Second-Order Perturbation Analysis of In-Plane Blade-Hub Dynamics of Horizontal-Axis Wind Turbines

2018 ◽  
Author(s):  
Ayse Sapmaz ◽  
Brian F. Feeny
Keyword(s):  
Perturbation Analysis ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Second Order ◽  
Horizontal Axis ◽  
Dynamic Responses ◽  
Order Perturbation ◽  
Resonance Case ◽  
Horizontal Axis Wind Turbine ◽  
Rotor Angle

This paper deals with a second-order perturbation analysis of the in-plane dynamic responses of both tuned and mistuned three-blade-hub horizontal-axis wind-turbine equations. The blades are under effect of gravitational and cyclic aerodynamics forces and centrifugal forces. Although the blades and hub equations are coupled, they can be decoupled by changing the independent variable from time to rotor angle and by using a small parameter approximation. A second-order method of multiple scales is applied in the rotor-angle domain to analyze in-plane blade-hub dynamics. A superharmonic resonance case at one third the natural frequency was revealed. This resonance case was not captured by a first-order perturbation expansion. The relationship between response amplitude and frequency is studied. The effect of blade mistuning on the coupled blade-hub dynamics are taken into account.

Second Order Perturbation Analysis of a Forced Nonlinear Mathieu Equation

2012 ◽  
Author(s):  
Venkatanarayanan Ramakrishnan ◽  
Brian F. Feeny
Keyword(s):  
Perturbation Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Mathieu Equation ◽  
Second Order ◽  
Order Perturbation ◽  
Cubic Nonlinearity ◽  
First Order ◽  
Order Expansion ◽  
Direct Forcing

The present study deals with the response of a forced nonlinear Mathieu equation. The equation considered has parametric excitation at the same frequency as direct forcing and also has cubic nonlinearity and damping. A second-order perturbation analysis using the method of multiple scales unfolds numerous resonance cases and system behavior that were not uncovered using first-order expansions. All resonance cases are analyzed. We numerically plot the frequency response of the system. The existence of a superharmonic resonance at one third the natural frequency was uncovered analytically for linear system. (This had been seen previously in numerical simulations but was not captured in the first-order expansion.) The effect of different parameters on the response of the system previously investigated are revisited.

In-Plane Blade-Hub Dynamics of Horizontal-Axis Wind Turbine With Mistuned Blades

2017 ◽  
Author(s):  
Ayse Sapmaz ◽  
Gizem D. Acar ◽  
Brian Feeny
Keyword(s):  
Wind Turbine ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Turbine Blades ◽  
Horizontal Axis ◽  
Wind Turbine Blades ◽  
Horizontal Axis Wind Turbine ◽  
Direct Excitation ◽  
Independent Variable ◽  
Rotor Angle

Understanding vibration of the wind turbine blades is of fundamental importance. This paper regards the effect of blade mistuning on the coupled blade-hub dynamics. Unavoidably, at any stage of the wind turbine, the set of blades will not be precisely identical due to the inhomogeneous material, manufacturer tolerances, etc. This paper is based on blade-hub dynamics of a horizontal-axis wind turbine with mistuned blade. The equations of motion are derived for the wind turbine blades and hub exposed to centrifugal effects and gravitational and cyclic aerodynamic forces. The equations are coupled. To decoupled them, the independent variable is changed from time to rotor angle. The resulting blade equations include parametric and direct excitation terms. The method of multiple scales is applied to examine response of the system. This analysis shows that superharmonic and primary resonances exist and are influenced by the mistuning. Resonance cases and the relations between response amplitude and frequency are studied.

Numerical Study of Superharmonic Resonances in a Mistuned Horizontal-Axis Wind-Turbine Blade-Rotor Set

2019 ◽  
Author(s):  
Ayse Sapmaz ◽  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Wind Turbine ◽  
Initial Conditions ◽  
Numerical Study ◽  
Horizontal Axis ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
First Order ◽  
Direct Excitation ◽  
Rotor Angle ◽  
Perturbation Solutions

Abstract This paper is on a simplified model of an in-plane blade-hub dynamics of a horizontal-axis wind turbine with a mistuned blade. The model has cyclic parametric and direct excitation due to gravity and aerodynamics. This work follows up a previous perturbation study applied to the blade equations written in the rotor-angle domain and decoupled from the hub, in which superharmonic and primary resonances were analyzed. In this work, the effects of mistuning, damping, and forcing level are illustrated. The first-order perturbation solutions are verified with comparisons to numerical simulations at superharmonic resonance of order two. Additionally, the effect of rotor loading on the rotor speed and blade amplitudes is investigated for different initial conditions and mistuning cases.

scholarly journals Investigating the loads and performance of a model horizontal axis wind turbine under reproducible IEC extreme operational conditions

2021 ◽  
Vol 6 (2) ◽  
pp. 477-489
Author(s):  
Kamran Shirzadeh ◽  
Horia Hangan ◽  
Curran Crawford ◽  
Pooyan Hashemi Tari
Keyword(s):  
Power Generation ◽  
Wind Turbine ◽  
Extreme Event ◽  
Horizontal Axis ◽  
Force Balance ◽  
Dynamic Responses ◽  
Horizontal Shear ◽  
Horizontal Axis Wind Turbine ◽  
Operational Conditions ◽  
Wind Shears

Abstract. The power generation and loading dynamic responses of a 2.2 m diameter horizontal axis wind turbine (HAWT) under some of the IEC 61400-1 transient extreme operational conditions, more specifically extreme wind shears (EWSs) and extreme operational gust (EOG), that were reproduced at the WindEEE Dome at Western University were investigated. The global forces were measured by a multi-axis force balance at the HAWT tower base. The unsteady horizontal shear induced a significant yaw moment on the rotor with a dynamic similar to that of the extreme event without affecting the power generation. The EOG severely affected all the performance parameters of the turbine.

Parametric Resonances of a Three-Blade-Rotor System With Reference to Wind Turbines

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Gizem D. Acar ◽  
Mustafa A. Acar ◽  
Brian F. Feeny
Keyword(s):  
Multiple Scales ◽  
Rotor System ◽  
Degree Of Freedom ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
Direct Excitation ◽  
Parametric Resonances ◽  
Parametric Effects ◽  
Rotor Angle ◽  
First Order Method

Abstract Coupled blade-hub dynamics of a coupled three-blade-rotor system with parametric stiffness, which is similar to a horizontal-axis wind turbine, is studied. Blade equations have parametric and direct excitation terms due to gravity and are coupled through the hub equation. For a single degree-of-freedom blade model with only in-plane transverse vibrations, the reduced-order model shows parametric resonances. A small parameter is established for large blades, which enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. Therefore, it is more convenient to use the rotor angle as the independent variable. By expressing the system dynamics in the rotor angle domain and assuming small variations in rotor speed, the blade equations are decoupled from the rotor equation. The interdependent blade equations constitute a three-degree-of-freedom system with periodic parametric and direct excitation. The response is analyzed by using a first-order method of multiple scales (MMS). The system has a superharmonic and a subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitude-frequency relations and stabilities of these resonances are studied. The MMS solutions are compared with numerical simulations for verification.

Second-Order Perturbation Analysis of Low-Amplitude Traveling Waves in a Periodic Nonlinear Chain

2013 ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Traveling Waves ◽  
Perturbation Analysis ◽  
Multiple Scales ◽  
Periodic Structures ◽  
Second Order ◽  
Quadratic Nonlinearity ◽  
Wave Number ◽  
Nonlinear Chain ◽  
Multiple Scales Analysis ◽  
Low Amplitude

Traveling waves in one-dimensional nonlinear periodic structures are investigated for low-amplitude oscillations using perturbation analysis. We use second-order multiple scales analysis to capture the effects of quadratic nonlinearity. Comparisons with the linear and cubical nonlinear cases are presented in the dispersion relationship, group velocity and phase velocity and their dependence on wave number and amplitude of oscillation. Quadratic nonlinearity is shown to have a significant effect on the behavior.

In-Plane Blade-Hub Dynamics in Horizontal-Axis Wind-Turbines

2016 ◽  
Author(s):  
Gizem Acar ◽  
Mustafa A. Acar ◽  
Brian F. Feeny
Keyword(s):  
Multiple Scales ◽  
Horizontal Axis ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
Direct Excitation ◽  
Horizontal Axis Wind Turbines ◽  
Parametric Effects ◽  
Cyclic Variations ◽  
Independent Variable ◽  
Three Degree Of Freedom

Blade-hub dynamics of a horizontal-axis wind turbine is studied. Blade equations are coupled through the hub equation, and have parametric terms due to cyclic aerodynamic forces, centrifugal effects and gravitational forces. Blade inertia is usually small compared to the rotor inertia, which enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. Therefore, it is more convenient to use the rotor angle as the independent variable. By doing so, and assuming small variations in rotor speed, the blade equations are decoupled from the rotor equation. The inter-dependent blade equations constitute a three-degree-of-freedom system with periodic parametric and direct excitation. The response is analyzed by using method of multiple scales. The system has a superharmonic and a subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitude frequency relations and stabilities of these resonances are studied.

scholarly journals Investigating the loads and performance of a model horizontal axis wind turbine under IEC extreme operational conditions

2020 ◽  
Author(s):  
Kamran Shirzadeh ◽  
Horia Hangan ◽  
Curran Crawford ◽  
Pooyan Hashemi Tari
Keyword(s):  
Wind Turbine ◽  
Extreme Event ◽  
Horizontal Axis ◽  
Force Balance ◽  
Dynamic Responses ◽  
Horizontal Shear ◽  
Power Performance ◽  
Horizontal Axis Wind Turbine ◽  
Time Duration ◽  
Wind Shears

Abstract. The power performance and loading dynamic responses of a 2.2 m scaled horizontal axis wind turbine (HAWT) under the IEC 61400-1 transient operational extreme conditions were investigated. Extreme wind shears (EWS) and extreme operational gust (EOG) inflow conditions, generated in the WindEEE dome at Western University. The global forces were measured by a multi axis force balance at the HAWT tower base. The unsteady horizontal shear induced a significant yaw moment on the rotor with similar dynamic loads as the extreme event with no serious effect on the power generation. The EOG severely affected all the performance parameters of the turbine which were highly dependent on the operational TSR and the time duration of the event.

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