## Wheels and Castors

The chassis is supported by two back wheels, with a castor in the back. In this analysis, Alex will analyze the structural integrity of the wheels and castors under realistic loads, and determine critical loads. In doing this analysis, one must take into account the Von-Mises stresses so that we can evaluate whether the stresses incurred are close to the failure stress. For some materials, we do not know the failure stress, so we are going to compare the Von-Mises stress to the yield stress. This analysis is done in ANSYS Workbench 19.1. First, we will perform the analysis on the wheels.

We are going to make an assumption that the wheels that we have 3D printed are made up of ABS plastic instead of PLA. This is because PLA is not available for analysis on the ANSYS platform. The geometry uploaded on ANSYS is from the above mentioned file CAD model. The forces act at the center, where the shaft resides.

We are going to make an assumption that the wheels that we have 3D printed are made up of ABS plastic instead of PLA. This is because PLA is not available for analysis on the ANSYS platform. The geometry uploaded on ANSYS is from the above mentioned file CAD model. On the wheel, the forces act at the center where the shaft is put into place. The castor we are using is made up of steel, and thus we have modeled it in ANSYS as structural steel.

The total mass of the robot along with the maximum 6 kg of payload is 8.3 kg, which can be converted into force by multiplying by the gravitational acceleration, 9.81ms^{-2}. This gives us a total force of 81.423N. For calculations, this will be approximated as 80N. Since there are two wheels at the back and one castor in the front, half of this weight is on the castor and the other 40N acts on the two wheels. This means that each of the wheel carries approximately 20N. This has been applied onto ANSYS. The spokes of the wheel each carry 20/4 = 5N of force. These are shown in the appendix. A fixed support was added at the bottom of the wheel.

**Reality check – **With these forces and constraint, we are able to model the real situation quite accurately because the forces have been divided in a way that it represents the true nature of the robot. Similarly, the constraint on the bottom of the wheel to have a fixed support represents the reality as well. The materials used to create these models also accurately depict the real models that we have used.

**Results **– We performed two tests on the wheel – total displacement in all directions and Von-Mises stress. With the total deformation, we can gauge how much is the part going to move under the loading conditions. The Von-Mises stress provides us an approximation of the stress under ductility. If this stress is less than the yield stress, the part should not undergo any failure.

We have plotted the total deformation of the wheel along the conditions specified above.

**Figure 1 – **Wheel Total Deformation

**Limitation of ANSYS – **one of the limitations of ANSYS is that it highly exaggerates the visual effects of the object being analyzed. For example, in the figure 1, the wheel looks quite deformed, however, if we look at the legend on the left, maximum deformation is 1.57 * 10^{-6} m, which is a really small number. This misrepresentation is confusing at first, but is going to be in every figure in the Finite Element Analysis.

On the left side of the figure 4.13, we can see that there are 4 forces acting at the center of the wheel and one fixed support at the edges of the wheel. From all this, the maximum deformation is at center of the wheel. However, this deflection is so small that we can simply ignore it. Similar can be said about the figure 4.14 with the Von-Mises Stress.

**Figure 2 – **Von-Mises Stress on the Wheel

In the figure 2, the maximum stress takes place at the center of the wheel. This is realistic as that is the area where the maximum deflection took place also in figure 1. This maximum stress is 0.182 MPa. This wheel is made up of APL, which is Acrylonitrile butadiene styrene.[i] This has a tensile strength of 46MPA (TestStandard). Therefore, we are well below the tensile strength of the material and safe for the competition that we are using the robot for.

**Failure point – **In order to determine the maximum loading condition when the Von-Mises stress will be above tensile strength, we found through our analysis that we would need a force of 800N or 80kg until the failure point. This helps us justify that the APL wheel that we are using is very durable and can withstand incredible amounts of weights.

A similar analysis was conducted for the castor. For the castor, we assumed that it is made up of Structural steel on ANSYS. The castor analysis was a little easier because there is only one force acting on it from the top. This can be observed in the appendix. Similarly, a constraint of fixed support has been added on the outside of the wheel. Once again, the displacement that we observe is greatly exaggerated in comparison to the true displacement. This can be seen below in the figure 3.

**Figure 4.3 – **Castor Total Deformation

The maximum total deformation in this castor is 4.307*10^{-6}m, which is incredibly small. Such a small deflection in our robot is not going to cause any harm to the robot or its long term use. It can also be observed that the maximum deflection takes place at the top instead of the wheel/castor. A similar result is observed in the Von-Mises stress also, below in the figure 4.

**Figure 4 – **Castor Von Mises Stress

From the figure above, we observe that the maximum Von-Mises stress takes place at axle of the castor. However, the rest of the robot stays under really small stress of 4 units of Pascals. The maximum stress is 9.95MPa. The ultimate tensile strength of the steel is 420MPa so we quite far away from that number, meaning that we are safe from any kinds of failures during the robot competition (Matweb Data sheet).

**Failure point – **Through the use of ANSYS, we can determine for what stress, we might exceed the above mentioned ultimate tensile strength of 420MPa. This we found to be 1750N when the maximum stress reached to a point of 420MPa. This means that when a mass of 1750kg is placed on the robot, then the castor is likely to fail. We have purchased a really strong and durable castor and this represents the true conditions.

From the above analysis, it can be observed that the wheels and the castor that we are using are safe to be used for our competition.

## Chassis

The chassis is arguably the most important component of a robot since it ties together every other piece. Since we plan to gain the most points out of the competition, we must test whether it will be able to withstand the maximum payload of 8.4 kg, which will be the total mass of the robot and payload. To carry out this analysis, we have decided to use ANSYS.

For this analysis, we are going use Oak Hardwood as the chassis material. The actual chassis material is birch ply wood, however as ANSYS does not have that material available, we chose the closest approximation. The wood that we are using is quite sturdy and durable. As a basic, preliminary test, we stood on top of the robot to check if it can hold our weight, which it did. However, we are going to conduct an in-depth analysis of the chassis with finite element analysis to understand under what conditions will it actually fail – and try to avoid that situation.

Since the chassis supports different elements of the robot, the challenge with this design is that different forces act at different spots on the chassis. This is why an individual weight of each individual component has to be added. In order to proceed with this, we had to find the weight of each of the components including the battery, Arduino microprocessor, sonar sensors and payloads. Once these have been calculated, each force has been added to the chassis, as can be observed from the figure in the appendix. The 4 following total forces have been added.

Object | Force (N) |

9 V batteries | 1 |

Aduino microprocessor | 1 |

Rechargeable batteries | 2 |

Added Payload | 80 |

**Reality check – **there are many assumptions that we have made here, however, they are close enough to be justified. The materials that we are using are close to the real material and therefore, our analysis is likely to be correct. We have approximated the weight of each object accurately and placed them at different locations, which is likely to give us an accurate deformation and stress graph of the chassis.

**Results – **As discussed previously, the deformations observed in the robot are exaggerated to more clearly show what is occurring. The figure 5 below demonstrates the deformation graph of the chassis when the component loads act on it.

**Figure 5 –** Chassis total deformation

As it can be observed from the deformation figure above, we observe that the maximum deformation takes place in the middle. This is because the heaviest weight acts in the middle of the robot due to the payloads that we add. The maximum deformation is 5.8*10^{-6}m, which is extremely small and therefore, not going to affect our robot. We observe a similar result in the Von-Mises stress graph generated through the same forces and constraints in the figure 4.18 below. In this figure, we observe that the maximum Von-Mises stress is 3.8MPa. Theoretically, we find that the ultimate stress of American White Oakwood is 5.3MPa (Matweb). Oak hardwood and American White Oakwood might not have exactly the same ultimate tensile strength but it is a good approximate as both as wood and finding an approximate value for material properties of wood is extremely tedious since making standards is really hard.

**Failure point – **After changing the various payloads weight to 200N, we found that the Oakwood went beyond the maximum Von-Mises stress of 5.3MPa. Since we are not planning the robot to hold such immense weights, our robot should be fine on the competition day. The result that we have observed from ANSYS is probably not accurate because it was described previously that one of us actually stood on the robot and nothing happened to the robot. This means that the birch plywood that we are using has a much higher ultimate tensile strength than we have estimated here. Nevertheless, this concludes that our robot should perform well under the presented conditions.

**Figure 6 – **Chassis Von-Mises Stress

## Motor Shaft

Motor shafts are responsible for driving the robot forward and navigating around the track. All the frictional force that acts on the robot must be able to be overcome by the motor to drive the robot forward, and this shaft must also support a portion of the robot’s mass. These forces that act on the shaft are where the importance of the motor shaft comes into the play. This shaft must be properly protected and modeled to prevent any kind of damage. Ideally, shock absorbers should be installed to prevent damage, however, that is not under our budget constraints. Thus, it is important to conduct a finite element analysis of the motor shaft to understand under what conditions our motor could stop working.

We are going to assume that the motor that we are is using made of structural steel, as it is available in the ANSYS materials library. This is also appropriate because our motor shaft actually made of steel. Some materials inside the motor might be made of other substances, however the implications of taking these into account are unfeasible given our constraints on time and resources. We are going to look at the deformation and Von-Mises stresses on the motor and motor shaft to understand under what conditions could the robot could fail.

There are two forces that act on the motor. One is on the top of the motor from the load that the bottom of the chassis puts on the motor casing, and the second is at the shaft due to the corresponding upward force from the wheel. These have been approximated and shown towards the end of the appendix. These forces are each given 20N as explained in Alex’s wheel section on how the total weight of the robot is divided into the different parts of the robot. One constraint has also been added on the motor shaft where it is held, as the construction does not allow it to move. This can also be observed in the figure in the appendix.

**Reality check – **We are making an approximation that the entirety of the motor is constructed from steel. However, this is not necessarily true as many of the materials inside the motor may not be steel. Making this approximation is important under the time and resources constraint with which we are working in. The constraints that we have defined are accurate and represent the true nature of what the motor and its shaft is experiencing.

**Figure 7 – **Motor shaft total displacement

This case is like the previous section where the maximum displacement is incredibly small – 1.06*10^{-5}m. ANSYS does not represent the deformation very well because it shows a very exaggerated case. As expected, since the top of the shaft is given a fixed support, it experiences the least deformation. However, due to the rotation, the other end of the motor experiences the most deformation. This result is different, in terms of the stress as shown in figure 8.

Due to the twisting motion, we expect the most amount of moment to develop at the shaft. It is this shear moment that causes the maximum stress at the shaft on the left, as represented in figure 8. The maximum Von-Mises stress gained is 23.35MPa. This is the maximum stress that we have seen at any point in our finite element analysis. Yet, the ultimate tensile strength of steel is 420MPa and our gained value is very far away from it.

**Figure 8 – **Motor Von-Mises stress

**Failure point – **Using ANSYS features, we can assign different forces at different points and this can tell us how the material is going to behave under numerous conditions. We tweaked the load involved until the maximum Von-Mises stress that we achieved went over 420MPa. The 857N necessary is equivalent to 85kg, and we are not planning to load our robot with such heavy conditions. Therefore, we can be carefree about any anticipated loading conditions and our robot should perform well mechanically under those in the competition.

## Blade

The interesting part of this project is that the course is trying to guide students into thinking more about renewable energy. Our robot must be able to convert the wind energy from its environment to mechanical energy to eventually run our robot. The turbine blades play a crucial role in providing a maximum energy conversion for our robot and must be sturdy enough to withstand normal use. This energy conversion is crucial in making our robot run for a longer time, which is ultimately what will earn us the best possible grade and coerce us into learning as much as possible about the efficiency of wind-powered vehicles. Therefore, we must perform a critical analysis on the blade to understand if it is likely to undergo any failure during the competition.

The blades that we have developed have been 3D printed out of PLA plastic. However as previously specified, PLA is not available in the ANSYS package, so I chose to approximate it as APA plastic. A similar assumption was made in the wheel analysis since the wheel was 3D printed as well. The geometry of the blade used to perform the analysis is congruent with the blade shown in the above CAD models in previous sections and the engineering drawings in Appendix C. In order to do calculate the force acting on the blade, we would have to delve into fluid dynamics and convert the wind speed to the pressure that is created. Therefore, the force acting on the blade has not been described and has not been included in the appendix.

From the specification provided, we are aware of the different wind speeds at different points of the turbine. To make our calculations easier, we represented all the velocities into one by taking an average.

We can convert this to miles per hour, which is 5.11 mph. Then we can use the following formula to find the pressure in psf.

Convert this pressure into more favorable SI units yields 3348Pa. This pressure is then divided into the 12 different blades that we are using at 279Pa. This pressure acts on the front of the blade and has been added as a condition onto ANSYS. Another condition that has been added is a fixed support on the end of the blade, since the blade will be rigid due to a solid attachment to the hub.

**Reality check – **We are making an approximation with the material that we are using. However, we are aware that they are similar materials with similar properties, which is why this is a valid approximation. The resultant pressure gradient on the blade is approximated with some error but does a good job in finding an approximation. The final pressure should not have been divided by exactly 12 because some air passes through. We do not have data to carry out that calculation, therefore the final pressure has been divided by 12 as an approximation.

As mentioned earlier, the deformation drawings from ANSYS can be visually misleading, due to the emphasis on gradient. The gradient will still go all the way from navy to red no matter how small the deformation is, unless it is zero. In the total deformation in Figure 9, we observe that the maximum deformation is 2.04*10^{-7}m, which is an incredibly small deflection relative to the size of the blade and therefore we should not be concerned. A small amount of deflection is to be expected when working with flexible materials such as PLA plastic, which are designed to bend to avoid plastic deformation.

**Figure 9 – **Blade total deformation

The pivoting around the base of the blade is the fixed support, which is why it is 0 deformation. The maximum deformation is at the tip of the blade, as was expected.

**Figure 10 – **Blade Von-Mises

This blade has a maximum Von-Mises stress of 471Pa, where as the ultimate tensile strength of APA is 46MPa. We do not even require a failure analysis as an incredibly strong pressure would be required to cause this blade to fatigue. APA might not be exactly same as the PLA that we are using, however, since both are similar materials, we can appropriately assume that APA represents the true turbine scenario that we will observe during physical testing.

**Failure point – **Through the use of ANSYS, we can identify what pressure would eventually lead to the failure of this blade, which means that the Von-Mises stress observed would be more than the ultimate tensile strength of the APA that we are assuming. This was found to be 1.05MPa, which is incredibly large compared to what we had estimated to be 279Pa. Working backwards, the speed of the air would have to be 140mph. For our application where a household fan is providing the moving air, such a speed cannot be reached. Therefore, it is plausible to conclude that the blades are safe against any damage for our competition.