A Four-Rigid-Body Element Model and Computer Simulation for Flexible Components of Wind Turbines

2011 ◽  
Author(s):  
Songyi Jiang ◽  
Shanzhong Shawn Duan
Keyword(s):  
Rigid Body ◽  
Wind Turbines ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Element Model ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Horizontal Axis Wind Turbine ◽  
Body Element ◽  
Flexible Components

In this paper, a four-rigid-body element model is presented for description of flexible components of a horizontal axis wind turbine (HAWT). The element consists of four rigid bodies arranged in a chain structure fashion. The bodies of each element are linked by two universal joints at two ends, and one cylindrical joint at the middle. Thus each element has six degrees of freedom. They are four degrees of freedom for bending, one degree of freedom for torsion, and one degree of freedom for axial stretching. For each degree of freedom, a spring is used to describe the stiffness of the component. Stiffness of each spring is obtained by using potential energy equivalence between a Timoshenko beam and these springs. With these considerations, flexible components of a HAWT such as blades and tower may then be represented by connecting several such elements together. Based on four-rigid-body element model, the tower and blades of a HAWT are constructed. Their equations of motion are then derived via Kane’s dynamical method. Commercial computational multibody dynamic analysis software Autolev has been used for motion simulation of tower and blades under given initial conditions. Simulation results associated with the tower indicate that four-rigid-body element model is suitable for analysis of dynamic loads, modal, and vibration of wind turbines with respect to fixed and moving references at high computational efficiency and low simulation costs. The approach is also a good candidate for simulating dynamical behaviors of wind turbines and preventing their fatigue failures in time domain.

A Multibody Dynamics Approach for Vibration Analysis of Horizontal Axis Wind Turbine Blades

2016 ◽  
Author(s):  
Songyi Jiang ◽  
Shanzhong (Shawn) Duan
Keyword(s):  
Wind Turbine ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Turbine Blades ◽  
Chain Structure ◽  
Rigid Bodies ◽  
Horizontal Axis ◽  
Degree Of Freedom ◽  
Horizontal Axis Wind Turbine ◽  
Segment Model

This paper presents a 4-rigidbody segment model to describe a generic flexible blade of a horizontal axis wind turbine (HAWT). The element is made up of four rigid bodies in a chain structure fashion. The bodies of each element are connected by two universal joints at two ends, and one cylindrical joint in the middle. So each element possesses six degrees of freedom, including four degrees of freedom for bending, one degree of freedom for axial stretching, and one degree of freedom for torsion. A spring is applied for each degree of freedom to describe the stiffness of the component. Through potential energy equivalence between a Timoshenko beam and these springs, the stiffness of each spring is calculated. A blade can then be simplified to several such elements connecting together. With the 4-rigidbody segment model, blades of a HAWT are built up. Their equations of motion are then derived through Kane’s equations. The commercial computational multibody dynamic analysis software Autolev is applied for motion and vibration simulation of blades under given initial conditions. Simulation results indicate that the 4-rigidbody segment model is appropriate to analyze dynamic loads, modal, and vibration of HAWT blades for fixed and moving references at high computational efficiency and low simulation costs. The method can also be served as a good solution to simulate dynamical behaviors of wind turbines and avoid their fatigue failures in time domain.

On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

Contact-space resolution model for a physically consistent view of simultaneous collisions in articulated-body systems: theory and experimental results

2020 ◽  
Vol 39 (10-11) ◽  
pp. 1239-1258
Author(s):  
Shameek Ganguly ◽  
Oussama Khatib
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Rigid Bodies ◽  
Computationally Efficient ◽  
Space Resolution ◽  
Resolution Model ◽  
Space Dynamics ◽  
Contact Space

Multi-surface interactions occur frequently in articulated-rigid-body systems such as robotic manipulators. Real-time prediction of contact-interaction forces is challenging for systems with many degrees of freedom (DOFs) because joint and contact constraints must be enforced simultaneously. While several contact models exist for systems of free rigid bodies, fewer models are available for articulated-body systems. In this paper, we extend the method of Ruspini and Khatib and develop the contact-space resolution (CSR) model by applying the operational space theory of robot manipulation. Through a proper choice of contact-space coordinates, the projected dynamics of the system in the contact space is obtained. We show that the projection into the dynamically consistent null space preserves linear and angular momentum in a subspace of the system dynamics complementary to the joint and contact constraints. Furthermore, we illustrate that a simultaneous collision event between two articulated bodies can be resolved as an equivalent simultaneous collision between two non-articulated rigid bodies through the projected contact-space dynamics. Solving this reduced-dimensional problem is computationally efficient, but determining its accuracy requires physical experimentation. To gain further insights into the theoretical model predictions, we devised an apparatus consisting of colliding 1-, 2-, and 3-DOF articulated bodies where joint motion is recorded with high precision. Results validate that the CSR model accurately predicts the post-collision system state. Moreover, for the first time, we show that the projection of system dynamics into the mutually complementary contact space and null space is a physically verifiable phenomenon in articulated-rigid-body systems.

Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Line Trajectories

1987 ◽  
Vol 109 (1) ◽  
pp. 116-124 ◽  
Author(s):  
Ashitava Ghosal ◽  
Bernard Roth
Keyword(s):  
Rigid Body ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Two Degrees Of Freedom ◽  
Global Properties ◽  
New Concepts ◽  
Line Trajectory

A general framework is presented for the study of the properties of trajectories generated by lines embedded in rigid bodies undergoing multi-degrees-of-freedom motions. Several new concepts, such as a line’s angular and linear velocities and accelerations, are introduced and used to (1) characterize the differences between line trajectories generated by different mechanisms; (2) distinguish trajectories generated by different lines in the same rigid body; (3) distinguish properties at different positions in the same trajectory. Line trajectories are classified according to the number of degrees of freedom of the motion, and local and global properties are discussed. These techniques are illustrated in an example of a line trajectory generated by a two-degrees-of-freedom manipulator.

Rigid body refinements in GSAS/EXPGUI

2011 ◽  
Vol 26 (S1) ◽  
pp. S13-S21 ◽  
Author(s):  
Charles H. Lake ◽  
Brian H. Toby
Keyword(s):  
Rigid Body ◽  
Software Package ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Atomic Motion ◽  
Bond Lengths

Rigid bodies provide a way to simplify the model used in a crystallographic refinement by removing parameters that describe degrees of freedom that are unlikely to change based on chemical experience. The GSAS software package provides a powerful implementation of rigid bodies that allows for refinement of classes of bond lengths, grouping of bodies to further reduce parameterization and where atomic motion can be described from group displacement parameters (TLS) representation. However, use of rigid bodies in GSAS is complex to learn and time-consuming to perform. This paper describes how the rigid body definition process has been simplified and extended through implementation in the EXPGUI interface to GSAS.

METHODS OF QUALITATIVE ANALYSIS IN THE PROBLEM OF RIGID BODY MOTION IN MEDIUM

2011 ◽  
Vol 21 (10) ◽  
pp. 2955-2961 ◽  
Author(s):  
VITALY A. SAMSONOV ◽  
MARAT Z. DOSAEV ◽  
YURY D. SELYUTSKIY
Keyword(s):  
Qualitative Analysis ◽  
Rigid Body ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Classical Problem ◽  
Rigid Body Motion ◽  
Horizontal Axis ◽  
Body Motion ◽  
Horizontal Axis Wind Turbine ◽  
And Behavior

The present paper describes the application of methods of qualitative analysis in the classical problem of rigid body motion in medium. Three particular problems are used as examples: bolides flight, galloping of aeroelastic constructions, and behavior of horizontal axis wind turbine. It is shown that this approach reveals the general properties of the behavior of objects studied, such as impossibility of translational deceleration of bolides and the presence of hysteretic phenomena in the operation of wind turbines.

scholarly journals Exact Augmented Perpetual Manifolds: Corollary about Different Mechanical Systems with Exactly the Same Motions

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Fotios Georgiades
Keyword(s):  
Differential Equation ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Mechanical Engineering ◽  
Initial Conditions ◽  
Mechanical Systems ◽  
Perfect Agreement ◽  
Ongoing Research ◽  
Rigid Body Motions ◽  
Perpetual Points

Perpetual points have been defined in mathematics recently, and they arise by setting accelerations and jerks equal to zero for nonzero velocities. The significance of perpetual points for the dynamics of mechanical systems is ongoing research. In the linear natural, unforced mechanical systems, the perpetual points form the perpetual manifolds and are associated with rigid body motions. Extending the definition of perpetual manifolds, by considering equal accelerations, in a forced mechanical system, but not necessarily zero, the solutions define the augmented perpetual manifolds. If the displacements are equal and the velocities are equal, the state space defines the exact augmented perpetual manifolds obtained under the conditions of a theorem, and a characteristic differential equation defines the solution. As a continuation of the theorem herein, a corollary proved that different mechanical systems, in the exact augmented perpetual manifolds, have the same general solution, and, in case of the same initial conditions, they have the same motion. The characteristic differential equation leads to a solution defining the augmented perpetual submanifolds and the solution of several types of characteristic differential equations derived. The theory in a few mechanical systems with numerical simulations is verified, and they are in perfect agreement. The theory developed herein is supplementing the already-developed theory of augmented perpetual manifolds, which is of high significance in mathematics, mechanics, and mechanical engineering. In mathematics, the framework for specific solutions of many degrees of freedom nonautonomous systems is defined. In mechanics/physics, the wave-particle motions are of significance. In mechanical engineering, some mechanical system’s rigid body motions without any oscillations are the ultimate ones.

Selective Sensitivity for Model Updating With Modal Data

1995 ◽  
Author(s):  
Muzio M. Gola ◽  
Aurelio Somà
Keyword(s):  
Degrees Of Freedom ◽  
Model Updating ◽  
Structural Parameters ◽  
Selection Procedure ◽  
Element Model ◽  
Degree Of Freedom ◽  
Data Set ◽  
Minimum Number ◽  
Selective Sensitivity ◽  
Updating Procedure

Abstract In the present work a criterion for the minimum measured data set (modes and degree of freedom) required for a successful updating is established in the case of the inverse sensitivity method. The finite element model is used as a tool for the pre-analysis in order to plan the modal experiments, the selection of modes and degree of freedom to put into play in the updating procedure are obtained though the evaluation covariance matrix of the estimated parameters. A two stage procedure is proposed, in the first part of the work the modal sensitivity problem is reviewed in order to illustrate a systematic procedure capable of enucleating the set of modes that effectively contributes to the updating procedure. Then the procedure is extended to the determination of the minimum number of degrees of freedom to be measured in relation to a desired upper limit for the standard deviation of the structural parameters which are to be updated. Simple frame structures with different parameter locations are used as examples, the convergence on two parameters maps is used as demonstration of the powerful of the selection procedure to predict the chances of the successful updating.

scholarly journals Vector Rotators of Rigid Body Dynamics with Coupled Rotations around Axes without Intersection

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Katica R. (Stevanović) Hedrih ◽  
Ljiljana Veljović
Keyword(s):  
Nonlinear Dynamics ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Rigid Body Dynamics ◽  
Degree Of Freedom ◽  
Inertia Moment ◽  
Vector Method ◽  
Mass Moment ◽  
Body Dynamics ◽  
Angular Velocities

Vector method based on mass moment vectors and vector rotators coupled for pole and oriented axes is used for obtaining vector expressions for kinetic pressures on the shaft bearings of a rigid body dynamics with coupled rotations around axes without intersection. Mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis are defined by K. Hedrih in 1991. These kinematical vectors rotators are defined for a system with two degrees of freedom as well as for rheonomic system with two degrees of mobility and one degree of freedom and coupled rotations around two coupled axes without intersection as well as their angular velocities and intensity. As an example of defined dynamics, we take into consideration a heavy gyrorotor disk with one degree of freedom and coupled rotations when one component of rotation is programmed by constant angular velocity. For this system with nonlinear dynamics, a series of tree parametric transformations of system nonlinear dynamics are presented. Some graphical visualization of vector rotators properties are presented too.

Vibration Analysis of Wind Turbine via a Multibody Dynamics Approach

2009 ◽  
Author(s):  
Shanzhong Shawn Duan
Keyword(s):  
Potential Energy ◽  
Data Storage ◽  
Wind Turbines ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Beam Model ◽  
Element Analysis ◽  
Plastic Properties ◽  
Lumped Model

In this paper, a lumped model of horizontal axis wind turbines (HAWT) is presented for modal and vibration analysis. Motion modes such as tower fore and aft, tower side to side, blade flap, blade edge, and tower axial torsion are considered. A multibody modeling approach is used to represent the structure and components of a HAWT. A continuous component in wind turbines may be divided as discrete rigid bodies linked by proper types of joints with springs and dampers for couplings. Joints are used to describe the degrees of freedom of the component’s deformation. Springs and dampers are added to accommodate the component’s elastic and plastic properties. For example the tower is modeled as discrete rigid bodies linked by universal joints, which allow three degrees of freedom (DOF) from one torsional and two bending motions of the tower, and torsional springs are added between bodies to accommodate elastic property of the tower. The potential energy of the springs equals to the potential energy of the continuous tower, which may be represented by Timoshenko-beam model. Thus the spring stiffness is calculated based on the potential energy equivalence. Equations of motion of wind turbines are derived via Kane’s dynamical method. Modal and vibration analysis are further carried out based on this lumped multibody model. As a comparison with other approaches such as finite element analysis (FEA) that requires high data storage and long simulation time, this approach may provide a low fidelity simulation model and tool, which is suitable for analysis of dynamic loads, modal, and vibration of wind turbines with respect to fixed and moving references at high computational efficiency and low simulation costs. The approach is also a good candidate for simulating dynamical behaviors of wind turbines and preventing their fatigue failures in time domain.

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