Application of Dry-Friction Whip and Whirl Solution Methods to Systems With Support Asymmetry

Dry-friction whip and whirl occurs when a rotor contacts a stator across a clearance annulus. In a general sense, the relative motion between the two bodies is described by a circular precessing motion. While this problem is generally well understood, the author is unaware of any papers that discuss the problem for systems having asymmetric rotor or stator supports. The current work will investigate a general model to describe dry-friction whip and whirl for the case of continuous contact between a rotor and stator in the presence of asymmetry. This paper will show that for light asymmetry, the rotor and stator motions are elliptical; however, the relative motion between the two bodies remains circular.

Rotordynamic Characterization of Labyrinth Seals in Steam Turbines: Effects of Thermal and Mechanical Loads

Over the last few decades, the increasing demand on efficiency and performance for steam turbines has resulted in OEMs operating machines near critical conditions of their structural and thermal capabilities. Consequently, a more accurate estimation of the dynamic behavior of the machine has become mandatory as well as the stability assessment. Steam turbines are subjected to high temperatures, high pressures and centrifugal forces that could change the nominal geometry, especially the clearance profile in correspondence of the sealing components, occasionally generating a convergent or divergent annulus. In this paper, a new thermo-elasto bulk-flow model for labyrinth seals has been introduced. The model includes the bulk-flow model for estimating the dynamic coefficients, heat transfer model for evaluating the temperature distribution in the rotating and stationary parts and structural-mechanics model for calculating the radial growth. By considering a staggered labyrinth seal installed in the balancing drum of a steam turbine, different inlet pre-swirl ratios, as well as the stability of the seal are investigated in this paper. The model can be extremely useful for the dynamic characterisation of a wide class of labyrinth seals considering the effect of the surrounding environment on the rotordynamic coefficient prediction.

A CFD Based Approach for Estimation of Rotor Dynamic Coefficients for Liquid Annular Seals in Turbomachinery

Seals are used to control leakage across stages in pumps and other rotating machinery such as turbomachines. However, while acting to control leakage, the seals generate a reaction force on the rotating members. The rotordynamic forces produced by fluid impact the stability behaviour of the high-speed turbomachinery, therefore precise estimation of rotordynamic parameters is important to ensure vibrational stability and desired dynamic performance of rotors having annular seals. Studies on seals have so far mainly focused on bulk flow model based on Hirs turbulent lubrication theory for calculating leakage flow rate and rotordynamic coefficients. However, it is incapable to deal complex geometries and is less efficient in predicting precise rotor dynamic parameters for high speed rotating systems due to its basic assumptions. The experiments performed for calculating rotordynamic coefficients show their dependence on many physical and mechanical properties such as working fluid properties, pressure drop, seal clearance, rotor speed, eccentricity and misalignments. With the latest high performance computing facilities it is now relatively easy to simulate the flow in seal and evaluate the dynamic coefficients at high rotational speeds and with complex geometries. This paper proposes a 3-D CFD based transient stimulation method to capture the experimental conditions in virtual environment. The fluid force is calculated by integrating pressure to the rotor surface and the stiffness and damping coefficients are evaluated by appropriate curve fitting of fluid forces for various eccentricity values. The coefficients obtained from the present method show better correlation with experimental data compared to the existing steady state CFD and theoretical models. Variation of these rotordynamic coefficients with eccentricity helps in assessing the safe design of turbomachinery.

Improvement of Low Frequency Vibration Isolation Capability of AMB Using a Cascade PID Controller

In contrast with traditional mechanical bearing, Active magnetic bearing (AMB) has no friction and lubrication, and its dynamic performance can be adjusted by active control. To isolate low frequency vibration of the rotating machinery under 50Hz, a novel design of cascade PID controller (CPC) with two control loops for AMB is proposed. The main loop is a position loop and the secondary loop is a transmission force loop. According to the theoretical derivations in this study, the CPC controls both the rotor position and the transmission force. Even when the control parameters maintain constant, the dynamic characteristic parameters, equivalent stiffness and equivalent damping, vary with frequency continuously and smoothly. Therefore, they can be adjusted in a wide range to achieve isolation of low frequency vibration when using proper control parameters. A simulation example shows that the transmission force with a CPC is lower in the 8–50Hz when the rotor displacement is almost same as with a single stage PID controller (SSPC). Experimental verification was carried out in an experimental bench of AMB under unbalanced rotor condition. Results show that a CPC can reduce the vibration acceleration at 15–50Hz especially near the peaks. Simulation and experimental results well demonstrate the effectiveness and guaranteed stability of the CPC in the present study.

Degradation Feature Extraction of Rolling Bearings Based on Optimal Ensemble Empirical Mode Decomposition and Improved Composite Spectrum Analysis

Rolling bearing is a key part of turbomachinery. The performance and reliability of the bearing is vital to the safe operation of turbomachinery. Therefore, degradation feature extraction of rolling bearing is important to prevent it from failure. During rolling bearing degradation, machine vibration can increase, and this may be used to predict the degradation. The vibration signals are however complicated and nonlinear, making it difficult to extract degradation features effectively. Here, a novel degradation feature extraction method based on optimal ensemble empirical mode decomposition (EEMD) and improved composite spectrum (CS) analysis is proposed. Firstly, because only a few IMFs are expected to contain the information related to bearing fault, EEMD is utilized to pre-process the vibration signals. An optimization method is designed for adaptively determining the appropriate EEMD parameters for the signal, so that the significant feature components of the faulty bearing can be extracted from the signal and separated from background noise and other irrelevant components to bearing faults. Then, Bayesian information criterion (BIC) and correlation kurtosis (CK) are employed to select the sensitive intrinsic mode function (IMF) components and obtain fault information effectively. Finally, an improved CS analysis algorithm is used to fuse the selected sensitive IMF components, and the CS entropy (CSE) is extracted as degradation feature. Experimental data on the test bearings with single point faults separately at the inner race and rolling element were studied to demonstrate the capabilities of the proposed method. The results show that it can assess the bearing degradation status and has good sensitivity and good consistency to the process of bearing degradation.

Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude

Rotor-dynamic fluid force (RD fluid force) of turbo-machinery is one of the causes of the shaft vibration problem. Bulk flow theory is the method for analyzing this RD fluid force, and it has been widely used in the design stage of machine. Conventional bulk flow theory has been carried out under the assumption of concentric circular shaft’s orbit with small amplitude. However, actual rotating machinery’s operating condition often does not hold this assumption, for example, existence of static load on the machinery causes static eccentricity. In particular, when such a static eccentricity is significant, the nonlinearity of RD fluid force may increase and become non-negligible. Therefore, conventional bulk flow theory is not applicable for the analysis of RD fluid force in such situation. In this paper, RD fluid force of the annular plain seal in the case of circular whirling orbit with static eccentricity is investigated. The case with both the significant static eccentricity and the moderate whirling amplitude is considered, and the perturbation analysis of the bulk-flow theory is extended to investigate RD fluid force in such cases. In this analysis, the assumption of the perturbation solution is extended to both static terms and whirling terms up to the third order. Then, the additional terms are caused by the coupling of these terms through nonlinearity, and these three kinds of terms are considered in the extended perturbation analysis of the bulk flow theory. As a result, a set of nonlinear analytical equations of the extended perturbation analysis of the bulk flow theory, for the case with both the significant static eccentricity and the moderate whirling amplitude, is deduced. RD fluid force for such cases are analyzed, and the occurrence of constant component, backward synchronous component and super-harmonic components in RD fluid force is observed in addition to the forward synchronous component. The representation of RD fluid force coefficients (RD coefficients) are modified for the case with significant static eccentricity, and the variation of RD fluid force coefficients for the magnitude of static eccentricity is analyzed. These analytical results of RD fluid force and its RD coefficients are compared with the numerical results using finite difference analysis and experimental results. As a result, the validity of the extended perturbation analysis of the bulk-flow theory for the case with both the significant static eccentricity and the moderate whirling amplitude is confirmed.

Predictions for Non-Contacting Mechanical Face Seal Vibration With External Excitation From Pump Vibration: Part I — Flexibly Mounted Stator

Stability and response predictions are presented for a Flexibly Mounted Stator (FMS) mechanical seal ring using the model developed by Childs in 2018. The seal ring is excited by external vibration from the rotor/housing. The model includes a frequency dependent stiffness and damping model for the O-ring and a frequency independent model for the fluid film. The dynamic coefficients depend on both speed and excitation frequency. Data used in defining the model are representative of a typical FMS mechanical seal. Parameters for radius and O-Ring placement are varied. The predictions show an insignificant dependency on speed. The predictions are strongly frequency dependent with a critical speed of 90 kRPM. The FMS is predicted to be stable to frequencies below 140 kRPM. The distance between the O-Ring and seal ring inertia center doz couples lateral and pitch-yaw motion of the seal ring. Overall, if doz is kept small, the seal ring is predicted to not have any stability or response issues.

Rotordynamic Characterization of a Staggered Labyrinth Seal: Experimental Test Data and Comparison With Predictions

As well known, the stability assessment of turbomachines is strongly related to internal sealing components. For instance, labyrinth seals are widely used in compressors, steam and gas turbines and pumps to control the clearance leakage between rotating and stationary parts, owing to their simplicity, reliability and tolerance to large thermal and pressure variations. Labyrinth seals working principle consists in reducing the leakage by imposing tortuous passages to the fluid that are effective on dissipating the kinetic energy of the fluid from high-pressure regions to low-pressure regions. Conversely, labyrinth seals could lead to dynamics issues. Therefore, an accurate estimation of their dynamic behavior is very important. In this paper, the experimental results of a long-staggered labyrinth seal will be presented. The results in terms of rotordynamic coefficients and leakage will be discussed as well as the critical assessment of the experimental measurements. Eventually, the experimental data are compared to numerical results obtained with the new bulk-flow model (BFM) introduced in this paper.

Evaluation of Coated Top Foil Bearings: Dry Friction, Drag Torque, and Dynamic Force Coefficients

Despite their many advantages, bump-type foil bearings (BFBs) have issues of dry-friction during sliding contact at rotor start/stop cycles. To prevent premature wear of both shaft and the BFB, the proper selection and application of a coating on the top foil is of importance to ensure bearing long life. This thesis presents measurements characterizing the static and dynamic load performance of a Generation I BFB having uncoated and coated (VN, TiSiN, MoS2) top foils. The bearing, with length L and diameter D = 38 mm, integrates a 360° 0.127 mm thick top foil made of Inconel X-750, and a 27 bumps strip layer, 0.47 mm in height, made of the same stock as for the top foils. The VN and TiSiN coating, 0.005 mm thick, applies to the front and back surfaces of a top foil. The MoS2 coating, 0.020 mm thick, is sacrificial. The tests were conducted at room temperature (21°C), determined by the existing test facility. The dry-sliding torque (T) increases linearly with an increase in applied static load, max W/(LD) = 25.6 kPa. The bearing with a VN coated top foil shows the largest turning torque. The dry-sliding friction factor f = T/(½WD) decreases as the specific load (W/(LD)) increases. As expected, journal rotation towards the top foil free end (clockwise) produces a larger f than for rotations in reverse. A test-rig records the BFB drag torque during rotor acceleration and deceleration procedures to/from 70 krpm (138 m/s). The vertical load applied into a bearing equals W/(LD) = −8.0 kPa, 0 kPa and 8.0 kPa. In general, the bearing with a coated top foil shows a lesser drag torque than that of the uncoated top foil bearing. Among the coated foil bearings, the one with VN coating shows the highest drag torque, whereas another with MoS2 coating shows the lowest. When the rotor starts up, the dry-sliding friction coefficient (f) of the bearing with VN coating is ∼0.4 while f for the bearing with TiSiN coating is 0.3∼0.4. The uncoated bearing shows the largest f ∼0.6, and the MoS2 coated one has the lowest f = 0.2∼0.3. The drag torque, increasing with an increase in applied static load, is small when the rotor is airborne (lesser than ∼10% of peak torque). Dynamic load tests spanning excitation frequencies (ω) from 200 Hz to 400 Hz serve to identify force coefficients for the test BFBs with a specific load of 16 kPa and operating with shaft speed at 50 krpm (833 Hz). Baseline measurements correspond to a null applied load and no shaft rotation. The test bearings show a remarkable behavior with nearly isotropic direct coefficients and very small cross-coupled ones. The bearing direct stiffnesses (K) increase with frequency whereas the direct damping coefficients (C) quickly decrease. The bearing material loss factor, γ = ωC/K, represents best the BFB ability to dissipate mechanical energy. Over the excitation frequency range, γ = 0.34, 0.28, and 0.12 for the uncoated top foil, VN coated and TiSiN coated bearings. The test data show the bearing loss factor correlates with the dry friction coefficient as γ ∼ (0.71 × f) at a rotor speed of 50 krpm (95 m/s). Since the top foils with VN or TiSiN are coated on both sides, kinetic friction between the back of a top foil and the bumps’ crests likely lessens during sustained contact.

Turbulence Input Parameters Correction Methodology in Water Lubricated Thrust Bearings

Oil-lubricated bearings are widely used in high speed rotating machines such as those found in the aerospace and automotive industries. However, environmental issues and risk-averse operations are resulting in the removal of oil and the replacement of all sealed oil bearings with reliable water-lubricated bearings. Due to the different fluid properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. This requires finer meshes when compared to oil-lubricated bearings as the low-viscosity fluid produces a very thin lubricant film. Analyzing water-lubricated bearings can also produce convergence and accuracy issues in traditional oil-based analysis codes. Thermal deformation largely affects oil-lubricated bearings, while having limited effects on water lubrication; mechanical deformation largely affects water lubrication, while its effects are typically lower than thermal deformation with oil. One common turbulence model used in these analysis tools is the eddy-viscosity model. Eddy-viscosity depends on the wall shear stress, therefore effective wall shear stress modeling is necessary in determining an appropriate turbulence model. Improving the accuracy and efficiency of modeling approaches for eddy-viscosity in turbulence models is of great importance. Therefore, the purpose of this study is to perform mesh refinement for water-lubricated bearings based on methodologies of eddy-viscosity modeling to improve their accuracy. According to Szeri [1], εm/v for the Boussinesq hypothesis is given by Reichardt’s formula. Fitting the velocity profile with experiments having a y+ in the range of 0–1,000 results in Ng-optimized Reichardt’s constants k = 0.4 and δ+ = 10.7. He clearly states that for y+ > 1000 theoretical predictions and experiments have a greater variance. Armentrout and others [2] developed an equation for δ+ as a function of the pivot Reynolds number, which they validated with CFD simulations. The definition of y+ can be used to approximate the first layer thickness calculated for a uniform mesh. Together with Armentrout’s equation, the number of required elements across the film thickness can be obtained. For typical turbulence models, the y+ must be within a certain range to be accurate. On the condition that the y+ is fixed to that of a standard oil bearing for which an oil bearing code was validated, the number of elements across the film thickness and coefficients used in the eddy-viscosity equation can be adjusted to allow for convergence with other fluids other than that which the traditional oil bearing code was designed for. In this study, the number of required elements across the film for improved prediction quality was calculated based on the proposed eddy-viscosity model mesh correction from the known literature. A comparison between water lubrication using the parameter correction and oil lubrication was also made. The results of this study could aid in improving future designs and models of water-lubricated bearings.