Forced Vibration of Elastic Structures With Friction Contacts

1999 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Relative Motion ◽  
Dry Friction ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Point Contact ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Contact Model ◽  
Elastic Structures ◽  
Normal Forces

Abstract In many technical contacts energy is dissipated because of dry friction and relative motion. This can be used to reduce the vibration amplitudes. For example, shrouds with friction interfaces are used to reduce the dynamic stresses in turbine blades. The three-dimensional motion of the blades results in a three-dimensional relative motion of the contact planes. The developed Point-Contact-Model is used to calculate the corresponding tangential and normal forces for each contact element. This Point-Contact-Model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffness in normal and tangential direction and dry friction. An experiment with two non-Hertzian contacts is used to verify the developed contact model. The comparison between measured and calculated frequency response functions for three-dimensional forced vibrations of the elastic structures shows a very good agreement.

The Calculation of the Forced Response of Shrouded Blades With Friction Contacts and its Experimental Verification

2000 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Dry Friction ◽  
Turbine Blades ◽  
Life Time ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Model ◽  
Spatial Motion ◽  
Normal Contact

Shrouds with a frictional interface are used to reduce the dynamic stresses in turbine blades. Due to dry friction energy is dissipated, which can be used to decrease vibration amplitudes and, hence, to increase the life time of turbine blades. The spatial motion of the blades results in a spatial motion of the contact planes. Due to the non-linearity of the problem, the contact planes are discretized. For each contact area, the developed contact model is used to calculate the corresponding tangential and normal contact forces. This contact model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffnesses in normal and tangential direction and dry friction. Due to the roughness of the contact planes the normal contact forces and the contact stiffnesses in normal and tangential direction are nonlinear dependent on the relative displacements in the normal direction. This effect is verified by experiments. An experiment with one shrouded blade and two non-Hertzian contacts is used to verify the developed contact model and the calculation method. The comparison between measured and calculated frequency response functions for bending and torsional vibrations of the blade show a very good agreement. A bladed disk assembly with shrouds is investigated and optimized with respect to the vibration amplitudes and alternating stresses. Varying the normal contact force best damping effects are obtained. Separation of the contacts leads to an increase of the alternating stresses and, thus, has to be avoided.

Development and Experimental Validation of a Point Contact Model for Dynamical Problems With Friction

2001 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Pressure Distribution ◽  
Relative Motion ◽  
Contact Area ◽  
Point Contact ◽  
Contact Problems ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Contact Model ◽  
Impact Oscillator ◽  
Normal Contact

Abstract The contact forces are dependent on many parameters, such as contact stiffnesses, surface profiles, material parameters, temperature distribution, relative motion and normal pressure distribution. These parameters can change within the contact area and from here, it is impossible to derive a general force law. The only possibility to overcome this problem is to discretize the contact areas, since in general the relative motion and the contact parameters are not constantly distributed within the contact surface. This leads to a point contact model, which has to include all main physical effects as described above, which are important, when simulating dynamical contact problems with friction. The friction model includes the main parameters such as the roughness of the contact surfaces, the nonlinear friction law, the contact stiffnesses in normal and tangential direction. The decreasing characteristic of the friction coefficient with respect to the relative velocity has to be modeled in a sufficient way. With respect to the dissipation of energy, the hysteretic behavior is studied with respect to the normal and tangential direction. Separation of the contact is included. This point contact model is be applied to real dynamical contact problems. In the first example, a simple impact oscillator with an elastic contact is used to check the overall modeling with respect to the elastic normal contact. Then, a self excited friction oscillator is investigated with respect to the tangential contact. Here, the modeling of surface waviness leads to high periodic solutions, which is also observed within the experiments. In both examples, the comparison of measurements and calculated phase plots is good. Furthermore, the influence of wear on to the surface profile, contact area and normal pressure distribution is investigated. From here, it follows, that friction leads to time dependent systems.

scholarly journals Prediction of Periodic Response of Blades Having 3D Nonlinear Shroud Constraints

1999 ◽  
Author(s):  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Relative Motion ◽  
Dimensional Space ◽  
Time Integration ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Hysteresis Loops ◽  
Contact Model ◽  
Algebraic Equations ◽  
Stick Slip ◽  
Periodic Response

In this paper, a 3D shroud contact model is employed to predict the periodic response of blades having 3D nonlinear shroud constraint. When subjected to periodic excitation, the resulting relative motion at the shroud contact is assumed to be periodic in three-dimensional space. Based on the 3D shroud contact model, analytical criteria are used to determine the transitions between stick, slip, and separation of the contact interface and are used to simulate hysteresis loops of the induced constrained force, when experiencing periodic relative motion. The constrained force can be considered as a feedback force that influences the response of the shrouded blade. By using the Multi-Harmonic Balance Method along with Fast Fourier Transform, the constrained force can be approximated by a series of harmonic functions so as to predict the periodic response of a shrouded blade. This approach results in a set of nonlinear algebraic equations, which can be solved iteratively to yield the periodic response of blades having 3D nonlinear shroud constraint. In order to validate the proposed approach, the predicted results are compared with those of the direct time integration method. The resonant frequency shift, the damping effect, and the jump phenomenon due to nonlinear shroud constraint are examined. The implications of the developed solution procedure to the design of shroud contact are also discussed.

Periodic Response of Blades Having Three-Dimensional Nonlinear Shroud Constraints

1999 ◽  
Vol 123 (4) ◽  
pp. 901-909 ◽  
Author(s):  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Relative Motion ◽  
Dimensional Space ◽  
Time Integration ◽  
Three Dimensional ◽  
Hysteresis Loops ◽  
Solution Procedure ◽  
Contact Model ◽  
Algebraic Equations ◽  
Stick Slip ◽  
Periodic Response

In this paper, a three-dimensional shroud contact model is employed to predict the periodic response of blades having three-dimensional nonlinear shroud constraint. When subjected to periodic excitation, the resulting relative motion at the shroud contact is assumed to be periodic in three-dimensional space. Based on the three-dimensional shroud contact model, analytical criteria are used to determine the transitions between stick, slip, and separation of the contact interface and are used to simulate hysteresis loops of the induced constrained force, when experiencing periodic relative motion. The constrained force can be considered as a feedback force that influences the response of the shrouded blade. By using the multiharmonic balance method along with Fast Fourier Transform, the constrained force can be approximated by a series of harmonic functions so as to predict the periodic response of a shrouded blade. This approach results in a set of nonlinear algebraic equations, which can be solved iteratively to yield the periodic response of blades having three-dimensional nonlinear shroud constraint. In order to validate the proposed approach, the predicted results are compared with those of the direct-time integration method. The resonant frequency shift, the damping effect, and the jump phenomenon due to nonlinear shroud constraint are examined. The implications of the developed solution procedure to the design of shroud contact are also discussed.

scholarly journals Comparison of Two-Equation Turbulence Models for Prediction of Heat Transfer on Film-Cooled Turbine Blades

1997 ◽  
Author(s):  
Vijay K. Garg ◽  
Ali A. Ameri
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Computer Time ◽  
Suction Surface ◽  
The Heat Transfer Coefficient

A three-dimensional Navier-Stokes code has been used to compute the heat transfer coefficient on two film-cooled turbine blades, namely the VKI rotor with six rows of cooling holes including three rows on the shower head, and the C3X vane with nine rows of holes including five rows on the shower head. Predictions of heat transfer coefficient at the blade surface using three two-equation turbulence models, specifically, Coakley’s q-ω model, Chien’s k-ε model and Wilcox’s k-ω model with Menter’s modifications, have been compared with the experimental data of Camci and Arts (1990) for the VKI rotor, and of Hylton et al. (1988) for the C3X vane along with predictions using the Baldwin-Lomax (B-L) model taken from Garg and Gaugler (1995). It is found that for the cases considered here the two-equation models predict the blade heat transfer somewhat better than the B-L model except immediately downstream of the film-cooling holes on the suction surface of the VKI rotor, and over most of the suction surface of the C3X vane. However, all two-equation models require 40% more computer core than the B-L model for solution, and while the q-ω and k-ε models need 40% more computer time than the B-L model, the k-ω model requires at least 65% more time due to slower rate of convergence. It is found that the heat transfer coefficient exhibits a strong spanwise as well as streamwise variation for both blades and all turbulence models.

scholarly journals Improved Reliability of Bladed Disks due to Friction Dampers

1997 ◽  
Author(s):  
Walter Sextro ◽  
Karl Popp ◽  
Ivo Wolter
Keyword(s):  
Dry Friction ◽  
Three Dimensional ◽  
Line Contact ◽  
Two Dimensional ◽  
Centrifugal Forces ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Bladed Disk ◽  
Bladed Disk Assembly

Friction dampers are installed underneath the blade platforms to improve the reliability. Because of centrifugal forces the dampers are pressed onto the platforms. Due to dry friction and the relative motion between blades and dampers, energy is dissipated, which results in a reduction of blade vibration amplitudes. The geometry of the contact is in many cases like a Hertzian line contact. A three-dimensional motion of the blades results in a two-dimensional motion of one contact line of the friction dampers in the contact plane. An experiment with one friction damper between two blades is used to verify the two-dimensional contact model including microslip. By optimizing the friction dampers masses, the best damping effects are obtained. Finally, different methods are shown to calculate the envelope of a three-dimensional response of a detuned bladed disk assembly (V84.3-4th-stage turbine blade) with friction dampers.

Inferring Structure from Motion in Two-View and Multiview Displays

Perception ◽  
1993 ◽  
Vol 22 (12) ◽  
pp. 1441-1465 ◽  
Author(s):  
Jeffrey C Liter ◽  
Myron L Braunstein ◽  
Donald D Hoffman
Keyword(s):  
Relative Motion ◽  
Apparent Motion ◽  
Structure From Motion ◽  
Three Dimensional ◽  
Rigid Motion ◽  
Parameter Family ◽  
Image Motion ◽  
Heuristic Analysis

Five experiments were conducted to examine constraints used to interpret structure-from-motion displays. Theoretically, two orthographic views of four or more points in rigid motion yield a one-parameter family of rigid three-dimensional (3-D) interpretations. Additional views yield a unique rigid interpretation. Subjects viewed two-view and thirty-view displays of five-point objects in apparent motion. The subjects selected the best 3-D interpretation from a set of 89 compatible alternatives (experiments 1–3) or judged depth directly (experiment 4). In both cases the judged depth increased when relative image motion increased, even when the increased motion was due to increased simulation rotation. Subjects also judged rotation to be greater when either simulated depth or simulated rotation increased (experiment 4). The results are consistent with a heuristic analysis in which perceived depth is determined by relative motion.

Wheel-Rail Multi-Point Contact Method for Railway Turnouts

2011 ◽  
Vol 97-98 ◽  
pp. 378-381
Author(s):  
Zhi Wei Chen ◽  
Linan Li ◽  
Shi Gang Sun ◽  
Jun Long Zhou
Keyword(s):  
Calculation Method ◽  
Normal Force ◽  
Contact Point ◽  
Point Contact ◽  
Contact Model ◽  
Contact Method ◽  
Elastic Contact ◽  
Simulation Calculation ◽  
Acute Change

A calculation method of wheel-rail multi-point contact based on the elastic contact model is introduced. Moreover, the simulation calculation of vehicles passing through branch lines of No.18 turnouts is carried out. The result showed that the acute change of wheel-rail normal force caused by the transfers of wheel-rail contact point between two rails can be avoid by wheel-rail multi-point contact method, and the transfers of wheel-rail normal force between two rails is smoother. The validity of wheel-rail multi-point contact method is verified.

3D Permeability of Thick-Section Glass Fabric Reinforced Polymer Composite by Vacuum-Assisted Resin Infusion Molding

2021 ◽  
pp. 1-15
Author(s):  
Ethan R Pedneau ◽  
Su Su Wang
Keyword(s):  
Wind Turbine ◽  
Composite Structures ◽  
Complex Geometry ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Glass Fabric ◽  
Thick Section ◽  
Flow Front ◽  
Resin Infusion ◽  
Principal Axes

Abstract Determination of permeability of thick-section glass fabric preforms with fabric layers of different architectures is critical for manufacturing large, thick composite structures with complex geometry, such as wind turbine blades. The thick-section reinforcement permeability is inherently three-dimensional and needs to be obtained for accurate composite processing modeling and analysis. Numerical simulation of the liquid stage of vacuum-assisted resin infusion molding (VARIM) is important to advance the composite manufacturing process and reduce processing-induced defects. In this research, the 3D permeability of thick-section E-glass fabric reinforcement preforms is determined and the results are validated by a comparison between flow front progressions from experiments and from numerical simulations using ANSYS Fluent software. The orientation of the principal permeability axes were unknown prior to experiments. The approach used in this research differs from those in literature in that the through-thickness permeability is determined as a function of flow front positions along the principal axes and the in-plane permeabilities and is not dependent on the inlet radius. The approach was tested on reinforcements with fabric architectures which vary through-the-thickness direction, such as those in a spar cap of a wind turbine blade. The computational simulations of the flow-front progression through-the-thickness were consistent with experimental observations.

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