Data-Driven Approach for Identifying Mistuning in As-Manufactured Blisks

Sector-to-sector geometry or material property variations in as-manufactured bladed disks, or blisks, can result in significantly greater vibration responses during operation compared to nominally cyclic symmetric designs. The dynamics of blisks are sensitive to these unavoidable deviations, known as mistuning, making the identification of mistuning in as-manufactured blisks necessary for accurately predicting their vibration. Previous approaches to identify such mistuning parameters often require the identification of modal information or blade-isolation techniques such as blade detuning using masses or adding damping pads. However, modal information can be difficult to obtain accurately even in optimal bench conditions. Additionally, in practice it can be difficult to isolate individual blades by restricting blade motion or detuning individual blades through added masses due to geometric constraints. In this paper, we present a method for mistuning identification using a data-driven approach based on a neural network. Here, mistuning in all sectors of blisks with the same nominal geometry can be identified by using a small number of forced responses and the forcing phase information from traveling-wave excitation. In this approach, no system or sector-level modal response information, restrictive blade isolation, or mass detuning are required. Validation of this approach is presented using a finite element blisk model containing stiffness mistuning within the blades to create computationally generated surrogate data. It is shown that mistuning can be predicted accurately using forced responses containing a significant amount of absolute and relative measurement noise, mimicking responses collected from experimental measurements.

Impact of Mistuned Underplatform Dampers On the Nonlinear Vibration of Bladed Disks

Before the final experimental validation and certification of a turboengine, designers perform a numerical simulation of its vibratory properties, among other things, in order to estimate its lifespan and adjust the design in an optimization process. One possible practical solution to decrease the vibratory response is to add underplatform dampers to the system. These components dissipate energy by friction and are widely employed in turbomachinery. However, a specific underplatform damper is usually efficient only for a specific mode. The purpose of this work is to investigate the possibility of adding different kinds of underplatform dampers to the cyclic structure in order to decrease the vibratory energy over a larger panel of modes. Different methods exist to determine the vibrations of nonlinear cyclic symmetric systems, but creating a robust methodology to account for the additional effect of mistuning remains a big challenge in the community. In this paper, the structure is mistuned through the friction coefficient of the dampers and not by altering its geometry, as is usually done in the literature. First, assuming a cyclic symmetric structure, the performance of the dampers is assessed for specific modes. Then, employing a method recently developed, the efficiency of an intentional mistuning pattern of underplatform dampers is studied and an optimal pattern proposed.

Development of a Multi-Shaker-Control to Investigate the Influence of the Interblade Phase Angle on Frictionally Damped Turbine Blades

Constructive damper concepts are developed and integrated in turbomachinery to reduce vibration amplitudes generated by dynamic loads. The potential damping effectiveness of friction-based damper concepts is strongly dependent on the relative motion between adjacent blades, besides other factors such as normal force. In cyclic symmetric structures the phase difference is determined by the excited nodal diameter, which leads to different damper movements and efficiencies for given mode shapes. Several studies on the investigation of the damper performance of different underplatform damper geometries have been carried out on non-rotating test stands consisting usually of two blades in order to reduce the experimental effort before setting up rotational tests. Based on the existing modes of the two blades and the application of commonly just one shaker, the investigations are limited to the in-phase and out-of-phase modes. In this paper an experimental approach is developed to reduce the gap of transferability between non-rotating and rotational tests to analyze the effects of a variable interblade phase angle on the damping effect of underplatform dampers. For this purpose, a cascaded control system using two shakers is being developed to control the force amplitudes and the phase difference between the response of the two blades. The control algorithm is designed in a model-based way by using a two degrees of freedom oscillator with friction contact and is subsequently integrated in the non-rotating test stand.

Impact of Mistuned Underplatform Dampers on the Nonlinear Vibration of Bladed Disks

Before the final experimental validation and certification of a turboengine, designers perform a numerical simulation of its vibratory properties, among other things, in order to estimate its lifespan and adjust the design in an optimization process. One possible practical solution to decrease the vibratory response is to add underplatform dampers to the system. These components dissipate energy by friction and are widely employed in turbomachinery. However, a specific underplatform damper is usually efficient only for a specific mode. The purpose of this work is to investigate the possibility of adding different kinds of underplatform dampers to the cyclic structure in order to decrease the vibratory energy over a larger panel of modes. Different methods exist to determine the vibrations of nonlinear cyclic symmetric systems, but creating a robust methodology to account for the additional effect of mistuning remains a big challenge in the community. In this paper, the structure is mistuned through the friction coefficient of the dampers and not by altering its geometry, as is usually done in the literature. First, assuming a cyclic symmetric structure, the performance of the dampers is assessed for specific modes. Then, employing a method recently developed, the efficiency of an intentional mistuning pattern of underplatform dampers is studied and an optimal pattern proposed.

Crack identification in cyclic symmetric structures based on relative indicators of frequency separation

Cyclic symmetric structures are an important class of structures in the fields of civil and mechanical engineering. In order to avoid accidents due to cracks in such structures, an effective method for crack identification is presented in this paper. First, the dynamic model of cyclic symmetric structures with gapless cracks is developed using a structure's sector model and rotation transformation. Then, the effects of cracks on the free vibration characteristics of a cracked cyclic symmetric structure are addressed, with particular interests in the distortion of mode shapes and the shift and split of natural frequencies. On the basis of crack-induced phenomena, an effective method based on relative indicators of frequency separation is developed for quantitative crack identification. Numerical results illustrate that the relative indicators are sensitive to small cracks and insensitive to the predicting model used during analysis. Finally, the method is validated by experiments conducted on an impeller-shaft assembly. The results show the effectiveness of the frequency separation indicators in crack identification in cyclically symmetric structures.

Active detection of small imperfections in structures with cyclic symmetry

Structures possessing cyclic symmetry such as turbine bladed disks, ultrasonic motors, and toothed gear wheels can experience elevated vibration levels when small deviations from circumferential periodicity exist. Detection of these perturbations via classical system identification approaches is time-consuming, indirect, and exhibits low sensitivity to defects and are affected by measurement noise. The present work utilizes low-level forces that automatically lock onto a weighted rotating projection of the system modes at resonance frequency to enhance the detectability of small structural imperfections. The spatial localization of defects is exploited to identify multiple, localized, isolated defects' locations. The defects' severities are estimated based on the deviation from the circular structure's analytical mode shapes. Fast and enhanced precision of defect identification is obtained by employing the modal filtered Autoresonance technique. To validate the presented method, an experimental system consisting of a ring of coupled Helmholtz acoustic resonators was developed. Experimental results show good agreement with numerical simulations, verifying the method's capabilities to identify the location and severity of multiple defects. Thus, implementation of the suggested method provides fast and precise structural health monitoring of cyclic symmetric systems.

Interaction Between Coriolis Forces and Mistuning on a Cyclic Symmetric Structure with Geometrical Nonlinearity

An investigation of the interaction between Coriolis forces and mistuning on a cyclic symmetric structure is presented in this paper. The sensitivity of the eigenvalues and eigenvectors to mistuning is first studied with the perturbation method. A lumped parameter model is used to perform a modal analysis using a numerical approach after which geometrical nonlinearity is added to compare behavior with the linear case. Two different modes are thoroughly investigated for different rotational speeds, the first with an eigenvalue isolated from the others and the second presenting a frequency veering zone. The evolution from a standing wave domination at low speeds to a travelling wave domination at high speeds is observed for the isolated mode, whereas a standing wave domination remains around the veering zone for the second mode studied. It is also shown that the geometrical nonlinearity reinforces the mistuning effect versus the Coriolis forces.