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.

scholarly journals Some Progress on Parallel Modal and Vibration Analysis Using the JAUMIN Framework

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xuanhua Fan ◽  
Keying Wang ◽  
Shifu Xiao ◽  
Qingkai Liu ◽  
Zeyao Mo
Keyword(s):  
Vibration Analysis ◽  
Numerical Experiments ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
High Efficiency ◽  
Parallel Implementation ◽  
Solution System ◽  
Element Analysis ◽  
Parallel Solution ◽  
Complex Equipment

In the development of large and complex equipment, a large-scale finite element analysis (FEA) with high efficiency is often strongly required. This paper provides some progress on parallel solution of large-scale modal and vibration FE problems. Some predominant algorithms for modal and vibration analysis are firstly reviewed and studied. Based on the newly developed JAUMIN framework, the corresponding procedures are developed and integrated to form a parallel modal and vibration solution system; the details of parallel implementation are given. Numerical experiments are carried out to evaluate the parallel scalability of our procedures, and the results show that the maximum solution scale attains ninety million degrees of freedom (DOFs) and the maximum parallel CPU processors attain 8192 with favorable computing efficiency.

Free Vibration Analysis of Frame Structures Using BSWI Method

2008 ◽  
Author(s):  
Farhang Daneshmand ◽  
Abdolaziz Abdollahi ◽  
Mehdi Liaghat ◽  
Yousef Bazargan Lari
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Frame Structures ◽  
Shape Functions ◽  
Element Analysis ◽  
B Spline ◽  
Multi Level ◽  
Element Method

Vibration analysis for complicated structures, or for problems requiring large numbers of modes, always requires fine meshing or using higher order polynomials as shape functions in conventional finite element analysis. Since it is hard to predict the vibration mode a priori for a complex structure, a uniform fine mesh is generally used which wastes a lot of degrees of freedom to explore some local modes. By the present wavelets element approach, the structural vibration can be analyzed by coarse mesh first and the results can be improved adaptively by multi-level refining the required parts of the model. This will provide accurate data with less degrees of freedom and computation. The scaling functions of B-spline wavelet on the interval (BSWI) as trial functions that combines the versatility of the finite element method with the accuracy of B-spline functions approximation and the multiresolution strategy of wavelets is used for frame structures vibration analysis. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. To verify the proposed method, the vibrations of a cantilever beam and a plane structures are studied in the present paper. The analyses and results of these problems display the multi-level procedure and wavelet local improvement. The formulation process is as simple as the conventional finite element method except including transfer matrices to compute the coupled effect between different resolution levels. This advantage makes the method more competitive for adaptive finite element analysis. The results also show good agreement with those obtained from the classical finite element method and analytical solutions.

Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part I — General Theory

1992 ◽  
Author(s):  
Jiechi Xu ◽  
Joseph R. Baumgarten
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Local Level ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Moving Frame ◽  
Element Analysis ◽  
Highly Nonlinear ◽  
Geometric Boundary ◽  
System Equations

Abstract In the present paper a general systematic modeling procedure has been conducted in deriving dynamic equations of motion using Lagrange’s approach for a spatial multibody structural system involving rigid bodies and elastic members. Both the rigid body degrees of freedom and the elastic degrees of freedom are considered as unknown generalized coordinates of the entire system in order to reflect the nature of mutually coupled rigid body and elastic motions. The assumption of specified rigid body gross motion is no longer necessary in the equation derivation and the resulting differential equations are highly nonlinear. Finite element analysis (FEA) with direct stiffness method has been employed to model the flexible substructures. Nonlinear coupling terms between the rigid body and elastic motions are fully derived and are explicitly expressed in matrix form. The equations of motion of each individual subsystem are formulated based on a moving frame instead of a traditional inertial frame. These local level equations of motion are assembled to obtain the system equations with the implementation of geometric boundary conditions by means of a compatibility matrix.

Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre ◽  
Olivier Poudou
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Vibration Response ◽  
New Method ◽  
Beam Model ◽  
Element Analysis

The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig–Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical degrees of freedom. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multiharmonic hybrid frequency∕time-domain technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack, shifts in resonant frequencies, and the existence of multiple solutions. For the cases considered, it is found that the nonlinear vibration response exhibits the jump phenomenon only when rotation is included in the model.

Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades

2006 ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Piecewise Linear ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
New Method ◽  
Beam Model ◽  
Element Analysis

The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig-Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical DOF. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multi-harmonic, hybrid frequency/time-domain (HFT) technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack and the existence of multiple solutions.

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Quentin T. Aten ◽  
Shannon A. Zirbel ◽  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Potential Energy ◽  
Equilibrium Position ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Virtual Work ◽  
Compliant Mechanism ◽  
Numerical Approach ◽  
Element Analysis ◽  
Loop Equation ◽  
Body Model

An underactuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudorigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for underactuated 1-DOF and 2-DOF pseudorigid-body models. Experimental force-deflection data are presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudorigid-body model, a 13-DOF pseudorigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with nonlinear finite element analysis and experimental force-displacement data.

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 two degrees of freedom comb capacitive-type accelerometer with low cross-axis sensitivity

2019 ◽  
Vol 13 (3) ◽  
pp. 5334-5346
Author(s):  
M. N. Nguyen ◽  
L. Q. Nguyen ◽  
H. M. Chu ◽  
H. N. Vu
Keyword(s):  
Degrees Of Freedom ◽  
Proof Mass ◽  
Vibration Modes ◽  
Electrode Structure ◽  
Element Analysis ◽  
Mechanical Coupling ◽  
Fully Differential ◽  
Mode Effects ◽  
The Finite Element Analysis ◽  
Cross Axis

In this paper, we report on a SOI-based comb capacitive-type accelerometer that senses acceleration in two lateral directions. The structure of the accelerometer was designed using a proof mass connected by four folded-beam springs, which are compliant to inertial displacement causing by attached acceleration in the two lateral directions. At the same time, the folded-beam springs enabled to suppress cross-talk causing by mechanical coupling from parasitic vibration modes. The differential capacitor sense structure was employed to eliminate common mode effects. The design of gap between comb fingers was also analyzed to find an optimally sensing comb electrode structure. The design of the accelerometer was carried out using the finite element analysis. The fabrication of the device was based on SOI-micromachining. The characteristics of the accelerometer have been investigated by a fully differential capacitive bridge interface using a sub-fF switched-capacitor integrator circuit. The sensitivities of the accelerometer in the two lateral directions were determined to be 6 and 5.5 fF/g, respectively. The cross-axis sensitivities of the accelerometer were less than 5%, which shows that the accelerometer can be used for measuring precisely acceleration in the two lateral directions. The accelerometer operates linearly in the range of investigated acceleration from 0 to 4g. The proposed accelerometer is expected for low-g applications.

Driving Torsion Scans with Wavefront Propagation

2020 ◽  
Author(s):  
Yudong Qiu ◽  
Daniel Smith ◽  
Chaya Stern ◽  
mudong feng ◽  
Lee-Ping Wang
Keyword(s):  
Potential Energy ◽  
Force Field ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Initial Guess ◽  
Field Development ◽  
Force Field Development ◽  
Wavefront Propagation ◽  
Open Source Software Package

<div>The parameterization of torsional / dihedral angle potential energy terms is a crucial part of developing molecular mechanics force fields.</div><div>Quantum mechanical (QM) methods are often used to provide samples of the potential energy surface (PES) for fitting the empirical parameters in these force field terms.</div><div>To ensure that the sampled molecular configurations are thermodynamically feasible, constrained QM geometry optimizations are typically carried out, which relax the orthogonal degrees of freedom while fixing the target torsion angle(s) on a grid of values.</div><div>However, the quality of results and computational cost are affected by various factors on a non-trivial PES, such as dependence on the chosen scan direction and the lack of efficient approaches to integrate results started from multiple initial guesses.</div><div>In this paper we propose a systematic and versatile workflow called \textit{TorsionDrive} to generate energy-minimized structures on a grid of torsion constraints by means of a recursive wavefront propagation algorithm, which resolves the deficiencies of conventional scanning approaches and generates higher quality QM data for force field development.</div><div>The capabilities of our method are presented for multi-dimensional scans and multiple initial guess structures, and an integration with the MolSSI QCArchive distributed computing ecosystem is described.</div><div>The method is implemented in an open-source software package that is compatible with many QM software packages and energy minimization codes.</div>

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

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