Modeling Contact Dynamics of Vanes With Adjustable Upstream Flow Angles

2012 ◽  
Author(s):  
Daniel Schurzig ◽  
Sebastian Tatzko ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Coulomb Friction ◽  
Nonlinear Behavior ◽  
Simulation Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Flow Angle ◽  
Complementarity Conditions ◽  
Time Stepping ◽  
Upstream Flow

In this paper, a simulation method is proposed for a sub-category of compressor vanes showing nonlinear behavior due to an adjustable upstream flow angle. The proposed algorithm computes the forced response of a single vane based on the New-mark time stepping scheme after reducing the structural matrices using the Craig-Bampton method. The contacts are modeled by Coulomb friction and Newton impact constraints. Contact forces are determined using linear complementarity conditions with decoupled orthogonal friction force directions. Different discretization methods for the cylindrical contact partners are proposed. Finally, numerical results are shown in order to validate the proposed algorithms.

A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

2021 ◽  
Author(s):  
Gregory L. Altamirano ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Nonlinear Response ◽  
Piecewise Linear ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
New Method ◽  
Analysis Tools ◽  
Compatibility Constraint

Abstract Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

The elastic contact influences on passive walking gaits

Robotica ◽  
2010 ◽  
Vol 29 (5) ◽  
pp. 787-796 ◽  
Author(s):  
Feng Qi ◽  
Tianshu Wang ◽  
Junfeng Li
Keyword(s):  
Coulomb Friction ◽  
Dynamic Models ◽  
Contact Stiffness ◽  
Contact Forces ◽  
Hertz Contact ◽  
Walking Gait ◽  
Routes To Chaos ◽  
Coulomb Friction Law ◽  
Contact Parameters ◽  
Passive Model

SUMMARYThis paper presents a new planar passive dynamic model with contact between the feet and the ground. The Hertz contact law and the approximate Coulomb friction law were introduced into this human-like model. In contrast to McGeer's passive dynamic models, contact stiffness, contact damping, and coefficients of friction were added to characterize the walking model. Through numerical simulation, stable period-one gait and period-two gait cycles were found, and the contact forces were derived from the results. After investigating the effects of the contact parameters on walking gaits, we found that changes in contact stiffness led to changes in the global characteristics of the walking gait, but not in contact damping. The coefficients of friction related to whether the model could walk or not. For the simulation of the routes to chaos, we found that a small contact stiffness value will lead to a delayed point of bifurcation, meaning that a less rigid surface is easier for a passive model to walk on. The effects of contact damping and friction coefficients on routes to chaos were quite small.

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.

Unilateral Impact and Contact of Elastic Structures Using Lagrangian Multipliers

2011 ◽  
Author(s):  
Sebastian Tatzko
Keyword(s):  
Equations Of Motion ◽  
Structural Equations ◽  
Contact Forces ◽  
Integration Scheme ◽  
Lagrangian Multiplier ◽  
Elastic Structures ◽  
Lagrangian Multipliers ◽  
Linear Elastic ◽  
Time Stepping ◽  
Numerical Effort

This paper deals with linear elastic structures exposed to impact and contact phenomena. Within a time stepping integration scheme contact forces are computed with a Lagrangian multiplier approach. The main focus is turned on a simplified solving method of the linear complementarity problem for the frictionless contact. Numerical effort is reduced by applying a Craig-Bampton transformation to the structural equations of motion.

scholarly journals Imbalance Response of a Test Rotor Supported on Squeeze Film Dampers

1998 ◽  
Vol 120 (2) ◽  
pp. 397-404 ◽  
Author(s):  
L. San Andre´s ◽  
D. Lubell
Keyword(s):  
Chaotic Behavior ◽  
Nonlinear Behavior ◽  
Theoretical Models ◽  
Forced Response ◽  
Analytical Models ◽  
Squeeze Film ◽  
Test Rig ◽  
Critical Speeds ◽  
Highly Nonlinear ◽  
Squeeze Film Dampers

Squeeze film dampers (SFDs) provide vibration attenuation and structural isolation to aircraft gas turbine engines which must be able to tolerate larger imbalances while operating above one or more critical speeds. Rotor-bearing-SFD systems are regarded in theory as highly nonlinear, showing jump phenomena and even chaotic behavior for sufficiently large levels of rotor imbalance. Yet, few experimental results of practical value have verified the analytical predictions. A test rig for measurement of the dynamic forced response of a three-disk rotor (45 kg) supported on two cylindrical SFDs is described. The major objective is to provide a reliable data base to validate and enhance SFD design practice and to allow a direct comparison with analytical models. The open-ends SFD are supported by four-bar centering structures, each with a stiffness of 3.5 MN/m. Measured synchronous responses to 9000 rpm due to various imbalances show the rotor-SFD system to be well damped with amplification factors between 1.6 and 2.1 while traversing cylindrical and conical modes critical speeds. The rotor amplitudes of motion are found to be proportional to the imbalances for the first mode of vibration, and the damping coefficients extracted compare reasonably well to predictions based on the full-film, open-ends SFD. Tight lip (elastomeric) seals contribute greatly to the overall damping of the test rig. Measured dynamic pressures at the squeeze film lands are well above ambient values with no indication of lubricant dynamic cavitation as simple theoretical models dictate. The measurements show absence of nonlinear behavior of the rotor-SFD apparatus for the range of imbalances tested.

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.

Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Christian Siewert ◽  
Lars Panning ◽  
Jörg Wallaschek ◽  
Christoph Richter
Keyword(s):  
Frequency Domain ◽  
Nonlinear Equations ◽  
Forced Response ◽  
Vibration Response ◽  
Contact Forces ◽  
Dynamic Loads ◽  
Response Analysis ◽  
Dynamic Stresses ◽  
Nonlinear Contact ◽  
Turbine Blading

In turbomachinery applications, the rotating turbine blades are subjected to high static and dynamic loads. The static loads are due to centrifugal stresses and thermal strains whereas the dynamic loads are caused by the fluctuating gas forces resulting in high vibration amplitudes, which can lead to high cycle fatigue failures. Hence, one of the main tasks in the design of turbomachinery blading is the reduction in the blade vibration amplitudes to avoid high dynamic stresses. Thus, coupling devices like underplatform dampers and tip shrouds are applied to the blading to reduce the vibration amplitudes and, therefore, the dynamic stresses by introducing nonlinear contact forces to the system. In order to predict the resulting vibration amplitudes, a reduced order model of a shrouded turbine blading is presented including a contact model to determine the nonlinear contact forces. To compute the forced response, the resulting nonlinear equations of motion are solved in the frequency domain using the multiharmonic balance method because of the high computational efficiency of this approach. The transformation from the time domain into the frequency domain is done by applying Galerkin’s method in combination with a multiharmonic approximation function for the unknown vibration response. This results in an algebraic system of nonlinear equations in the frequency domain, which has to be solved iteratively in order to compute the vibration response. The presented methodology is applied to the calculation of the forced response of a nonlinear coupled turbine blading in the frequency domain.

Load Control–Strain Control Isochronous Stress–Strain Curves for High Temperature Nonlinear Analysis

1995 ◽  
Vol 117 (2) ◽  
pp. 364-370 ◽  
Author(s):  
G. S. Bechtel ◽  
T. S. Cook
Keyword(s):  
Rupture Life ◽  
Nonlinear Behavior ◽  
General Purpose ◽  
Operating Conditions ◽  
Time Dependent ◽  
Load Control ◽  
New Techniques ◽  
Time Stepping ◽  
The Past ◽  
Computer Resources

Aircraft gas turbine components are subjected to severe operating conditions. High temperatures, large thermal strains, and mechanical loads combine to cause the material to undergo significant nonlinear behavior. In order to assure safe, durable components, it is necessary that analysis methods be available to predict the nonlinear deformation. General purpose finite element codes are available to perform elastic and viscoplastic analyses, but the analyses are expensive. Both large plastic and creep strain analyses can require significant computer resources, but typically a plastic solution is more economical to run than a time-stepping creep or viscoplastic model solution. For those applications where the deformation is principally time dependent, it is advantageous to include time-dependent creep effects in a “constant time” or “isochronous” analysis. Although this approach has been used in the past to estimate rupture life, this paper will present several significant new techniques for doing an isochronous analysis to analyze time-dependent deformation.

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