Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers

1997 ◽  
Vol 119 (1) ◽  
pp. 96-103 ◽  
Author(s):  
K. Y. Sanliturk ◽  
M. Imregun ◽  
D. J. Ewins
Keyword(s):  
Harmonic Balance ◽  
Turbine Blades ◽  
Numerical Test ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Friction Damper ◽  
Friction Dampers ◽  
Equivalent Time ◽  
Time Marching ◽  
Detailed Assessment

Although considerable effort has been devoted to the formulation of predictive models of friction damper behavior in turbomachinery applications, especially for turbine blades, the problem is far from being solved due to the complex nonlinear behavior of the contact surfaces. This paper primarily focuses on analytical and numerical aspects of the problem and addresses the problem in the frequency domain while exploring the viability of equivalent time-domain alternatives. The distinct features of this work are: (i) the modelling of nonlinear friction damper behavior as an equivalent amplitude-dependent complex stiffness via a first-order harmonic balance method (HBM), (ii) the use of sine sweep excitation in time-marching analysis, (iii) the application of the methodology to numerical test cases, including an idealised 3D turbine blade model with several friction dampers, (iv) the verification of the numerical findings using experimental data, and (v) a detailed assessment of the suitability of HBM for the analysis of structures with friction dampers.

scholarly journals Friction Damper Optimisation: Simulation of Rainbow Tests

1999 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
David J. Ewins ◽  
Robert Elliott ◽  
Jeff S. Green
Keyword(s):  
Harmonic Balance Method ◽  
Lumped Parameter Model ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Lumped Parameter ◽  
Engine Order ◽  
Resonance Response ◽  
Theoretical Predictions ◽  
Different Characteristics

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimisation via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called ‘rainbow tests’ where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disc assembly. A new method of analysis — a combination of Harmonic Balance Method and structural modification approaches — is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called ‘rainbow tests’ in turbomachinery applications. A simple lumped-parameter model of a bladed-disc model was used and different damper weights were modelled using friction elements with different characteristics. Resonance response levels were obtained for bladed discs with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disc assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disc is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

Efficient Damping Prediction of Bolted Structures Using Harmonic Balance Method

2012 ◽  
Author(s):  
Pascal Reuss ◽  
Jens Becker ◽  
Lothar Gaul
Keyword(s):  
Harmonic Balance ◽  
Normal Force ◽  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Computation Time ◽  
Nonlinear Effects ◽  
Element Model ◽  
Balance Method ◽  
Friction Damper ◽  
Step Size

In this paper damping induced by extensive friction occurring in the interface between bolted structures is considered by simulations and experiments. A friction damper is attached to a beam-like flexible structure by screws such that the normal force in the interface can be varied by the clamping force of the screws. Contact and friction force parameters are identified by the comparison of simulated and experimentally determined FRFs for a particular normal force. Afterward a prediction of damping for different configurations is established. For simulations a finite element model is used where suitable contact and friction models are implemented. A time simulation of the system is expensive due to the large number of DoFs of the discretized substructures and the required small step size due to the high contact stiffness. Therefore model reduction methods are used. A further reduction of the computation time can be achieved by using the Harmonic Balance Method (HBM) for a direct frequency domain computation of FRFs. This enables an efficient procedure to approximate the reachable damping as well as to search the optimal damper position and the optimal normal force. The dependency of the friction to the vibration amplitude is therefore taken into account. A more detailed investigation of the nonlinear effects, e.g. higher harmonic response, is then accomplished by transient simulations for the optimal configured system in the time domain and the results are compared to experimental results.

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.

scholarly journals Use and Limitations of the Harmonic Balance Method for Rub-Impact Phenomena in Rotor-Stator Dynamics

2012 ◽  
Author(s):  
Loïc Peletan ◽  
Sebastien Baguet ◽  
Georges Jacquet-Richardet ◽  
Mohamed Torkhani
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Current Form ◽  
Transient Simulations ◽  
Future Extension ◽  
Periodic Behaviour ◽  
State Behaviour ◽  
Impact Phenomena ◽  
Time Marching

In the present paper, a Harmonic Balance Method (HBM) coupled with a pseudo-arc length continuation algorithm is presented for the prediction of the steady state behaviour of a rotor-stator contact problem. The ability of the HBM to reproduce the four most common phenomena encountered during rotor to stator contact situations (i.e. ‘no-rub’, ‘full annular rub’, ‘partial rub’ and ‘backward whirl/whip’) is investigated. A modified Jeffcott rotor model is used and results of the proposed algorithm are compared with traditional time marching solutions and analytical predictions. The advantages and limitations of the HBM for this kind of problem are analyzed. It is shown that the HBM is orders of magnitude faster than transient simulations, and provides very accurate results. However, in its current form it is unable to predict quasi-periodic behaviour. Detailed analysis of the transient solutions yields valuable information for the future extension of the HBM to efficient quasi-periodic simulations.

Friction Dampers: Measurement, Modelling and Application to Blade Vibration Control

1995 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
Anthony B. Stanbridge ◽  
David J. Ewins
Keyword(s):  
Harmonic Balance Method ◽  
Theoretical Modelling ◽  
Dynamic Force ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Response Characteristics ◽  
Joint Characteristics ◽  
Contact Behaviour ◽  
Better Than

Abstract This paper describes a procedure that combines the measurement of dry-friction contact behaviour, its theoretical modelling and the analysis of structures with friction joints. The experimental part describes a friction damper test rig which is specifically designed for measuring the dynamic force-response characteristics of a joint. A hybrid mathematical model, which is a combination of the traditional macro- and micro-slip models, is proposed to represent the joint characteristics and it is shown that such a model represents the measured behaviour better than any of the traditional ones. The final part of the paper demonstrates the procedure applied to a blade-damper test structure and which includes testing, analysis and correlation of both sets of results. The non-linear response levels are predicted using a dedicated program based on the Harmonic Balance Method and it is found that the proposed analysis procedure can predict the amount of response reduction, the optimum friction damper load and the locked natural frequency quite accurately.

Feasibility Research on Coupled Friction/Piezoelectric Dampers

2018 ◽  
Author(s):  
Lin Li ◽  
Yaguang Wu ◽  
Yu Fan
Keyword(s):  
Dry Friction ◽  
Harmonic Balance ◽  
Vibrational Mode ◽  
Piezoelectric Materials ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Friction Dampers ◽  
Feasibility Research ◽  
Aero Engines ◽  
Better Than

A new passive damper coupling the energy dissipative mechanisms of dry friction and piezoelectric shunting circuit is proposed. The idea is to embed the shunted piezoelectric materials to the dry friction dampers at appropriate positions, so that the elastic deformation of the dry friction dampers can be utilized to generate additional damping. Moreover, this provides a more practical way to install the piezoelectric dampers into realistic mechanical systems such as aero-engines. A five Degree-of-freedom (DOFs) lumped system model is introduced to demonstrate the feasibility of such an idea. The damping performance is revealed using the forced response results obtained by the Multi Harmonic Balance Method (MHBM). We show that the coupled damper significantly outperforms the standalone piezoelectric or dry friction dampers. The coupled damper is better than, at least equivalent to, the case where both piezoelectric and dry friction dampers are applied but in uncoupled manner. Eventually, the mechanism of the proposed damper is further explained from the perspective of vibrational mode and energy conversion.

A Time Marching Integration for Semi-Analytical Solutions of Nonlinear Oscillators Based On Synchronization

2021 ◽  
Author(s):  
R.Z. Yao ◽  
Y.M. Chen ◽  
Q.X. Liu
Keyword(s):  
Fourier Series ◽  
Analytical Solutions ◽  
Harmonic Balance ◽  
Numerical Scheme ◽  
Harmonic Balance Method ◽  
Nonlinear Oscillators ◽  
Harmonic Oscillators ◽  
Time Marching ◽  
Novel Method ◽  
Basic Ideas

Abstract A novel method is proposed in this study for solving the semi-analytical solutions of periodic responses of nonlinear oscillators. The basic ideas comes from the fact that any periodic response can be described by Fourier series. By transforming the Fourier series into a system of harmonic oscillators, we thus establish a novel numerical scheme for tracking the periodic responses, as long as a synchronized motion can be achieved between the system of harmonic oscillators and the nonlinear oscillators considered. The presented method can be implemented by conducting time marching integration only, but it is capable of providing semi-analytical solutions straightforwardly. Different from some widely used methods such as harmonic balance method and its improved forms, this method can solve solutions involving high order harmonics without incorporating any tedious derivations as it is totally a numerical scheme. Several typical oscillators with smooth as well as non-smooth nonlinearities are taken as numerical examples to test the validity and efficiency.

scholarly journals Parametric Analysis of the Nonlinear Behavior of Rotating Structures

2015 ◽  
Author(s):  
Lihan Xie ◽  
Sébastien Baguet ◽  
Benoit Prabel ◽  
Régis Dufour
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Equation System ◽  
Jacobian Determinant ◽  
State Behavior ◽  
Mass Unbalance ◽  
Stability Change ◽  
Sign Change ◽  
Continuation Technique

In nonlinear rotordynamics, techniques can take advantage of the periodic steady state behavior to predict quickly and accurately the mass unbalance response to a series of parameters, especially with the presence of certain nonlinearities which leads to nonlinear dynamics and complicated responses. The method proposed here calculates the response curve by combining Harmonic Balance Method, Alternating Frequency-Time method and continuation. The singular points where a stability change often arises are detected with the sign change of the Jacobian determinant and then located through a penalty method that increases the solving equation system by a completing constraint. Tracking these points, which provides an efficient way to analyze parametrically the nonlinear behavior of a system, can be fulfilled, once again, by the continuation technique.

Friction Damper for Fatigue Damage Mitigation in Steel Jacket Platforms

2008 ◽  
Author(s):  
A. A. Golafshani ◽  
A. Gholizad
Keyword(s):  
Nonlinear Behavior ◽  
Ocean Waves ◽  
Realistic Model ◽  
Offshore Platforms ◽  
Friction Damper ◽  
Friction Dampers ◽  
Optimal Values ◽  
Hysteretic Dampers ◽  
Wave Induced ◽  
Random Nature

The performance of friction dampers to mitigate the wave induced vibrations in jacket type offshore platforms has been investigated in this study. Due to the random nature of ocean waves, a full stochastic analysis method has been intended to evaluate the response of the structures utilized with these devices and also a stochastic linearization technique has been used to take the nonlinear behavior of these hysteretic dampers into account. At last, the developed mathematic formulation has been practiced to evaluate the response of a realistic model and to find out the optimal values for the adjustive parameters of the friction dampers to dissipate the wave induced vibrations of the platform.

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