Pulling Rod
The rivet rod is the part that applies a load to the rivet in order to break the mandrel. The part features a cylinder with a transverse circular hole cut 0.5 inches from the top. An axial load is applied on the top and bottom of the part, placing the material in tension. Because there is only axial loading present and not bending or shear forces, there is no need to calculate the stress using a shear or moment diagram. Instead the stress was calculated using equation 1:
The stress will not be constant across the part due to changing geometry, so two points were selected for analysis. The first point was at the normal cylinder without the hole as in Figure 1, for which the area and stress was calculated to be:
The second point was the edge of the hole as seen in Figure 1, for which the area and stress was calculated to be:
Since the second stress is higher, the part will most likely break at that point, so the rest of the calculations use this stress. Please note that normally the presence of the hole would cause stress concentration, thereby increasing the stress at point 2. There were no concentration factor tables to be found that included a cylinder with a transverse circular hole with an axial load that fit the dimensions used, so the stress used for point two may be less conservative than in real life.
The Von Mises stress is calculated using the three principle stresses. Due to the sole presence of axial loading, the principle stress equation simplifies to:
From these principle stresses the Von Mises stress was calculated:
The principle purpose of the Von Mises is finding the factor of safety. The material used for the rivet rod is AISI 1045, which has a yield strength of 63ksi and an ultimate strength of 107ksi, yielding a safety factor of:
A safety factor of 1.89 shows that the part will be able to withstand a force of 1,400lb once. The rivet gun will be used time and time again, so the parts must be designed to withstand continual use. Finding the number of times that the part can be used before failure is done by finding the σrev and Se as in the equations below. The max stress is 33.3kpsi and the minimum stress is 0.
The Soderberg criteria was chosen to calculate σrev because it is more conservative than Gerber, ASME, or m-Goodman, forcing the design to be safer. Because the σrev is lower than Se, the part will break after infinite uses.
The S-N Diagram pictured shows how σrev compares to Sut and Se.
