Use of the Harmonic Balance Method for Flexible Aircraft Engine Rotors With Nonlinear Squeeze Film Dampers

2014 ◽  
Author(s):  
Feng He ◽  
Paul Allaire ◽  
Timothy Dimond
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Aircraft Engine ◽  
Balance Method ◽  
Squeeze Film ◽  
Spring Stiffness ◽  
Squeeze Film Damper ◽  
Flexible Rotors ◽  
Squeeze Film Dampers ◽  
Nonlinear Transient

Squeeze film dampers in flexible rotors such as those in compressors, steam turbines, aircraft engines and other rotating machines are often modeled as linear devices. This linearization is valid only for a specified orbit where appropriate equivalent stiffness and damping coefficients can be found. However, squeeze film dampers are inherently nonlinear devices which complicates the analysis. This paper develops the harmonic balance method with a direct force model of the SFDs. This model is used for flexible rotors with squeeze film dampers where the rotor is treated as linear and the squeeze film damper is treated as nonlinear. The predictor-corrector method is employed to obtain the system forced response in the frequency domain after separating the nonlinear components from the linear components of the equations of motion. This approach is much more efficient than conventional full nonlinear transient analysis. The application considered in this paper is the low pressure (LP) compressor of an aircraft engine. The LP compressor rotor has two roller bearings with squeeze film dampers and one ball bearing without a squeeze film damper. Orbits at the fan end dampers and the turbine end dampers for both the harmonic balance and nonlinear transient modeling are compared for accuracy and calculation time. The HB method is shown to be 5 to 12 times faster computationally for similar results. Fast Fourier transform results were obtained for various shaft operating speeds. Results were also obtained for the unbalance response at different locations with gravity loading. Finally, unbalance response of the rotor with varying centering spring stiffness values were obtained. The results show that the centering spring stiffness for the turbine end damper is less sensitive than the fan end damper.

A theoretical and experimental investigation into the vibration response of a flexible rotor and squeeze-film damper assembly

2001 ◽  
Vol 215 (10) ◽  
pp. 1251-1269 ◽  
Author(s):  
C-C Siew ◽  
M Hill ◽  
R Holmes ◽  
M Brennan
Keyword(s):  
Harmonic Balance ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Vibration Response ◽  
Mode Shapes ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Linear Vibration ◽  
Squeeze Film Damper ◽  
Good Agreement

This paper presents two efficient methods to calculate the unbalance vibration response of a flexible rotor provided with a squeeze-film damper (SFD) with retainer springs. Both methods are iterative and combine the harmonic balance and receptance approaches. The first method, called the modified iteration method (MIM), is suitable for predicting the three-dimensional mode shapes of a concentric SFD-rotor system. The second method, called the modified harmonic balance method (MHBM), is developed to calculate the non-linear vibration response of a flexible shaft provided with either a concentric or eccentric SFD. The system is also investigated experimentally under different conditions. The predictions computed by these methods are compared with experimental measurements and reasonably good agreement is obtained.

Design of Nonlinear Squeeze-Film Dampers for Aircraft Engines

1977 ◽  
Vol 99 (1) ◽  
pp. 57-64 ◽  
Author(s):  
E. J. Gunter ◽  
L. E. Barrett ◽  
P. E. Allaire
Keyword(s):  
Reynolds Equation ◽  
Nonlinear Effects ◽  
Aircraft Engine ◽  
Squeeze Film ◽  
Aircraft Engines ◽  
Transient Method ◽  
Squeeze Film Damper ◽  
Wide Range ◽  
Squeeze Film Dampers ◽  
Bearing Stiffness

This paper examines the effect of squeeze-film damper bearings on the steady state and transient unbalance response of aircraft engine rotors. The nonlinear effects of the damper are examined, and the variance of the motion due to unbalance, static pressurization, retainer springs, and rotor preload is shown. The nonlinear analysis is performed using a time-transient method incorporating a solution of the Reynolds equation at each instant in time. The analysis shows that excessive stiffness in the damper results in large journal amplitudes and transmission of bearing forces to the engine casing which greatly exceed the unbalance forces. Reduction of the total effective bearing stiffness through static pressurization and rotor preload is considered. The reduction in stiffness allows the damping generated by the bearing to be more effective in attenuating rotor forces. It is observed that in an unpressurized damper, the dynamic transmissibility will exceed unity when the unbalance eccentricity exceeds approximately 50 percent of the damper clearance for the relatively wide range of conditions examined in this study.

A Study of the Influence of Static Eccentricity and Unbalance on Cavitation Effects in a Squeeze Film Damped Flexible Rotor

2002 ◽  
Author(s):  
Philip Bonello ◽  
Michael J. Brennan ◽  
Roy Holmes
Keyword(s):  
Dynamic Systems ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Test Rig ◽  
Squeeze Film Damper ◽  
Static Eccentricity ◽  
Rotor Dynamic ◽  
Rigid Rotors

The study of eccentric squeeze film damped rotor dynamic systems has largely concentrated on rigid rotors. In this paper, a newly developed receptance harmonic balance method is used to efficiently analyze a squeeze film damped flexible rotor test rig. The aim of the study is to investigate the influence of damper static eccentricity and unbalance level on cavitation and its resulting effect on the vibration level. By comparing predictions for the rotor vibration levels obtained respectively with, and without, lower pressure limits for the eccentric squeeze film damper model, it is demonstrated that cavitation is promoted by increasing static eccentricity and/or unbalance level. This, in turn, is found to have a profound effect on the predictions for the critical vibration levels, which such dampers are designed to attenuate. The reported findings are backed by experimental evidence from the test rig.

Optimum Design of Squeeze Film Dampers Supporting Multiple-Mode Rotors

2002 ◽  
Vol 124 (4) ◽  
pp. 992-1002 ◽  
Author(s):  
A. El-Shafei ◽  
R. Y. K. Yakoub
Keyword(s):  
Optimum Design ◽  
Critical Speed ◽  
Aircraft Engine ◽  
Squeeze Film ◽  
Operating Speed ◽  
Spring Stiffness ◽  
Search Technique ◽  
Amplitude Response ◽  
Design Program ◽  
Squeeze Film Dampers

In this paper a study of the optimum design of squeeze film dampers for multimode rotors is presented. The optimum design program obtains the best possible damper parameters for a given rotor to satisfy the minimization requirements for the objective function. The objectives are to minimize the amplitude response of the rotor at the critical speed, minimize the force transmitted to the support at the operating speed, or maximize the power dissipated by the damper. A combination of these objectives can also be used, with weighting factors to weigh the importance of each of these objectives. These are the possible objectives for the design of squeeze film dampers for aircraft engine applications. The basis of the optimum design program is an extremely fast algorithm which is able to quickly calculate the unbalance response of a rotor, for circular centered orbits of the journal in the damper. A commercial routine is used for the optimization, and is based on a complex direct search technique. The variation of the optimum clearance, length, and retainer spring stiffness are plotted against various rotor parameters. Recommendations for the design of squeeze film dampers are made. Applications to an aircraft engine illustrate the power of the developed algorithm.

A Finite Length Bearing Correction Factor for Short Bearing Theory

1980 ◽  
Vol 102 (3) ◽  
pp. 283-287 ◽  
Author(s):  
L. E. Barrett ◽  
P. E. Allaire ◽  
E. J. Gunter
Keyword(s):  
Correction Factor ◽  
Finite Length ◽  
Transient Analysis ◽  
Nonlinear Response ◽  
Reynolds Equation ◽  
Analytic Solution ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Flexible Rotors ◽  
Nonlinear Transient

A rapid method for calculating the general nonlinear response of finite-length plain journal and squeeze film damper bearings is presented. The method incorporates a finite-length correction factor which modifies the nonlinear forces obtained from short bearing theory. The steady-state rotational, precessive squeeze, and radial squeeze forces obtained with the correction factor compare extremely well with the forces obtained from an analytic solution of Reynolds equation using a variational approach up to L/D of 1.25 and hence covers the most commonly encountered L/D ratios. The method is no more time consuming than the short bearing analysis and is especially suited to nonlinear transient analysis of flexible rotors.

scholarly journals Parallel Harmonic Balance Method for Analysis of Nonlinear Dynamical Systems

2020 ◽  
Author(s):  
J. Blahoš ◽  
A. Vizzaccaro ◽  
L. Salles ◽  
F. El Haddad
Keyword(s):  
Harmonic Balance ◽  
Solid Mechanics ◽  
Nonlinear Dynamical Systems ◽  
Parallel Implementation ◽  
Harmonic Balance Method ◽  
Aircraft Engine ◽  
Balance Method ◽  
Computationally Efficient ◽  
Nonlinear Dynamical ◽  
Engine Design

Abstract Controlling vibration in jet engine remains one of the biggest challenges in aircraft engine design and conception. Methods dealing with vibration modelling usually rely on reduced order modelling techniques. This paper aims to provide a high fidelity method to solve vibration problems. It presents a parallel harmonic balance method applied to a full size problem. In order to be computationally efficient, a parallel harmonic balance method is used for the first time in solid mechanics. First, the parallel implementation of harmonic balance method is described in detail. The algorithm is designed to minimize communication between cores. Then, the software is tested for both beam and blade geometries. Finally, a scalability study shows promising acceleration when increasing the number of cores.

Optimum Design of Squeeze Film Dampers Supporting Multiple-Mode Rotors

2001 ◽  
Author(s):  
A. El-Shafei ◽  
R. Y. Yakoub
Keyword(s):  
Optimum Design ◽  
Critical Speed ◽  
Aircraft Engine ◽  
Squeeze Film ◽  
Spring Stiffness ◽  
Search Technique ◽  
Amplitude Response ◽  
Design Program ◽  
Squeeze Film Dampers ◽  
Multi Mode

In this paper a study of the optimum design of squeeze film dampers for multi-mode rotors is presented. The optimum design program obtains the best possible damper parameters for a given rotor to satisfy the minimization requirements for the objective function. The objectives are to: minimize the amplitude response of the rotor at the critical speed, minimize the force transmitted to the support at the operating speed or maximize the power dissipated by the damper. A combination of these objectives can also be used, with weighting factors to weigh the importance of each of these objectives. These are the possible objectives for the design of squeeze film dampers for aircraft engine applications. The basis of the optimum design program is an extremely fast algorithm which is able to quickly calculate the unbalance response of a rotor, for circular centered orbits of the journal in the damper. A commercial routine is used for the optimization, and is based on a complex direct search technique. The variation of the optimum clearance, length, and retainer spring stiffness are plotted against various rotor parameters. Recommendations for the design of squeeze film dampers are made. Application to an aircraft engine, illustrate the power of the developed algorithm.

A Study of the Nonlinear Interaction Between an Eccentric Squeeze Film Damper and an Unbalanced Flexible Rotor

2004 ◽  
Vol 126 (4) ◽  
pp. 855-866 ◽  
Author(s):  
Philip Bonello ◽  
Michael J. Brennan ◽  
Roy Holmes
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Interaction ◽  
Harmonic Balance ◽  
Linear Part ◽  
Harmonic Balance Method ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Test Rig ◽  
Squeeze Film Damper ◽  
Static Eccentricity

In this paper, the nonlinear interaction between an eccentric squeeze film damper and an unbalanced flexible rotor is investigated, paying particular attention to the effect of cavitation in the damper. A harmonic balance method that uses the receptance functions of the rotating linear part of the system to determine periodic solutions to the nonlinear problem is used to predict vibration levels in a test rig. By comparing predictions obtained respectively with, and without, lower pressure limits for the squeeze film damper model, it is concluded that cavitation is promoted by increasing static eccentricity and/or unbalance level. This, in turn, is found to have a profound effect on the predictions for the critical vibration levels, which such dampers are designed to attenuate. Experimental results are presented to support the findings.

Imbalance Response of Nonlinear Rotor-SFD Dynamic Systems With Structure Modelled As FRFs Using Harmonic Balance Method

2017 ◽  
Author(s):  
Manoj Settipalli ◽  
Rahul Chandran ◽  
Venkatarao Ganji ◽  
Theodore Brockett
Keyword(s):  
Dynamic Systems ◽  
Harmonic Balance ◽  
Degrees Of Freedom ◽  
Fourier Coefficients ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Balance Method ◽  
Squeeze Film ◽  
Static Structure ◽  
The Impact

Squeeze-film-dampers (SFDs) used to couple rotor dynamic systems to linear static structures, such as those in aircraft engines and turbochargers, are often approximated as linear connections in dynamic simulations. Linearized stiffness and damping coefficients of the SFDs can be reasonably estimated for circular centered orbits. Selection of linearized properties for the SFD is challenged under more general whirling conditions, such as those occurring in non-centered dampers with steady gravity loading. In this paper, an efficient method for coupling the rotor system to a static structure modeled as frequency-response-functions (FRFs) through nonlinear SFDs is illustrated. The harmonic balance method (HBM) with arc length continuation technique is employed in the frequency domain to obtain the system periodic response. Degrees-of-freedom participating in the non-linear SFD model, when separated from the remaining linear degrees-of-freedom, are expanded in terms of Fourier coefficients. The algorithm allows the Fourier coefficients approximating the nonlinearity to be iteratively determined at each frequency of interest. The approach has a tremendous time advantage over a traditional nonlinear transient analysis. The method can be used to efficiently predict vibration response on the engine static structure to typical imbalance on the rotors to assess the risk of meeting the low vibration requirements typical of new designs. The prediction includes the primary driving frequencies and their harmonics in the vibration estimate. A flexible rotor system connected to structure through an SFD is used to demonstrate the approach and discuss the impact of results.

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