Analytical formulation of the Jacobian matrix for non-linear calculation of the forced response of turbine blade assemblies with wedge friction dampers

2006 ◽  
Vol 41 (10) ◽  
pp. 1118-1127 ◽  
Author(s):  
J.M. Borrajo ◽  
S. Zucca ◽  
M.M. Gola
Keyword(s):  
Turbine Blade ◽  
Jacobian Matrix ◽  
Forced Response ◽  
Friction Dampers ◽  
Analytical Formulation ◽  
Non Linear

scholarly journals Test-Model Correlation of Dry-Friction Damping Phenomena in Aero-Engines

2008 ◽  
Author(s):  
P. Jean ◽  
C. Gibert ◽  
C. Dupont ◽  
J.-P. Lombard
Keyword(s):  
Dry Friction ◽  
Forced Response ◽  
Test Model ◽  
Friction Damping ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Bladed Disk ◽  
Resonance Frequencies ◽  
Non Linear ◽  
Aero Engines

In order to control the risk of high cycle fatigue of bladed disks, it is important to predict precisely the vibration levels and to design damping solutions to attenuate them. Therefore, Snecma has made some efforts in the last years in order to characterize better the damping in aero-engines. Among the various damping sources, friction damping is particularly difficult to model due to its non-linear behaviour [1]. For that purpose, two methods based on multi-harmonic balance strategy have been especially developed for Snecma, dedicated to the study of the non-linear forced response of bladed disks. The first one enables to model the bladed disk equipped with dry-friction dampers [2], and the second one takes into account intrinsic friction located in disk-blade interface [3]. To validate both models experimentally, a test campaign has been carried out in a vacuum chamber on a rotating bladed disk excited by piezoelectric actuators. The blade shanks have been softened in order to increase friction effects. Experimental results show a regular and reproducible behaviour of the non-linear forced response, over various rotation speed and excitation levels. The contributions of friction dampers and friction in blade attachment have been decoupled thanks to glue applied in the blade root. Both friction phenomena that were observed experimentally at resonance of the blade first bending mode have been reproduced numerically. After updating modeling parameters, an acceptable correlation was found on resonance frequencies, amplitudes and damping levels over the full experimental setup range, which validates these numerical tools for their use in design process.

Non-Linear Vibrations of Multi-Stage Bladed Disks Systems With Friction Ring Dampers

2007 ◽  
Author(s):  
Denis Laxalde ◽  
Fabrice Thouverez
Keyword(s):  
Harmonic Balance Method ◽  
Forced Response ◽  
Bladed Disks ◽  
Friction Forces ◽  
Friction Dampers ◽  
Multi Stage ◽  
Non Linear ◽  
Time Domains ◽  
Linear Vibrations ◽  
Stage System

In this paper, we study the non-linear dynamics of a multi-stage system of turbomachinery bladed disks with friction dampers. We focus on the quasi-periodic forced response of this system under multi-frequency rotating excitations. The system’s equations of the motion are expressed in the multi-frequency domain using a multi-frequency harmonic balance method in combination a multi-stage cyclic symmetry reduction. A Dynamic Lagrangian formulation in alternating frequency/time domains is also used for the calculation of the contact and friction forces. In applications we consider a system of two HP compressor stages of integrally bladed disks with friction ring dampers.

scholarly journals Machine Learning for Turbulence Model Development Using a High-Fidelity HPT Cascade Simulation

2017 ◽  
Author(s):  
Jack Weatheritt ◽  
Richard Pichler ◽  
Richard D. Sandberg ◽  
Gregory Laskowski ◽  
Vittorio Michelassi
Keyword(s):  
High Pressure ◽  
Evolutionary Algorithm ◽  
Turbine Blade ◽  
A Priori ◽  
Model Development ◽  
Boussinesq Approximation ◽  
High Pressure Turbine ◽  
Stress Strain ◽  
Non Linear ◽  
Anisotropy Tensor

The validity of the Boussinesq approximation in the wake behind a high-pressure turbine blade is explored. We probe the mathematical assumptions of such a relationship by employing a least-squares technique. Next, we use an evolutionary algorithm to modify the anisotropy tensor a priori using highly resolved LES data. In the latter case we build a non-linear stress-strain relationship. Results show that the standard eddy-viscosity assumption underpredicts turbulent diffusion and is theoretically invalid. By increasing the coefficient of the linear term, the farwake prediction shows minor improvement. By using additional non-linear terms in the stress-strain coupling relationship, created by the evolutionary algorithm, the near-wake can also be improved upon. Terms created by the algorithm are scrutinized and the discussion is closed by suggesting a tentative non-linear expression for the Reynolds stress, suitable for the wake behind a high-pressure turbine blade.

Innovative Design, Structural Optimization and Additive Manufacturing of New-Generation Turbine Blades

2020 ◽  
Author(s):  
Andrea Amedei ◽  
Enrico Meli ◽  
Andrea Rindi ◽  
Benedetta Romani ◽  
Lorenzo Pinelli ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Structural Optimization ◽  
Turbine Blade ◽  
Turbine Blades ◽  
Forced Response ◽  
Mode Shapes ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
New Generation

Abstract The need for high performances is pushing the complexity of mechanical design at very high levels, especially for turbomachinery components. In this field, structural topology optimization methods together with additive manufacturing techniques for high resistant alloys are considered very promising tools, but their potentialities have not been deeply investigated yet for critical rotating components like new-generation turbine blades. In this framework, this research work proposes a methodology for the design, the optimization and the additive manufacturing of extremely stressed turbomachinery components like turbine blade-rows. The presented procedure pays particular attention to important aspects of the problems as fluid-structure interactions (forced response and flutter phenomena) and fatigue of materials, going beyond the standard structural optimization approaches found in the literature. The new design strategy enables a substantial reduction of the component mass, limiting the maximum stress and improving the vibrational behaviour of the system in terms of eigenfrequencies, modal shapes and fatigue life. Furthermore, the numerical procedure shows robustness and efficiency, making the proposed methodology a good tool for rapid design and prototyping, and for reducing the design costs and the time-to-market typical of this kind of mechanical elements. The procedure has been applied to a low-pressure turbine rotor to improve the aeromechanical behavior while keeping the aerodynamic performance. From the original geometry, mode-shapes, forcing functions (due to rotor/stator interactions) and aerodynamic damping have been numerically evaluated and are used as input data for the following topological optimization. Finally, the optimized geometry has been verified in order to confirm the improved aeromechanical design. After the structural topology optimization, the final geometries provided by the procedure have been then properly rendered to make them suitable for additive manufacturing. Some prototypes of the new optimized turbine blade have been manufactured from aluminum to be tested mechanically and in terms of fatigue.

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.

Design Methods of Friction Damping at Blade-Disk Joints

2009 ◽  
Author(s):  
Jie Hong ◽  
Lulu Chen ◽  
Yanhong Ma ◽  
Xin Yang
Keyword(s):  
Low Frequency ◽  
Harmonic Balance Method ◽  
Large Error ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Tracking Motion ◽  
Nonlinear Force ◽  
Free Mode

Friction at blade-disk joints is an important source of damping that reduces low frequency resonant amplitudes to acceptable levels in blade-disk assemblies. An effective method is proposed to predict nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints in frequency domain, which syncretizes the excellencies of harmonic balance method, dynamic softness method and tracking motion method. Constrained Mode Shapes are introduced to express the relative motion which occurs at the contact interfaces of blade roots. Compared to using free mode shapes, fewer number of constrained mode shapes is required in order to obtain the accurate resonant response of a system with friction dampers when the contact state is fully stick. It is more efficient to predict the nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints. Based on this method, the effect of Boundary Conditions on the resonant frequencies and forced response levels under different engine rotational speeds is investigated. Large error in the prediction of forced response levels under low engine rotational speed by using traditional methods is found. The effects of preload distribution at blade roots and excitation level are also investigated.

A Resonance Tracking Algorithm for the Prediction of Turbine Forced Response With Friction Dampers

2000 ◽  
Author(s):  
C. Bréard ◽  
J. S. Green ◽  
M. Vahdati ◽  
M. Imregun
Keyword(s):  
Rotor Blade ◽  
Turbine Blades ◽  
Turbine Rotor ◽  
Forced Response ◽  
Rotor Blades ◽  
Test Case ◽  
Friction Damper ◽  
Blade Vibration ◽  
Frequency Shifts ◽  
Friction Dampers

This paper presents an iterative method for determining the resonant speed shift when non-linear friction dampers are included in turbine blade roots. Such a need arises when conducting response calculations for turbine blades where the unsteady aerodynamic excitation must be computed at the exact resonant speed of interest. The inclusion of friction dampers is known to raise the resonant frequencies by up to 20% from the standard assembly frequencies. The iterative procedure uses a viscous, time-accurate flow representation for determining the aerodynamic forcing, a look-up table for evaluating the aerodynamic boundary conditions at any speed, and a time-domain friction damping module for resonance tracking. The methodology was applied to an HP turbine rotor test case where the resonances of interest were due to the 1T and 2F blade modes under 40 engine-order excitation. The forced response computations were conducted using a multi-stage approach in order to avoid errors associated with “linking” single stage computations since the spacing between the two bladerows was relatively small. Three friction damper elements were used for each rotor blade. To improve the computational efficiency, the number of rotor blades was decreased by 2 to 90 in order to obtain a stator/rotor blade ratio of 4/9. However, the blade geometry was skewed in order to match the capacity (mass flow rate) of the components and the condition being analysed. Frequency shifts of 3.2% and 20.0% were predicted for the 1T/40EO and 2F/40EO resonances in about 3 iterations. The predicted frequency shifts and the dynamic behaviour of the friction dampers were found to be within the expected range. Furthermore, the measured and predicted blade vibration amplitudes showed a good agreement, indicating that the methodology can be applied to industrial problems.

Sign in / Sign up

Export Citation Format

Share Document