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How to calculate maximum torque capability on square drives ? ? ?

  1. Sep 24, 2007 #1
    Hi all,

    I'm hoping this is a relatively simple question, but the usual Google search has not really offered me any hints ?

    I need to make a shaft with a connection at one end. The type of connection is not critical as the shaft it will connect to is to be specially made as well. So, I have no limiting factors of compatibility with existing components, only that of torque.

    The shaft must be no larger that 16mm dia. which pretty much rules out 1/2" square drive, but I would like to be able to calculate max torque on a number of different sized squares or hex's. It would only be a guess, but I would imagine the calcs to include details about contact points and / or surface area ?

    The maximum torque I expect to see is 80Nm

    Any hints would be much appreciated.
  2. jcsd
  3. Sep 24, 2007 #2


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  4. Sep 24, 2007 #3
    I did read that thread earlier today, but its not so much the shaft that I need to know about, more the end fitting.

    I "think" I'm right in saying that the torque capabilities of a shaft are different to those of a square / hex. Again, I "think" I need a calculation which takes into account the number of contact points ?
  5. Sep 24, 2007 #4


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    The amount of torque that a shaft can handle is related to the material properties of the shaft. The shear strength (or resistance) of the shaft is dependant on the ultimate tensile strength of the shaft. Normally this value is found empirically. You cannot apply more force to the end connection, what ever it is, than the shaft can handle. If you do, you will shear the shaft (or yield it).

    Now that being said, the end connection may not be able to handle the amount of torque you are applying to it. Is that the question you are asking...how much torque can a square or hex shaped connection handle before stripping out?
  6. Sep 24, 2007 #5
    Yes, thats right. I beleive the shaft is more than capable of withstanding the torque. The question is focused on the end connection and at what point it would be stripped out.

    The problem lies in the fact that whatever connection method I choose (square drive / hex etc.) I must be able to machine the female form of the connection into a 16mm dia shaft, so I would like to be able to use a formula to estimate the torque capability of a number of connection types before I commit to costly CAD analysis. Unfortunately, the CAD analysis is a requirement of the job, but if I were able to have an "educated guess" at the best connection type I would be able to limit the amount of time that a FEA engineer sits at a screen costing me my precious pennies !
  7. Sep 24, 2007 #6


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  8. Sep 24, 2007 #7
    Not sure where to get the info for this one besides calculating the moment for the hex manually. You may instead of looking for info on hex bores try to look for a spline bore formula. Only places I ever see hex bores used is agg applications so maybe you can try that in your search as well.
  9. Sep 24, 2007 #8


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    You have to be careful with the assumptions you make with regards to non-circular cross sections in torsion. The elastic theory gets pretty nasty. However, there is our handy friend Roark's.

    For a square drive of side dimension 2a, the angular deflection, [tex]\theta[/tex] and the max shear stress [tex]\tau[/tex] are the following:

    [tex]\theta = \frac{TL}{KG}[/tex] where

    [tex]T[/tex] = applied torque
    [tex]L[/tex] = Length
    [tex]K[/tex] = Calculated constant in this case [tex]k=2.25a^4[/tex]
    [tex]G[/tex] = Modulus of rigidity

    [tex]\tau_{max} = \frac{.601T}{a^3}[/tex]
    Despite what many people think, the max shear stress is located at the mid point on each side! It is not located at the corners.
  10. Sep 28, 2007 #9
    Almost any square type end you make will have the force only on the corners . Thus, you have 1/2 the end-to-end distance as the moment arm. There might be a problem if the contact area is small and local pressure exceeds the plastic strength of the metal. If that is the case, you need some type of splined coupling or a welded one, or a tapered bushing, etc.
  11. Sep 28, 2007 #10


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    I'm confused by your concern. 80 Nm is not a scary torque level unless you are using a plastic shaft or some other soft material. Torque wrenches with 3/8" square drive are routinely rated to 100 Nm so you should have no trouble with 16 mm.

    Do select a high strength steel alloy. Square female holes are usually formed by broaching. Use coolant during machining it so you don't overheat the metal ("draw the temper"). You'll be fine.
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