Reduced Order Modeling of Bladed Disks With Friction Ring Dampers

2016 ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Friction Model ◽  
Contact Friction ◽  
Bladed Disks ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Bladed Disk

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ring-like substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector level calculation, and allows pre-calculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution method. A model of a bladed disk and damper, is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis in ANSYS with the full order model.

Reduced-Order Modeling of Bladed Disks With Friction Ring Dampers

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Friction Model ◽  
Contact Friction ◽  
Bladed Disks ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Bladed Disk ◽  
Steady State Responses ◽  
State Responses

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed-disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ringlike substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced-order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector-level calculations and allows precalculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution methods. A model of a bladed disk and damper is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis (TDA) in ansys with the full-order model. It is found that the steady-state responses predicted from the ROMs and the results from ansys are in good agreement, and that the ROMs reduce computation time significantly.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
O. G. McGee ◽  
C. Fang ◽  
Y. El-Aini
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Equations Of Motion ◽  
Response Prediction ◽  
Companion Paper ◽  
Energy Model ◽  
Forced Response ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

Comparative Performance of Isotropic and Composite Bladed Disks

1989 ◽  
Author(s):  
P. Seshu ◽  
V. Ramamurti
Keyword(s):  
Steady State ◽  
Shell Element ◽  
Cyclic Symmetry ◽  
Bladed Disks ◽  
Comparative Performance ◽  
Composite Blade ◽  
Bladed Disk ◽  
Plate And Shell ◽  
Representative Model ◽  
Symmetry Method

Abstract Using a 3-noded, multilayered anisotropic triangular plate and shell element combined with cyclic symmetry method, a comparison has been drawn on the steady state as well as free vibration behaviour of isotropic and composite bladed disks, taking into account all the geometric and material complexities. Results are presented for a representative model for three cases – isotropic bladed disk, isotropic disk-composite blade, and composite bladed disk.

Effect of Rubber Material Properties on Steady-State Flat Belt Response

2019 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy
Keyword(s):  
Steady State ◽  
Internal Combustion Engines ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Solution Procedure ◽  
Friction Model ◽  
Rigid Bodies ◽  
Rubber Matrix ◽  
Belt Drive

Abstract Belt-drives are used to transmit power between rotational machine elements in many mechanical systems such as industrial machines, home appliances, and internal combustion engines. The belt cross-section typically consists of axially stiff tension cords (made of steel or polyester strands) embedded in a rubber matrix. The rubber matrix provides the friction interface between the belt and the pulleys through which mechanical torque is transmitted. In this paper, the effect of the rubber’s Young’s modulus and Poisson’s ratio on the steady-state belt normal, tangential and axial stresses, average belt slip, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of a flat belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s cords are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as rigid bodies with a cylindrical contact surface. The equations of motion are integrated using a time-accurate explicit solution procedure.

scholarly journals Investigation of vibration characteristics for bladed-disks with dry friction nonlinearity

2018 ◽  
Vol 207 ◽  
pp. 04009
Author(s):  
Tianyuan Liu ◽  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Dry Friction ◽  
Normal Load ◽  
Frequency Domain Analysis ◽  
Friction Model ◽  
Load Level ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Qualitative Assessment ◽  
Bladed Disk ◽  
Harmonic Equation

This paper focuses on the vibration characteristics of the bladed-disk subjected to the dry friction damping under periodic excitation. Firstly, the multi-harmonic equation basing on the frequency-domain analysis is established to predicate the steady response of the bladed-disk. Then, the algorithm to solve the nonlinear multi-harmonic balance equation is given step by step. In the numerical simulation, a simplified lumped parameter model of a turbine bladed-disk as well as the elastic Coulomb friction model between the root and disk contacting surfaces are applied. The normal load level of the friction interfaces, which are the focal points of the bladed-disk design, is analysed for the nonlinear vibration characteristics of the blades. The results show that vibration response of bladed-disk is affected significantly by normal load, and there exists an optimal value of the normal load under the operating condition of the turbomachinery, which can provide a qualitative assessment for the design practice of friction dampers.

High-Fidelity Modeling of a Backhoe Digging Operation Using an Explicit Multibody Dynamics Code With Integrated Discrete Particle Modeling Capability

2013 ◽  
Author(s):  
Shahriar G. Ahmadi ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Multibody Dynamics ◽  
Search Algorithm ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Friction ◽  
Contact Detection ◽  
High Fidelity ◽  
Normal Contact ◽  
Contact Search

A high-fidelity multibody dynamics model for simulating a backhoe digging operation is presented. The backhoe components including: frame, manipulator, track, wheels and sprockets are modeled as rigid bodies. The soil is modeled using cubic shaped particles for simulating sand with appropriate inter-particle normal and frictional forces. A penalty technique is used to impose both joint and normal contact constraints (including track-wheels, track-terrain, bucket-particles and particles-particles contact). An asperity-based friction model is used to model joint and contact friction. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm is used to allow fast contact detection between polygonal contact surfaces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model can help improve the performance of construction equipment by predicting the actuator and joint forces and the vehicle stability during digging for various vehicle design alternatives.

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

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.

On Damping Entire Bladed Disks Through Dampers on Only a Few Blades

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Javier Avalos ◽  
Marc P. Mignolet
Keyword(s):  
Optimum Design ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Bladed Disks ◽  
Single Degree Of Freedom ◽  
Reduced Order ◽  
Bladed Disk ◽  
Single Degree ◽  
Random Mistuning

The focus of this paper is on demonstrating the potential to damp entire bladed disks using dampers on only a fraction of the blades. This problem is first considered without the presence of random mistuning, and it is demonstrated that a few dampers at optimized locations can lead to a significant reduction in the forced response of the entire bladed disk. Unfortunately, this optimum design may not be robust with respect to random mistuning and a notable fraction of the reduction in forced response obtained may disappear because of mistuning. To regain the reduction in forced response but with mistuning present, robustness to mistuning is enhanced by using intentional mistuning in addition to dampers. The intentional mistuning strategy selected here is the A/B pattern mistuning in which the blades all belong to either type A or B. An optimization effort is then performed to obtain the best combination of A/B pattern and damper location to minimize the mistuned forced response of the disk. The addition of intentional mistuning in the system is shown to be very efficient, and the optimum bladed disk design does indeed exhibit a significant reduction in mistuned forced response as compared with the tuned system. These findings were obtained on both single-degree-of-freedom per blade-disk models and a reduced order model of a blisk.

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