An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients

In this work, a novel methodology for the identification of stiffness and damping rotordynamic coefficients in a rotor-bearing system is proposed. The mathematical model for the identification process is based on the algebraic identification technique applied to a finite element (FE) model of a rotor-bearing system with multiple degree-of-freedom (DOF). This model considers the effects of rotational inertia, gyroscopic moments, shear deformations, external damping and linear forces attributable to stiffness and damping parameters of the supports. The proposed identifier only requires the system’s vibration response as input data. The performance of the proposed identifier is evaluated and analyzed for both schemes, constant and variable rotational speed of the rotor-bearing system, and numerical results are obtained. In the presented results, it can be observed that the proposed identifier accurately determines the stiffness and damping parameters of the bearings in less than 0.06 s. Moreover, the identification procedure rapidly converges to the estimated values in both tested conditions, constant and variable rotational speed.

Effects of Increased Tooth Clearance on the Performance of a Labyrinth Seal With Oil-Rich Bubbly Laminar Flow

In recent years, multiphase pumps have become more and more popular because of the capability to simplify the process, reduce the footprint, and lower the cost. To compensate for the axial thrust force, an annular seal is normally used as a balance piston seal, and the labyrinth seal is one of the choices. A typical labyrinth seal consists of a surface with teeth and a smooth surface. The teeth are either on the rotor or the stator. To protect the machine, one side (either the teeth or the smooth surface) is made of a material that can be safely sacrificed during a rub. After the rub, the teeth clearance is increased. This paper studies the impact of the increased teeth clearance on the performance of the labyrinth seal under oil-rich bubbly flow conditions. The test fluid is a mixture of silicone oil (PSF 5cSt) and air with inlet Gas Volume Fraction GVF up to 9%. Tests are conducted with pressure drop PD = 34.5 bars, rotor speed ω = 5 krpm, and radial tooth clearance Cr = 0.102 mm and 0.178 mm. Test results show that, for all test conditions (before and after injecting air bubbles into the oil flow), increasing Cr from 0.102 mm to 0.178 mm increases the mass flow rate by about 40% but barely changes the test seal’s rotordynamic coefficients; i.e., the increased tooth clearance would not change the pump vibration performance.

A Novel Hybrid Seal: Design and Experimental Validation on a High Pressure Rotordynamic Test Rig

The design and experimental activity presented in this paper is related to a novel hybrid seal which is intended to work as a balance piston seal in an AMBs levitated high-pressure (about 300 bar delivery pressure) motor-compressor. The typical solution adopted for balance piston application is a damper seal (e.g. honeycomb seal), as the rotordynamic stability is a primary focus. However, due to interactions between the AMB controller and seal high stiffness level, the aforementioned selection is not so straightforward. After a review of the state of the art it was found that a combination of some conventional geometries (e.g. labyrinth and honeycomb) can be adopted to achieve the desired target. The design was done using a novel tool combining the validated bulk flow codes for each geometry. Moreover, a CFD analysis, based on some literature references, was carried out as a final verification of the design. The experimental activity was then performed at the Authors’ internal seal test rig. As in typical rotordynamic seal testing activity, the operating parameters leveraged to explore performance sensitivity are rotational speed, inlet pressure, pressure ratio and inlet swirl level. The outcome was satisfactory both in terms of leakage and rotordynamic coefficients.

System Level Analysis of Compressor Eye-Labyrinth Seal Rotordynamic Forces: A Computational Fluid Dynamics Approach

Accurate characterization of compressor rotordynamic coefficients during the design phase reduces the risk of sub-synchronous vibration (SSV) problems occurring in the field. Although rotordynamists extensively investigate discrete compressor components (such as seals and front shrouds) to tackle instability issues, integrated or system-level analysis of compressor rotordynamics is rare. In reality, the impeller, eye labyrinth seal, and the front shroud heavily influence one another; and the collective dynamic behavior of the system differs from the sum of the dynamic behavior of isolated components. To further investigate, a CFD-based approach is taken to evaluate the dynamic behavior of the system as a whole. The geometry and operating conditions in this work are based on the recent experimental study of Song et al. (2019) on compressor seal and front shroud stiffness values. The compressor impeller is redesigned utilizing turbomachinery design software CFturbo. The commercial CFD code CFX 19.0 is used to resolve Reynolds Averaged Navier-Stokes (RANS) equations to quantify eye labyrinth seal and front cavity stiffness, damping, and added mass, while the whole compressor stage is modeled to uncover the coupled behavior of the components, and assess the stability of the whole system instead of any discrete components. The coupled system is constructed by modeling the interacting upstream and downstream components to accurately capture key rotordynamic parameters such as damping, axial pressure, and pressure distribution evolution inside the cavities. Effect of turbulence is captured utilizing the shear stress transport (SST) k-ω model. In the current work, three CFD approaches, namely quasi-steady, transient static eccentric, and transient mesh deformation technique are tested, and predictions are made on stiffness, damping, and virtual mass. Effectiveness of each CFD method is evaluated by comparison with the experimental data. CFD results provide the non-axisymmetric pressure perturbation for the shroud and seal surfaces. Furthermore, rotordynamic coefficients are derived utilizing correlations from the literature, and compared with CFD based and experimental results.

Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals

The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

An Accelerating Sweep Frequency Excitation Method for the Rotordynamic Coefficients Identification of Annular Gas Seals Based On Computational Fluid Dynamics

This paper proposes a rotordynamic identification method using the accelerating sweep frequency excitation method (ASFE). The CFD transient solution combined with the moving grid method is utilized to obtain the transient flow field of the seal excited by the whirling rotor with an accelerating frequency. Rotordynamic coefficients at swept frequencies are obtained by analyzing the transient response force acting on the rotor. Rotordynamic coefficients of three published experimental seals including a labyrinth seal (LABY), a fully partitioned pocket damper seal (FPDS) and a honeycomb seal (HC) are identified to validate the proposed method. The results show that the predicted rotordynamic coefficients are all well agreement with the experimental data. Compared with the existing numerical models based on transient solutions, the CPU consumption of the proposed method is substantially reduced by 98% when achieving the same frequency resolution. In addition, the impact of the exciting acceleration on the identification accuracy is also illustrated.

Influence of Manufacturing Variation On the Dynamic and Tribological Performance of Tilting Pad Journal Bearings

A systematic approach of a Tilting Pad Journal Bearing (TPJB) as a whole tolerance stack up assembly is presented. Normal component variation within actual design tolerances is considered. The vector loop is expanded via Taylor series for sensitive analysis. The bearing shell and tilting pad machined radiuses for each pad are found to be the more influential dimensional characteristics on the assembled clearance and preload. A leading edge relief was used to avoid unloaded pads fluttering, while maintaining a satisfactory bearing assembled clearance in the loaded pads throughout the resultant preload variation. Pivot flexibility and preload loss due to pad wear in service life were considered in the preload variation assessment. Surface response multivariate multi-response models were built for a 4-pad TPJB under Load Between Pad (LBP) and Load On Pad (LOP) configurations. Desirability functions rendered the maximum and minimum rotordynamic coefficient and tribological parameter responses across speed. The LOP configuration showed more variation in the direct rotordynamic coefficients, while the LBP configuration indicated more sensitive cross-coupled coefficients with strong sign change in some cases. Among the tribological performance parameters, the eccentricity and pad maximum pressure were more affected, followed by the minimum film thickness, and weakly by the power loss, and oil film temperature. The dispersion of the tribology parameters under normal manufacturing variation is found of importance. Four, and seven extreme geometrical state cases were identified for the LBP, and LOP bearing configurations, respectively.