In this lecture, I will talk about material requirements for wind turbine blades. After this lecture, you will be able to calculate the loads working on a wind turbine blade, calculate the stresses working in the blade material, estimate the number of load cycles in a wind turbine blade. Here are shown a number of existing wind turbine blades plotted as a function of lenght versus the weight of the blades. If you look at the smallest blade, then you can see that growth weight regarding weight versus length, is following nearly a power of three, a power of three will be the case for pure upscaling of the blade. If you look at a longer blade, then we have actually growth rate which is a little lower. If you zoom in on the longest blades then we have two cases here. Which is made of pure glass, epoxy, or polyester. So this is 70 plus long blade. This is 80 plus long blade. This blade is actually also consists of some part of carbon fiber in the load carrying laminates. The final point up here, which is a 86-meter-long blade, is a virtual blade, so that's not being produced, but is a reference blade which will be used in an example later in this lecture. The reference to the work describing this blade, can be seen here. First, we will look at the aerodynamic load working on a wind turbine blade, meaning the flap-wise loading of the blade. You will learn earlier in the course that the maximum load on a wind turbine blade is reached when the wind speed is equal to the rated wind speed for the wind turbine blade. This speed corresponds to the point where the max production is reached for the turbine, meaning that we are reaching the power of the generator in a turbine. The corresponding loading on this point is given by this small equation here. Only consisting of the density of the air, shown here as 1.2 kilograms per cubic meter, the rated wind speed and the length of the blade. This load will be distributed onto the three wind turbine blades. And actually distribution will be while a linear function coming from zero load at the root up to a certain load intensity at the blade tip. This is shown in the equation describing this variation as a function of x. When we zoom into one blade and, Plot the load intensity on the blade, then we can cut the blade and find the forces working inside the blade. We would like to calculate the moment which is resulting in stresses in the blade material. This can be calculated after the equation shown here, where the red part is coming from the uniform part. Of the linear distribution of the load and the blue part is coming from the linear variation part of the loading. It's found by actually finding the total value of the loads given by the intensity multiplied with the length of the section and then the point where this load is working. So for the uniform distribution load we have that the max load would work movement-wise in the mid-point while for the linear distribution it will work in the 2/3rd point in the blade. This equation can be derived as this one where we put in the values for the load intensity. So this is giving the moment in a arbitrary point in our blade. In order to make a wind turbine blade, we need to have some materials. And this will generate some gravity load on the wind turbine blade. This loading would be in the edge-wise direction of the blade. Illustrated here on a wind turbine and on one blade. If you assume that the amount of material used is constant per unit length of the blade, then you have a uniformally distributed load, and the intensity of this load can be written as a function of the density of the material and the amount of material used and the g constant, which is equal to 10 meters per second squard. Do the similar cutting as we was doing before in the blade material and we can get out the moment working in the blade material on the cross section. So here's the equation shown for that and again we have those uniform loads Intensity here and we have that the load will work in the middle point as the intensity multiplied by the length of the section we're looking at and then the point where the force will work moment-wise. This equation can be derived in short form here and this would give the moment in an arbitrary point in our blade. Now we would like to go from the moment in the cross section to actual stresses in the material. In order to do that, you need to look into the cross section of a wind turbine blade. I have an example here where you can see that the load carrying part is the top part here and the bottom part here and the two parts in the ends. So the top part and the bottom part Is taking care of the aerodynamic load while the two parts in the end is take care of the gravity load. This point I illustrated as green points of materials on the sketch. And also to simplify this structure or this cross-section. I drawn a picture here showing some materials which are the flap-wise. The material taking care of the flap-wise loading and which have the height which is the bhight of the thickness of the blade and then some material taking care of the edge-wise loading with a distance which is corresponding to the width of the blade. The sum of these four materials is the sum of the material used in the wind turbine blade. Now we'd like to go from the moment to the stresses in the material. And we have the equation for the moment in an arbitrary point in our cross-section. This moment can be recalculated as stresses in a wind turbine blade material as shown here, with compression stresses in the top and tensile stresses in the bottom. In order to calculate the relation between the moment in a place section and the corresponding stresses, we have that the stresses will work as forces given by the stress multiplied by the cross section area here, and then movement-wise given by the arm from the center line to the point, as shown here. This equation can be derived in this form here where we have the stresses in an arbitrary point along the length of the blade. We can now put the equation in for the flap-wise moment. In this equation here and get the stresses in the arbitrary point. In a similar way we have found the moment coming from the gravity load on the blade. And we can find the corresponding stresses coming from the edge-wise loading of the blade. The wind turbine blade materials not only loaded statically, it's highly loaded with fatigue and regarding the number of cycles. Of working on a wind turbine, I will show here a small estimate on a number of cycles throughout the lifetime of a wind turbine blade. As an example again take the DTU 10 Megawatt reference blade. If you look at the material at the tip of the blade, then normally 100 meter per second is considered as a max speed, in order to avoid a erosion of the polymeric surface on the wind turbine blade. Knowing the length of the blade, then this limit will then give the rotation time of a wind turbine blade. And this is 5 seconds for this specific turbine. Hours of production is here set to 3000 hours. That's nearly 9000 hours in a year, but only partially the time is used when the turbine is running. And this is normally the number of hours considered for full production of a wind turbine. And then we are considering the lifetime, 25 years. Putting this together then we're getting a number of load cycles due to the gravity force equal to 50 millions. Following the gravity load, and we also have a wind introduced fatigue. When we are estimating the number of load cycle, the starting point will be the Eigen frequency of the blade, which will be the order of one Hertz for this given turbine. Again, taking the hour of production equal to 3,000 hours per year and a lifetime, 25 years, then we are reaching a number of load cycle, coming from the wind load on 300 millions. In this lecture you have learn how to calculate the loads working on a wind turbine blade, calculate the stresses working in the blade material, estimate the number of load cycles on a wind turbine blade.
