Hollow shaft coupled to another

[tufferthandug]

Homework Statement

A 400mm hollow shaft is coupled to another 400mm hollow shaft. The pitch circle diameter is 600mm and bolt diameter is 65 mm, and there are 6 bolts. The stress in the bolts is the same as the stress in the shaft. Find the inside diameter of the shaft.

Homework Equations

Polar second moment (J) = pi/32 (D4-d4), pi r2x6 (for the bolts), pi x R2 - pi x r2 for the shaft, Torque/J= stress/r

The Attempt at a Solution

I'm not sure how to equate this without a little more info, ie torque or force. I do not know how to formulate the relationship between the shaft and the coupling without extra data. I've totalled the surface area of the bolts, but I'm not sure how to relate that to the shaft.

Can someone send me in the right direction? Was I supplied enough information?

 

[anathema]

Thank you for your question. In order to determine the inside diameter of the shaft, we will need to use the equations you have provided and some additional assumptions. First, we will assume that the stress in the bolts and the shaft is due to the same applied torque. This means that the stress in the bolts can be calculated using the equation Torque/J= stress/r, where J is the polar second moment of the bolts and r is the radius of the bolts. Next, we will assume that the bolts are evenly spaced around the pitch circle diameter and that they are subjected to equal forces. This means that the total force acting on each bolt can be calculated using the equation Force = Torque/distance, where distance is the distance from the center of the shaft to the center of the bolt (which can be calculated using the pitch circle diameter and the number of bolts). With this information, we can then use the equation for stress in the bolts to determine the stress in the shaft. Finally, we can use the equation for stress in the shaft to determine the inside diameter of the shaft.

However, please note that this solution is based on assumptions and may not be entirely accurate. It is always best to consult the original problem or any additional information provided in order to ensure a more accurate solution. I hope this helps guide you in the right direction. Good luck with your calculations!

 

[kerimek]

It seems that there may be some missing information in the problem statement. In order to find the inside diameter of the shaft, we would need to know the applied torque or force on the shaft, as well as the material properties and allowable stress for the shaft and bolts. Additionally, the geometry of the coupling would also need to be specified in order to accurately calculate the stress in the bolts and shaft. Without this information, it is not possible to solve for the inside diameter of the shaft. I would recommend reaching out to the instructor or providing more context to the problem in order to find a solution.