ME Analysis Project #2

Christian Seymour

Due Date: December 12, 2013

Abstract:
The diameter for my shaft design was hand calculated to be 0.8756” for a factor of safety or 2. This factor of safety was expected to be the outcome in FEA SolidWorks and it was not. The reason for this is simply SolidWorks is not the best tool to use for complex designs and loads as ours was. It worked great for the simple beam deflection in the last project. Many times hand calculations are the long way of doing things. In this case, it took much longer to figure out the correct way of adding fixtures, load, and connections in SolidWorks. Many of the material properties in SolidWorks are also not the same as they are in our book. Simply said, choosing which method to use is the hardest decision to make. Sometimes FEA analysis is better, and in some cases, hand calculations are the easiest.
Background:
We have been given the task to design a shaft to specific guidelines using inch size pillow blocks. We will perform appropriate calculations using modeling techniques and verify the design in SolidWorks FEA program. The problem is 7-5 in the book and is shown below:

The problem statement: A geared industrial roll shown in the figure is driven at 300 rev/ min by force F acting on a 3-in-diamter pitch circle as shown. The roll exerts a normal force of 30 lbf/in of roll length on the material being pulled through. The material passes under the roll. Design a shaft for the situation of the industrial roll with a design factor of 2 and a reliability goal of 0.999 against fatigue failure. Pick a shaft size that does not deflect greater than 2”.
We have been given this problem to see how we will approach a design problem like this and I hope I have approached it correctly. I plan to figure out all of the statics, and back solve for a diameter using a factor of safety of 2.
Experimental Techniques:
The first step in designing this shaft is to calculate the statics of the shaft. You will have to pay extra attention to the areas you think are of concern. In this case, it will be the area of the shaft right before the roller. The maximum moment will be calculated from shear and bending diagrams. Once the alternate moment and mean torsion are calculate the endurance limit must be calculated. Here is where the material of the shaft will be chosen. Stress risers will be calculated next for the area of concern right before the roller. Once all of this data is hand calculated it can be placed into an excel worksheet. The worksheet will back solve an appropriate diameter given a factor of safety. This shaft will be created in SolidWorks will be compared to see how well FEA SolidWorks performs.

Results and Discussions:
Statics has been calculated below in both the x-y and x-z planes. The mean torque is equal to 192 lbf. The alternating moment is equal to 375 lbf-in. Both the alternating torque and mean moments are equal to zero.

Once the Statics was figured out I went straight to choose the material. I chose 1020 CR steel because it is very often used as a shaft. The Endurance limit was calculated next. I left k_b as an equation in my excel program so it would change with the diameter. Stress concentration factors were used for the fillets between the shaft and roller and also the rise from the shaft diameter to the 4” roller.

Once all calculated data was found they were simply placed into my excel spreadsheet. I back solved for a diameter by setting the factor of safety to a value of 2, as stated in the problem. It gave me the diameter of 0.8756”.

Once the hand calculations were finished, the model in SolidWorks could be created. The shaft, roller, and gear were all created as one part, because in reality, whether welded, hot pressed, etc., they act as one part. Appropriate bearings were found at McMasterCarr.com. Once the assembly was created the FEA study could begin. Appropriate loads had to be applied, which we found in the calculations we performed. Bearing connections and fixed points also had to be created. The assembly was meshed and our results were displayed.
Conclusion:
The diameter for my shaft design was hand calculated to be 0.8756” for a factor of safety or 2. This factor of safety was expected to be the outcome in FEA SolidWorks and it was not. In SolidWorks it was calculate to be 25. Many of the material properties in SolidWorks are not the same as they are in our book. Also, the calculations can be different by how we fix and connect our model. There are so many options in SolidWorks it is easy to become lost. The positive of this FEA analysis is that my shaft did not exceed the 2” deflection limit. Our shaft was a good choice.