Evaluation of free interface-based reduction techniques for nonlinear forced response analysis of shrouded blades

2019 ◽  
Vol 233 (23-24) ◽  
pp. 7459-7475 ◽  
Author(s):  
Fahimeh Mashayekhi ◽  
Stefano Zucca ◽  
Ali S Nobari
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Computational Cost ◽  
Forced Response ◽  
Contact Forces ◽  
Component Mode Synthesis ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Free Interface ◽  
Reduction Techniques

The efficient dynamic stress assessment of turbine blades is of prime importance in turbomachinery design. An accurate prediction of forced response level of shrouded blades requires a very detailed finite element model in addition to a nonlinear solver. In order to perform nonlinear forced response analysis of blades at an affordable computational cost, applying a model order reduction technique is essential. The appeal for component mode synthesis methods in dimension reduction of structures with friction contacts is due to the possibility of retaining a subset of physical degrees of freedom (e.g. the contact degrees of freedom) in the set of generalized coordinates. In this paper, a reduction method recently developed for nonlinear forced response analysis of structures with local nonlinearity is evaluated and compared with two classical component mode synthesis reduction techniques. All three methods have the same projection basis, which includes residual flexibility attachment modes and free interface modes, but different implementation. The response is computed in the frequency domain using multiharmonic balance method and periodic contact forces are modeled with a node-to-node 3D friction contact model. In order to demonstrate the efficiency of the three formulations, a rod and a simplified shrouded turbine blade are considered as case studies.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Detection of Cracks in Mistuned Bladed Disks Using Reduced Order Models and Vibration Data

2011 ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the un-cracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reducedorder) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated, and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

A Comparison of Component Mode Synthesis Methods for Cyclic Structures

2000 ◽  
Author(s):  
Duc-Minh Tran
Keyword(s):  
Forced Response ◽  
Component Mode Synthesis ◽  
Synthesis Methods ◽  
Cyclic Symmetry ◽  
Cyclic Structure ◽  
Free Interface ◽  
New Methods ◽  
Symmetry Properties ◽  
Eigen Solutions ◽  
Hybrid Interface

Abstract Several component mode synthesis methods with fixed, free and hybrid interface are used to compute the eigen solutions and the frequency response of a cyclic structure in combination with the cyclic symmetry properties. In particular, a procedure based on the use of a truncated basis of interface modes has been developed to reduce the number of interface coordinates in the component mode synthesis methods. Both classical and new methods provide very good results and are more efficient than the use of the cyclic symmetry properties only or the combination of the cyclic symmetry with the modal projection method for computing the forced response. For the eigen solutions, the free interface methods are more accurate than the fixed and the hybrid interface methods.

Non-Linear Forced Response Analysis of Mistuned Bladed Disk Assemblies

2010 ◽  
Author(s):  
M. Ersin Yu¨mer ◽  
Ender Cig˘erog˘lu ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Degrees Of Freedom ◽  
Linear Equations ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Disk Model ◽  
Bladed Disk ◽  
Non Linear ◽  
Linear Elements

Forced response analysis of bladed disk assemblies plays a crucial role in rotor blade design, and therefore has been investigated by researchers extensively. However, due to lack of computation power, several studies in the literature utilize either linear mistuned models which are short of capturing nonlinear effects, or non-linear tuned models which do not catch the effects of mistuning. Studying the combined effect of the two, namely non-linearity and mistuning, is relatively recent and generally conducted with methods whose convergence and accuracy depend highly on the number of degrees of freedom related with the non-linear elements. In this paper, a new approach is proposed to predict forced response of frictionally damped mistuned bladed disk assemblies in modal domain. A friction element, which enables normal load variation and separation of the contact interface, is utilized to determine the non-linear contact forces in three-dimensional space, and harmonic balance method is used to obtain a relationship between the non-linear contact forces and the relative motion. As mistuning phenomenon destroys the cyclic symmetry, modeling the whole assembly rather than a sector of it is necessary, which increases the number of non-linear elements required considerably. In the proposed approach, the analysis is carried out in modal domain where the differential equations of motions are converted to a set of non-linear algebraic equations using harmonic balance method and modal superposition technique. Thus, the number of non-linear equations to be solved is proportional to the number of modes retained, rather than the number of degrees of freedom related with the nonlinear elements. Therefore, the proposed approach can be applied to realistic bladed disk models without increasing the number of non-linear equations. Moreover, to accomplish this it is not required to use a reduced order model in the method suggested. Two case studies are presented to illustrate the implementation of the method: a lumped parameter bladed disk model and an academic bladed disk model with shrouds.

Regeneration-Induced Forced Response in Axial Turbines

2013 ◽  
Author(s):  
Jens Aschenbruck ◽  
Christopher E. Meinzer ◽  
Linus Pohle ◽  
Lars Panning-von Scheidt ◽  
Joerg R. Seume
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Response Analysis ◽  
Geometrical Parameters ◽  
Turbine Stage ◽  
Structural Dynamic ◽  
Air Turbine ◽  
Axial Turbines ◽  
Interaction Approach ◽  
Stagger Angle

The regeneration of highly loaded turbine blades causes small variations of their geometrical parameters. To determine the influence of such regeneration-induced variances of turbine blades on the nozzle excitation, an existing air turbine is extended by a newly designed stage. The aerodynamic and the structural dynamic behavior of the new turbine stage are analyzed. The calculated eigenfrequencies are verified by an experimental modal analysis and are found to be in good agreement. Typical geometric variances of overhauled turbine blades are then applied to stator vanes of the newly designed turbine stage. A forced response analysis of these vanes is conducted using a uni-directional fluid-structure interaction approach. The effects of geometric variances on the forced response of the rotor blade are evaluated. It is shown that the vibration amplitudes of the response are significantly higher for some modes due to the additional wake excitation that is introduced by the geometrical variances e.g. 56 times higher for typical MRO-induced variations in stagger-angle.

Interface Reduction in Craig-Bampton Component Mode Synthesis by Orthogonal Polynomial Series

2017 ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Reduction Techniques ◽  
Interface Reduction ◽  
Reduction Methods ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

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.

An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes

1993 ◽  
Vol 207 (1) ◽  
pp. 41-52
Author(s):  
H K Kim ◽  
Y-S Park
Keyword(s):  
Equations Of Motion ◽  
Forced Response ◽  
Suggested Method ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Lumped Mass ◽  
State Equations ◽  
Mass Model ◽  
Non Linear ◽  
Forced Responses

An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.

Range of Variability in the Dynamics of Semi-Cylindrical Friction Dampers for Turbine Blades

2008 ◽  
Author(s):  
Stefano Zucca ◽  
Daniele Botto ◽  
Muzio M. Gola
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Numerical Test ◽  
Forced Response ◽  
Numerical Code ◽  
Test Case ◽  
Force Coefficient ◽  
System A ◽  
Flat Side ◽  
Fatigue Failures

Under-platform dampers are used to reduce resonant stresses in turbine blades to avoid high cycle fatigue failures. In this paper a model of semi-cylindrical under-platform damper (i.e. with one flat side and one curved side) for turbine blades is described. The damper kinematics is characterized by three degrees of freedom (DOFs): in-plane translations and rotation. Static normal loads acting on the damper sides are computed using the three static balance equations of the damper. Non-uniqueness of normal pre-loads acting on the damper sides is highlighted. Implementation of the model in a numerical code for the forced response calculation of turbine blades with under-platform dampers shows that non-uniqueness of normal pre-loads leads to non-uniqueness of the forced response of the system. A numerical test case is presented to show the capabilities of the model and to analyze the effect of the main system parameters (damper mass, excitation force, coefficient of friction and damper rotation) on the damper behavior and on the system dynamics.

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

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

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.

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