Influence of Different Parametrizations on the Optimum Design of a High Pressure Turbine Blade Firtree

Today the design processes in the aero industry face many challenges. Apart from automation itself, a suitable parametric geometry setup plays a significant role in making workflows usable for optimization. At the same time there are tough requirements against the parametric model. For the lowest number of possible parameters, which should be intuitively ascertainable, a high flexibility has to be ensured. Within the parameter range an acceptable stability is necessary. Under these constraints the creation of such parametric models is a challenge, which should not be underestimated especially for a complex geometry. In this work different kinds of parametrization with different levels of complexity will be introduced and compared. Thereby several geometry elements will be used to handle the critical regions of the geometry. In the simplest case a combination of lines and arcs will be applied. These will be replaced by superior elements like a double arc construct or different formulations of b-splines. There will be an additional focus on the variation of spline degree and control points. To guarantee consistency a set of general parameters will be used next to the specific ones at the critical regions. The different parameter boundaries have a influence on the possible geometries and should therefore be tested separately before an optimization run. The analysis of the particular parametrization should be compared against the following points: • effort for the creation of the parametrization in theory • required time for the implementation in the CAD software • error-proneness/robustness of the parametrization • flexibility of the possible geometries • accuracy of the results • influence of the number of runs on the optimization • comparison of the best results Even though this assessment matrix is only valid for the considered case, it should show the general trend for the creation of these kinds of parametric models. This case takes a look at a firtree of a high pressure turbine blade, which is a scaled version of the first row from a small to medium aero engine. The failure of such a component can lead to a critical engine failure. For that reason, the modeling/meshing must be done very carefully and the contact between the blade and the disc is of crucial importance. It is possible to use scaling factors for three dimensional effects to reduce the problem to a two dimensional problem. Therefore the contact description is shortened from face-to-line to line-to-point. The main aim of the optimization is the minimization of the tension (notch stress) at the inner bends of the blade respectively at the outer bends of the disc. This has been the limiting factor in previous investigations. At this part of the geometry the biggest improvement are expected from a superior parametrization. Another important constraint in the optimization is the pressure contact (crushing stress) between blade and disc. Additionally the geometry is restricted with measurements of the lowest diameter at specific fillets to fulfill manufacturing requirements.

A Multi-Scale Approach for Nonlinear Dynamic Response Predictions With Fretting Wear

Accurate prediction of the vibration response of aircraft engine assemblies is of great importance when estimating both the performance and the lifetime of its individual components. In the case of underplatform dampers, for example, the motion at the frictional interfaces can lead to a highly nonlinear dynamic response and cause fretting wear at the contact. The latter will change the contact conditions of the interface and consequently impact the nonlinear dynamic response of the entire assembly. Accurate prediction of the nonlinear dynamic response over the lifetime of the assembly must include the impact of fretting wear. A multi-scale approach that incorporates wear into the nonlinear dynamic analysis is proposed, and its viability is demonstrated for an underplatform damper system. The nonlinear dynamic response is calculated with a multiharmonic balance approach, and a newly developed semi-analytical contact solver is used to obtain the contact conditions at the blade-damper interface with high accuracy and low computational cost. The calculated contact conditions are used in combination with the energy wear approach to compute the fretting wear at the contact interface. The nonlinear dynamic model of the blade-damper system is then updated with the worn profile and its dynamic response is recomputed. A significant impact of fretting wear on the nonlinear dynamic behaviour of the blade-damper system was observed, highlighting the sensitivity of the nonlinear dynamic response to changes at the contact interface. The computational speed and robustness of the adopted multi-scale approach are demonstrated.

Support Vibration Diagnostics and Limits in Gas Turbines

The paper deliberates vibration limits for non-rotating parts in application to industrial gas turbines. As a rule such limits follow ISO 10816-4 or API616, although in field operation it is not well known relationship between these limits and failure modes. In many situations, the reliability function is not well-defined, and more comprehensive methods of determining the harmful effects of support vibrations are desirable. In the first part, the undertaken approach and the results are illustrated based on the field and theoretical experience of the authors about the failure modes related to alarm level of vibrations. Here several failure modes and diagnostics observations are illustrated with the examples of real-life data. In the second part, a statistical approach based on correlation of support vs. shaft vibrations (velocity / displacement) is demonstrated in order to assess the risk of the bearing rub. The test data for few gas turbine models produced by General Electric Oil & Gas are statistically evaluated and allow to draw an experimentally based transfer function between vibrations recorded by non-contact and seismic probes. Then the vibration limit with objectives like bearing rub is scrutinized with aid of probabilistic tools. In the third part, the attention is given to a few examples of the support vibrations — among other gas turbine with rotors supported on flexible pedestals and baseplate. Here there is determined a transfer coefficient between baseplate and bearing vibrations for specific foundation configurations. Based on the test data screening as well as analysis and case studies thereof, the conclusions about more specific vibration limits in relation to the failure modes are drawn.

An Integrated Software Tool for High Fidelity Probabilistic Assessments of Metallic Aero-Engine Components

Most current tools and methodologies to predict the life and reliability of fracture critical gas turbine engine components rely on stress intensity factor solutions that assume highly idealized component and crack geometries, and this can lead to highly conservative results in some cases. This paper describes a new integrated methodology to perform these assessments that combines one software tool for creating high fidelity crack growth simulations (FRANC3D) with another software tool for performing probabilistic fatigue crack growth life assessments of turbine engine components (DARWIN). DARWIN employs finite element models of component stresses, while FRANC3D performs automatic adaptive re-meshing of these models to simulate crack growth. Modifications have been performed to both codes to allow them to share and exchange data and to enhance their shared computational capabilities. Most notably, a new methodology was developed to predict the shape evolution and the fatigue lifetime for cracks that are geometrically complex and not easily parameterized by a small number of degrees of freedom. This paper describes the integrated software system and the typical combined work flow, and it shows the results from a number of analyses that demonstrate the significant features of the system.

Suppression of Subsynchronous Vibrations in a 11 MW Steam Turbine Using Integral Squeeze Film Damper Technology at the Exhaust Side Bearing

The presence of high subsynchronous vibrations and other rotordynamic instabilities in steam turbines can prevent operation at full speed and/or full load. The destabilizing forces generating subsynchronous vibrations can be derived from bearings, seals, impellers or other aerodynamic sources. The present paper describes the case of an 11 MW steam turbine, driving a syngas centrifugal compressor train, affected by subsynchronous vibrations at full load. After the occurrence of anomalous vibrations at high load and a machine trip due to the high vibrations, the analysis of data collected at the site confirmed instability of the first lateral mode. Further calculations identified that the labyrinth seal at the balance drum was the main source of destabilizing effects, due to the high pre-swirl and the relatively tight seal clearance. The particular layout of the turbine, a passing-through machine with a combined journal/double thrust bearing on the steam admission side, together with the need for a fast and reliable corrective action limited the possible solutions. Based on the analyses performed, adjusting the clearance and preload of the journal bearings could not have ensured stable operation at each operating condition. The use of swirl brakes to reduce the steam pre-swirl at the recovery seal entrance would have required a lengthy overhaul of the unit and significant labor to access and modify the parts. The final choice was a drop-in replacement of only the rear bearing (on the steam exhaust side) with a bearing featuring integral squeeze film damper (ISFD) technology. In addition to being a time efficient solution, the ISFD technology ensured an effective tuning of stiffness and damping, as proven by the field results. The analyses carried out to understand the source of the subsynchronous vibrations and to identify possible corrective actions, as well as the comparison of rotordynamic data before and after the application of the bearing with ISFD technology, are discussed.

Torsional Robustness of the Combined Cycle Power Train Arrangement: Application of Statistical Methods to Accelerate Shaft-Line Design Cycles

This article presents the application of statistical methods to guide the rotordynamic design of a turbo-generator shaft-line. One of the basic requirements is all shaft components must survive the event of a short circuit at the terminals of the generator. This is typically assessed via a transient response simulation of the complete machine train (including generator’s electrical model) to check the calculated response torque against the allowable value. With an increasing demand of a shorter design cycle and competition in performance, cost, footprint and safety, the probabilistic approach is starting to play an important role in the power train design process. The main challenge arises with the size of the design space and complexity of its mapping onto multiple objective functions and criteria which are defined for different machines. In the presented paper, the authors give an example demonstrating the use of statistical methods to explore (Design of Experiment) and understand (Surface Response Methods) the design space of the Combined Cycle Power Train with respect to the typically most severe constraint (fault torque torsional response), which leads to a quicker definition of a turbo-generator’s arrangement. Further statistical analyses are carried out to understand the robustness of the chosen design against future modifications as well as parameters’ uncertainties.

A Fractal Contact Friction Model and Nonlinear Vibration Response Studies of Loosely Assembled Blade With Dovetail Root

To investigate the friction damping effect of a loosely assembled blade with dovetail root, a fractal contact friction model is proposed to describe the friction force. In the proposed model, the friction contact interface is discretized to a series of friction contact pairs and each of them can experience stick, slip, or separate. Fractal geometry is used to simulate the topography of contact surfaces. The contact stiffness, which is related to the parameters of contact interfaces including normal load, roughness, Young’s modulus, and Poisson’s ratio, is calculated using Hertz contact theory and fractal geometry. The nonlinear vibration response of loosely assembled blade with dovetail root is predicted using the proposed model, the multiharmonic balance method and Newton iterative algorithm. The effect of centrifugal force, friction coefficient and exciting force on the forced response of a loosely assembled blade with dovetail root is studied. The numerical vibration responses are compared to the experimental results. It will verify the reliability of the numerical method and provide theoretical basis for structure design of the loosely assembled blade with dovetail root.

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

Forced Response Analysis of a Mistuned Compressor Blisk Comparing Three Different Reduced Order Model Approaches

Accurate structural modeling of blisk mistuning is critical for the analysis of forced response in turbomachinery. Apart from intentional mistuning, mistuning can be due to the manufacturing tolerances, corrosion, foreign object damage and in-service wear in general. It has been shown in past studies that mistuning can increase the risk of blade failure due to energy localization. For weak blade to blade coupling, this localization has been shown to be critical and higher amplitudes of vibration are expected in few blades. This paper presents a comparison of three reduced order models for the structural modeling of blisks. Two of the models assume cyclic symmetry while the third model is free of this assumption. The performance of the reduced order models for cases with small and large amount of mistuning will be examined. The benefits and drawbacks of each reduction method will be discussed.

Forced Vibration of Mistuned Bladed Discs in Last Stage LP Steam Turbine

During the exploitation of a commercial LP steam turbine, self-excitation occurred in the last stage of slender blades, inducing high vibration amplitudes. These problems were solved by changing the geometry of certain blades (feathering) and arranging them in a specific order (alternating mistuning). This paper presents free and forced vibrations of various mistuned steam turbine bladed discs. The natural frequencies and mode shapes of the steam turbine bladed discs were calculated using FEM models. Two different approaches to mistuning were applied: either the blade geometry or the Young’s Modulus were changed. Next, the results were compared. This showed that blade geometry mistuning gave the best results for long blades in the case of higher mistuning. The forced vibration analysis showed that the maximal blade stress location differed, depending on the kind of mistuning. The application feathering and alternating mistuning showed lower stress levels than the tip-timing measured standard mistuning pattern.