Landing Gear
The landing gear of an aircraft needs to be strong enough to survive a reasonably hard landing while absorbing the kinetic energy from the aircraft. Landing gear that is too rigid will result in excessive stresses on the frame. An excess of stresses could affect the structural integrity of the aircraft. Also, overly ridged landing gear could add too much weight. On the other hand, landing gear that is too ductile could yield and gears that are too brittle could break. That being said, an appropriate design and material needs to be chosen for the landing gear in order to maintain structural integrity and effectiveness.
Flexible landing gears (FLG) are commonly used in RC helicopters and quadrotors. FLGs are light because they utilize the mechanical properties of the material in which they are made and not heavy hydraulics in order to absorb the energy of landing. FLGs where chosen for this project due to their light weight and simplicity, and the final design is shown in Figure 8.
The first step in choosing an appropriate material for the landing gear is to determine the conditions of a reasonably hard landing. Unlike a soft landing where the propellers are producing an upward thrust upon touchdown, a hard landing is defined as a one foot drop without propeller thrust. A simple kinetic and potential energy Equation is used to determine the velocity of the aircraft just before a hard touchdown. The result of the energy balance which is given in Equation 11 is 2.44 m/s or 5.46 mph.
Table 5 shows the different metals considered for the landing gear. This table includes density which is important for weight and yield strength which is important for integrity.
From Table 5, it is clear that steel is too dense for a small aircraft like AirWolf II. Also, the increase of yield strength vs. density of the aluminum indicates that 7075T6 is the best choice for this project.
The next step involves modeling the landing gear as a nonlinear spring. This nonlinear behavior is due to an increasing moment arm as the displacement increases. A general force vs. displacement response for flexible landing gears is given in Figure 9.
A Finite Element Analysis (FEA) method was used to model the landing gear. This analysis was performed in SolidWorks using the SimulationXpress tool. In this analysis, various forces were applied to the gear which resulted in different displacements. These forces and displacements were then graphed, and the corresponding bestfit curves for different thicknesses of 7075T6 aluminum were found. The results of the model are given in Figure 10 below.
One interesting result is seen from the near linear force vs. displacement curves. One reason for the linear behavior is that the displacements are relatively small in comparison to the size of the landing gear. This indicates that the range of forces tested falls in the left most region of the general curve given in Figure 9. In other words, the curve in Figure 9 could be seen as linear if a small region at the left most portion of the curve is looked at.
Now that the landing gear has been modeled as a spring in the form F=kx+c, a new workenergy analysis can be performed. Figure 11 shows the two states of the quadcopter modeled as a spring and mass combination. State 1 represents the quadcopter just before it touches down. In this state, the spring is uncompressed and the velocity of the mass is 2.44 m/s. In State 2, the velocity of the mass is zero, the height has decreased, and a force is applied to the mass by the spring.
The work done by the spring from State 1 to State 2 is given in Equation 12 where x is the displacement given in Equation 15. The integration in Equation 12 is already simplifies because there is no work done by the spring in State 1.
The following workenergy equation is used to derive displacement.
Solving Equation 17 with the different values of k and c from Table 6 yields displacements that are then plugged back into the landing gear models found in Figure 10. The resulting forces are then plugged back into SimulationXpress. From the simulation, the safety factor from yielding, maximum deflection, and mass are found. The results of this process are summed up in Table 7 below.
Landing gear made out of the 1.6002mm thick 7075T6 aluminum resulted in a large force of 193N which could cause damage to the frame. The 1.016mm thick aluminum exhibits a low safety factor which could lead to the landing gear breaking. The 1.27mm aluminum shows a high safety factor while maintaining a low maximum force and was chosen as the material used in this project.
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Is there any way to increase the flexibility of aluminum landing gear, either by bending and rebending them in a vise, or by cutting the sides off, making the gears thinner across?
–Tom Boyden
Good question. Thanks for checking out my blog by the way. There are some things that you can do to change the behavior of metal, but those things are beyond the average man’s capabilities (super hot ovens or stain hardening equipment). So we have to look at the materials that are available to use. Flexibility is a property of a material and can be estimated by the materials Young’s Modulus (or Elastic Modulus). To better explain this please check out the link below.
The linked picture shows two general stressstrain curves for two different materials. To explain the graphs, a material is pulled (stress) which results in the material elongating (Strain). The AB portion of both curves is known as the elastic portion, and the slope of this line is Young’s modulus (E). It is called elastic because the material will stretch under stress below point B and return to its original shape when the stress is relieved (kind of like a spring). If the stress exceed point B then plastic deformation occurs such that the material will not return back to its original form.
The Point? We want a material that has a low Young’s Modulus (E or slope from point A to B). Basically we want a material that will stretch a lot under stress and return back to its original shape like the material representing the right curve. In addition, the material should have a high yield strength (the stress that occurs at point B). A high yield strength, which is another material property that distributers will give you, insures that the material will not fail while under the stresses of landing. So basically, choose a material that looks like it has the right material properties then do an FAE analysis to confirm your suspicions.
In regards to increasing flexibility by bending, what you are actually doing is decreasing the crosssectional area of the material by introducing micro imperfections like microcracks that propagate throughout the material. This is not recommended because it ruins the integrity of the material and leads to an accelerated failure (the landing gear just broke).
A better way to reduce the crosssectional area of the material is to do your last suggested: cut down the width of the gear. The only problem is that you will reach the materials yield strength with less force. As a crude example, my landing gear is designed to take a hit from a 1 ft dead drop. If the gear is reduced in size, a safe drop distance might be reduced to 0.5 ft or something. Basically, the width and thickness of the gear was chosen for design intent in order to withstand a hard landing.
What I suggest you do is look at different materials like Plastics, or there is this steel that is used for bailing that is super springy.
Thats all I have right now. Please let me know If there is anything that I explain better. Thanks