Investigation of Engine–Airframe Vibration Due to Main Rotor Hub Loads Using a Substructuring Framework

2019 ◽  
Vol 64 (4) ◽  
pp. 1-16
Author(s):  
Stacy Sidle ◽  
Ananth Sridharan ◽  
Inderjit Chopra ◽  
Matt Feshler ◽  
Peter Kull
Keyword(s):  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Element Model ◽  
Forced Response ◽  
Main Rotor ◽  
Structural Dynamic ◽  
Engine Vibration ◽  
Parametric Studies ◽  
Engine Mount ◽  
Stiffness And Damping

This paper presents a methodology to analyze the coupled structural dynamic response of an elastic airframe and engines of a helicopter in response to main rotor hub loads. Transfer functions of individual components (airframe, engine, mount struts, and torque tube) are coupled together using a substructuring approach to obtain consistent coupled solutions of the entire system. Using this approach, a twin-engine, four-bladed helicopter is analyzed using NASTRAN-based models of the airframe and engines. This efficient substructuring approach is validated against the fully coupled NASTRAN model using forced response studies. Characteristics of the mount properties, i.e., the torque tube stiffness, and aft mount stiffness and damping are systematically varied to study their effect on the engine vibration response. The fore and aft mount element properties for minimizing the 8P engine response are identified without increasing 4P response. A compromise between 4P and 8P response is also identified from parametric studies of rear mount properties, using just three parameters to represent the design space. Using the substructuring approach presented here, future studies can be performed to rapidly match airframe characteristics with available engines at approximately 1000 times the speed of running a detailed finite element model (millions of degrees of freedom), without any reduction in accuracy.

Dynamic Analysis of Engine-Mount Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 79-83 ◽  
Author(s):  
H. Ashrafiuon ◽  
C. Nataraj
Keyword(s):  
Circular Plate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Forced Response ◽  
Engine Vibration ◽  
Airplane Engine ◽  
Engine Mount ◽  
Industrial Rubber ◽  
Stiffness And Damping

This paper examines the forced response of an airplane engine supported by an elastic foundation. It is assumed that the vibrations of the engine and the foundation are small enough such that the equations of motion are linear. The engine is modeled as a rigid body connected to the foundation by standard industrial rubber mounts which act as three-dimensional springs with a significant amount of hysteresis damping. Three fundamental models of the foundation are considered; rigid, statically flexible, and dynamically flexible. In the flexible cases, the foundation is modeled as a clamped circular plate, infinite plate, or any structure identified by a finite element stiffness matrix. In all cases, the mass, stiffness, and damping matrices of the engine-mount system are constructed and the frequency response to the rotating unbalance is determined. For the infinite and clamped circular plate cases, analytical methods are used to determine the real and imaginary parts of the flexibility matrix at different frequencies in response to the harmonic forces transmitted to the plate through the rubber mounts. It is shown here that the foundation elasticity may have a significant effect on the engine vibration and the mounting forces transmitted from the engine to the structure. It is also shown that only the dynamic model of the foundation is able to capture the correct response of the system at frequencies close to the foundation’s natural frequencies.

Dynamic Analysis of Engine-Mount Systems

1991 ◽  
Author(s):  
Hashem Ashrafiuon ◽  
C. Nataraj
Keyword(s):  
Circular Plate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Forced Response ◽  
Engine Vibration ◽  
Airplane Engine ◽  
Engine Mount ◽  
Industrial Rubber ◽  
Stiffness And Damping

Abstract This paper examines the forced response of an airplane engine supported by an elastic foundation. It is assumed that the vibrations of the engine and the foundation are small enough such that the equations of motion are linear. The engine is modeled as a rigid body connected to the foundation by standard industrial rubber mounts which act as three dimensional springs with a significant amount of hysteresis damping. Three fundamental models of the foundation are considered: rigid, statically flexible, and dynamically flexible. In the flexible cases, the foundation is modeled as a clamped circular plate, infinite plate, or any structure identified by a finite element stiffness matrix. In all cases, the mass, stiffness, and damping matrices of the engine-mount system are constructed and the frequency response to the rotating unbalance is determined. For the infinite and clamped circular plate cases, analytical methods are used to determine the real and imaginary parts of the flexibility matrix at different frequencies in response to the harmonic forces transmitted to the plate through the rubber mounts. It is shown here that the foundation elasticity may have a significant effect on the engine vibration and the mounting forces transmitted from the engine to the structure. It is also shown that only the dynamic model of the foundation is able to capture the correct response of the system at frequencies close to the foundation’s natural frequencies.

scholarly journals Structural Reanalysis Based on FRFs Using Sherman–Morrison–Woodbury Formula

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jun Ren ◽  
Qianghao Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Salient Feature ◽  
Original System ◽  
Modal Testing ◽  
Structural Dynamic ◽  
Structural Dynamic Modification ◽  
Modal Model ◽  
Dynamic Modification ◽  
One Step ◽  
Stiffness And Damping

Structural dynamic modification is a popular approach to obtain desire frequencies and dynamic characteristics. It has been observed that reanalyzing the modified structure usually involves complicated calculations when modifications are concerned with numerous degrees of freedom (DOFs), especially adding substructures to these DOFs. This paper proposed a method to reanalyze the frequency response functions (FRFs) of structures with multiple co-ordinates modifications. Two different cases are taken into consideration in the modifications, including adding (or decreasing) masses, stiffness, and damping, as well as adding spring-mass substructures, which makes the method more practical. This method is developed by employing Sherman–Morrison and Woodbury (SMW) formula based on the FRFs related to the modifications coordinates of the original system. The advantage of this method is that neither a physical model nor a modal model is required; instead, it needs only the FRFs, which can be directly measured by experimental modal testing. Another salient feature of this proposed strategy is that the FRFs of the modified structure can be calculated in only one step. Validation of this proposed method is demonstrated using various numerical examples. It is shown that the method is very effective and can be considered for real applications.

Beam Element Structural Dynamics Modification Using Experimental Modal Rotational Data

1995 ◽  
Vol 117 (3A) ◽  
pp. 265-271 ◽  
Author(s):  
John A. Cafeo ◽  
Martin W. Trethewey ◽  
H. Joseph Sommer
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Structural Dynamic ◽  
Modal Data ◽  
Structural Dynamic Modification ◽  
Dynamic Modification ◽  
Rotational Degrees Of Freedom ◽  
Fixed Beam

Structural dynamic modification (SDM) of a fixed-free (cantilever) beam to convert it into a fixed-fixed beam with experimental modal data is presented. The SDM focuses on incorporating experimental rotational degrees-of-freedom (DOF) measured with a novel laser measurement technique. A cantilever beam is tested to develop the experimental modal database including rotational degrees of freedom. A modal database from a finite-element model also is developed for comparison. A structural dynamic modification, with both databases, is performed using a Bernoulli-Euler beam to ground the free end of the cantilever beam. The hardware is then modified and a second experimental modal analysis of the resulting fixed-fixed beam performed. A finite-element model of the fixed-fixed beam also was created. Comparison of results from these four tests are used to assess the effectiveness of SDM using experimental modal rotational data. The evaluation shows that provided high quality experimental rotational modal data can be acquired, SDM work with beam elements can be effective in yielding accurate results.

Geometric Mistuning Reduced-Order Models for Integrally Bladed Rotors With Mistuned Disk–Blade Boundaries

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Charles J. Cross ◽  
Joseph C. Slater
Keyword(s):  
Degrees Of Freedom ◽  
Principal Component ◽  
Element Model ◽  
Forced Response ◽  
Solid Model ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Small Areas ◽  
Eigen Analysis ◽  
Connection Type

New geometric mistuning modeling approaches for integrally bladed rotors (IBRs) are developed for incorporating geometric perturbations to a fundamental disk–blade sector, particularly the disk–blade boundary or connection. Reduced-order models (ROMs) are developed from a Craig–Bampton component mode synthesis (C–B CMS) framework that is further reduced by a truncated set of interface modes that are obtained from an Eigen-analysis of the C–B CMS constraint degrees of freedom (DOFs). An investigation into using a set of tuned interface modes and tuned constraint modes for model reduction is then performed, which offers significant computational savings for subsequent analyses. Two configurations of disk–blade connection mistuning are investigated: as-measured principal component (PC) deviations and random perturbations to the interblade spacing. Furthermore, the perturbation sizes are amplified to investigate the significance of incorporating mistuned disk–blade connections during solid model generation from optically scanned geometries. Free and forced response results are obtained for each ROM and each disk–blade connection type and compared to full finite element model (FEM) solutions. It is shown that the developed methods provide accurate results with a reduction in solution time compared to the full FEM. In addition, results indicate that the inclusion of a mistuned disk–blade connection deviations are small or conditions where large perturbations are localized to a small areas of the disk–blade connection.

scholarly journals A Study on Fluid Self-Excited Flutter and Forced Response of Turbomachinery Rotor Blade

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Chih-Neng Hsu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Power Plants ◽  
Single Mode ◽  
Element Model ◽  
Forced Response ◽  
Structural Dynamic ◽  
Turbine Engine ◽  
Forcing Function ◽  
Structural Dynamic Characteristics

Complex mode and single mode approach analyses are individually developed to predict blade flutter and forced response. These analyses provide a system approach for predicting potential aeroelastic problems of blades. The flow field properties of a blade are analyzed as aero input and combined with a finite element model to calculate the unsteady aero damping of the blade surface. Forcing function generators, including inlet and distortions, are provided to calculate the forced response of turbomachinery blading. The structural dynamic characteristics are obtained based on the blade mode shape obtained by using the finite element model. These approaches can provide turbine engine manufacturers, cogenerators, gas turbine generators, microturbine generators, and engine manufacturers with an analysis system to remedy existing flutter and forced response methods. The findings of this study can be widely applied to fans, compressors, energy turbine power plants, electricity, and cost saving analyses.

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.

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.

Quantitative Assessment of Mass Discretization in Structural Dynamic Modeling

1986 ◽  
Vol 108 (4) ◽  
pp. 401-405 ◽  
Author(s):  
K. M. Vashi
Keyword(s):  
Degrees Of Freedom ◽  
Quantitative Assessment ◽  
Natural Frequencies ◽  
Exact Analytical Solution ◽  
Discrete Problem ◽  
Span Length ◽  
Structural Dynamic ◽  
Simply Supported ◽  
Parametric Studies ◽  
Modeling Rule

For dynamic analysis of majority of structures, a dynamic model is developed by discretizing the distributed mass and elastic properties. For assessing the adequacy of mass discretization, several procedures are used. These procedures include a comparison of analysis with test, parametric studies using finer mass discretizations, and lump mass spacing according to a frequency-controlled span length of a simply supported beam. This paper presents a quantitative assessment of mass discretization by utilizing exact analytical solution to the discrete problem of beam and bar vibrations. The assessment examines the effect of mass discretization on the accuracy of natural frequencies, modes and participation factors. In one modeling rule, the total number of dynamic degrees of freedom is taken to be twice the number of lower frequencies to be computed with a reasonable amount of accuracy. The assessment in this paper provides support for this rule.

The Influence of Blade Properties on the Forced Response of Mistuned Bladed Disks

2011 ◽  
Author(s):  
Andreas Hohl ◽  
Benedikt Kriegesmann ◽  
Jo¨rg Wallaschek ◽  
Lars Panning
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Degrees Of Freedom ◽  
Vibrational Energy ◽  
Normal Modes ◽  
Element Model ◽  
Forced Response ◽  
Optimization Approach ◽  
Bladed Disks ◽  
Value Decomposition

In turbomachinery applications bladed disks are subjected to high dynamic loads due to fluctuating gas forces. Dynamic excitation can result in high vibration amplitudes which can lead to high cycle fatigue (HCF) failures. Herein, the blades are almost identical but differ due to wear or small manufacturing tolerances. Especially, after regeneration and repair procedures the properties of the blades can differ with a high variance. These deviations of the blade properties can lead to a localization of the vibrational energy in single blades and even higher risk of HCF. A recently developed substructure model with a combination of the Hurty transformation or Component Mode Synthesis (CMS) and the so called Wave Based Substructuring (WBS) is used to obtain a Reduced Order Model (ROM) with a reasonable low number of degrees of freedom. The CMS of the disk can be calculated with one cyclic disk segment of the underlying finite element model. The WBS is used to describe the numerous coupling degrees of freedom between the disk and the blades with a truncated set of waves. The orthogonal waves are derived by a Singular Value Decomposition or a QR decomposition from the coupling nodes normal modes calculated by a cyclic modal analysis of the full structure. The blade eigenvalues of the clamped blade can be mistuned individually under consideration of the variance as well as the correlation between the different eigenvalues of the blades. Monte-Carlo-Simulations are performed to calculate the effect of these parameters on the forced response of a mistuned bladed disk for blade dominated modes. Furthermore, Monte-Carlo-Simulations and a constraint optimization approach is used to calculate the worst and best case blade patterns for specific blade patterns and blade patterns with distributed blade properties.

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