Whirl Frequency Research Articles

Modeling of Multibody Lubrication Dynamics in Cylindrical Roller Bearings

As a typical multibody system, rolling bearing consists of several lubricated frictional pairs which transmit motions and forces among components. In this paper, a multibody lubrication dynamics (MLD) model of cylindrical roller bearings (CRBs) is developed by coupling the bearings dynamics sub-model and several lubrication sub-models of each frictional pairs in real-time. The lubrication sub-models are discretized by using finite difference and solved by numerical iteration methods of Gauss-Seidel with line relaxation and discrete convolution-fast Fourier transform (DC-FFT) technique. What’s more, a parallel algorithm is also designed to enhance the calculation efficiency. Its results are validated by the experimental results in literature, and further compared by the results from other dynamics models. It is revealed that the film formation changes not only friction but also geometrical constraints and pressure distribution, which may introduce additional load inside bearing and increase rolling friction under high-speed conditions. As the dynamic oil film stiffness and damper are took into account by MLD, the cage has a lower whirl frequency and forces. The curve-fitting formulas of EHL film thickness are overestimates the thickness value, and thus change the load distribution and friction between roller and raceway.

Dynamic characteristics of a flexible rotor supported on surface textured journal bearings

Abstract This paper presents the dynamic characteristics of a flexible rotor supported on surface textured journal bearings. Oil lubricated journal bearings exhibit the self-exited whirling of rotor, leading to instability. Understanding the threshold speed of instability is crucial in mitigating excessive vibration in rotating machinery. In this work, a simple model of a flexible rotor with central disc is studied. Modal analysis is carried out to obtain the whirl frequencies of the system, mode shapes, and stability limit speed. The addition of surface textures to the journal bearing stands out as a significant modification aimed at improving performance. Fully textured and partially textured bearing surfaces are considered in the investigation and compared with the performance of smooth journal bearings. Notably, fully textured bearings enhance stability limits. This study offers insights essential for optimizing machinery performance and minimizing operational risks.

Analysis of Reverse Whirl Characteristics of a Rub-Impact Rotor System

The rub-impact fault between the rotor and stator of the aeroengine can lead to a reverse whirl phenomenon, which will induce the instability of the rotor system. This paper uses the bending–torsion coupled vibration signal to analyze the reverse whirl characteristics of the single-rotor system under single-disc and multidisc rub-impact faults. In the full-spectrum analysis of the bending direction, the reverse whirl frequency, which is the nonpower frequency component caused by rubbing, is found. This whirl frequency leads to the period-doubling bifurcation and the reverse whirl phenomenon of the system. In the analysis of the torsional direction, it is found that the torsional signal can better reflect the different types of rub-impact faults. Further research shows that the unbalanced phase between the rubbing discs is a crucial parameter influencing the bending–torsion coupled vibration and the whirl characteristics of the rotor system. An experimental platform with nonuniform clearance is designed and manufactured to reproduce the reverse whirl phenomenon. The reverse whirl motion near the second-order superharmonic resonance speed is designed to verify the mechanism of the reverse whirl.

Dynamic and stability analysis of crescent geometry-possessing textured journal bearing using nanolubricant

PurposeThis study aims to find the dynamic performance parameters of the journal bearing with micro geometries patterning the arc (crescent) shape textures provided in three specific regions of the journal bearing: the full, the second half and the increasing pressure region. The dynamic behavior of textured journal bearings has been analyzed by computing dynamic parameters and linear and non-linear trajectories.Design/methodology/approachThe lubricant flows between the bearing and journal surface are governed by Reynold’s equation, which has been solved by finite the element method. The dynamic performance parameters such as stiffness, damping, threshold speed, critical mass and whirl frequency ratio are examined under various operating conditions by considering various ranges of eccentricity ratios and texture depths. Linear and non-linear equations of motion have been solved with Ranga–Kutta method to get journal motion trajectories. Also, the impact of adding aluminum oxide and copper oxide nanoparticles to the base lubricant in combination with arc-shaped textures is analyzed to further see any enhancement in the performance parameters.FindingsThe findings demonstrated that direct stiffness and damping parameters increased to their maximum level with six textures in the pressure-increasing region when compared with the untextured surface. Also, nanoparticle additives showed improvements above the highest value attained with no inclusion of additives in the same region or quantity of textures.Originality/valueEngineers may design bearings with improved stability and overall performance if they understand how texture form impacts dynamic properties.

Enhanced rotordynamic performance under various structural arrangements of hole diaphragm labyrinth seal

In this study, we study the influence of five drilling hole arrangements on the rotordynamic and leakage performance of hole diaphragm labyrinth seal (HDLS) type seals with precise CFD analysis. Key findings reveal that hole distance significantly affects direct and cross-coupled stiffness, thereby impacting stability and leakage. Notably, the smallest hole in rectangle four holes(RF)-HDLS does not yield the minimum leakage. Vortex structure analysis, employing the Q-criterion, elucidate horizontal two holes(HT)-HDLS's superior leakage reduction owing to enhanced turbulence eddy dissipation. Seals with larger hole diameters, down single hole(DS)-HDLS and up single hole(US)-HDLS, demonstrate stable rotordynamic performance, with DS-HDLS exhibiting a notable 106.3% improvement in cross-coupled stiffness. In contrast, seals with holes positioned farther away, DS-HDLS, US-HDLS and vertical two holes(VT)-HDLS, experienced increased leakage with whirl frequency. HT-HDLS and RF-HDLS displayed a decrease, attributed to the stronger centrifugal effect. Comparing to center single hole(CS)-HDLS, VT-HDLS and US-HDLS achieved a significant 159.3% direct stiffness improvement and 432.7% reduction in cross-coupled stiffness. Despite a maximum 4.2% leakage increase, this substantial enhancement in rotor stability should not be overlooked. Moreover, all seals exhibited lower leakage rates than the traditional labyrinth seal.

Stability analysis of partial journal bearings lubricated with micropolar fluid

PurposeThis study aims to investigate the stability performance of partial journal bearings of 120° and 180° partial angles with micropolar lubricant.Design/methodology/approachTo investigate the stability characteristics of partial journal bearing, a MATLAB source code is written. To solve the Reynolds’ equation, the finite element method is used. Stability performances of 120° and 180° partial journal bearings are computed for a wide range of non-dimensional micropolar fluid parameters and working eccentricities.FindingsThe presented results provide design data for stability parameters in terms of equivalent stiffness, whirl frequency ratio, critical mass and threshold speed of the rotor with respect to eccentricities and material size of the lubricant. The stability of 180° partial journal bearing is found to be higher than 120° partial journal bearing.Originality/valueIn open literature, it is rare to find the stability of a partial journal bearing lubricated with micropolar fluid. Very few researchers have studied the combined effect of eccentricities and micropolar lubricant parameters on the dynamic performance of such bearings. Hence, it is important to study the dynamic stability to explore the complete investigation of the performance of partial journal bearings with micropolar fluid.

Leakage and Rotordynamic Force Coefficients of a Labyrinth Seal and a Pocket Damper Seal Operating With Wet Gas

Abstract Subsea centrifugal compressors commonly using labyrinth seals (LS) and pocket damper seals (PDS) must withstand the flow of oil in gas mixtures with a liquid volume fraction (LVF) up to 5%. This paper presents experimental results for the leakage and rotordynamic coefficients of a uniform clearance PDS and a similar size LS both supplied with wet gas. The shaft diameter D = 127 mm and the seal axial length L = 48 mm. In the tests, the seals' pressure ratio (inlet/exit) = 2.5, and the shaft speed reaches 5.25 krpm (surface speed = 35 m/s). The LS has a 17% larger radial clearance (Cr,LS = 0.230 mm > Cr,PDS = 0.196 mm) due to a manufacturing error. This paper extends prior work by Torres et al. (2022, “A Stepped Shaft Labyrinth Seal versus a Pocket Damper Seal: Leakage and Dynamic Force Coefficients Under Wet Gas Operation,” ASME J. Eng. Gas Turbines Power, 145(1), p. 011006) for the same two seal types with a stepped clearance configuration that promotes damping. When supplied with a dry gas, the LS leaks more because of its larger clearance. A loss coefficient (cd) is a fraction of the physical clearance that characterizes a seal's effectiveness in reducing leakage. The cd of both seals is nearly identical for operation with pure gas; the small differences are well within the experimental uncertainty. For operation with wet gas, the PDS cd decreases as the LVF increases whereas the LS cd increases, thus indicating the PDS is more effective to restrict wet gas leakage. When operating with pure gas, the direct stiffness (K) and effective damping (Ceff) of both seals are small in magnitude (K < 0.5 MN/m, Ceff < 2 kN-s/m) and often less than the experimental uncertainty. For wet gas operation and with shaft speed = 3 krpm and 5.25 krpm, the PDS produces Ceff < 0 for whirl frequencies below 50 Hz. In contrast, the LS Ceff > 0, although small in magnitude. The experimental results under wet gas operation are similar for operation with LVF equal to 3% and 5%. Unexpected low-frequency broadband motions appear when supplying the PDS with a wet gas. Although small in amplitude (<5 μm), the motions increase in severity as the mixture inlet LVF and shaft speed increase. The motions are entirely absent for tests with the LS. Experiments in which the mixture is drawn from the PDS cavities rule out liquid accumulation as the cause of the observed motions. The current test results serve as a reference for turbomachinery design engineers and aid in the validation of analytical predictive tools.

Dynamic Forced Performance of an O-Rings Sealed Squeeze Film Damper Lubricated With a Low Supply Pressure and a Simple Method to Quantify Air Ingestion

Abstract Contemporary squeeze film dampers (SFDs) in air-breathing engines are short in length to limit weight and part count and lubricated with a low feed pressure to reduce oil storage and pumping power. In SFDs, O-rings (ORs) restrict side leakage and increase the viscous damping while a adding a modest centering stiffness. Continuing a long-term project characterizing SFDs for aircraft engines and extending the original work (San Andrés and Rodríguez, 2021, “On the Experimental Dynamic Force Performance of a Squeeze Film Damper Supplied Through a Check Valve and Sealed With O-Rings,” ASME J. Eng. Gas Turb. Power, 143(11), p. 111011) the paper details measurements of the forced performance of an OR sealed damper (OR-SFD) with diameter D = 127 mm, land length L = 0.2 D, and radial clearance c = 0.0022 D. Lubricant ISO VG 2 supplied at 0.69 bar(g) fills an upstream oil plenum and flows into the middle of the land through a single orifice configured with a check valve. Measurements of applied single-frequency dynamic loads, along with the ensuing damper displacements and accelerations serve to identify the parameters of the test structure, ORs, and SFD. The tests encompass centered whirl motions with amplitude r = 0.05–0.45c, and a range of whirl frequencies, ω = 10–130 Hz. Note the squeeze velocity vs = rω reaches 102 mm/s. The ORs force coefficients are nearly invariant with frequency but do depend on the orbit amplitude. The ORs' stiffness (KOR) decreases by 75% as the motion amplitude increases, r → 0.45c, likely due to the large elastic deformations and slow recovery of the ORs material. For small amplitude motions (r/c = 0.05 and 0.10), the ORs damping coefficient (COR) is ∼10% of the overall coefficient for the lubricated system (CL), while for r/c > 0.25, COR ∼ 0.03CL. For small amplitudes of whirl (r ≤ 0.25c), the SFD experimental viscous damping (CSFD) and added mass (MSFD) coefficients, identified over a shorter frequency range (vs<30 mm/s) equal theoretical magnitudes for a fully sealed damper. As the orbit size grows to r = 0.45c MSFD drops nearly by 75% and CSFD decreases by ∼40% due to the onset of both lubricant cavitation and air ingestion occurring for squeeze velocities vs ≥ 24.5 mm/s, as also seen in the recorded dynamic pressures and video recordings of a bubbly mixture leaving the damper. A comprehensive flow model predicts CSFD and MSFD about 8% and 12% larger than the experimentally identified coefficients. A novel approach enables the estimation of the gas volume fraction (GVF) generated in the damper which rapidly increases as vs grows. The simple procedure draws into a deflated balloon the material contents in the squeeze film, weighs the sample, and identifies its volume to produce an estimate of the GVF. The procedure to quantify the GFV will assist in the validation of predictive tools.

On the Added Modal Coefficients of a Rotating Submerged Cylinder Induced by a Whirling Motion—Part 2: Numerical Investigation

Part 2 of this work presents a numerical methodology, validated using the experimental results presented in Part 1, to calculate the added modal coefficients of a submerged cylinder in water both when it oscillates and when it rotates with a whirling motion. The numerical methodology is based on computational fluid dynamic simulations that obtain the added modal forces on the cylinder when it is forced to vibrate with mode shapes calculated using acoustic-structural modal analysis. Then, these forces are processed with a curve-fitting algorithm to extract all the coefficients. Most numerical coefficients presented a close agreement with the corresponding experimental ones, although the added modal damping was overestimated. In general, the added modal mass was found to be independent of both the rotating speed and the whirling frequency except for low whirling frequencies when it increased. The added modal damping was found to depend on both parameters, and the rest of the coefficients were independent of the whirling frequency and only depended on the rotating speed. As a conclusion, this numerical approach has permitted the study of particular conditions that could not be experimentally tested and thus broadened the knowledge of the behavior of the added modal coefficients of rotating submerged cylinders.

Influence of pivot support stiffness on dynamic characteristics of vertical rotor system

The pivot-jewel bearing pair is the only dynamic and static contact component of the flexible vertical rotor system, and its support stiffness directly affects the dynamic response of the rotor system. A non-linear dynamic model of the vertical rotor system is established, and the effect of different elastic pivot stiffnesses on the dynamic behavior of the rotor system is investigated in combination with experiments. The results show that with the increase of rotational speed, the system has the dynamic characteristics of alternating period 1 and quasi period, and when the speed reaches 550 r/s, 1/3 times low frequency whirl occurs and when the speed rises to 675 r/s, the low frequency amplitude is higher than the rotational frequency amplitude. With the increase of the elastic pivot stiffness, the amplitude of the low frequency whirl at the lower end of the rotor decreases continuously but the proportion of the “width” gradually increases. The rotational speed corresponding to the large amplitude quasi periodic motion of the rotor is delayed from 550 r/s to 650 r/s. The research results can provide a theoretical basis for the optimal design of the bearing subsystem of the vertical rotor system.

Effects of manufacturing errors and micro-groove surfaces on the static and dynamic characteristics of water-lubricated bearings

In this paper, the effects of manufacturing error and micro-groove on the static, dynamic and stability characteristics of water-lubricated journal bearings (WLJBs) are investigated. Mathematical expressions of manufacturing errors and surface micro-groove are presented, and the Reynolds equations with steady and unsteady states are calculated by using the linear perturbative method and the finite difference technology. According to the developed model, the effects of the waviness magnitude, spatial number, and phase angle for circumferential errors, as well as the concavity, convexity, and taper for axial errors on the film thickness distribution, fluid pressure distribution, bearing capacity, coefficient of friction, side leakage flow rate, attitude angle, stiffness coefficient, damping coefficient, threshold speed and whirl frequency ratio of WLJBs are evaluated. Simulation results demonstrate that fluid film thickness distribution and fluid pressure distribution are significantly affected by manufacturing errors and micro-groove. Compared with axial manufacturing errors, circumferential manufacturing errors cause an inhomogeneous distribution of fluid pressure and morphological transformation in the high-pressure zone. The variation rules for the lubrication performance of bearings with circumferential waviness, concavity, convexity, and taper errors are not consistent at various eccentricity ratios. The magnitude of the concavity and taper errors may have an improving effect on the bearing performance, whereas circumferential waviness and convexity error play a negative role. Moreover, the micro-groove with partial distribution enhances the hydrodynamic effect in the bearing clearance. Numerical simulations can provide a valuable reference for the manufacturing and design of bearing systems.

Vibration and Stability Analysis of a Spinning Hollow Functionally Graded Beam with Exponentially Varying Cross-Section

This paper presents an analytical investigation of the whirl characteristics and flexural instability of a spinning functionally graded (FG) hollow beam with exponentially varying cross-section. Applying Rayleigh beam theory, the governing equation of motion of the spinning beam with eccentricity is formulated via the Hamilton principle. The dimensionless whirl frequency equation is obtained for the FG beam with pinned–pinned end supports. On the basis of the obtained model, the whirl frequency, critical spinning speed, and stability conditions of the system are studied. Also, the effects of the main parameters on the whirl characteristics and stability of the system are evaluated. Results show that the unbalanced mass is the main source of system instability. It is also shown that the whirl frequency, critical spinning speed, and stability boundaries of the system are strongly dependent on the slenderness ratio, taper parameter, gradient index, hollow ratio, and eccentricity effects.

Comparative study on static and dynamic characteristics of pumping-out and pumping-in herringbone grooved journal bearings

The aim of this paper is to compare the static and dynamic performances of two types of herringbone grooved journal bearings (HGJBs), that is, pumping-out HGJB and pumping-in HGJB. Firstly, based on finite control volume method and the principle of flow balance, an equivalent Reynolds equation considering the turbulence effect is derived. Then, the journal motion considering angular displacement is analyzed with linear perturbation method. The equivalent Reynolds equation is linearized into static-form one and perturbed-form ones. These equations are solved by finite difference method and their solutions are integrated on the bearing surface to determinate the static characteristics and dynamic coefficients of HGJB. Additionally, the critical mass and critical whirl frequency are defined for evaluating the stability and rigidity of bearing by solving a motion equation with four degree of freedoms (DOFs). Finally, the static and dynamic characteristics of two types of HGJBS are analyzed and compared symmetrically in consideration of effects of eccentricity ratio, length to diameter ratio, groove angle, groove depth, the width of sealing damp, tilting degree of journal, and rotation speed. The results show that, within the interested range of investigated parameters, static performances of pumping-out HGJB are superior to that of pumping-in HGJB generally. Stability of pumping-in HGJB is better than pumping-out HGJB but bearing rigidity of pumping-in HGJB is inferior to pumping-out HGJB.

Vibration and stability of a spinning functionally graded cylinder in a liquid-filled concentric drum

The vibration and stability of an axially functionally graded (AFG) cylinder with whirl motion in the annular liquid environment are investigated. The model of the performed system is given by the spinning Rayleigh beam assumptions with the rotary inertia and the gyroscopic effects. The fluid forces exerted on the cylinder, as a result of the external fluid, are calculated analytically. The coupled governing equation of motion for the system is developed via Hamilton's principle. The exact and approximate whirl frequency equations are presented for vibration and stability analysis of the AFG cylinder. The validity of the proposed model is confirmed by comparing it with the numerical solutions available in the literature. Detailed parameter discussions are conducted to evaluate the effects of the density ratio, outer-to-inner radius ratio, hollowness ratio, and slenderness ratio on the whirl characteristics and stability of the system. The results show that the whirl characteristics and instability of the AFG cylinder are strongly dependent on the external fluid.

Multi-scale contact induced period-doubling vibrations in rotor systems: Numerical and experimental studies

Bolted disk structure has the advantages of easy production and assembly and it is widely adopted in the design of gas turbine rotors. However, the discontinuity of bolted structure and the contact effects between the disks produce complex nonlinear properties to the rotor system, resulting in difficulties in solving the vibration dynamics of the rotors. In this paper, in order to reflect the contact effect between the rotor disks more accurately, a multi-scale contact mechanics model considering the whole deformation process of the material is deduced based on the skewed distribution theory. The contact effect between disks is considered by introducing an equivalent material layer. Newmark-β method is applied to obtain the dynamic response of the rotor system under different preloads. A multi-disk rotor-bearing test bench is designed to conduct dynamic tests to verify the accuracy of the contact modeling method and obtained dynamic results. Numerical and experimental results show that adjusting the preloads has the effect to change the bifurcation state of the rotor system and the increase in the preloads leads to the period-doubling bifurcation phenomenon moving toward low speed, and leads to the early appearance of some combined frequency components (such as 2fn-fr, where fn is the working frequency and fr is the oil film whirl frequency). This research provides a theoretical reference for the modeling, dynamic behavior prediction as well as fault diagnosis of rod-fastened gas turbine rotor systems.

Vibration and stability analysis of a spinning shaft with arbitrary boundaries subjected to partial load

This paper deals with the flexural vibration and dynamic stability of a spinning shaft subjected to partial load. Based on the theorem of moment of momentum and the theorem of motion of center of mass, the governing equation of motion for the spinning shaft system is obtained. Four kinds of boundary conditions including pinned-pinned, clamped-clamped, free-free, and elastic supports are considered. The exact whirl frequency equation is derived analytically for different boundary conditions. The obtained model is confirmed by comparing with the results reported in the available literature, and excellent agreement is presented. A numerical investigation is carried out to examine the effects of support stiffness, mass ratio, eccentric distance, and slenderness ratio on the whirl characteristics and stability of the system in terms of the obtained model. The results show that the whirl frequency and critical spinning speed of the system are dependent on these parameters, and the stability is mainly governed by the mass ratio and eccentric distance.

Modified Fourier Approach for Vibration Analysis of Spinning Beam with Elastic Restraints

This paper presents a unified method for analyzing the dynamic behavior of spinning beams under elastic constraints. Based on the Timoshenko beam theory, a dynamic model of a spinning beam with elastic constraints is established. The displacement and bending angle are represented by a modified Fourier series. Compared with the traditional Fourier series, the improved Fourier series eliminates the discontinuity of the derivative at the boundary by introducing auxiliary polynomials, making it more suitable for elastic constraints. The governing equations and boundary conditions are coupled together using the energy method to form a set of standard linear equations. By solving this equation, the modes of the spinning beam structure under elastic constraints can be concisely and quickly obtained. Finally, by comparing with other methods, it is proved that the method has good convergence and practicability. Then, the effects of spinning speed, boundary stiffness and slenderness ratio on the whirling characteristics are analyzed. The results show that the linear spring has a more pronounced effect on the whirl frequency than the torsion spring. Different boundary constraints produce different elastic intervals. Mode exchange was found with increasing spinning speed. In the case of elastic constraints, the mode exchange occurs at lower spinning speed. This method has a certain universal applicability to the dynamic analysis of spinning beams under elastic constraints, and the research results can provide theoretical reference for subsequent research.

Dynamic Behavior of a Spinning Exponentially Functionally Graded Shaft With Unbalanced Load

Abstract The dynamic behaviors of a pinned–pinned spinning exponentially functionally graded shaft with unbalanced loads are investigated. The shaft is simulated in the Rayleigh beam model considering rotary inertia and gyroscopic effects. The governing equation for the flexural vibration of the shaft is derived via the Hamilton principle. Based on the boundary conditions, both the exact and approximate whirl frequency equations of the system are obtained analytically. Also, the validity of the proposed model is confirmed by comparing it with the results reported in the literature. Finally, a numerical study on the basis of the analytical solutions is performed to evaluate the main parameters, including slenderness ratio (α), gradient index (β), mass ratio (μ), and eccentric distance (γ) on the whirl frequency, critical spinning speed, mode shapes, and stability of the system. The results reveal that the vibration and instability of the spinning shaft are strongly dependent on the unbalanced load and material gradient.

Measured Leakage and Rotordynamic Force Coefficients for Two Liquid Annular Seal Configurations: Smooth-Rotor/Grooved-Stator Versus Grooved-Rotor/Smooth-Stator

Abstract This paper reports and compares the experimental results of leakage and dynamic force coefficients for two liquid annular pressure seals, one having a smooth-rotor/circumferentially grooved stator (SR/GS), the other one with a circumferentially grooved rotor/smooth-stator (GR/SS). Differing only in the grooves’ location, the GR/SS seal’s geometry and operating conditions are representative of those in electrical submersible pumps (ESPs) used for oil recovery. Supplied with an ISO VG2 oil at 46 °C, both seals have the same diameter D = 102 mm, length-to-diameter ratio L/D = 0.5, and nominal land clearance Cr = 0.203 mm. The seals have 15 circumferential grooves with grooves and land lengths equal to 1.52 mm. Test variable ranges include (a) shaft speeds (ω) ranging from 2 to 8 krpm (shaft surface speed ∼ 43 m/s), and (b) pressure differences (ΔP) from 2 to 8 bar. Upstream of the test seals, three separate prerotation rings generate a range of inlet circumferential velocities (entrance swirl). Under all conditions, the GR/SS seal leaks about 10% less than the SR/GS seal. For both seals, the direct stiffnesses (KXX, KYY) have low magnitudes that drop with increasing ω; in some cases, they turn negative at 6 krpm. The GR/SS seal produces cross-coupled stiffnesses (KXY, KYX) that are ∼1.5 times larger than those for the SR/GS seal. Under the same conditions, the SR/GS seal is more stabilizing as its direct damping, and added mass coefficients are ∼ 20% larger than those for the GR/SS seal. Instability issues are likely to arise with either seal geometry because negative KXX and KYY drop a pump critical speed, aggravating the well-known destabilizing coefficients KXY and KYX. The whirl frequency ratio (WFR) combines the effects of the cross-coupled stiffness, direct damping and cross-coupled mass terms, thus providing a good basis for comparing two seals’ stability characteristics. Overall, the WFR magnitudes for the GR/SS seal are about three times higher than those for the SR/GS seal. Note that, irrespective of the inlet swirl condition, the GR/SS approaches a WFR ∼ 0.50 for operating shaft speeds greater than 4 krpm. At the lowest shaft speed (2 krpm), the WFR ≪ 0.5 for the low inlet preswirl ring, whereas WFR > 0.8 for the medium and high preswirl rings. For the SR/GS seal, the WFR ∼ 0.2 at the highest shaft speed of 6 krpm, and not affected by the inlet preswirl condition. On the other hand, at the lowest shaft speed, the WFR ranges from 0.5 to 0.75 for the SR/GS seal with medium and high preswirl rings. At this speed, the WFR = 0 with the low inlet preswirl ring. Hence, to enhance the operational stability, an effective swirl brake that could drop the inlet preswirl ratio upstream of a seal is helpful for the GR/SS seal out to 4 krpm and for the SR/GS seal out to 6 krpm.

Dynamic and Thermal Investigations of the Forward Dry-Friction Whirl/Whip of a Vertical Rotor-AMB System during Touchdowns

When an active magnetic bearing (AMB) rotor drops, it impacts the touchdown bearing (TDB) and produces friction on its surface. The vertical AMB rotor has no stable support in the radial direction, and the rotor exhibits a violent whirl motion in the gap of the TDB. In this study, a complete dynamic and thermal model of the AMB-rotor-TDB system was established, and the complete drop process was simulated. When the rotor dropped, it obtained stable support after several bounces on the thrust surface of the TDB inner ring in the axial direction. In the radial direction, the rotor entered whirl motion after the initial collisions. There is a natural whirl frequency so that the drop forward whirl is divided into the dry-friction whirl and whip states. The contact force and heat generation of the TDB were monitored in the simulation and had different performancs in the two states. Both the initial collisions and the stabilized whirl motions were studied to evaluate the reliability of the TDB. Finally, a series of drop tests were performed, and the experimental results were in good agreement with the simulation.