Dynamic Simulation of Reeving Systems With the Extension of the Modal Approach in the Axial Direction

2021 ◽  
Author(s):  
Narges Mohammadi ◽  
José Luis Escalona
Keyword(s):  
Axial Strain ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Rigid Bodies ◽  
Arbitrary Lagrangian Eulerian ◽  
Absolute Nodal Coordinates ◽  
Lagrange’S Equation ◽  
Axial Forces ◽  
Nodal Coordinates ◽  
Modal Coordinates

Abstract In this work, the simulation of reeving systems has been studied by including axial modes using the Arbitrary Lagrangian-Eulerian (ALE) description. The reeving system is considered as a deformable multibody system in which the rigid bodies are connected by the elastic wire ropes through sheaves and reels. A set of absolute nodal coordinates and modal coordinates is employed to describe the motion and deformation in the axial direction. This new method allows the analysis of elements with non-constant axial strain along its length. In addition, modal coordinates are employed to describe the dynamic motion in the transverse direction. The non-constant axial displacement within the wire rope is computed in terms of the absolute position coordinates, longitudinal material coordinates, and modal deformation coordinates. To derive the governing equations of motion, Lagrange’s equation is employed. The formulation is validated for a simple pendulumlike motion actuated by an initial velocity. The simulation results are provided to trace the movements of the payload. It can be seen that by adding modal coordinates, the axial force within the element changes. Moreover, the effects of modal coordinates in the axial direction are presented for a different number of nodes, and the resulting axial forces are compared with reference solution.

Advances In The Modeling And Dynamic Simulation of Reeving Systems Using The Arbitrary Lagrangian-Eulerian Modal Method

2021 ◽  
Author(s):  
José L. Escalona ◽  
Narges Mohammadi
Keyword(s):  
Finite Elements ◽  
Axial Force ◽  
Axial Direction ◽  
Rotary Inertia ◽  
Arbitrary Lagrangian Eulerian ◽  
Original Formulation ◽  
Absolute Position ◽  
Axial Forces ◽  
Modal Coordinates ◽  
Modal Method

Abstract This paper presents new advances in the arbitrary Lagrangian-Eulerian modal method (ALEM) recently developed for the systematic simulation of the dynamics of general reeving systems. These advances are related to a more convenient model of the sheaves dynamics and the use of axial deformation modes to account for non-constant axial forces within the finite elements. Regarding the sheaves dynamics, the original formulation uses kinematic constraints to account for the torque transmission at the sheaves by neglecting the rotary inertia. One of the advances described in this paper is the use of the rotation angles of the sheaves as generalized coordinates together with the rope-to-sheave no-slip assumption as linear constraint equations. This modeling option guarantees the exact torque balance the sheave without including any non-linear kinematic constraint. Numerical results show the influence in the system dynamics of the sheave rotary inertia. Regarding the axial forces within the finite elements, the original formulation uses a combination of absolute position coordinates and transverse local modal coordinates to account for the rope absolute position and deformation shape. The axial force, which only depends on the absolute position coordinates, is constant along the element because linear shape functions are assumed to describe the axial displacements. For reeving systems with very long rope spans, as the elevators of high buildings, the constant axial force is inaccurate because the weight of the ropes becomes important and the axial force varies approximately linearly within the rope free span. To account for space-varying axial forces, this paper also introduces modal coordinates in the axial direction. Numerical results show that a set of three modal coordinates in the axial direction is enough to simulate linearly varying axial forces.

Dynamic Analysis of Flexible Multi-Body Systems With Time-Variant Mode Shapes

1991 ◽  
Author(s):  
F. M. L. Amirouche ◽  
M. Xie
Keyword(s):  
Equations Of Motion ◽  
Rate Of Change ◽  
Mode Shapes ◽  
Flexible Body ◽  
Governing Equations ◽  
Dynamical Equations ◽  
Application Problem ◽  
Nodal Coordinates ◽  
Multi Body ◽  
Modal Coordinates

Abstract The paper extends the theory of flexible multi-body systems to include time-variant mode shapes to account for the changes of boundary conditions that a flexible body undergoes while in motion. The method presented herein makes use of finite element methods to discretize the elastic body, then the nodal coordinates are related to the modal coordinates through the mode shapes. The latter are computed separately and their rate of change is accounted for in the dynamical equations of motion. The resulting governing equations of motion are presented in a computer form and a possible application problem is proposed.

scholarly journals Use of mixed coordinates in modeling wind turbines including tubular tower

2019 ◽  
Vol 10 (1) ◽  
pp. 35-46
Author(s):  
Ayman Nada ◽  
Ali Al-Shahrani
Keyword(s):  
Wind Turbine ◽  
Equations Of Motion ◽  
Body Motion ◽  
Computational Time ◽  
Proposed Model ◽  
Nodal Model ◽  
Nodal Coordinates ◽  
Mixed Coordinates ◽  
Modal Coordinates ◽  
Turbine Model

Abstract. This paper studies the effect of the tower dynamics upon the wind turbine model by using mixed sets of rigid and/or nodal and/or modal coordinates within multibody system dynamics approach. The nodal model exhibits excellent numerical properties, especially in the case where the rotation of the rotor-blade is extremely high, and therefore, the geometric stiffness effect can not be ignored. However, the use of nodal models to describe the flexibility of large multibody systems produces huge size of coordinates and may consume massive computational time in simulation. On the other side, the dynamics of the tower as well as other components of wind turbine remain exhibit small deformations and can be modeled using Cartesian and/or reduced set of modal coordinates. The paper examines a method of using mixed sets of different coordinates in the same model, although there are differences in the scale and the physical interpretation. The equations of motion of the wind-turbine model is presented based on the floating frame of reference formulation. The mixed coordinates vector consists of three sets: Cartesian coordinates set to present the rigid body motion (nacelle and rotor bodies), elastic nodal coordinates for rotating blades, and reduced-order modal coordinates for low speed components and those that deflect by simple motion shapes (circular Tower). Experimental validation has been carried out successfully, and consequently, the proposed model can be utilized for design process, identification and health monitoring aspects.

Review of Finite Elements Using Absolute Nodal Coordinates for Large-Deformation Problems and Matching Physical Experiments

2005 ◽  
Author(s):  
Wan-Suk Yoo ◽  
Oleg Dmitrochenko ◽  
Dmitry Yu. Pogorelov
Keyword(s):  
Finite Elements ◽  
Large Deformation ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Absolute Nodal Coordinates ◽  
Current State ◽  
Physical Experiments ◽  
Spatial Beams ◽  
Nodal Coordinates ◽  
Large Deformation Problems

A review of the current state of the absolute nodal coordinate formulation (ANCF) is proposed for large-displacement and large-deformation problems in flexible multibody dynamics. The review covers most of the known implementations of different kinds of finite elements including thin and thick planar and spatial beams and plates, their geometrical description inherited from FEM, and formulations of the most important elements of equations of motion. Much attention is also paid to simulation examples that show the reasonableness and accuracy of the formulation applied to real physical problems and that are compared with experiments having significant geometrical non-linearity. Current and further development directions of the ANCF are also briefly outlined.

scholarly journals Driven Pile Effects on Nearby Cylindrical and Semi-Tapered Pile in Sandy Clay

2021 ◽  
Vol 11 (7) ◽  
pp. 2919
Author(s):  
Massamba Fall ◽  
Zhengguo Gao ◽  
Becaye Cissokho Ndiaye
Keyword(s):  
Coupling Effect ◽  
Lateral Displacement ◽  
Bending Moment ◽  
Adaptive Mesh ◽  
Pile Driving ◽  
Arbitrary Lagrangian Eulerian ◽  
Axial Forces ◽  
Tapered Pile ◽  
Driven Pile ◽  
The Impact

A pile foundation is commonly adopted for transferring superstructure loads into the ground in weaker soil. They diminish the settlement of the infrastructure and augment the soil-bearing capacity. This paper emphases the pile-driving effect on an existing adjacent cylindrical and semi-tapered pile. Driving a three-dimensional pile into the ground is fruitfully accomplished by combining the arbitrary Lagrangian–Eulerian (ALE) adaptive mesh and element deletion methods without adopting any assumptions that would simplify the simulation. Axial forces, bending moment, and lateral displacement were studied in the neighboring already-installed pile. An investigation was made into some factors affecting the forces and bending moment, such as pile spacing and the shape of the already-installed pile (cylindrical, tapered, or semi-tapered). An important response was observed in the impact of the driven pile on the nearby existing one, the bending moment and axial forces were not negligible, and when the pile was loaded, it was recommended to consider the coupling effect. Moreover, the adjacent semi-tapered pile was subjected to less axial and lateral movement than the cylindrical one with the same length and volume for taper angles smaller than 1.0°, and vice versa for taper angles greater than 1.4°.

Absolute Nodal Coordinates in Digital Image Correlation

2012 ◽  
Vol 53 (5) ◽  
pp. 807-818 ◽  
Author(s):  
M. Langerholc ◽  
J. Slavič ◽  
M. Boltežar
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Image Correlation ◽  
Absolute Nodal Coordinates ◽  
Nodal Coordinates

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.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

Co-Simulation Procedure for Multibody Reeving Systems

2018 ◽  
Author(s):  
Grzegorz Orzechowski ◽  
Aki M. Mikkola ◽  
José L. Escalona
Keyword(s):  
Multibody System ◽  
Wire Rope ◽  
Rigid Bodies ◽  
Arbitrary Lagrangian Eulerian ◽  
Transverse Deformation ◽  
Absolute Position ◽  
Eulerian Approach ◽  
Wire Ropes ◽  
Simulation Procedure ◽  
Flexible Wire

In this paper, co-simulation procedure for a multibody system that includes reeving mechanism will be introduced. The multibody system under investigation is assumed to have a set of rigid bodies connected by flexible wire ropes using a set of sheaves and reels. In the co-simulation procedure, a wire rope is described using a combination of absolute position coordinates, relative transverse deformation coordinates and longitudinal material coordinates. Accordingly, each wire rope span is modeled using a single two-noded element by employing an Arbitrary Lagrangian-Eulerian approach.

scholarly journals A Simulation Model for Computing the Loads Generated at Landing Site During Helicopter Take-Off or Landing Operation

2019 ◽  
Vol 2019 (2) ◽  
pp. 59-75
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Landing Site ◽  
Simulation Method ◽  
Rigid Bodies ◽  
Landing Gear ◽  
Rotor Blades ◽  
Wind Gust ◽  
The Galerkin Method ◽  
Lumped Masses ◽  
And Control

Summary The paper presents simulation method and results of calculations determining behavior of helicopter and landing site loads which are generated during phase of the helicopter take-off and landing. For helicopter with whirling rotor standing on ground or touching it, the loads of landing gear depend on the parameters of helicopter movement, occurrence of wind gusts and control of pitch angle of the rotor blades. The considered model of helicopter consists of the fuselage and main transmission treated as rigid bodies connected with elastic elements. The fuselage is supported by landing gear modeled by units of spring and damping elements. The rotor blades are modeled as elastic axes with sets of lumped masses of blade segments distributed along them. The Runge-Kutta method was used to solve the equations of motion of the helicopter model. According to the Galerkin method, it was assumed that the parameters of the elastic blade motion can be treated as a combination of its bending and torsion eigen modes. For calculations, data of a hypothetical light helicopter were applied. Simulation results were presented for the cases of landing helicopter touching ground with different vertical speed and for phase of take-off including influence of rotor speed changes, wind gust and control of blade pitch. The simulation method may help to define the limits of helicopter safe operation on the landing surfaces.

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