Rotational sampling in wind turbines: Difference between revisions

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{{Further|Wind turbine design}}

{{Issues|

{{UnderlinkedMore citations needed|date=JuneOctober 20232013}}

The loads on both [[horizontal-axis wind turbine]]s (HAWTs) and [[vertical-axis wind turbine]]s (VAWTs) are cyclic; the [[thrust]] and [[torque]] acting on the blades depend on where the blade is. In a horizontal axis wind turbine, both the apparent [[wind speed]] seen by the blade and the [[angle of attack]] depends on the blade's position. This phenomenon is described as [[Rotational sampling in wind turbines|'''rotational sampling]]'''. This article will provide insight into the cyclic nature of the loads that arise because of rotational sampling for a horizontal axis wind turbine.

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The loads on both [[horizontal-axis wind turbine]]s (HAWTs) and [[vertical-axis wind turbine]]s (VAWTs) are cyclic; the [[thrust]] and [[torque]] acting on the blades depend on where the blade is. In a horizontal axis wind turbine, both the apparent wind speed seen by the blade and the [[angle of attack]] depends on the blade's position. This phenomenon is described as [[Rotational sampling in wind turbines|rotational sampling]]. This article will provide insight into the cyclic nature of the loads that arise because of rotational sampling for a horizontal axis wind turbine.

Rotational sampling can be divided into two parts: [[Deterministic system|deterministic]] and [[Stochastic process|stochastic]]. Deterministic processes present themselves as spikes on a [[Power spectral density|power spectrum]], where as stochastic processes spread over a wider [[frequency range]].

{{Further|Wind turbine design}}

==Background==

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Upon completing a single revolution, a blade has produced an ever-changing [[torque]], and so power. Some of these changes are due to deterministic processes, i.e., processes that can be determined and do not require statistical methods. Examples of deterministic processes are listed below:

* [[Mass|Gravitational loading]]

* Tower shadow <ref>Time-Domain Modeling of Tower Shadow and Wind Shear in Wind Turbines,

Swagata Das, Neeraj Karnik, and Surya Santoso</ref>

* [[Wind shear]] <ref>Time-Domain Modeling of Tower Shadow and Wind Shear in Wind Turbines,

Swagata Das, Neeraj Karnik, and Surya Santoso</ref>

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The [[drivetrain]] of a wind turbine comprises the hub, the low speed shaft, the [[Transmission (mechanical device)|gearbox]], the high speed shaft, and the generator. The torque at the hub is strongly influenced by the [[Rotordynamics|rotor dynamics]]. The instantaneous hub torque is found by summing all the torques from all the blades of the wind turbine at any instant in time.

Consider an <math>n</math> bladed wind turbine. Each [[blade]] is separated angularly from a neighbouringneighboring blade by <math>360/n</math> degrees. That is, for a 3-bladed wind turbine, the blades are 120 degrees apart.

The [[torque]] acting on the blade is defined as the z-component of <math>\textbf{r}\times\mathbf{F}</math>, where '''r''' is the radius from the axis of rotation (in this case the hub), and '''F''' is the force acting on the blade. If the torque is defined as the z-component of this cross product, then the torque is simply ''rF''_perp where ''F''_perp is the force perpendicular to the radius vector, or tangential to the instantaneous velocity of the blade (See figure below)

From the figure above, it can be seen that the torque, ''T'', due to gravitational forces acting on a single blade is given by the following expression:

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</math>

The [[covariance]] function of a sum of [[Sinusoidal model|sinusoids]] is itself a sum of [[sinusoidal functionsfunction]]s. Thus, the power spectral density function is a set of Dirac delta functions. The locations of these are at multiples of ''n''. Thus, on a power spectrum, deterministic processes such as gravitational loading manifest themselves as spikes. This can be seen from analysing generator torque.

====Blades====

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==Structural loads==

[[Spectral analysis (disambiguation)|Spectral analysis]] of component loading is useful in [[fatigue analysis]].

==References==

{{Reflist}}

[[Category:Wind turbines]]

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[[Category:Wind turbines]]