Structural Dynamics Analysis of Rotating Blades Using Fully Intrinsic Equations, Part I: Formulation and Verification of Single-Load-Path Configurations

2013 ◽  
Vol 58 (3) ◽  
pp. 1-9 ◽  
Author(s):  
Zahra Sotoudeh ◽  
Dewey H. Hodges
Keyword(s):  
Structural Dynamics ◽  
Equations Of Motion ◽  
Turbine Blades ◽  
Rotor Blades ◽  
Load Path ◽  
Dynamics Modeling ◽  
Governing Equations ◽  
Wind Turbine Blades ◽  
First Order ◽  
Infinite Degree

As part of an ongoing investigation into potential advantages of so-called fully intrinsic formulations, this paper presents an application of the fully intrinsic equations of motion and kinematics for beams to rotor blades. A fully intrinsic formulation is devoid of displacement and rotation variables. Although the governing equations are geometrically exact, they are free of the attendant singularities and infinite-degree nonlinearities found in other types of formulations. These nonlinear, first-order partial differential equations are suitable for analyzing initially curved and twisted, anisotropic beams and thus are very attractive for analysis of both helicopter and wind turbine blades. This two-part paper is devoted to the structural dynamics modeling of rotor blades with a wide variety of boundary conditions—in particular hingeless and bearingless rotor configurations. In Part I, the theory and the formulation are presented, along with verification of single-load-path configurations. Part II is devoted to the verification of dual-load-path configurations.

Structural Dynamics Analysis of Rotating Blades Using Fully Intrinsic Equations, Part II: Dual-Load-Path Configurations

2013 ◽  
Vol 58 (3) ◽  
pp. 1-9 ◽  
Author(s):  
Zahra Sotoudeh ◽  
Dewey H. Hodges
Keyword(s):  
Structural Dynamics ◽  
Equations Of Motion ◽  
Turbine Blades ◽  
Rotor Blades ◽  
Load Path ◽  
Dynamics Modeling ◽  
Governing Equations ◽  
Wind Turbine Blades ◽  
First Order ◽  
Infinite Degree

As part of an ongoing investigation into potential advantages of so-called fully intrinsic formulations, this paper presents an application of the fully intrinsic equations of motion and kinematics for beams to rotor blades. A fully intrinsic formulation is devoid of displacement and rotation variables. Although the governing equations are geometrically exact, they are free of the attendant singularities and infinite-degree nonlinearities found in other types of formulations. These nonlinear, first-order partial differential equations are suitable for analyzing initially curved and twisted, anisotropic beams and thus are very attractive for analysis of both helicopter and wind turbine blades. This two-part paper is devoted to the structural dynamics modeling of rotor blades with a wide variety of boundary conditions—in particular hingeless and bearingless rotor configurations. Part II is devoted to verification of certain dual-load-path configurations suggested by Bell Helicopter Textron.

scholarly journals A Robot-Assisted Large-Scale Inspection of Wind Turbine Blades in Manufacturing Using an Autonomous Mobile Manipulator

2021 ◽  
Vol 11 (19) ◽  
pp. 9271
Author(s):  
Heiko Engemann ◽  
Patrick Cönen ◽  
Harshal Dawar ◽  
Shengzhi Du ◽  
Stephan Kallweit
Keyword(s):  
Wind Turbine ◽  
Rotor Blade ◽  
Large Scale ◽  
Turbine Blades ◽  
Rotor Blades ◽  
Mobile Manipulator ◽  
Wind Turbine Blades ◽  
Left Hand ◽  
Planning Strategy ◽  
Execution Strategy

Wind energy represents the dominant share of renewable energies. The rotor blades of a wind turbine are typically made from composite material, which withstands high forces during rotation. The huge dimensions of the rotor blades complicate the inspection processes in manufacturing. The automation of inspection processes has a great potential to increase the overall productivity and to create a consistent reliable database for each individual rotor blade. The focus of this paper is set on the process of rotor blade inspection automation by utilizing an autonomous mobile manipulator. The main innovations include a novel path planning strategy for zone-based navigation, which enables an intuitive right-hand or left-hand driving behavior in a shared human–robot workspace. In addition, we introduce a new method for surface orthogonal motion planning in connection with large-scale structures. An overall execution strategy controls the navigation and manipulation processes of the long-running inspection task. The implemented concepts are evaluated in simulation and applied in a real-use case including the tip of a rotor blade form.

scholarly journals Damage tolerance and structural monitoring for wind turbine blades

2015 ◽  
Vol 373 (2035) ◽  
pp. 20140077 ◽  
Author(s):  
M. McGugan ◽  
G. Pereira ◽  
B. F. Sørensen ◽  
H. Toftegaard ◽  
K. Branner
Keyword(s):  
Wind Turbine ◽  
Damage Tolerance ◽  
Turbine Blades ◽  
Turbine Rotor ◽  
Rotor Blades ◽  
Offshore Wind ◽  
Tolerance Index ◽  
Wind Turbine Blades ◽  
Efficient Operation ◽  
Reliable Design

The paper proposes a methodology for reliable design and maintenance of wind turbine rotor blades using a condition monitoring approach and a damage tolerance index coupling the material and structure. By improving the understanding of material properties that control damage propagation it will be possible to combine damage tolerant structural design, monitoring systems, inspection techniques and modelling to manage the life cycle of the structures. This will allow an efficient operation of the wind turbine in terms of load alleviation, limited maintenance and repair leading to a more effective exploitation of offshore wind.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

Optimal Tuning of Centrifugal Pendulum Vibration Absorbers

2013 ◽  
Author(s):  
Chengzhi Shi ◽  
Robert G. Parker ◽  
Steven W. Shaw
Keyword(s):  
Equations Of Motion ◽  
Turbine Blades ◽  
Vibration Absorbers ◽  
Wind Turbine Blades ◽  
Optimal Tuning ◽  
Translational Vibration ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Rotational Vibration ◽  
Reaction Forces ◽  
Analytical Proof

This note provides an analytical proof of the optimal tuning of centrifugal pendulum vibration absorbers (CPVAs) to reduce in-plane translational and rotational vibration for a rotor with N cyclically symmetric substructures attached to it. The reaction forces that the substructures (helicopter or wind turbine blades, for example) exert on the rotor are first analyzed. The linearized equations of motion for the vibration are then solved by a gyroscopic system modal analysis procedure. The solutions show that the rotor translational vibration at order j is reduced when one group of CPVAs is tuned to order jN − 1 and the other is tuned to order jN + 1. Derivation of this result is not available in the literature. The current derivation also yields the better known result that tuning CPVAs to order jN reduces rotational rotor vibration at order j.

scholarly journals Active Aerodynamic Load Control of Wind Turbine Blades

2007 ◽  
Author(s):  
Dale E. Berg ◽  
Jose R. Zayas ◽  
Donald W. Lobitz ◽  
C. P. van Dam ◽  
Raymond Chow ◽  
...  
Keyword(s):  
Turbine Blades ◽  
Cost Effective ◽  
Rotor Blades ◽  
Load Control ◽  
Aerodynamic Load ◽  
Wind Turbine Blades ◽  
Trailing Edge ◽  
Trailing Edge Flaps ◽  
Control Devices ◽  
The Cost

The cost of wind-generated electricity can be reduced by mitigating fatigue loads acting on the rotor blades of wind turbines. One way to accomplish this is with active aerodynamic load control devices that supplement the load control obtainable with current full-span pitch control. Thin airfoil theory suggests that such devices will be more effective if they are located near the blade trailing edge. While considerable effort in Europe is concentrating on the capability of conventional trailing edge flaps to control these loads, our effort is concentrating on very small devices, called microtabs, that produce similar effects. This paper discusses the work we have done on microtabs, including a recent simulation that illustrates the large impact these small devices can exert on a blade. Although microtabs show promise for this application, significant challenges must be overcome before they can be demonstrated to be a viable, cost-effective technology.

scholarly journals Nonlinear Vibration of the Blade with Variable Thickness

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaobo Jie ◽  
Wei Zhang ◽  
Jiajia Mao
Keyword(s):  
Variable Thickness ◽  
Conical Shell ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Dynamic Responses ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Relationship ◽  
Governing Equations ◽  
First Order

In this paper, the nonlinear dynamic responses of the blade with variable thickness are investigated by simulating it as a rotating pretwisted cantilever conical shell with variable thickness. The governing equations of motion are derived based on the von Kármán nonlinear relationship, Hamilton’s principle, and the first-order shear deformation theory. Galerkin’s method is employed to transform the partial differential governing equations of motion to a set of nonlinear ordinary differential equations. Then, some important numerical results are presented in terms of significant input parameters.

scholarly journals Experimental Investigation of Finite Aspect Ratio Cylindrical Bodies for Accelerated Wind Applications

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 25 ◽  
Author(s):  
Michael Parker ◽  
Douglas Bohl
Keyword(s):  
Aspect Ratio ◽  
Wind Turbine ◽  
Turbine Blades ◽  
Cylindrical Body ◽  
Turbine Rotor ◽  
Flow Speed ◽  
The Body ◽  
Rotor Blades ◽  
Wind Turbine Blades ◽  
Smooth Cylinder

The placement of a cylindrical body in a flow alters the velocity and pressure fields resulting in a local increase in the flow speed near the body. This interaction is of interest as wind turbine rotor blades could be placed in the area of increased wind speed to enhance energy harvesting. In this work the aerodynamic performance of two short aspect ratio (AR = 0.93) cylindrical bodies was evaluated for potential use in “accelerated wind” applications. The first cylinder was smooth with a constant diameter. The diameter of the second cylinder varied periodically along the span forming channels, or corrugations, where wind turbine blades could be placed. Experiments were performed for Reynolds numbers ranging from 1 × 105 to 9 × 105. Pressure distributions showed that the smooth cylinder had lower minimum pressure coefficients and delayed separation compared to the corrugated cylinder. Velocity profiles showed that the corrugated cylinder had lower peak speeds, a less uniform profile, and lower kinetic energy flux when compared to the smooth cylinder. It was concluded that the smooth cylinder had significantly better potential performance in accelerated wind applications than the corrugated cylinder.

Fluid-Structure Interaction Forces at Pump-Impeller-Shroud Surfaces for Rotordynamic Calculations

1989 ◽  
Vol 111 (3) ◽  
pp. 216-225 ◽  
Author(s):  
D. W. Childs
Keyword(s):  
Equations Of Motion ◽  
Perturbation Expansion ◽  
Momentum Equation ◽  
Governing Equations ◽  
Pump Impeller ◽  
First Order ◽  
Pressure Distributions ◽  
Pump Housing ◽  
Reaction Forces ◽  
Ring Seal

Governing equations of motion are derived for a bulk-flow model of the leakage path between an impeller shroud and a pump housing. The governing equations consist of a path-momentum, a circumferential-momentum, and a continuity equation. The fluid annulus between the impeller shroud and pump housing is assumed to be circumferentially symmetric when the impeller is centered; i.e., the clearance can vary along the pump axis but does not vary in the circumferential direction. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leakage rate and the circumferential and path velocity distributions and pressure distributions for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to either a radial-displacement perturbation or a tilt perturbation of the impeller. Integration of the perturbed pressure and shear-stress distribution acting on the rotor yields the reaction forces and moments acting on the impeller face. Calculated results yield predictions of possible resonance peaks of the fluid within the annulus formed by the impeller shroud and housing. Centrifugal acceleration terms in the path-momentum equation are the physical origin of these unexpected predictions. For normalized tangential velocities at the inlet to the annulus, uθ0(0) = Uθ0(0)/Riω of 0.5, the phenomenon is relatively minor. As uθ0(0) is increased to 0.7, sharp peaks are predicted. Comparisons for rotordynamic coefficient predictions with test results of Bolleter et al. show reasonable agreement for cross-coupled stiffness and direct damping terms. Calculated results are provided which make comparisons between seal forces and shroud forces for a typical impeller/wear-ring-seal combination.

Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation

2017 ◽  
Vol 29 (5) ◽  
pp. 774-786 ◽  
Author(s):  
M Arefi ◽  
MH Zamani ◽  
M Kiani
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
First Order ◽  
Size Dependent ◽  
Inhomogeneity Parameter ◽  
Exponentially Graded

This work is devoted to the free vibration nonlocal analysis of an elastic three-layered nanoplate with exponentially graded graphene sheet core and piezomagnetic face-sheets. The rectangular elastic three-layered nanoplate is resting on Pasternak’s foundation. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on first-order shear deformation theory. In addition, Eringen’s nonlocal piezo-magneto-elasticity theory is used to consider size effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is scrutinized for different side length ratio, nonlocal parameter, inhomogeneity parameter, and parameters of foundation numerically. The comparison with various references is performed for validation of our analytical results.

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