Analysis Continued
Gear Sizing
A key constraint on the chosen design is the amount of power that can be transfer through the gears. From the dimensional constraints shown in appendix B approximant gear dimension were specified as a pitch diameter of one inch and a face width of one half inch. PowerGear software (http://www.gear-doc.com/powergear.html) was used to analyze the amount of power that could be transferred with these sized gears. This analysis lead to the selection of helical gears to transfer more power. From PowerGear, a value of 7.9 ft-lbs is the maximum allowable torque. However it was realized that due to the depth of the catapult cylinder pocket at least a 2:1 gear ratio would be needed. This would cut the maximum torque by more than half which lead to a search for alternative methods of power transfer.
Sprocket Selection
In order to fulfill the geometric requirements, particularly the socket offset requirement, a roller chain and sprocket were analyzed to determine if this would be more advantageous than helical gearing. The maximum sprocket diameter that could be used is one inch due to the thickness limitation. This makes the ANSI chain #25 the heaviest COT chain that can be used. The working load is 22lbf for this chain. This means this sprocket and roller chain pair can transfer eleven ft-lbs of torque. This is higher than what could be transferred using helical gearing. Sprockets are also more convenient since a 1:1 ratio can be used to achieve the needed offset.
Shaft Analysis
The drive shaft and socket shaft were analyzed to insure that the required torque could be transferred. The torque of seven ft-lbs is the only significant force acting on these shafts. The critical point in these shafts is the smallest diameter which is constrained by the sprocket inner diameters to be 0.25 inches. To find a factor of safety for this section, first, the shear stress due to the torque was calculated. Von Mises theorem was then used to find the equivalent axial stress. Next, an endurance limit was calculated accounting for the size, surface finish, and reliability required. Finally, the Goodman criterion was used to find a factor of safety. The factor of safety for both shafts was 3.5.
Finite Element Analysis
A finite element analysis was performed on the socket portion of the tool. The analysis was done to determine the stresses and strains on the socket caused by the torque applied. To simplify the model of applying a torque to the socket, instead of an actual distributed load being applied, two point forces were applied on opposite nodes. From previous analysis, it was determined that a maximum torque that would be applied is 8 ft*lbs. From this load the point forces were calculated. The value for the two point forces applied is 123 lbf. These two point forces are applied at opposite nodes and in opposite directions to model an equivalent torque that would be applied. The figure below shows a diagram of the socket in ANSYS meshed, where the forces are applied.
Maximum deformation is determined to be 112 micro-inches. Since deformation is very small it can be neglected