Blades

Objective:

Low Cost

Wind generators in today's market are overpriced and never meets the rated power promised to their users. Our design is to minimize the costs and produce a resourceful and effective renewable energy. The overarching project goal to beat market competitors is to offer better results with less costs.

Maximum Power Output

The power produced by a wind generator, P, is related to the swept area of the blade using the following equation:

The swept area is directly proportional to the length of the blade. The longer the blade, the more swept area will occur, thus the more power will be produced. The velocity of the wind, v, is not something we can control but does make the biggest impact on power output. Another factor that cannot be controlled is the air density, ρ. These factors are considered when optimizing generators.

Longevity/Reduced component wear

Since the portable turbine is designed for outdoor and prolonged use, the longevity and wear resistance of the product is of importance. Not only should it be resistant to wear from various weather conditions, it should also be resistant to degradation from UV light as well as abrasion from particles in the air.

Constraints:

• Minimize turbine blade mass moment of inertia
  • Rotational turbine/propeller mass moment of inertia = mass*radius^2

• Rotational mass moment of inertia is essentially the turbine's resistance to changes in rotational speed
• Radius is fixed by turbine power production requirements based on 3-blade design
• Mass must be minimized to reduce mechanical wear on the generator and bearing structure to ensure product longevity
• High stiffness to ensure full blade sweep area, regardless of wind speed
  • Each turbine blade can be modeled as a rectangular beam in bending, with loading on one end, where total deflected is a function of force, F, length, l, E, elastic modulus, and I, moment of inertia:

• As explained in the objective section, the total area swept by the turbine blade is directly proportional to the power produced by the turbine unit
• High blade stiffness will ensure blade deformation/bending is minimized, and as a result a maximum sweep area is maintained

Equation Development:

For material selection parameters, the turbine blades were modeled as rectangular rods with length of 16cm and average cross sectional area of 2.4cm height and 0.2cm width. An average wind velocity for this model was expected to be in the range of 5-20mph, with 30mph (13.4m/s) as the maximum. In addition, to maintain the structural stiffness of the turbine blades, the maximum deflection at the free end was chosen to be no larger than 0.2cm. Based on extensive research by the Technical University of Denmark ("A simplified model predicting the weight of the load carrying beam in a wind turbine," 2016), the maximum force a turbine blade will experience in operation was found to be the following:

The maximum force was found to be 7.86 N. Next, the estimated beam moment of inertia was calculated to mimic the behavior of each turbine blade:

Finally, this moment of inertia value was plugged into the beam deflection equation, solved for the elastic modulus (E):

As a result, the blade material must have an absolute minimum elastic modulus of 0.39 GPa. In order to ensure a significant factor of safety (2.5) considering the application of the material (high-speed turbine blades), it was determined that our Ashby chart analysis should be limited to the range of E = >1 GPa to ensure proper material function.

Material Analysis:

After considering the objectives of the blade are stiffness and low mass, the constraints were focused on increasing the length while maintaining blade stiffness and keeping the density low. By implementing the equations described above and combining each of them, it was determined that all variables could be held constant (by design) except density and elastic modulus. The blade length and specific cross sectional area were both fixed due to power constraint requirements. As a result, the material index was found to be:

For optimum results, this material index will be maximized. In summary, the elastic modulus is fixed based on stiffness requirements, and the density should be minimized based on blade shape and size requirements. The Ashby line equation calculations were conducted below, which resulted in a slope of +2:

The unfiltered Ashby chart producing the relationship between elastic modulus and density is shown below:

Everything above the sloped line as shown below, represents the materials that could be suitable for the project. Foam materials are the cheapest and lowest density option. However, they also has a lower modulus of elasticity, which results in less stiffness and will not meet the material requirements of >1 GPa. There were many wood and metal options such as pine and aluminum that have a good trade off between stiffness and weight. Polymers are also good candidates which have relatively high modulus for their lower density compared to most metals.

The above information is not enough to decide which material would work best. However, using the limits of modulus of elasticity calculated, the option of foam is easily dismissed because it does not meet the minimum requirement needed to be sufficient, even if it is the most cost effective option. Metals have the reversed trade off as they have high modulus, but cost and weigh more.

The next limiting factor is the material processing. Injection molding is the most practical and common mass production for the specific shapes designed. This processing is the also the cheapest and still very effective. Using this information, the Ashby chart narrowed down even more as shown below:

The mass production of wood is much more expensive than the mass production of PLA and TPO, leaving them as the material finalists for this design and processing technique. Further research where looked into these two materials to analyze which material would be the optimal option.

A constraint that is important to consider is the material's durability with UV radiation. Since the wind turbine is set outside, having at least good sunlight durability plays an important role. TPO may be cheaper and less dense, but it has poor radiation. Even though PLA is slightly more expensive, it can withstand the sunlight better and therefor extend the lifetime of the product. Therefor PLA is the best option for the wind turbine blades.

Process Selection

Although 3-D printing is ideal for prototyping, with large-scale production in mind, polymer injection molding was chosen as the manufacturing method for the components.

Other possible manufacturing methods that were considered include extrusion and rotational molding, but due to the design constraints involving the geometry, they were eliminated from the possible methods. Extrusion is a powerful primary shaping process, but is not suitable for manufacturing the geometries that we have designed. Although the housing may possibly be rotational molded, PLA, the selected material, is not compatible with this method.

Injection molding is a very versatile manufacturing method that can handle various polymers such as thermoplastics, thermosets and elastomers. Although capital and tooling costs are high, the cost per unit after the initial investment will be extremely low in comparison to additive manufacturing methods. The relative simplicity of our design also leads to low initial moulding costs.

In addition, since the possible tolerance for thermoplastics is +/-0.2mm to +/-0.5mm and smooth surface finishes are possible, our components can be manufactured at the required tolerances and finishes.

Due to the high throughput potential as well as the low manufacturing costs at large batch sizes, injection molding was chosen as the manufacturing methods of choice for the turbine components including the blades as well as the housing.

Other Components

Process selection, functionality, and quality are qualities that were analyzed when deciding which material(s) would best suit each component.

Consistency is valued in this project when considering the material selection; since price and longevity are desired characteristics for not only the blades, but all other components as well. The blades are the most critical aspect and needs the most consideration because of their small thickness and precise design. The other component that required material analysis was the casing. Deciding to keep the project uniformly composed of one material ensures the desire of consistency is met and causes the manufacturing process to be more predictable and less expensive.

The components that will be made up of PLA are the blades and housing. The stand is optional and can vary depending on the users choice. The casing includes a universal thread so different types of tripods, stands, and mounts can be easily attached. This gives the user the freedom to customize the portable wind generator to their meet their specific needs. This also allows for potential room to grow as a company, rather than stay as one product.