Reduced Order Model for a Two Stage Gas Turbine Including Mistuned Bladed Disks and Shaft Interaction

2009 ◽  
Author(s):  
Luis A. Boulton ◽  
Euro Casanova
Keyword(s):  
Finite Element ◽  
Gas Turbine ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Order Model ◽  
Two Stage ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk ◽  
The Impact

A number of previous works have suggested that in some cases the interaction between shaft and bladed disk modes could significantly modify the dynamics of the whole assembly i.e. the bladed disks mounted on a flexible shaft. This paper presents the application of a previously published reduced-order modeling technique to the dynamical modeling of a real two stage gas turbine, including the bladed disks and the shaft. In the resulting reduce order model, mistuning is included in the bladed disk models and the shaft is modeled using beam finite elements according to the classical rotordynamic approach. Generation of finite element parent model for the real turbine is presented and discussed as well as simplifications used in order to generate the reduced order model. Comparisons are made between the reduced model and the full finite element solution for free response frequencies and mode shapes in order to assess the methodology and to evaluate the impact of simplifying hypothesis considered in model generation. Finally, this work also shows interaction between shaft modes and bladed disk modes, therefore confirming that stage independent analysis might not be adequate for predicting the global dynamic response of some turbomachinery rotors.

A Reduced-Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

2003 ◽  
Vol 125 (3) ◽  
pp. 772-776 ◽  
Author(s):  
P. Marugabandhu ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Finite Element Analyses ◽  
Order Model ◽  
Reduced Order ◽  
Low Aspect Ratio ◽  
Centrifugal Stiffening ◽  
Fan Blade

A reduced-order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

Prediction of Geometrically Induced Localization Effects Using a Subset of Nominal System Modes

2019 ◽  
Author(s):  
Thomas Maywald ◽  
Christoph R. Heinrich ◽  
Arnold Kühhorn ◽  
Sven Schrape ◽  
Thomas Backhaus
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Reduced Order Model ◽  
Vibration Measurement ◽  
Mode Shapes ◽  
Compressor Stage ◽  
Order Model ◽  
Reduced Order ◽  
Numerical Predictions

Abstract It is widely known that the vibration characteristics of blade integrated discs can dramatically change in the presence of manufacturing tolerances and wear. In this context, an increasing number of publications discuss the influence of the geometrical variability of blades on phenomena like frequency splitting and mode localization. This contribution is investigating the validity of a stiffness modified reduced order model for predicting the modal parameters of a geometrically mistuned compressor stage. In detail, the natural frequencies and mode shapes, as well as the corresponding mistuning patterns, are experimentally determined for an exemplary rotor. Furthermore, a blue light fringe projector is used to identify the geometrical differences between the actual rotor and the nominal blisk design. With the help of these digitization results, a realistic finite element model of the whole compressor stage is generated. Beyond that, a reduced order model is implemented based on the nominal design intention. Finally, the numerical predictions of the geometrically updated finite element model and the stiffness modified reduced order model are compared to the vibration measurement results. The investigation is completed by pointing out the benefits and limitations of the SNM-approach in the context of geometrically induced mistuning effects.

A Nonlinear Dynamic Reduced-Order Model for a Large Gas Turbine Outer Casing Low Cycle Fatigue Prediction

2021 ◽  
Author(s):  
Aditya Dubey ◽  
Rishi Relan ◽  
Uwe Lohse ◽  
Jaroslaw Szwedowicz
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Gas Turbine ◽  
Nonlinear Dynamic ◽  
Low Cycle Fatigue ◽  
Reduced Order Model ◽  
Cycle Fatigue ◽  
Order Model ◽  
Element Analysis ◽  
Reduced Order

Abstract The secondary stresses that result from nonlinear and transient thermal gradients during the start-up and shut down of the large gas turbine engines drive low-cycle fatigue at specific locations of the outer casing. Typical service inspection of the outer casing is primarily based on finite element analysis estimates, considering various safety factors. However, as finite element analysis includes the worst possible combination of loading scenarios and operating conditions any engine may encounter in actual operation, this results in a conservative estimation of the service interval. Therefore, a generic preventive maintenance plan for the whole fleet often underutilises the casing capability and added cost. Hence, this paper proposes a data-driven nonlinear dynamic reduced-order model developed using the temperature data from low-cycle fatigue critical casing locations, ramp rates, and the percentage load of operation to predict the stresses. As a result, a reduced-order model can assess the damage for low-cycle fatigue critical locations in real-time using the operational data and propose an appropriate service intervention plan for each casing in a fleet.

A Reduced Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

2000 ◽  
Author(s):  
P. Marugabandhu ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Finite Element Analyses ◽  
Order Model ◽  
Reduced Order ◽  
Low Aspect Ratio ◽  
Centrifugal Stiffening ◽  
Fan Blade

A reduced order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

On Damping Entire Bladed Disks Through Dampers on Only a Few Blades

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Javier Avalos ◽  
Marc P. Mignolet
Keyword(s):  
Optimum Design ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Bladed Disks ◽  
Single Degree Of Freedom ◽  
Reduced Order ◽  
Bladed Disk ◽  
Single Degree ◽  
Random Mistuning

The focus of this paper is on demonstrating the potential to damp entire bladed disks using dampers on only a fraction of the blades. This problem is first considered without the presence of random mistuning, and it is demonstrated that a few dampers at optimized locations can lead to a significant reduction in the forced response of the entire bladed disk. Unfortunately, this optimum design may not be robust with respect to random mistuning and a notable fraction of the reduction in forced response obtained may disappear because of mistuning. To regain the reduction in forced response but with mistuning present, robustness to mistuning is enhanced by using intentional mistuning in addition to dampers. The intentional mistuning strategy selected here is the A/B pattern mistuning in which the blades all belong to either type A or B. An optimization effort is then performed to obtain the best combination of A/B pattern and damper location to minimize the mistuned forced response of the disk. The addition of intentional mistuning in the system is shown to be very efficient, and the optimum bladed disk design does indeed exhibit a significant reduction in mistuned forced response as compared with the tuned system. These findings were obtained on both single-degree-of-freedom per blade-disk models and a reduced order model of a blisk.

On Damping Entire Bladed Disks Through Dampers on Only a Few Blades

2008 ◽  
Author(s):  
Javier Avalos ◽  
Marc P. Mignolet
Keyword(s):  
Optimum Design ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Bladed Disks ◽  
Single Degree Of Freedom ◽  
Reduced Order ◽  
Bladed Disk ◽  
Single Degree ◽  
Random Mistuning

The focus of this paper is on demonstrating the potential to damp entire bladed disks using dampers on only a fraction of the blades. This problem is first considered without the presence of random mistuning and it is demonstrated that a few dampers at optimized locations can lead to a significant reduction in the forced response of the entire bladed disk. Unfortunately, this optimum design may not be robust with respect to random mistuning and a notable fraction of the reduction in forced response obtained may disappear because of mistuning. To regain the reduction in forced response but with mistuning present, robustness to mistuning is enhanced by using intentional mistuning in addition to dampers. The intentional mistuning strategy selected here is the A/B pattern mistuning in which the blades all belong to either type A or B. An optimization effort is then performed to obtain the best combination of A/B pattern and damper location to minimize the mistuned forced response of the disk. The addition of intentional mistuning in the system is shown to be very efficient and the optimum bladed disk design does indeed exhibit a significant reduction of mistuned forced response as compared to the tuned system. These findings were obtained on both single-degree-of-freedom per blade disk models and a reduced order model of a blisk.

A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed-Disks

2000 ◽  
Author(s):  
François Moyroud ◽  
Torsten Fransson ◽  
Georges Jacquet-Richardet
Keyword(s):  
Finite Element ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Mode Localization ◽  
Reduced Order ◽  
Bladed Disk ◽  
Reduction Techniques ◽  
Modal Reduction

The high performance bladed-disks used in today’s turbomachines must meet strict standards in terms of aeroelastic stability and resonant response level. One structural characteristic that can significantly impact on both these area is that of bladed-disk mistuning. To predict the effects of mistuning, computationally efficient methods are necessary to make it feasible, especially in an industrial environment, to perform free vibration and forced response analyses of full assembly finite element models. Due to the size of typical finite element models of industrial bladed-disks, efficient reduction techniques must be used to systematically produce reduced order models. The objective of this paper is to compare two prevalent reduction methods on representative test rotors, including a modern design industrial shrouded bladed-disk, in terms of accuracy (for frequencies and mode shapes), reduction order, computational efficiency, sensitivity to inter-sector elastic coupling, and ability to capture the phenomenon of mode localization. The first reduction technique employs a modal reduction approach with a modal basis consisting of mode shapes of the tuned bladed-disk which can be obtained from a classical cyclic symmetric modal analysis. The second reduction technique is based on a Craig and Bampton substructuring and reduction approach. The results show a perfect agreement between the two reduced order models and the non-reduced finite element model. It is found that the phenomena of mode localization is equally well predicted by the two reduction models. In terms of computational cost, reductions from 1 to 2 orders of magnitude are obtained for the industrial bladed-disk, with the modal reduction method being the most computationally efficient approach.

A Reduced Order Model for Nonlinear Dynamics of Mistuned Bladed Disks With Shroud Friction Contacts

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
S. Mehrdad Pourkiaee ◽  
Stefano Zucca
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Reduced Model ◽  
Synthesis Methods ◽  
Order Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk

A new reduced order modeling technique for nonlinear vibration analysis of mistuned bladed disks with shrouds is presented. The developed reduction technique employs two component mode synthesis methods, namely, the Craig-Bampton (CB) method followed by a modal synthesis based on loaded interface (LI) modeshapes (Benfield and Hruda). In the new formulation, the fundamental sector is divided into blade and disk components. The CB method is applied to the blade, where nodes lying on shroud contact surfaces and blade–disk interfaces are retained as master nodes, while modal reductions are performed on the disk sector with LIs. The use of LI component modes allows removing the blade–disk interface nodes from the set of master nodes retained in the reduced model. The result is a much more reduced order model (ROM) with no need to apply any secondary reduction. In the paper, it is shown that the ROM of the mistuned bladed disk can be obtained with only single-sector calculation, so that the full finite element model of the entire bladed disk is not necessary. Furthermore, with the described approach, it is possible to introduce the blade frequency mistuning directly into the reduced model. The nonlinear forced response is computed using the harmonic balance method and alternating frequency/time domain approach. Numerical simulations revealed the accuracy, efficiency, and reliability of the new developed technique for nonlinear vibration analysis of mistuned bladed disks with shroud friction contacts.

Vibration reduction optimization of the mistuned bladed disk considering the prestress

2017 ◽  
Vol 233 (1) ◽  
pp. 226-239 ◽  
Author(s):  
Hongyuan Zhang ◽  
Huiqun Yuan ◽  
Wenjun Yang ◽  
Tianyu Zhao
Keyword(s):  
Finite Element ◽  
Optimization Algorithm ◽  
Synthesis Method ◽  
Reduced Order Model ◽  
Component Mode Synthesis ◽  
Order Model ◽  
Blade Vibration ◽  
Reduced Order ◽  
Vibration Localization ◽  
Bladed Disk

Ignoring the effect of prestress can increase the gap between the actual results and research results, which is not conducive to improve the vibration localization of bladed disk system and the finite element calculation. To improve the vibration localization and computational efficiency, the prestressed component mode synthesis method (PCMSM) was adopted to establish the finite element reduced-order model considering prepress. Since the main calculation precision of the prestressed component mode synthesis method was the mode truncation number, calculation was made to the eigenfrequency of different mode truncations; the contrast and analysis were made to the calculation result of blisk model, minimum mode truncation number under the above calculation precision was obtained, and freedom of the model was greatly reduced. The finite element reduced-order model was collocated to make an analysis of the vibration response characteristics of mistuned bladed disk. From the aforementioned analysis, the maximum amplitude of mistuned bladed disk was not only associated with the mistuning value of blade but also related to the frequency of adjacent blade; on the basis of such a rule, the finite element reduced-order model was adopted to raise an optimization algorithm for the blade vibration reduction and arrangement. Results have revealed that the optimization algorithm has made an adequate consideration of both model precision and calculation speed. The maximum dimensionless amplitude of blade vibration under three mistuning patterns and upon optimization is greatly reduced by 32.8%, 30.1%, and 28%. The localization factor of blade vibration under three mistuning patterns and upon optimization is greatly reduced by 64%, 68.5%, and 57.2%. The optimization algorithm based on the prestressed component mode synthesis method gets the optimization value by not more than 15 iterations. The optimization algorithm has greatly reduced the amplitude of the blade and obviously dampened vibration localization of the bladed disk system.

A Reduced Order Model for Nonlinear Dynamics of Mistuned Bladed Disks With Shroud Friction Contacts

2018 ◽  
Author(s):  
S. Mehrdad Pourkiaee ◽  
Stefano Zucca
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Reduced Model ◽  
Order Model ◽  
Bladed Disks ◽  
Statistical Characterization ◽  
Reduced Order ◽  
Bladed Disk

A new reduced order modeling technique for nonlinear vibration analysis of mistuned bladed disks with shrouds is presented. It has been shown in the literature that the loss of cyclic symmetry properties which is known as mistuning could considerably increase the response level, localize the vibration around few number of blades and finally bring high cyclic fatigue. The developed reduction technique employs two component mode synthesis methods, namely, the Craig-Bampton (CB) method followed by a modal synthesis based on loaded interface modeshapes (Benfield and Hruda). In the new formulation the fundamental sector is divided into blade and disk components. The CB method is applied to the blade, where nodes lying on shroud contact surfaces and blade-disk interfaces are retained as master nodes, while modal reductions is performed on the disk sector with loaded interfaces. The use of loaded interface component modes allows removing the blade-disk interface nodes from the set of master nodes retained in the reduced model. The result is a much more reduced order model with no need to apply any secondary reduction. In the paper it is shown that the reduced order model of the mistuned bladed disk can be obtained with only single-sector calculation, so that the full finite element model of the entire bladed disk is not necessary. Furthermore, with the described approach it is possible to introduce the blade frequency mistuning directly into the reduced model. In this way, reduction is performed only once in case of multiple analyses, necessary for statistical characterization of the nonlinear response of the system. The nonlinear forced response is computed using the harmonic balance method (HBM) and alternating frequency/time domain (AFT) approach. Friction contacts are introduced into the FE model using a 3D contact element. Numerical simulations revealed the accuracy, efficiency and reliability of the new developed technique for nonlinear vibration analysis of mistuned bladed disks with shroud friction contacts.

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