connection with key(theory)

[Domenico Garofalo]

I am studying the oral construction of machines 1 and I have stuck on the key, in practice I cannot understand this formula as it was found (I attached the photo).
m= fp×(d-h)/2+p×e+fpd/2=fpd
I hope some of you can help me.
Thank you.

 

[meccanicamg]

It's all written on the book page. are all forces for friction rather than reactions. Keep in mind that you're planting a wedge that works head and base everything for friction. then the balance of moments was made with respect to the tree center. It's all very basic.

 

[Stan9411]

It seems to me well explained. simply wrote the balance at the moments around the center of the tree given by the forces exchanged by the stick.
the first term comes from the force exchanged between the stick and the tree;
the third between key and hub;
the second is the possible disassesment that however is always in balance with fph/2 (first equation at the top) then those two terms go away (there is a less).

what remains is fpd/2 + fpd/2 = fpd

 

[PiE81]

is the balance of the moments of the forces acting on the tree, compared to the center.
fp tangential to the key and that is d-h/2 from the center
p that is normal to the key with arm and (no disassesment has nothing to do with it), as explained in the forehead
fp acting between hub and shaft, of tangential closure with arm d/2
the sum of these moments is equivalent to the moment m.

 

[Domenico Garofalo]

Thank you so much guys now I'm clear.