Wedge Damper Modeling and Forced Response Prediction of Frictionally Constrained Blades

2007 ◽  
Author(s):  
Ender Cigeroglu ◽  
Ning An ◽  
Chia-Hsiang Menq
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Harmonic Balance ◽  
Contact Stiffness ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Points ◽  
Contact Surfaces

In this paper, an improved wedge damper model is presented, based on which the effects of wedge dampers on the forced response of frictionally constrained blades are investigated. In the analysis, while the blade is modeled as a constrained structure, the damper is considered as an unconstrained structure. The model of the damper includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the damper is not artificially constrained. When modeling the contact surfaces of the wedge damper, discrete contact points along with contact stiffness are evenly distributed on the two contact surfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the engine rpm, quasi-static contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the centrifugal force. A friction model is employed to determine the three-dimensional nonlinear contact forces and the relationship between the contact forces and the relative motion is utilized by the Harmonic Balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations, in the Harmonic Balance method is in proportion to the number of modes employed, and therefore the number of contact points used is irrelevant. The developed method is applied to tuned bladed disk system and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that, the effect of rotational motion is significant, particularly for the in-phase vibration modes.

Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Ender Cigeroglu ◽  
Ning An ◽  
Chia-Hsiang Menq
Keyword(s):  
Harmonic Balance ◽  
Normal Load ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Response Prediction ◽  
Forced Response ◽  
Contact Forces ◽  
Balance Method ◽  
Frictional Contacts ◽  
Contact Points

In this paper, a forced response prediction method for the analysis of constrained and unconstrained structures coupled through frictional contacts is presented. This type of frictional contact problem arises in vibration damping of turbine blades, in which dampers and blades constitute the unconstrained and constrained structures, respectively. The model of the unconstrained/free structure includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the free structure is not artificially constrained. When modeling the contact surfaces between the constrained and free structure, discrete contact points along with contact stiffnesses are distributed on the friction interfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the normal force acting on the contact interfaces, quasistatic contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the normal load. A friction model is employed to determine the three-dimensional nonlinear contact forces, and the relationship between the contact forces and the relative motion is utilized by the harmonic balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations in the harmonic balance method, are in proportion to the number of modes employed. Therefore the number of contact points used is irrelevant. The developed method is applied to a bladed-disk system with wedge dampers where the dampers constitute the unconstrained structure, and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that the effect of rotational motion is significant, particularly for the in-phase vibration modes. Moreover, the effect of partial slip in the forced response analysis and the effect of the number of harmonics employed by the harmonic balance method are examined. Finally, the prediction for a test case is compared with the test data to verify the developed method.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

A Contact Model for Nonlinear Forced Response Prediction of Turbine Blades: Calculation Techniques and Experimental Comparison

2008 ◽  
Author(s):  
Christian M. Firrone ◽  
Marco Allara ◽  
Muzio M. Gola
Keyword(s):  
Normal Load ◽  
Contact Stiffness ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Model ◽  
Experimental Comparison ◽  
Normal Contact ◽  
Contact Models

Dry friction damping produced by sliding surfaces is commonly used to reduce vibration amplitude of blade arrays in turbo-machinery. The dynamic behavior of turbine components is significantly affected by the forces acting at their contact interfaces. In order to perform accurate dynamic analysis of these components, contact models must be included in the numerical solvers. This paper presents a novel approach to compute the contact stiffness of cylindrical contacts, analytical and based on the continuous contact mechanics. This is done in order to overcome the known difficulties in simultaneously adjusting the values of both tangential and normal contact stiffness experimentally. Monotonic loading curves and hysteresis cycles of contact forces vs. relative displacement are evaluated as a function of the main contact parameters (i.e. the contact geometry, the material properties and the contact normal load). The new contact model is compared with other contact models already presented in literature in order to show advantages and limitations. The contact model is integrated in a numerical solver, based on the Harmonic Balance Method (HBM), for the calculation of the forced response of turbine components with friction contacts, in particular underplatform dampers. Results from the nonlinear numerical simulations are compared with those from validation experiments.

Evaluation of Friction Damping in Dovetail Root Joints Based on Dissipation Energy on Contact Surfaces

2009 ◽  
Author(s):  
Kunio Asai ◽  
Shigeo Sakurai ◽  
Takeshi Kudo ◽  
Norihiko Ozawa ◽  
Taizo Ikeda
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Relative Displacement ◽  
Contact Angles ◽  
Forced Response ◽  
Contact Forces ◽  
Friction Damping ◽  
Normal Contact ◽  
Tangential Contact ◽  
Contact Surfaces

It is necessary to increase and estimate friction damping at contact interfaces to reduce vibratory stresses in turbines. The hysteresis behavior between tangential contact force and relative displacement should be precisely estimated to improve the accuracy of fiction-damping estimates. There is a difficulty in establishing a general model of hysteresis because tangential contact stiffness depends on many parameters, such as normal contact force, contact geometry, surface roughness, and wear status. We discuss a procedure to empirically calculate friction damping in dovetail root joints using the tangential contact stiffness estimated from measured natural frequencies and the micro-slip model whose coefficients were experimentally obtained from special fretting tests. Instead of the multi-harmonic balance methods, we calculated the friction damping on the basis of the energy dissipation at contact surfaces to discuss the effects of the tangential contact stiffness on several physical values, i.e., tangential and normal contact forces, natural frequency, and micro-slip. In our model, the linear forced response analysis was conducted by taking into consideration the non-linearity between the tangential contact force and the relative displacement by defining the actual and imaginary tangential contact stiffness. We confirmed that the numerically calculated damping ratios are quantitatively in very good agreement with the measured ones under different contact angles, input gravity levels, and contact forces. This indicates that if the tangential contact stiffness is accurately estimated, friction damping with our method can be precisely estimated under different test conditions. We also showed that the estimated tangential contact stiffness for dovetail root joints are smaller than those obtained by the fretting tests at high input gravity. This is probably because the contact interface partially separates during a cyclic loading in the former case; this results in the decrease of the contact area and contact stiffness.

Influence of rail flexibility in a wheel/rail wear prediction model

2016 ◽  
Vol 231 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Javier F Aceituno ◽  
Pu Wang ◽  
Liang Wang ◽  
Ahmed A Shabana
Keyword(s):  
Prediction Model ◽  
Rigid Body ◽  
Contact Point ◽  
Three Dimensional ◽  
Contact Forces ◽  
Wear Model ◽  
Material Loss ◽  
Wear Prediction ◽  
Contact Points ◽  
Rail Wear

The aim of this paper is to study the influence of rail flexibility when a wheel/rail wear prediction model that computes the material loss based on an energy approach is used. The wheel/rail wear model used in this investigation is a simplified combined wear hypothesis that is based on the frictional energy loss in the contact patch. In order to account for wear and its distribution in a profiled wheel surface, the contact forces, creepages and location of the wheel/rail contact points are first calculated using a fully nonlinear multibody system (MBS) and three-dimensional contact formulations that account for the rail flexibility. The contact forces, creepages and contact point locations are defined as nonlinear functions of the rail deformations. These nonlinear expressions are used in the wear calculations. The wear distribution is considered to be proportional to the normal force in the contact area. Numerical simulations are first performed in order to compare between the results obtained using the simplified wheel/rail wear model and the results obtained using Archard’s wear model with a focus on sliding when the track is modeled as a rigid body. This simplified wear model is then used in the simulation of the MBS vehicle model in the case of a flexible body track, in which the rails are modeled using the finite element floating frame of reference approach and modal reduction techniques. The effect of the rail deformation on the wear results are examined by comparing these results with those obtained using the rigid-body track model.

A Contact Force Solution for Non-Colliding Contact Dynamics Simulation

2006 ◽  
Author(s):  
Inna Sharf ◽  
Yuning Zhang
Keyword(s):  
Rigid Body ◽  
Contact Force ◽  
Contact Point ◽  
Closed Form Solution ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Friction Forces ◽  
Contact Points

Rigid-body impact modeling remains an intensive area of research spurred on by new applications in robotics, biomechanics, and more generally multibody systems. By contrast, the modeling of non-colliding contact dynamics has attracted significantly less attention. The existing approaches to solve non-colliding contact problems include compliant approaches in which the contact force between objects is defined explicitly as a function of local deformation, and complementarity formulations in which unilateral constraints are employed to compute contact interactions (impulses or forces) to enforce the impenetrability of the contacting objects. In this article, the authors develop a novel approach to solve the non-colliding contact problem for objects of arbitrary geometry in contact at multiple points. Similarly to the complementarity formulation, the solution is based on rigid-body dynamics and enforces contact kinematics constraints at the acceleration level. Differently, it leads to an explicit closed-form solution for the normal forces at the contact points. Integral to the proposed formulation is the treatment of tangential contact forces, in particular the static friction. These friction forces must be calculated as a function of microslip velocity or displacement at the contact point. Numerical results are presented for three test cases: 1) a thin rod sliding down a stationary wedge; 2) a cube rotating off the stationary wedge under application of an external moment and 3) the cube and the wedge both moving under application of a moment. To ascertain validity and correctness, the solutions to frictionless and frictional scenarios obtained with the proposed formulation are compared to those generated by using a commercial simulation tool MSC ADAMS.

Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver

2018 ◽  
Author(s):  
Anna Engels-Putzka ◽  
Jan Backhaus ◽  
Christian Frey
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Unsteady Aerodynamics ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Algorithmic Differentiation ◽  
Design And Optimization ◽  
Initial Application ◽  
Reverse Mode ◽  
Geometric Changes

This paper describes the development and initial application of an adjoint harmonic balance solver. The harmonic balance method is a numerical method formulated in the frequency domain which is particularly suitable for the simulation of periodic unsteady flow phenomena in turbomachinery. Successful applications of this method include unsteady aerodynamics as well as aeroacoustics and aeroelasticity. Here we focus on forced response due to the interaction of neighboring blade rows. In the CFD-based design and optimization of turbomachinery components it is often helpful to be able to compute not only the objective values — e.g. performance data of a component — themselves, but also their sensitivities with respect to variations of the geometry. An efficient way to compute such sensitivities for a large number of geometric changes is the application of the adjoint method. While this is frequently used in the context of steady CFD, it becomes prohibitively expensive for unsteady simulations in the time domain. For unsteady methods in the frequency domain, the use of adjoint solvers is feasible, but still challenging. The present approach employs the reverse mode of algorithmic differentiation (AD) to construct a discrete adjoint of an existing harmonic balance solver in the framework of an industrially applied CFD code. The paper discusses implemen-tational issues as well as the performance of the adjoint solver, in particular regarding memory requirements. The presented method is applied to compute the sensitivities of aeroelastic objectives with respect to geometric changes in a turbine stage.

scholarly journals Dual Time Stepping Algorithms With the High Order Harmonic Balance Method for Contact Interfaces With Fretting-Wear

2011 ◽  
Author(s):  
Loi¨c Salles ◽  
Laurent Blanc ◽  
Fabrice Thouverez ◽  
Alexander M. Gouskov ◽  
Pierrick Jean
Keyword(s):  
Frequency Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Contact Forces ◽  
Balance Method ◽  
Fretting Wear ◽  
Rate Equations ◽  
Time Stepping ◽  
Dual Time Stepping

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-Harmonic Balance Method (mHBM). The Dynamic Lagrangian Frequency-Time method is used to calculate contact forces in the frequency domain. A new strategy for solving non-linear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.

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.

Complex Impact Response of a Beam and Rigid Body Structure to Harmonic Base Excitation

2005 ◽  
Author(s):  
Elizabeth Ervin ◽  
Jonathan Wickert
Keyword(s):  
Rigid Body ◽  
Contact Stiffness ◽  
Excitation Frequency ◽  
Period Doubling ◽  
Forced Response ◽  
The Body ◽  
Body Structure ◽  
Base Excitation ◽  
Response Dynamics ◽  
Contact State

This paper investigates the forced response dynamics of a clamped-clamped beam to which a rigid body is attached, and in the presence of periodic or non-periodic impacts between the body and a comparatively compliant base structure. The assembly is subjected to base excitation at specified frequency and acceleration, and the potentially complex responses that occur are examined analytically. The two sets of natural frequencies and vibration modes of the beam-rigid body structure (in its in- contact state, and in its not-in-contact state), are used to treat the forced response problem through a series of algebraic mappings among those states. A modal analysis based on extended operators for the (continuous) beam and (discrete) rigid body establishes a piecewise linear state-to-state mapping for transition between the in-contact and not-in-contact conditions. The contact force, impulse, and displacement each exhibit complex response characteristics as a function of the excitation frequency. Periodic responses occurring at the excitation frequency, period-doubling bifurcations, grazing impacts, sub-harmonic regions, fractional harmonic resonances, and apparently chaotic responses each occur at various combinations of damping, excitation frequency, and contact stiffness. Parameter studies are discussed for structural asymmetry and eccentricity of contact point’s location.

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