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.

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.

scholarly journals Development of Dynamics for Design Procedure of Novel Grating Tiling Device with Experimental Validation

2021 ◽  
Vol 11 (24) ◽  
pp. 11716
Author(s):  
Qingshun Bai ◽  
Mohamed Shehata ◽  
Ayman Nada ◽  
Zhongxi Shao
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Real Life ◽  
Design Procedure ◽  
Industrial Applications ◽  
Differential Algebraic Equations ◽  
System Stability ◽  
Design Parameters ◽  
Measuring Instruments ◽  
Algebraic Equations

The article proposes a dynamic for design (DFD) procedure for a novel aperture grating tiling device using the multibody system (MBS) approach. The grating device is considered as a rigid-flexible MBS that is built primarily based totally at the load assumptions because of grating movement. This movement is utilized in many industrial applications, such as the compression of laser pulse, precision measuring instruments, and optical communication. A new design procedure of tiling grating device frame is introduced in order to optimize its design parameters and enhance the system stability. The dynamic loads are estimated based on the Lagrange multipliers that are obtained from the solution of the MBS model. This model is fully non-linear and moves in the three-dimensional space, and the relative movement of its bodies is restricted by the description of the constraints function in the motion manifold. The mechanism of the grating device is structurally analyzed in keeping with the dynamic conduct and therefore the generated forces. The symbolic manipulation as well as the computational work of solving the obtained differential-algebraic equations (DAEs) is carried out using MATLAB Symbolic Toolbox. Once the preliminary design has been attained, the stress behavior of the grating device is examined using the MATLAB FEATool Multiphysics toolkit, regarding system stability and design aspects. Moreover, the design was constructed in real life, and the movement has been verified experimentally, which confirms the effectiveness of the proposed procedure. In conclusion, the DFD procedure with trade-off optimization is utilized successfully to design the grating unit for maximum ranges of grating movements.

Prediction of Resonant Response of Shrouded Blades With 3D Shroud Constraint

1998 ◽  
Author(s):  
B. D. Yang ◽  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Relative Motion ◽  
Normal Load ◽  
Three Dimensional ◽  
Force Model ◽  
Resonant Response ◽  
Equivalent Stiffness ◽  
Stick Slip ◽  
Contact Plane ◽  
Blade System ◽  
Stiffness And Damping

In this paper, the 3D shroud contact kinematics of a shrouded blade system is studied. The assumed blade motion has three components, namely axial, tangential, and radial components, which result in a three dimensional relative motion across the shroud interface. The resulting relative motion can be decomposed into two components. The first one is on the contact plane and can induce stick-slip friction. The other component is perpendicular to the contact plane and can cause variation of the contact normal load and, in extreme circumstances, separation of the two contacting surfaces. In order to estimate the equivalent stiffness and damping of the shroud contact an approach is proposed. In this approach, the in-plane slip motion is assumed to be elliptical and is decomposed into two linear motions along the principal major and minor axes of the ellipse. A variable normal load friction force model (Yang and Menq, 1996) is then applied separately to each individual linear motion, and the equivalent stiffness and damping of the shroud contact can be approximately estimated. With the estimated stiffness and damping, the developed shroud contact model is applied to the prediction of the resonant response of a shrouded blade system. The effects of two different shroud constraint conditions, namely 2D constraint and 3D constraint, on the resonant response of a shrouded blade system are compared and the results are discussed.

Contact Kinematics between Three-Dimensional Rigid Bodies with General Surface Parameterization

2020 ◽  
pp. 1-28
Author(s):  
Mubang Xiao ◽  
Ye Ding
Keyword(s):  
Reference Frame ◽  
Relative Motion ◽  
Screw Theory ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Frame Field ◽  
Contact Kinematics ◽  
Acceleration Analysis

Abstract This paper provides an improvement of the classic Montana's contact kinematics equations considering non-orthogonal object parameterizations. In Montana's model, the reference frame used to define the relative motion between two rigid bodies in three-dimensional space is chosen as the Gauss frame, assuming there is an orthogonal coordinate system on the object surface. To achieve global orthogonal parameterizations on arbitrarily shaped object surfaces, we define the relative motion based on the reference frame field, which is the orthogonalization of the surface natural basis at every contact point. The first- and second-order contact kinematics, including the velocity and acceleration analysis of the relative rolling, sliding, and spinning motion, are reformulated based on the reference frame field and the screw theory. We use two simulation examples to illustrate the proposed method. The examples are based on simple non-orthogonal surface parameterizations, instead of seeking for global orthogonal parameterizations on the surfaces.

Prediction of Resonant Response of Shrouded Blades With Three-Dimensional Shroud Constraint

1999 ◽  
Vol 121 (3) ◽  
pp. 523-529 ◽  
Author(s):  
B. D. Yang ◽  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Relative Motion ◽  
Normal Load ◽  
Three Dimensional ◽  
Force Model ◽  
Resonant Response ◽  
Equivalent Stiffness ◽  
Stick Slip ◽  
Contact Plane ◽  
Blade System ◽  
Stiffness And Damping

In this paper, the three-dimensional shroud contact kinematics of a shrouded blade system is studied. The assumed blade motion has three components, namely axial, tangential, and radial components, which result in a three dimensional relative motion across the shroud interface. The resulting relative motion can be decomposed into two components. The first one is on the contact plane and can induce stick-slip friction. The other component is perpendicular to the contact plane and can cause variation of the contact normal load and, in extreme circumstances, separation of the two contacting surfaces. In order to estimate the equivalent stiffness and damping of the shroud contact an approach is proposed. In this approach, the in-plane slip motion is assumed to be elliptical and is decomposed into two linear motions along the principal major and minor axes of the ellipse. A variable normal load friction force model (Yang and Menq, 1996) is then applied separately to each individual linear motion, and the equivalent stiffness and damping of the shroud contact can be approximately estimated. With the estimated stiffness and damping, the developed shroud contact model is applied to the prediction of the resonant response of a shrouded blade system. The effects of two different shroud constraint conditions, namely two-dimensional constraint and three-dimensional constraint, on the resonant response of a shrouded blade system are compared and the results are discussed.

Design of 3-Dimensional Guidance Law of Missile Based on Discrete Sliding Mode

2013 ◽  
Vol 816-817 ◽  
pp. 976-980
Author(s):  
Nuan Wen ◽  
Zheng Hua Liu ◽  
Le Chang
Keyword(s):  
Discrete Time ◽  
Relative Motion ◽  
Sliding Mode ◽  
Dimensional Space ◽  
Three Dimensional ◽  
New Approach ◽  
3 Dimensional ◽  
Guidance Law ◽  
Guidance Laws ◽  
Three Dimensional Space

In this article, a new approach to design discrete-time sliding-mode guidance laws is presented based on the target-missile relative motion equation in three-dimensional space. This method significantly reduced system chattering and could be easily achieved on engineering. Furthermore, effectiveness of the proposed guidance laws is demonstrated through simulation by comparing with the traditional proportional guidance laws.

scholarly journals Modelling workflow forest fire soil - thrower with energy-saving hydraulic drive

2018 ◽  
Vol 7 (4) ◽  
pp. 182-189
Author(s):  
Петр Попиков ◽  
P. Popikov ◽  
П. Гончаров ◽  
P. Goncharov ◽  
Андрей Шаров ◽  
...  
Keyword(s):  
Energy Saving ◽  
Forest Fire ◽  
Hydraulic System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Hydraulic Drive ◽  
Spherical Shape ◽  
Algebraic Equations ◽  
Working Bodies ◽  
Three Dimensional Space

The article is a schematic diagram of the hydraulic soil-thrower with connection air-charged accumulator which stores energy during overload when working bodies meeting with obstacles, while avoiding the operation of safety valves and conversion hydraulic energy into heat. Mathematical model that comprehensively describes the events taking place: the rotation and movement of the rotor soil-thrower rotor interaction with the ground and obstacles, the drive ground in space. In the method of the soil and the obstacles presented a collection of a large number (about 2000 ... 10000) spherical elements of small size, enabled communicate both among themselves and with the blades soil-thrower. The simulation is performed in three-dimensional space XYZ, where in the same elements have a spherical shape with the same diameter. With in the framework of the model developed by the working surfaces are represented as a set of elementary triangles. Rotor soil-thrower model with some degree of desensitization is represented by four rectangular blades, each of which consists of two triangles. In the process of simulation reproduced rotation of the rotor and the calculation of the interaction with the elements of triangular surfaces ground and obstacles. To solve the system of differential-social and algebraic equations, which laid the basis for the model, time-operated computer program "Program for modeling the work of forest fire soil-thrower with energy saving action hydraulic drive" program time to work in Borland Delphi environment 7.0 language Object Programming PascalIzucheny soil-thrower stage of interaction with the irresistible preption. Using the powering hydraulic system improves the uniformity of rotation of the rotor, to reduce energy costs for rotorus rotation by 12%.

DYNAMICS OF MULTIBODY SYSTEMS WITH UNILATERAL CONSTRAINTS

1999 ◽  
Vol 09 (03) ◽  
pp. 473-478 ◽  
Author(s):  
M. WÖSLE ◽  
F. PFEIFFER
Keyword(s):  
Contact Problem ◽  
Multibody Systems ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
Mathematical Form ◽  
Algebraic Equations ◽  
Unilateral Constraints ◽  
Stick Slip ◽  
Dynamics Of Multibody Systems

In couplings of machines and mechanisms, backlash and friction phenomena are always occurring. Whether stick–slip phenomena take place depends on the structure of such couplings. These processes can be modeled as multibody systems with a time-varying topology. Making use of Lagrange multiplier methods with a mathematical formulation of the contact problem is very efficient for large systems with many constraints. In the following, the differential-algebraic equations are transformed into a resolvable mathematical form by means of the contact laws in equation form. Ultimately we get a nonlinear system of equations for the three-dimensional contact problem with dependent constraints. For its solution, the homotopy method will be used and applied to a simple mechanical system.

Forced Response Analysis of Shrouded Blades by an Alternating Frequency/Time Domain Method

2006 ◽  
Author(s):  
Shi Yajie ◽  
Hong Jie ◽  
Shan Yingchun ◽  
Zhu Zigen
Keyword(s):  
Relative Motion ◽  
Time Domain ◽  
Dry Friction ◽  
Nonlinear Response ◽  
Harmonic Component ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Response Analysis ◽  
Stick Slip ◽  
Moving Contact

In turbine jet engine, the rotating blades are subjected to cyclic loading, which makes the blades experience the so-called High Cycle Fatigue (HCF). Dry friction is often employed in turbine design to attenuate the blade vibration and increase aeroclastic stability of the turbine. The dry friction dampers are often classified into four types, i.e., blade-to-blade, blade-to-ground, shrouds, and wedge damper, respectively. Compared with the under-platform dampers, shrouds make fan behavior be significantly more complex. It is very difficult to model and predict the nonlinear response of shrouded blades. In the present study, an efficient approach to investigate the nonlinear response of the shrouded blades is suggested using an alternating frequency/time domain (AFT) method. On one hand, the friction force between shrouds is numerically solved in time-domain. The trajectory of relative motion of the moving contact point is traced, and the stick-slip-separation transition for 3-D relative motion of the shroud-contact interface is considered. On the other hand, the response of the shrouded blades is iteratively solved in frequency-domain using Harmonic Balance Method (HBM). In this approach, the influence of high frequency modes of blade, and the coupling of each harmonic component on damping behavior can be taken into account. As an application, the performance of shroud damper is systematically investigated using the AFT method. The influence of shroud-to-shroud preload and contact stiffness on the shroud damping potential is studied. Some valuable results are got to the design of the shroud contact.

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