Tilting Pad Gas Bearings Research Articles

High-speed tilting-pad gas journal bearing flow field analysis

Tilting-pad gas journal bearing are widely used in the field of high-speed turbine machinery, especially in the special environment of low temperature. However, the performance is limited by structure, so a clear understanding of the field is particularly important. In this paper, finite volume method is used to simulate the three-dimensional flow field of high-speed tilting-pad gas bearing, then the effects of shaft speed, eccentricity and gas film thickness on the bearing capacity are studied. The simulation results show that the two factors of shaft speed and gas film clearance play a decisive role in producing sufficient bearing capacity of tilting tile radial gas bearings compared with other factors.

Theoretical and Experimental Investigation of Porous Tilting Pad Gas Bearings with Hermetic Squeeze Film Dampers Based on Multilayer Diaphragm Structure

A novel porous tilting pad gas bearing (PTPGB) with hermetic squeeze film dampers based on multilayer diaphragm structure (MLD-HSFD) is proposed for oil-free turbomachinery. A dynamic model of MLD-HSFDs including the frequency dependence effect is presented by considering the compressibility of the damper fluid. An experimental test rig was assembled to measure the performance of MLD-HSFDs. The model predicts well the test data, including the frequency dependence of force coefficients. A comprehensive theoretical model of PTPGBs with MLD-HSFDs is proposed based on the implementation of the isothermal compressible Reynolds equation coupled to a flexible support and porous models. The effects of thickness of diaphragms thickness, bearing clearance, and supply pressure on bearing performance are discussed.

Tilting pad gas bearing induced thermal bow- rotor instability (Morton effect)

Abstract The Morton effect ME is a thermally induced, rotordynamic instability, which is frequently reported in overhung machines supported with oil-lubricated bearings. Synchronous journal whirling results in an uneven viscous shearing of the lubricant film and temperature variation around the journal circumference. This bends the shaft and under certain conditions causes increasing synchronous vibration. Previous research focused solely on oil-lubricated bearings. A transient, high-fidelity ME methodology is presented to expand the scope to tilting pad gas bearing (TPGB) systems. Three dimensional finite element models are established to predict the rotor and bearing temperature and dynamic responses in the time domain. Simulations indicate that the ME can occur in the TPGB systems and may be sensitive to imbalance and overhung mass.

Bifurcation and nonlinear dynamic behaviours of a metal mesh damped flexible pivot tilting pad gas bearing system

The nonlinear dynamics of a rigid rotor supported on two identical metal mesh damped flexible pivot tilting pad gas bearings is investigated. This new type gas bearing is used because of high effective damping level and adequate compliance with variations in rotor geometry or misalignment. Time domain simulation that couples rotor motion equations, unsteady Reynolds equation and pad motion (considering dampers) equations is used. The nonlinear dynamic responses are analysed using rotor trajectories, fast Fourier transform plots, Poincare maps and bifurcation plots. The effects of different system parameters, including operating speed, rotor mass, imbalance radius, pad radial stiffness and pad preload, on nonlinear characteristics of the rotor–bearing system are studied. The numerical results reveal that rich and complex nonlinear behaviours are contained in the rotor responses. The rotor experiences T-periodic motion, KT-periodic motion and quasi-periodic motion with the variations of different system parameters. The bifurcation diagrams for different damper mesh densities are compared. For the bearing system with larger damper mesh density, both the speed range of subsynchronous vibrations and the amplitudes of rotor orbits are smaller. As rotor mass increases, the subsynchronous amplitudes increase. Quasi-periodic motion occurs when the imbalance radius is within the interval of $$0.2\times 10^{-6}\,\hbox {m}\le r_u \le 2\times 10^{-6}\,\hbox {m}$$ . Moreover, smaller pad radial stiffness and pad preload lead to larger subsynchronous vibration peaks. These studies can be used as guideline for designing and selecting suitable rotor, bearing and operating parameters of rotor–bearing system.

A Rotordynamic, Thermal, and Thrust Load Performance Gas Bearing Test Rig and Test Results for Tilting Pad Journal Bearings and Spiral Groove Thrust Bearings

A high-speed gas bearing test rig was developed to characterize rotordynamic, thermal, and thrust load performance of gas bearings being developed for an oil-free turboexpander. The radial bearings (RBs) tested in this paper were tilting pad journal bearings with radial compliance features that allow the bearing bore to increase to accommodate shaft growth, and the thrust bearings (TBs) were a spiral groove type with axial compliance features. The TB accounts for over 90% of the combined bearing power consumption, which has a cubic relationship with speed and increases with case pressure. RB circumferential pad temperatures increased approximately with speed to the fourth or fifth power, with slightly higher temperature rise for lower case pressure. Maximum steady-state bearing pad temperatures increase with increasing speed for similar cooling mass flow rates; however, only the TB showed a significant increase in temperature with higher case pressure. The TBs were stable at all speeds, but the load capacity was found to be lower than anticipated, apparently due to pad deformations caused by radial temperature gradients in the stator. More advanced modeling approaches have been proposed to better understand the TB thermal behavior and to improve the TB design. Finally, the RBs tested were demonstrated to be stable up to the design speed of 130 krpm, which represents the highest surface speed for tilting pad gas bearings tested in the literature.

Nonlinear Numerical Prediction of a Rotor–Bearing System Using Damped Flexure Pivot Tilting Pad Gas Bearings

ABSTRACTFlexure pivot tilting pad gas bearings with pad radial compliance (FPTPGB-Cs) and metal mesh dampers (MMDs) in parallel (FPTPGB-C-MMDs) have been considered for application to high-speed and high-performance turbomachinery because of their advantages of high effective damping level and adequate compliance with variations in rotor geometry or misalignment. Although the dynamic coefficients of FPTPGB-C-MMDs have been predicted using the linear method, a nonlinear study is urgently needed for their high nonlinear behavior. A nonlinear numerical investigation on the rotor–bearing system supported by FPTPGB-C-MMDs is presented in this study by using the time domain orbit simulation method that couples rotor motion equations, the unsteady Reynolds equation, and pad motion (considering MMDs) equations. The nonlinear predictions are verified by the prediction and experimental results of a published paper.FPTPGB-C-MMDs can effectively suppress the subsynchronous vibrations compared with the rotor system supported by FPTPGB-Cs. The prediction results show that a high damper mesh density has a more positive effect on improving the stability of the rotor system by reducing the subsynchronous vibrations. Investigation shows that MMDs can improve the ability of the rotor system to sustain the effect of destabilizing forces. A high damper mesh density can sustain large destabilizing forces. The simulation results also indicate that low pad radial stiffness or preload leads to high amplitudes of subsynchronous vibrations. A small clearance results in an increase in critical speed and its synchronous amplitude. Moreover, large clearance results in a wide speed range that leads to the occurrence of subsynchronous vibrations with large amplitudes.

Theoretical model of flexure pivot tilting pad gas bearings with metal mesh dampers in parallel

The application of flexure pivot tilting pad gas bearings (FPTPGBs) with metal mesh dampers (MMDs) in parallel in high-performance oil-free turbomachineries has been considered because of their high effective damping level and adequate compliance to the variations in rotor geometry. This study proposes a comprehensive theoretical model of these bearings by coupling the FPTPGB model and MMD model. The effects of many parameters, including damper mesh density, pad radial stiffness, MMD radial interference, bearing nominal clearance and pad preload, are discussed. Results show that the direct damping coefficients of the bearings in this study are higher than those of FPTPGBs.

Active control of unbalance response of rotor systems supported by tilting-pad gas bearings

This article establishes an optimal control model using piezoelectric actuators, proportional–derivative (PD) compensation, and gap sensors to control the vibration of rotor systems supported by tilting-pad gas bearings with active pads. The optimal control law between the voltage applied on the actuator and dynamic displacement of rotor is obtained by means of conventional optimal control theory. Using this active control model, the unbalance responses of rotor system are numerically controlled. Results show that the unbalance responses of system can be effectively suppressed by this optimal control system. This article provides a theoretical basis for further improving the stability of rotor systems supported by tilting-pad gas bearings.

Stability Analysis on Rotor Systems Supported by Self-acting Tilting-pad Gas Bearings with Frequency Effects

The recent research on stability of gas bearing-rotor systems still mostly adopts the same method as in oil-lubricated bearing-rotor systems.The dynamic coefficients of gas bearings in the case that the perturbation frequencies are same as the rotating speed are used to carry out the stability analysis of rotor systems.This method does not contact the frequency characteristics of dynamic stiffness and damping coefficients of gas bearings with the dynamical behaviors of rotor systems.Furthermore,the effects of perturbation frequencies on the stability of systems are not taken into account.In this paper,the dynamic stiffness and damping coefficients of tilting-pad gas bearings are calculated by the partial derivative method.On the base of solution of dynamic coefficients,two computational models are produced for stability analysis on rotor systems supported by tilting-pad gas bearings according to whether the degrees of the freedom of pads tilting motions are included in the equations of motion or not.In the condition of considering the frequency effects of dynamic coefficients of tilting-pad gas bearings,the corresponding eigenvalues of the rigid and first five vibration modes of the system with the working speeds of 8-30 kr/min are computed through iteratively solving the equations of motion of rotor-system by using two computational models,respectively.According to the obtained eigenvalues,the stability of rotor system is analyzed.The results indicate that the eigenvalues and the stability of rotor system obtained by these two computational models are well agreement each other.They all can more accurately analyze the stability of rotor systems supported by tilting-pad gas bearings.This research has important meaning for perfecting the stability analysis method of rotor systems supported by gas bearings.

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.

Limits of Dynamic Coefficients of Self-Acting Tilting-Pad Gas Bearings

Many previously published articles have studied the effects of perturbation frequency on the dynamic coefficients of gas bearing, but they all do not give the rounded definition of dynamic coefficients in the whole frequency range. In this article, the dynamic stiffness and damping coefficients of tilting-pad bearings are calculated by the partial derivative method and the limits of dynamic coefficients are obtained by using the limit theory. Furthermore, the equivalent dynamic coefficients of tilting-pad bearings are also calculated, which makes it possible to denote the dynamic characteristics of the tilting-pad bearing with eight dynamic coefficients. In the article, the dynamic coefficients of the bearing are investigated in the whole frequency range. The numerical results indicate that the changing trends of dynamic coefficients with perturbation frequency are well in agreement with their limits. With the increase of perturbation frequency, the dynamic stiffness coefficients are all close to their corresponding limits, and the limits of all dynamic damping coefficients are equal to zero. Moreover, the cross-coupling terms of dynamic coefficients of the tilting-pad gas bearing are close to zero, which further reveals the main reason that the performance of the tilting-pad bearings is better than the generic fixed-pad bearings.

Design and Manufacturing of Mesoscale Tilting Pad Gas Bearings for 100–200 W Class PowerMEMS Applications

This paper introduces a design and manufacturing of mesoscale flexure pivot tilting pad gas bearing with a diameter of 5 mm and a length of 1–2.5 mm for PowerMEMS (micro electromechanical systems for power generation) applications with power ranges of 100–200 W. Potential applications include power source for unmanned air vehicles, small robots, microgas turbines to be harnessed by very small solid oxide fuel cells, microblowers/compressors for microfuel cells, etc. The design studies involve scaling analysis, time-domain orbit simulations for stability analyses, and frequency-domain modal analyses for prediction of rotor-bearing natural frequencies. Scaling analysis indicates that direct miniaturization of macroscale tilting pad gas bearing can result in a large bearing number, which may render the rotor-bearing system unstable. However, the scaling analysis provides the baseline design from which the final design can be derived considering manufacturing issue. The generalized modal analysis using impedance contours predict damped natural frequencies close to those from orbit simulations, providing high fidelity to the developed numerical methods. It was predicted that the designed mesoscale tilting pad gas bearings would show very stable operation up to a maximum simulated speed of 1,000,000 rpm. The designed mesoscale tilting pad gas bearings were manufactured using X-ray lithography and electroplating.

Rotordynamic Performance of Flexure Pivot Tilting Pad Gas Bearings With Vibration Damper

Recently, gas-lubricated bearings have drawn enormous attention for clean energy conversion/process systems such as fuel cells, micro-gas-turbines, gas compressors, etc. Among many different types of gas bearings, tilting pad gas bearings have many attractive features such as high rotor-bearing stability and less severe thermal issues (due to multipad configurations) than foil gas bearings. However, extension of the application of the tilting pad gas bearings to flexible rotors and harsh environments with external vibrations/impacts poses significant design challenges. The design problem addressed in this paper is the vibration damper to be integrated with the flexure pivot tilting pad gas bearing (FPTPGB) with and without pad radial compliance. Linear and nonlinear dynamic models of the FPTPGB with vibration damper were developed, and rotordynamic performance was evaluated to prescribe design guidelines for the selection of bearing shell mass and damper properties. Direct numerical integration (time-domain orbit simulations) and linear analyses were employed to predict rotordynamic responses and other interesting behaviors relevant of rotor-bearing systems with the vibration damper. Rotor-bearing systems showed better performance with larger damper stiffness for both with and without radial compliance. However, bearing shell mass showed different tendencies; lower bearing shell mass was shown to be ideal for bearings with radial compliance, while the opposite trend was observed for bearings without radial compliance. Although increasing the degrees of freedom of the system by allowing the bearing shell to move introduces additional natural frequencies, careful design considerations could allow the placement of the natural frequencies outside of the operating range.

Analysis on Dynamic Performance of Hydrodynamic Tilting-Pad Gas Bearings Using Partial Derivative Method

Tilting-pad gas bearings are widely used in high-speed rotating machines due to their inherent stability characteristics. This paper advances the analytical method for prediction of the dynamic performances of tilting-pad gas bearings. The main advantage of the analytical method is that the complete set of dynamic coefficients of tilting-pad gas bearings can be obtained. The predictions show that the perturbation frequency has the strong effects on the dynamic coefficients of gas bearings. In general, at lower perturbation frequency, the equivalent direct stiffness coefficients increase with frequency, whereas equivalent direct damping coefficients dramatically reduce. For higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the equivalent dynamic coefficients of four-pad tilting-pad gas bearing obtained by the method in this paper are in good agreement with those obtained by Zhu and San Andres [(2007), “Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,” ASME J. Eng. Gas Turbines Power, 129(4), pp. 1020–1027] in the published paper. The results validate the feasibility of the method presented in this paper in calculating the dynamic coefficients of gas-lubricated tilting-pad bearings.

Thermohydrodynamic Analysis of Compliant Flexure Pivot Tilting Pad Gas Bearings

A new thermohydrodynamic (THD) analysis for compliant flexure pivot tilting pad gas bearings is presented. Unlike many previous THD analyses on oil-lubricated bearings and gas bearings, the new THD analysis solves the rotor and bearing pad temperatures as well as the gas film temperature simultaneously upon adequate thermal boundary conditions on the bearing shell and rotor ends are given. All the previous studies assume that the rotor and bearing temperatures are given as thermal boundary conditions to solve 2D or 3D energy equation in the bearing film. The developed computational method is unique because these boundary conditions are found internally through global energy balance around the bearing. A numerical procedure involves solving the generalized Reynolds equation, 3D energy equation, and heat flux equations around the bearings simultaneously through iterative process. Furthermore, rotor thermal and centrifugal expansions are also considered during the iteration. Parametric studies were performed for the various temperature fields, i.e., rotor temperature, gas film temperature, and pad temperature as a function of nominal clearance, external load, and various thermal boundary conditions. Nominal clearance showed the most significant influence on overall THD behavior. The analyses also show that the rotor-bearing system can go to thermal runaway if adequate cooling mechanism does not exist. Linear perturbation analysis was also performed to investigate the thermal effects on the rotordynamic performance. Rotor thermal growth and increased viscosity increased direct stiffness and damping coefficients compared to the isothermal case.

Numerical Analysis on Dynamic Coefficients of Self-Acting Gas-Lubricated Tilting-Pad Journal Bearings

Although gas-lubricated tilting-pad bearings are widely used in high-speed turbomachinery, the theoretical prediction of the dynamic characteristics of tilting-pad gas bearings is also a very difficult problem because of its structural complexity. Several approaches have been proposed to solve this problem such as the pad assembly method and the small perturbation method. A numerical method by combining the partial derivative method with the equivalent coefficient method is presented in this paper to evaluate the dynamic stiffness and damping coefficients of self-acting tilting-pad gas bearing. The dynamic coefficients with the pads fixed and with the pads perturbation are, respectively, obtained for a typical self-acting tilting-pad gas bearing by using the proposed method to mainly explain the dependency of the bearing dynamic coefficients on the perturbation frequency. For bearings with the pads perturbation, the cross-coupling stiffness and damping coefficients are almost negligible compared with the direct ones. At lower perturbation frequency, the stiffness coefficients increase, while the damping coefficients decrease with an increasing frequency. The higher perturbation frequencies have very little effects on the bearing dynamic coefficients. Dynamic stiffness coefficients approach to the constant and damping coefficients to zero. However, with the pads fixed, in a low range of frequency, the absolute values of cross-coupling stiffness coefficients decrease with frequency. Furthermore, the cross-coupling coefficients are not negligible compared with the direct ones. In addition, the effects of pad inertia on dynamic coefficients are studied and compared with the results of pad inertia neglected.

Dynamic stiffness and damping coefficients of aerodynamic tilting-pad journal bearings

The dynamic gas–film forces of aerodynamic bearing often can be characterized by eight linear stiffness and damping coefficients. How to theoretically predict these coefficients is a very difficult issue for tilting-pad gas bearing design because of its structural complexity. The current study presents a novel and universal theoretical analysis method for calculating the dynamic stiffness and damping coefficients of aerodynamic tilting-pad bearing. The gas–film pressure within the bearing is expressed in the form of dimensionless compressible gas-lubricated Reynolds equation, which is solved by means of the finite element method. With the assumption that the journal and the pads are disturbed with the same frequency, the dynamic coefficients of tilting-pad gas bearing are computed by using the partial derivative method and the equivalent coefficient method. Finally, the investigations are conducted about the effects of bearing number, perturbation frequency of the journal and the pads, eccentricity ratios, preload and length-to-diameter ratio of the bearing on the dynamic coefficients of aerodynamic tilting-pad journal bearing. The numerical results indicate that the dynamic stiffness and damping coefficients of tilting-pad gas bearing are closely related with these factors. The proposed analytical method provides a valuable means of predicting dynamic performances of tilting-pad gas bearing. The solution can be used for the purpose of prediction of dynamic behavior of the rotor systems supported by aerodynamic tilting-pad bearings.

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.

틸팅 패드 기체베어링의 정상상태 성능해석

In this paper, the steady-state performances analysis of a tilting pad gas bearing(TPGB) are analyzed by using finite element method for compressible Reynolds' equation. TPGB is used in a high-expansion-ratio expander running at a speed of 230,000 rpm. In order to solve the nonlinear finite element equations, the Newton-Raphson method is applied. The variations of the loading capacity, friction force and tilting angle of a single pad v.s. eccentricity direction of eccentricity and bearing number are investigated. The condition for the equilibrium of a pad, which is important for safe working of the bearing, is stated. The performances of the three pad bearing such as loading capacity, friction moment are predicted.

PZT 액추에이터를 이용한 로터계 동기진동의 강인제어

This paper presents the synchronous vibration control of a rotor system using an active air bearing(AAB). In order to suppress the synchronous vibration, it is necessary to actively control the air film pressure or the air film thickness. In this study, active pads are used to control the air film thickness. Active pads are supported by pivots containing piezoelectric actuators and their radial position can be actively controlled by applying voltage to the actuators. Thus, disturbances, i. e. various kinds of external force can cause shaft vibration as well as change of the air film thickness. The dynamic behavior of a rotary system supported by two tilting-pad gas bearings and its active stabilization using the tilting-pads as actuators are investigated numerically. The synthesis are applied to the AAB system with three pads, two of which contain piezoelectric actuators. To test the validity of the theoretical method, the performance of this control method is evaluated through experiments. The experimental results also show the effectiveness of the control system for suppressing the unbalanced response of the rigid modes.