system time constant.

Rotordynamic Coefficients Measurements Versus Predictions for a High-Speed Flexure-Pivot Tilting-Pad Bearing (Load-Between-Pad Configuration)

Experimental dynamic force coefficients are presented for a four pad flexure-pivot tilting-pad bearing in load-between-pad configuration for a range of rotor speeds and bearing unit loadings. Measured dynamic coefficients have been compared to theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes (NS) model. Predictions from two models—the Reynolds equation and a bulk-flow NS equation models are compared to experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added-mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32kg), but the bulk-flow NS equation predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency-independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The frequency dependency that is accounted for by the added mass coefficient is predicted by the models and arises (in the models) primarily because of the reduction in degrees of freedom from the initial 12 degrees (four pads times three degrees of freedom) to the two-rotor degrees of freedom. For the bearing and condition tested, pad and fluid inertia are secondary considerations out to running speed. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting-pad bearings or flexure-pivot tilting-pad (FPTP) bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. For the bearing tested and the load conditions examined, the present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations. Different results may be obtained for conventional tilting-pad bearings (or this bearing at higher load conditions).

Imbalance Response of a Rotor Supported on Flexure Pivot Tilting Pad Journal Bearings in Series With Integral Squeeze Film Dampers

Measurements of the imbalance responses of a massive 45 kg rotor supported on series (flexure pivot) tilting pad bearings and integral squeeze film dampers (SFDs) are presented. The rotor-bearing configuration is of interest in compressor applications where often oil lubricated dampers are introduced in series with fluid film bearings to relocate critical speeds, enhance the overall system damping, and reduce the risks of rotordynamic instabilities due to seals and impellers, for example. Coast-down experiments from 9000 rpm are conducted for increasing levels of rotor imbalance, and equivalent system damping coefficients identified from the peak amplitude of rotor response while traversing cylindrical mode critical speeds. The tests performed with locked (inactive) and active SFDs demonstrate the effectiveness of the flexible damped support in reducing the system critical speed and improving the overall rotor response with reduced transmitted forces to ground. The SFDs allow safe rotor operation with values of imbalance twice as large as the maximum sustained by the rotor supported on tilting pad bearings alone. The experiments reveal a linear relationship between the peak amplitude of vibration at the critical speeds and the imbalance displacement, even for rotor motions larger than 50% of the tilting pad bearing and damper clearances. The tests also show little cross-coupling effects with the shaft centerline moving along a nearly vertical path. The rotor-bearing system remained stable in the entire range of operation and without the appearance of subsynchronous vibration or nonlinear damper jump response.

Measurements of the Static Load (On Pad) Performance and Pad Temperatures in a Flexure-Pivot Tilting-Pad Bearing

Measurements of the bearing displacements and pad edge temperatures in a four-shoe flexure-pivot tilting-pad bearing under static loading toward a pad are presented. The test rig consists of a vertical rigid journal and shaft supported on precision ball bearings and driven by a variable speed motor. The housing is suspended by cables and holds the flexure-pivot bearing with four 80° arc length pads, 50% offset and null preload. The length, diameter, and nominal radial clearance of the bearing are equal to 46 mm, 127 mm, and 0.178 mm, respectively, with a pad flexural rotational stiffness equal to 1125 N-m/rad. Steady-state tests with an ISO VG 22 oil are conducted at three rotational speeds (1800, 3000, and 4500 rpm) with loads applied to the bearing with a simple jack and load cell mechanism. Measurements include the bearing displacements in two orthogonal directions, oil flow rate, lubricant inlet and discharge temperatures, and the leading and trailing edge pad temperatures for each pad. The measurements show the bearing displacements to be larger in the direction of the applied loan than in the orthogonal direction with an attitude angle of approximately 30°. This characteristic bearing operation is due to the relatively large size of the bearing clearance and the pad rotational stiffness. The test bearing does not show any subsynchronous whirl (hydrodynamic instability) including operation at the null bad condition. The pad temperatures follow well-known trends with the highest magnitude at the trailing edge of the loaded pad. A reduction of the lubricant viscosity in the tests at the largest speed (4500 rpm) produced a drop in the bearing load capacity because of the increase of the lubricant and pad temperatures. Overall, the experimental performance curve of bearing eccentricity versus Sommerfeld number agrees well with numerical predictions based on an effective viscosity method. Presented as a Society of Tribologists and Lubrication Engineers paper at the World Tribology Congress in London, United Kingdom, September 8–12, 1997