stresses in forced shaft-mode

[Frankie85]

Good morning, I have a doubt (more theoretical than anything) that I can't melt on the calettamento with tree- hub interference.
I did time ago calculations to transmit a couple between a tree and a semi-joint calettato with interference.
As noted, radial and circumferential sigma is calculated according to the theory of the cylinders to a large thickness and finally occurs with a seizure with sigma c - sigma r (which in fact are main sigma, the third is 0).
the most solicited point is the internal radius of the hub in which sigma c is positive and negative sigma r.

the doubt is why this verification is made statically and in no treatment is taken into account the addition of a possible tau due to a torque moment?
It is quite typical that, in the most solicited point mentioned above, the value of tau is very low compared to the value of sigma c and r obtained, but I never see it taken into account.
Does anyone know if there's a theoretical reason I miss? Does any tau tend to always reduce the value of the circumferential sigma?
Thank you.

 

[meccanicamg]

Bye. the solicitation agents find them at my post number 2 of This is what debate.
forced calettamento is mainly done to convey torque moment and therefore tau exist here.

 

[Mattymecc]

if you want to check the hub torsion and calettamento you have to do as said mechanicalmg: imposed a fem model because in touch objects like a hub it is difficult to calculate how to distribute the tau...

instead for a tree the distribution of the sigma due to the calettamento, at the torque moment and to the bending one we know them very well... on the niemann or on the shigley is all explained by thread and by sign.. .
combine these tensions and check with trespass or von mises.

 

[Frankie85]

thanks for the answers @meccanicamg e @mattymecc , formulas coincide with mine. I had to get them out of the basic formulas by imposing all the c.c. because my case was a little particular (to recover an existing joint I had to interpose a ring between tree and hole... ).
reasoning with your formulas:
1- the stress on the tree is very clear and simple also because both sigma r and sigma c are equal to -p, therefore with sigma gt,max is calculated easily.
2- In the hub, however, even in your formulas the comparison stress does not take into account the tau, but only the values of sigma c and sigma r which then reducing the equations become function only of pmax and a.
This is the point: why? since the most stressed point of the whole system is precisely the inner diameter of the hub. for simplicity if you calculate the tau on the hub as if it were a hollow tree, its value at that point is very low compared to the value that you already get of sigma gt-max. Why is it almost irrelevant?

 

[ultratech]

an additional explanation:

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Guida rapida al calettamento forzato (conico e non), collegamento albero mozzo per trasmissioni meccaniche e organi rotanti.

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