Bernd Beirow

Experimental and Numerical Analyses of Radial Turbine Blisks With Regard to Mistuning

The effect of blade frequency mistuning on the forced response of integral radial turbines is studied by means of experimental and numerical analyses. Blade dominated frequencies representing the mistuning are identified based on blade by blade measurements using the example of a MTU ZR140 turbine blisk. Based on these results, numerical simulations of the blade by blade measurements are performed, aiming to update the originally ideal (tuned) finite element model. The damping information to be considered in the update process is taken from results of an experimental modal analysis. The quality of the model is proved by well correlated frequency response functions (FRF) of numerical and experimental analyses. Finally, the models are used to simulate the forced response due to travelling wave excitations. As a result, mode localization phenomena and response amplifications compared to tuned blisks are proved. In order to round off the contribution to a more enhanced understanding of the radial turbine blisk dynamics optically based geometry measurements are performed to assess the influence of geometrical deviations on frequency mistuning. It is shown that geometric imperfections can be the main driver causing a mistuned response characteristic.Copyright

Numerical Investigations of Localized Vibrations of Mistuned Blade Integrated Disks (Blisks)

Blade-to-blade variations of bladed disk assemblies result in local zoning of vibration modes as well as amplitude magnifications, which primarily reduces the high cycle fatigue life of aeroengines. Criteria were introduced to determine the level of these mode localization effects depending on various parameters of a real high pressure compressor blisk rotor. The investigations show that blade vibration modes with lower interblade coupling, e.g., torsion modes or modes with high numbers of nodal diameter lines, have a significantly higher sensitivity to blade mistuning, which can be characterized by the higher percentage of blades on the total blisk strain energy.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, SNM-based reduced order models are used in which the disk remains unchanged while the Young’s modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient technique is employed to model aeroelastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades’ Young’s modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aeroelastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.Copyright

On the Influence of Strain Gauge Instrumentation on Blade Vibrations of Integral Blisk Compressor Rotors Applying a Discrete Model

The effect of blade frequency mistuning on the forced response of HPC-blisks is studied by means of experimental and numerical investigations applying discrete mechanical low degree of freedom models. Besides the mistuning resulting from manufacturing and inhomogeneous material also strain gauge (S/G) induced mistuning is considered. Blade by blade measurements supported by numerical calculations are used to determine mistuning distributions within an iterative approach. Due to the stiffness contribution of high temperature S/G, a significant increase of blade alone frequencies can be proved. It is shown within laser scanning measurements that this S/G induced mistuning can cause strongly localized mode shapes. Since S/G signals are used to monitor also non-instrumented blade resonances in engine-tests, it is reasonable to consider the S/G contribution within model-updates. The numerical models introduced in this paper are adjusted to experimentally determined blade alone frequency distributions. Within simulations of the forced response it is shown in principle, that the S/G-instrumentation also affects the response of non-instrumented blades which is important with regard to the S/G calibration process. Additional investigations are addressed to the consequences of small variations in measured mistuning distributions on the maximum forced response, i. e. resulting from a changing ambient temperature while measurement or a limited frequency resolution. In this context, a strong dependence on the engine order excited, the damping level and thus the flow conditions could be proved. As an example all investigations presented in this paper are carried out for two stages of a research compressor.Copyright

A Discrete Model to Consider the Influence of the Air Flow on Blade Vibrations of an Integral Blisk Compressor Rotor

The influence of the aerodynamic coupling in the forced response analysis of a HPC test-blisk is studied by means of a reduced order mechanical model. In the first step this equivalent blisk model (EBM) is derived based on a finite element analysis of the disk from design and an adjustment to experimentally determined blade alone frequencies in order to consider the real blade mistuning. Applying the EBM — so far not considering the air flow influence — to carry out forced response analyses due to a rotating excitation acting on the stationary blisk, a maximum blade displacement amplification of more than 50% has been calculated comparing the tuned and the mistuned blisk. Aiming at an additional consideration of the air flow, fully coupled computations of the fluid structure interaction (FSI) are exemplarily carried out for elastically supported blades in a cascade arrangement. The results are used to calibrate simple mass-spring-damper models from which quantities of additional aerodynamic elements in terms of a consideration of co-vibrating air masses, air stiffening and aerodynamic damping are derived. Based on this information the EBM is extended to a so called advanced EBM. Aerodynamic influences are considered assigning the aerodynamic properties to each blade in dependence on the inter blade phase angle (IBPA). Forced response analyses, now including all aerodynamic influences, show that for an extreme application of a rear blisk close to the combustion chamber and under MTO conditions a strong smoothing of originally localized vibration modes occurs. The maximum blade displacement amplification due to mistuning is decreased from more than 50% to below 12% for the first blade flap mode.© 2008 ASME

Design and Analysis of an Intentional Mistuning Experiment Reducing Flutter Susceptibility and Minimizing Forced Response of a Jet Engine Fan

Recent demands for a reduction of specific fuel consumption of jet engines have been opposed by increasing propulsive efficiency with higher bypass ratios and increased engine sizes. At the same time the challenge for the engine development is to design safe and efficient fan blades of high aspect ratios. Since the fan is the very first rotor stage, it experiences significant distortions in the incoming flow depending on the operating conditions. Flow distortions do not only lead to a performance and stall margin loss but also to remarkable low engine order (LEO) excitation responsible for forced vibrations of fundamental modes. Additionally, fans of jet engines typically suffer from stall flutter, which can be additionally amplified by reflections of acoustic pressure waves at the intake. Stall flutter appears before approaching the stall line on the fan’s characteristic and limits its stable operating range. Despite the fact that this “flutter bite” usually affects only a very narrow speed range, it reduces the overall margin of safe operation significantly. With increasing aspect ratios of ultra-high bypass ratio jet engines the flutter susceptibility will probably increase further and emphasizes the importance of considering aeromechanical analyses early in the design phase of future fans. This paper aims at proving that intentional mistuning is able to remove the flutter bite of modern jet engine fans without raising issues due to heavily increased forced vibrations induced by LEO excitation. Whereas intentional mistuning is an established technology in mitigating flutter, it is also known to amplify the forced response. However, recent investigations considering aeroelastic coupling revealed that under specific circumstances mistuning can also reduce the forced response due to engine order excitation. In order to allow a direct comparison and to limit costs as well as effort at the same time, the intentional mistuning is introduced in a non-destructive way by applying heavy paint to the blades. Its impact on the blade’s natural frequencies is estimated via finite element models with an additional paint layer. In parallel, this procedure is experimentally verified with painted fan blades in the laboratory. A validated SNM (subset of nominal system modes) representation of the fan is used as a computational model to characterize its mistuned vibration behavior. Its validation is done by comparing mistuned mode shape envelopes and frequencies of an experimental modal analysis at rest with those obtained by the updated computational model. In order to find a mistuning pattern minimizing the forced response of mode 1 and 2 at the same time and satisfying stability and imbalance constraints, a multi-objective optimization has been carried out. Finally, the beneficial properties of the optimized mistuning pattern are verified in a rig test of the painted rotor. Copyright

Forced Response Analysis of a Mistuned Compressor Blisk

The forced response of an E3E-type HPC-blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades namely stiffness and damping are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order and aerodynamic influences it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade alone frequencies as design variables are applied. The validity of the Whitehead-limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk’s stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.© 2013 ASME

Forced Response Reduction of a Compressor Blisk Rotor Employing Intentional Mistuning

Using the example of a compressor test blisk with 29 blades different sources of mistuning and their consequences for the forced response are analysed under consideration of aeroelastic effects. In particular the impact of superimposing intentional structural mistuning by both random structural mistuning and aerodynamic mistuning is studied. For this purpose reduced order models of the blisk are adjusted for different mistuning distributions. The mistuning itself is characterized by assigning individual stiffness parameters to each blade. The aeroelastic coupling is included employing aerodynamic influence coefficients. By means of genetic algorithm optimizations, structural mistuning patterns are found which yield a mitigation of the forced response below that of the tuned design reference. Ideally a nearly 50 % reduction of maximum response magnitudes is computed for the fundamental bending mode and large mistuning. The solutions found have been proven to be robust with respect to additional random and aerodynamic mistuning in case of large intentional structural mistuning.

Vacuum Spin Test Series of a Turbine Impeller With Focus on Mistuning and Damping by Comparing Tip Timing and Strain Gauge Results

This paper describes preparation, execution and evaluation of a comprehensive bladed disk spin test series. At the example of an turbine impeller the effects of rotation and temperature are analyzed with special focus on mistuning and damping. The forced response is measured synchronously via 13 identical positioned strain gauges on each blade as well as via blade tip-timing. Subsequently it is possible to compare the results of both systems. During the test series rotational speed varies in the range from 10.000 up to 19.000 RPM. Simultaneously, the wheel is heated up to 820 K by an oven. A number of pre-selected natural frequencies, damping ratios and operating deflection shapes are evaluated and compared with respect to different rotational speeds and impeller temperatures.Copyright

Effect of Mistuning and Damping on the Forced Response of a Compressor Blisk Rotor

The forced response of an E3E-type high pressure compressor blisk front rotor is analyzed with regard to intentional mistuning and its robustness towards additional random mistuning. Both a chosen alternating mistuning pattern and artificial mistuning patterns optimized concerning the forced response are considered. Focusing on three different blade modes, subset of nominal system mode-based reduced order models are employed to compute the forced response. The disk remains unchanged while the Young’s modulus of each blade is used to define the particular mistuning pattern. The well established aerodynamic influence coefficient technique is employed to model aeroelastic coupling and hence to consider the strongly mode- and inter blade phase angle-dependent aerodynamic damping contribution.It has been found that a reduction of the maximum forced response beyond that of the tuned reference can be achieved for particular mistuning patterns and all modes considered. This implies an exciting engine order which would cause a low nodal diameter mode in case of a tuned blisk. At best a nearly 50% reduction of maximum response magnitudes is computed for the fundamental bending mode and large mistuning. The solution proved to be robust towards additional random mistuning of reasonable magnitude, which is of particular interest with regard to a potential technical realization. In case of small mistuning as assumed for the first torsion and the longitudinal bending mode the advantage of achieving response magnitudes beyond the tuned reference gets lost indeed, if random mistuning is superimposed. However, mostly a lower response level is calculated compared to responses obtained from models adjusted to mistuning determined by experiment.© 2015 ASME