Forced Response of Turbine Engine Bladed Disks and Sensitivity to Harmonic Mistuning

2002 ◽  
Vol 125 (1) ◽  
pp. 113-120 ◽  
Author(s):  
J. A. Kenyon ◽  
J. H. Griffin
Keyword(s):  
Maximum Amplitude ◽  
Mathieu Equation ◽  
Forced Response ◽  
System Response ◽  
Analytical Prediction ◽  
Bladed Disks ◽  
Turbine Engine ◽  
Root Cause ◽  
Random Mistuning ◽  
Shear Spring

The mistuned forced response of turbine engine bladed disks is treated using harmonic perturbations in the properties of a continuous ring. A continuous shear spring is attached to the ring in which the stiffness is allowed to vary along the ring annulus. The modes of such a structure with a single harmonic mistuning pattern are shown to obey the Mathieu equation, which is solved to obtain the natural frequencies and modes of the mistuned system. The forced response of the system is then examined to determine the sensitivity of the system to small mistuning. The model is extended to include multiple harmonics, allowing for the possibility of general mistuning. An expression for the maximum amplitude magnification due to small mistuning is developed by showing that high response is caused by distortion of the structural modes. A method to intentionally mistune systems for maximum forced response is demonstrated, and numerical results demonstrate the accuracy of the analytical prediction. The intentionally mistuned system response is shown to be robust with respect to small random mistuning. Such a result might be useful for designing a test rotor for screening new bladed disk designs or for establishing the root cause of fatigue problems.

Forced Response of Turbine Engine Bladed Disks and Sensitivity to Harmonic Mistuning

2001 ◽  
Author(s):  
J. A. Kenyon ◽  
J. H. Griffin
Keyword(s):  
Maximum Amplitude ◽  
Mathieu Equation ◽  
Forced Response ◽  
System Response ◽  
Analytical Prediction ◽  
Bladed Disks ◽  
Turbine Engine ◽  
Root Cause ◽  
Random Mistuning ◽  
Shear Spring

The mistuned forced response of turbine engine bladed disks is treated using harmonic perturbations in the properties of a continuous ring. A continuous shear spring is attached to the ring in which the stiffness is allowed to vary along the ring annulus. The modes of such a structure with a single harmonic mistuning pattern are shown to obey the Mathieu equation, which is solved to obtain the natural frequencies and modes of the mistuned system. The forced response of the system is then examined to determine the sensitivity of the system to small mistuning. The model is extended to include multiple harmonics, allowing for the possibility of general mistuning. An expression for the maximum amplitude magnification due to small mistuning is developed by showing that high response is caused by distortion of the structural modes. A method to intentionally mistune systems for maximum forced response is demonstrated, and numerical results demonstrate the accuracy of the analytical prediction. The intentionally mistuned system response is shown to be robust with respect to small random mistuning. Such a result might be useful for designing a test rotor for screening new bladed disk designs or for establishing root cause of fatigue problems.

Comparative Studies of Surrogate Models for Response Analysis of Mistuned Bladed Disks

2020 ◽  
Vol 17 (10) ◽  
pp. 2050012 ◽  
Author(s):  
Shiyuan Deng ◽  
Jianyao Yao ◽  
Linlin Wang ◽  
Jianqiang Xin ◽  
Ning Hu
Keyword(s):  
Degrees Of Freedom ◽  
Surrogate Models ◽  
Forced Response ◽  
Statistical Characteristics ◽  
Kriging Interpolation ◽  
Response Analysis ◽  
Bladed Disks ◽  
Single Output ◽  
Random Mistuning ◽  
Forced Responses

The forced responses of bladed disks are highly sensitive to inevitable random mistuning. Considerable computational efforts are required for the sampling process to assess the statistical vibration properties of mistuned bladed disks. Therefore, efficient surrogate models are preferred to accelerate the process for probabilistic analysis. In this paper, four surrogate models are utilized to construct the relation between random mistuning and forced response amplitudes, which are polynomial chaos expansion (PCE), response surface method (RSM), artificial neural networks (ANN) and Kriging interpolation, respectively. A bladed disk with 2-degrees-of-freedom (2-DOF) each sector is used to validate the effectiveness of the surrogate models. The effects of number of training samples on the surrogate model accuracy are discussed. The responses results of one blade (single output) and maximum response of all blades (multi-output) indicate that PCE and Kriging interpolation could yield accurate and stable predictions of the statistical characteristics of the forced responses. PCE is recommended for the mistuned response predictions due to its accuracy and efficiency.

Robust Strategies for Forced Response Reduction of Bladed Disks Based on Large Mistuning Concept

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. Nikolic ◽  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Uncertainty Analysis ◽  
Reliability Assessment ◽  
Forced Response ◽  
Bladed Disks ◽  
Reduction Strategies ◽  
Random Mistuning ◽  
Robust Strategies

In this paper, robust maximum forced response reduction strategies based on a “large mistuning” concept are introduced, including both (i) random and (ii) deterministic approaches. An industrial bladed fan disk serves as an application example for a reliability assessment of the aforementioned strategies using two well-established tools for uncertainty analysis: (i) statistics and (ii) sensitivity and robustness. The feasibility and other practical aspects of implementing large mistuning as a means of preventing excessive forced response levels caused by random mistuning and ensuring the predictability of the response are discussed.

Effects of a Cracked Blade on Mistuned Turbine Engine Rotor Vibration

2007 ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Time Integration ◽  
Element Model ◽  
Forced Response ◽  
System Response ◽  
Turbine Engine ◽  
Reduced Order ◽  
Hybrid Interface ◽  
Engine Rotor

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The effects of small, random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of Component Mode Synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact interaction in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack, as well as vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared to those obtained with linear ROMs as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar those of mistuning, differences between the effects of mistuning and damage can be discerned by observing and comparing the response across different families of system modes.

Local/Global Effects of Mistuning on the Forced Response of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 131-141 ◽  
Author(s):  
A. J. Rivas-Guerra ◽  
M. P. Mignolet
Keyword(s):  
Maximum Amplitude ◽  
High Accuracy ◽  
Forced Response ◽  
Entire Population ◽  
Modeling Technique ◽  
Bladed Disks ◽  
High Level

The focus of the present investigation is on the assessment and modeling of the local (spanning only a few blades) and global (encompassing the entire disk) effects of mistuning on the forced response of bladed disks. To this end, the concept of localization is first revisited and a new measure of this effect is introduced in terms of the number of blades the mistuning of which actually affects the forced response of a central blade. Using this new metric, it is demonstrated that high responding blades typically exhibit a high level of localization and that the reverse is not necessarily true. Thus, localization is not only disk dependent but also varies from blade-to-blade on the same disk. This observation is then used to validate a partial mistuning approach to the determination of the maximum amplitude of response over the entire population of disks. The results of this study indicate that the largest amplification due to the mistuning occurs at very strong blade-to-blade coupling levels, at the contrary of a general perception, but is associated with large mistuning levels. Finally, the above phenomenological observations are used to devise a modeling technique of both local and global components of mistuning. An example of application is presented that demonstrates the high accuracy of this approach through the entire blade-to-blade coupling domain.

On the Individual and Combined Effects of Intentional Mistuning, Coupling and Damping on the Forced Response of Bladed Disks

2008 ◽  
Author(s):  
Changbo Yu ◽  
Jianjun Wang ◽  
Qihan Li
Keyword(s):  
High Cycle Fatigue ◽  
Numerical Study ◽  
Threshold Value ◽  
Forced Response ◽  
Combined Effects ◽  
Bladed Disks ◽  
Disk Model ◽  
Bladed Disk ◽  
Random Mistuning ◽  
The Individual

Random mistuning always exists in bladed disk structures. The maximum blade forced response amplitudes are often much larger than those of their perfectly tuned counterparts, which leads to eventual failure via high cycle fatigue (HCF). Therefore, it is of great importance to predict and, ultimately, to reduce the blade forced response levels as a result of random mistuning. In this paper, intentional mistuning is introduced into a simplified 12-bladed disk model by varying the stiffness of the blades in periodic harmonic patterns. The individual and combined effects of intentional mistuning, coupling and damping are examined in the absence and presence of random mistuning through numerical study. It is found that there is some threshold value of intentional mistuning and coupling that leads to maximum mistuning effects and certain relations among intentional mistuning strength, integer harmonics, coupling and damping can suppress the response levels of mistuned bladed disks, which provides useful guidelines for safe and reliable designs of bladed disk systems.

Effects of a Cracked Blade on Mistuned Turbine Engine Rotor Vibration

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Time Integration ◽  
Element Model ◽  
Forced Response ◽  
System Response ◽  
Turbine Engine ◽  
Reduced Order ◽  
Hybrid Interface ◽  
Engine Rotor

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The influence of small random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of component mode synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response of an example rotor are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack and the vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared with those obtained with linear ROMs, as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar to those of mistuning, the effects of mistuning and damage can be distinguished by observing and comparing the response across multiple families of system modes.

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.

Local/Global Effects of Mistuning on the Forced Response of Bladed Disks

2001 ◽  
Author(s):  
Alejandro J. Rivas-Guerra ◽  
Marc P. Mignolet
Keyword(s):  
Maximum Amplitude ◽  
High Accuracy ◽  
Forced Response ◽  
Entire Population ◽  
Modeling Technique ◽  
Bladed Disks ◽  
High Level

The focus of the present investigation is on the assessment and modeling of the local (spanning only a few blades) and global (encompassing the entire disk) effects of mistuning on the forced response of bladed disks. To this end, the concept of localization is first revisited and a new measure of this effect is introduced in terms of the number of blades the mistuning of which actually affects the forced response of a central blade. Using this new metric, it is demonstrated that high responding blades typically exhibit a high level of localization and that the reverse is not true. Thus, localization is not only disk dependent but also varies from blade-to-blade on the same disk. This observation is then used to validate a partial mistuning approach to the determination of the maximum amplitude of response over the entire population of disks. The results of this study indicate that the largest amplification due to mistuning occurs at very strong blade-to-blade coupling levels, at the contrary of a general perception, but is associated with extremely large mistuning levels. Finally, the above phenomenological observations are used to devise a modeling technique of both local and global components of mistuning. An example of application is presented that demonstrates the high accuracy of this approach through the entire blade-to-blade coupling domain.

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