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.

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.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Plain and Full Floating Bearing Simulations With Rigid Shaft Dynamics

2007 ◽  
Author(s):  
Ian McLuckie ◽  
Scott Barrett
Keyword(s):  
System Development ◽  
Equations Of Motion ◽  
Time Integration ◽  
Forced Response ◽  
Design Parameters ◽  
Integration Scheme ◽  
Damping Coefficients ◽  
Time Integration Scheme ◽  
Combined Solution ◽  
Stiffness And Damping

This paper shows a promising predictive bearing model that can be used to reduce turbocharger bearing system development times. Turbocharger development is normally done by varying design parameters such as bearing geometry in a very time consuming experimentation process. Full Floating Bearings (FFB) are used in most automotive turbochargers and, due to emissions regulations, there has been a push towards downsizing engines and applying turbo charging to generate optimized engine solutions for both gasoline and diesel applications. In this paper the turbocharger rotor is regarded as being rigid, and the equations of motion are solved using the Bulirsch Stoer time integration scheme. These equations are solved simultaneously with the bearing model which is used also to determine nonlinear stiffness and damping coefficients. The bearings are solved using a Rigid Hydro Dynamic (RHD) Finite Difference Successive Over Relaxation (SOR) scheme of Reynolds equation that includes both rotational and squeeze velocity terms. However the solver can also consider bearing and rotor elasticity in a Multi-Body Dynamic (MBD) and Elasto-Hydro Dynamic (EHD) combined solution. Two bearing types have been studied, a plain grooved (PGB) and a full floating bearing (FFB) for comparative purposes. The mathematical models used are generic and suitable for whole engine bearing studies. The results in this paper show they are suitable for determining the onset of turbocharger bearing instability, and also the means by which bearing instability may be suppressed. The current study has investigated forced response with the combined effects of gravity and unbalance. It is worth noting that the effects of both housing excitation and aerodynamic excitation from the compressor and turbine can be easily accommodated, and will be the subject of a future paper. Other topics introduced here that will be explored further in the future include the effect of bearing and rotor flexibility in the MBD and EHD solution and the use of automatically generated stiffness and damping coefficients for any bearing geometry.

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.

Forced Wave Propagation in Elastic Cables With Small Curvature

1995 ◽  
Author(s):  
M. Behbahani-Nejad ◽  
N. C. Perkins
Keyword(s):  
Nonlinear Response ◽  
Asymptotic Form ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Transverse Waves ◽  
Propagating Waves ◽  
Distinct Frequency ◽  
Elastic Cables

Abstract This study presents an investigation of the coupled longitudinal-transverse waves that propagate along an elastic cable. The coupling considered derives from the equilibrium curvature (sag) of the cable. A mathematical model is presented that describes the three-dimensional nonlinear response of a long elastic cable. An asymptotic form of this model is derived for the linear response of cables having small equilibrium curvature. Linear in-plane response is described by coupled longitudinal-transverse partial differential equations of motion, which are comprehensively evaluated herein. The spectral relation governing propagating waves is derived using transform methods. In the spectral relation, three qualitatively distinct frequency regimes exist that are separated by two cut-off frequencies. This relation is employed in deriving a Green’s function which is then used to construct solutions for in-plane response under arbitrarily distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves which propagate through the cable, one characterizing extension-compressive deformations (rod-type) and the other characterizing transverse deformations (string-type). These waves may propagate or attenuate depending on wave frequency. The propagation and attenuation of both wave types are highlighted through solutions for an infinite cable subjected to a concentrated harmonic excitation source.

Harmonically Forced Wave Propagation in Elastic Cables With Small Curvature

1997 ◽  
Vol 119 (3) ◽  
pp. 390-397 ◽  
Author(s):  
M. Behbahani-Nejad ◽  
N. C. Perkins
Keyword(s):  
Nonlinear Response ◽  
Asymptotic Form ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Periodic Waves ◽  
Transverse Waves ◽  
Propagating Waves ◽  
Elastic Cables

This study presents an investigation of coupled longitudinal-transverse waves that propagate along an elastic cable. The coupling considered derives from the equilibrium curvature (sag) of the cable. A mathematical model is presented that describes the three-dimensional nonlinear response of an extended elastic cable. An asymptotic form of this model is derived for the linear response of cables having small equilibrium curvature. Linear, in-plane response is described by coupled longitudinal-transverse partial differential equations of motion, which are comprehensively evaluated herein. The spectral relation governing propagating waves is derived using transform methods. In the spectral relation, three qualitatively distinct regimes exist that are separated by two cut-off frequencies which are strongly influenced by cable curvature. This relation is employed in deriving a Green’s function which is then used to construct solutions for in-plane response under arbitrarily distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves which propagate through the cable, one characterizing extension-compressive deformations (rod-type) and the other characterizing transverse deformations (string-type). These waves may propagate or attenuate depending on wave frequency. The propagation and attenuation of both wave types are highlighted through solutions for an infinite cable subjected to a concentrated harmonic excitation source.

Nonlinear Vibration Analysis of Gas Turbine Bladings With Shroud Coupling

2008 ◽  
Author(s):  
Andreas Hohl ◽  
Christian Siewert ◽  
Lars Panning ◽  
Andreas Kayser
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Gas Turbine ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Forced Response ◽  
Vibrational Amplitude ◽  
Friction Forces ◽  
Mapping Procedure

Rotating blades are subjected to vibrations caused by excitation forces due to a non-homogeneous pressure field of the fluid. Therefore, damping devices like tip shrouds are implemented which reduce the vibrational amplitude and apply additional stiffness and damping to the structure. To predict the resulting vibration response and stresses, a three dimensional contact model has been developed to determine the friction forces. The resulting equations of motion are solved in the frequency domain. The developed method has been implemented in a nonlinear forced response code called DATAR designed for the gas turbine division of Siemens Energy. In this paper, the transfer of common Finite Element models of bladings with shrouds or underplatform dampers to the DATAR code is presented. A mapping procedure based on Finite Element shape functions is used to couple the model with the regular contact grid used in the nonlinear vibration analysis performed with the DATAR code. As a practical example, the vibration behavior of a gas turbine blading with interlocked shrouds is investigated with the developed method.

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.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2007 ◽  
Vol 129 (4) ◽  
pp. 417-424 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Six Degree Of Freedom

In this paper, vibration behavior of engine on the nonlinear hydraulic engine mount, including inertia track and decoupler, is studied. In this regard, after introducing the nonlinear factors of this mount (i.e., inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between the rubber and the hydraulic engine mounts, a six-degree-of-freedom four-cylinder V-shaped engine under shaking and balancing mass forces and torques is considered. By solving the time domain nonlinear equations of motion of the engine on three inclined mounts, translational and rotational motions of an engine body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of a hydraulic one in the low-frequency region.

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