Determination of the Vibration Within a Squeeze-Film Damper Under Rotational Unbalance Conditions From Externally Mounted Sensors

Recently, there has been a focus on the use of inverse problem techniques in order to monitor rotor unbalance, and obtain a balancing solution, from vibration measurements on the casing and prior knowledge of the rotor-casing structure. In certain practical configurations that use nonlinear bearings like the squeeze-film damper (SFD) bearing, an inverse model of the bearing is an important part of the unbalance identification process. The inverse bearing model is used to estimate the journal vibration from casing vibration measurements, thus acting as a substitute for internal instrumentation in applications where the rotor is not accessible under operational conditions. Previous research has shown that an inverse bearing model can be identified using a trained Recurrent Neural Network (RNN) from experimental input/output data. However, the RNN was both trained and validated under simulated rotational conditions, wherein the motion was driven by two orthogonally-phased perpendicular shakers. In this paper, a RNN of an inverse bearing model that is identified from experimental data generated under simulated rotational conditions is validated under actual rotational (i.e. unbalance-driven) vibration conditions. The necessary modifications to the test rig are presented, together with the identification/training procedure. The results of the validation tests show that the RNN is capable of predicting the frequency spectrum of the dynamic nonlinear response of the journal with reasonable accuracy. This inverse SFD bearing model can be thus used in a future work to identify rotor unbalance.

Hydro Francis Runner Stability and Forced Response Calculations

Hydroelectric power generation accounts for 7% of the total world electric energy production. Francis turbines are often employed in large-scale hydro projects and represent 60% of the total installed base. Outputs up to 800 MW are available and efficiencies of 95% are common. Cost, performance, and design cycle time are factors that continue to drive new designs as well as retrofits. This motivates the development of more sophisticated analysis tools to better assess runner performance earlier in the design phase. The focus of this paper is to demonstrate high fidelity and time-efficient runner damping and forced response calculations based on one-way fluid-structure interaction (FSI) using loosely coupled commercial finite element analysis (FEA) and computational fluid dynamics (CFD) codes. The runner damping is evaluated based on the work done by the fluid on the runner. The calculation of the work first involves determining the runner mode shapes and natural frequencies using a cyclic symmetric FEA model with structural elements to represent the runner hardware, and acoustic fluid elements to represent the mass loading effect of the fluid. The mode shapes are then used in a transient CFD calculation to determine the damping which represents the work done by the fluid on the runner. Positive damping represents stability from flutter perspective while negative damping represents unstable operating conditions. A transient CFD calculation was performed on a runner to obtain engine order forcing function from upstream stationary vanes. This unsteady forcing function was mapped to the FEA model. Care is taken to account for the proper inter-blade phase angle on the cyclic symmetric model. The hydraulic damping from flutter calculations was also provided as input to the forced response. The forced response is then determined using this equivalent proportional damping and modal superposition of the FEA model that includes both the structural and acoustic elements. Results of the developed analysis procedure are presented based on the Tokke runner, that has been the basis of several studies through the Norwegian HydroPower Center. Unique features of the workflow and modeling approaches are discussed in detail. Benefits and challenges for both the FEA model and the CFD model are discussed. The importance of the hydraulic damping, that is traditionally ignored in previous analysis is discussed as well. No validation data is available for the forced response, so this paper is focused on the methodology for the calculations.

Simple Contact Stiffness Model Validation for Tie Bolt Rotor Design With Butt Joints and Pilot Fits

Tie bolt rotors for centrifugal compressors comprise multiple shaft components that are held together by a single tie bolt. The axial connections of these rotors — including butt joints, Hirth couplings, and Curvic couplings — exhibit a contact stiffness effect, which tends to lower the shaft bending frequencies compared to geometrically identical monolithic shafts. If not accounted for in the design stage, shaft bending critical speed margins can be compromised after a rotor is built. A previous paper had investigated the effect of tie bolt force on the bending stiffness of stacked rotor assemblies with butt joint interfaces, both with and without pilot fits. This previous work derived an empirical contact stiffness model and developed a practical finite element modeling approach for simulating the axial contact surfaces, which was validated by predicting natural frequencies for several test rotor configurations. The present work built on these previous results by implementing the same contact stiffness modeling approach on a real tie bolt rotor system designed for a high pressure centrifugal compressor application. Each joint location included two axial contact faces, with contact pressures up to five times higher than previously modeled, and a locating pilot fit. The free-free natural frequencies for different amounts of tie bolt preload force were measured, and the frequencies exhibited the expected stiffening behavior with increasing preload. However, a discontinuity in the data trend indicated a step-change increase in the contact stiffness. It was shown that this was likely due to one or more of the contact faces becoming fully engaged only after sufficient tie bolt force was applied. Finally, a design calculation was presented that can be used to estimate whether contact stiffness effects may be ignored, which could simplify rotor analyses if adequate contact pressure is used.

Improvement of Rotordynamic Performance of Integrally Geared Centrifugal Compressors Through a Systematic Design Modification Approach

Integrally geared centrifugal compressors have found wide applications in air separation plants and the petrochemical industry because they can be readily designed to run at a higher efficiency than in-line compressors. Many of these compressors with multiple stages are designed to meet the demands for high power and high speed applications with high efficiency and high reliability. These requirements are challenges for their rotordynamic designs. Some compressors may experience excessive synchronous or subsynchronous vibrations during commissioning or in a short period of service. This study starts with discussing the vibration characteristics of a compressor pinion-bearing system, including undamped critical speeds, unbalance responses, and rotordynamic stability. To improve the rotordynamic performance, a systematic and feasible approach for modifying a rotordynamic design has been proposed. It has been showed that damped modes at an operating speed are key indicators of the rotordynamic performance. The sensitivities of damped modes to main design variables, i.e. bearing geometry, shaft geometry and impeller mass properties, are thoroughly examined. A procedure for design modification is proposed for general guidance. The feasibility and effectiveness of this method have been demonstrated in the modification of a pinion-bearing system. In addition, this paper also proposes a method to evaluate the torsional natural frequencies of an equivalent pinion model and briefly discusses the application of optimal design methodology to the rotordynamic design modification.

A Crystal Visco-Plastic Model for Ni-Base Superalloys Under Low Cycle Fatigue

Components in gas turbines, specifically turbine blades are subjected to extreme loading conditions such as high temperatures and stresses over extended periods of time; therefore, predicting material behavior and life expectancy at these loading conditions are extremely important. The development of simulations that accurately predict monotonic response for these materials are highly desirable. Single crystal Ni-base superalloys used in the design of gas turbine blades exhibit anisotropic behavior resulting from texture development and dislocation substructures. A Crystal Visco-plastic (CVP) model has the capability of capturing both phenomena to accurately predict the deformation response of the material. The rate dependent crystal visco-plastic model consists of a flow rule and internal state variables. This model considers the inelastic mechanism of kinematic hardening which is captured using the Back stress. Crystal graphic slip is taken in to account by the incorporation of 12 Octahedral slip systems. An implicit integration structure that uses Newton Raphson iteration scheme is used to solve the desired solutions. The MATLAB model is developed in two parts, including a routine for the CVP constitutive model along with a separate routine which functions as an emulator. The emulator replicates a finite element analysis model and provides the initial calculations needed for the CVP. A significant advantage of the MATLAB model is its capability to optimize the modelling constants to increase accuracy. The CVP model has the capability to display material behavior for monotonic loading for a variety of material orientations and temperatures.

A Method to Evaluate the Sensitivity of Aerodynamic Damping to Mode Shape Perturbations

Turbomachinery blade mode shapes are routinely predicted by finite element method (FEM) programs and are then used in unsteady computational fluid dynamic (CFD) analyses to predict the aerodynamic damping. This flutter stability assessment process is critical for the last-stage blades (LSBs) of modern heavy-duty gas turbines (HDGTs) which can be particularly susceptible to flutter. Evidences suggest that actual mode shapes may deviate from the FEM predictions due to changes in the FEM boundary or loading conditions, effects of the nonlinear friction contacts, and blade-to-blade variations (mistuning), among others. This uncertainty in the mode shape is accompanied by a general lack of knowledge on the sensitivity of the aerodynamic damping to a small change in mode shape. This paper presents a method to perturb a mode shape and estimate the corresponding change in aerodynamic damping in a framework enabled by linear theories and a rigid-body, quasi-3D treatment of mode shapes. This method is of low computational cost and is suitable for use in the preliminary design cycle. The numerical validation and applications of the method are demonstrated on two LSB blades. Results suggest that the mode shape sensitivity can be substantial and may even exceed the change in aerodynamic damping of a frictionally damped system when subjected to various levels of excitation.

Experimental Investigation on the Creep and Low Cycle Fatigue Behaviors of a Serviced Turbine Blade

This paper experimentally investigated the creep and fatigue behaviors of a low-pressure turbine (LPT) blade with 600 hours of service using a novel test system. Pure low cycle fatigue (LCF), pure creep and creep-fatigue interaction (CFI) experiments on the full-scale serviced blades were conducted respectively. Test results showed that the increasing of deformation amplitude was divided into three stages under both pure LCF and creep-fatigue loadings. The deformation of each blade increased rapidly until failure when the test cycle exceeded the 80% of their overall life under the pure LCF and CFI condition. The hold period in creep-fatigue tests shortens the first stage of whole life and has no influence on the proportion of crack initiation life to overall life. The fractures in pure LCF, pure creep and creep-fatigue tests emerged transgranular, intergranular and both transgranular and intergranular behaviors respectively. The crack initiated and propagated in a specific zone of the blade under all the experimental loadings, which limited its creep-fatigue resistance. At last, the remaining life of turbine blade was estimated conservatively by introducing the safety limit into a statistical method.

Dynamic Analysis and Optimization on Assembly Parameters of Rod Fastening Rotor System With Manufacturing Tolerances

Rod fastening rotor (RFR), as a typical rotor structure of gas turbine which is different from the integral rotor, is comprised of a set of discs clamped together by a central tie rod or several tie rods on the pitch circle diameters. In process of machining, tolerances of the disc are inevitable, of which the parallelism error and mass imbalance are focused on in this paper. Firstly, the complex bending of RFR by accumulation of parallelism errors of discs is derived through the coordinate transmission. Then the static analysis of RFR is performed to obtain the additional pressure by the effect of unbalanced forces, which is related to the assembly angles and rotating speed, on contact surfaces using a linear hypothesis, based on which the distribution of contact pressure considering the original pre-tightening force is obtained. Then the Bifractal-Regular theory is adopted to acquire the micro-topography of the contact interface and derive the contact stiffness related to normal contact pressure, fractal upper length limit and regular shape of the contact interfaces. After that, the zero thickness element is introduced to obtain the equivalent stiffness matrices of the contact surface. In addition, the circumferential uniformly distributed rods are modeled as a spring element which provides additional bending stiffness for the RFR. Based on the analysis above, the dynamic model of the RFR-bearing system containing 10 discs is established using the Timoshenko beam element where the continuous part of the shaft is modeled by Timoshenko beam element considering shear effect. Finally, the multi-optimization is carried out on the vibration response by the coupled effects of both initial bending and mass imbalance of the RFR-bearing system through which the optimal assembly angles are obtained. The results show a good performance in decreasing vibration as well as bending of the RFR system.

Conceptual Flutter Analysis of Stepped Labyrinth Seals

A simple non-dimensional model to describe the flutter onset of two-fin straight labyrinth seals [1] is extended to stepped seals. The effect of the axial displacement of the seal is analyzed first in isolation. It is shown that this fundamental mode is always stable. In a second step, the combination of axial and torsion displacements is used to determine the damping of modes with arbitrary torsion centers. It is concluded that the classical Abbot’s criterion stating that seals supported in the low-pressure side of the seal are stable provided that natural frequency of the mode is greater than the acoustic frequency breaks down under certain conditions. An analytical expression for the non-dimensional work-per-cycle is derived and new non-dimensional parameters controlling the seal stability identified. It is finally concluded the stability of stepped seals can be assimilated to that of a straight through seal if the appropriate distance of the torsion center to the seal is chosen.

Novel and Applicable Method to Determine Equivalent Strain Range and Equivalent Strain Direction Under Multiaxial Non-Proportional Loading

When considering mechanical components that are subjected to complex loading conditions, it is difficult to achieve accurate predictions of low-cycle fatigue life. For multiaxial and non-proportional loads, the principal strain directions vary in three-dimensional space with time. The commonly accepted methods to determine fatigue life under such loading conditions are based on a critical plane approach, and they rely heavily on accurate strain range estimates. However, there is no singly accepted method to determine the critical plane, equivalent strain magnitude, or equivalent strain direction. Furthermore, current suggestions are computationally intensive and challenging to implement. This paper offers a novel and concise method to accurately determine equivalent strain range and equivalent strain direction under multiaxial, non-proportional loading in three-dimensional space. A practical approach is provided for implementing the method, and an example of an application using a finite element model of a first stage turbine blade is discussed. To demonstrate the approach, ANSYS Mechanical was used to simulate a turbine blade under transient loading conditions and to determine the resulting strains. Equivalent strain range results were applied to a Coffin-Manson relation to determine the low-cycle fatigue life of every node within the finite element model of the first stage turbine blade. The post-processing of the strain predictions, which yielded the equivalent strain range and equivalent strain direction, is discussed in detail.