ortabe:
RE: your 10JAN 7:32 post; that’s called pulling something out of your butt, but it may not be too bad a guess.
RE: your 10JAN 12:36 post, 1st para., last sentence; I think you read that right and have good memory.
To get your brain and thinking in gear; think of stress concentrations at shaft transitions, more generous radius means lower stresses; the point being, how do the stresses want to flow and if you pinch them down too much you have high stresses (concentrations). And you have that problem to consider in your shaft from the stress standpoint. But, assume no radius from 300mm to 900mm for our discussion, and still ask the question, how do the stresses and strains act; they do not turn 90° and go up to 900mm and turn 90° again and go down the length of the shaft. Rather, they will tend to make some nice gradual transition to a larger radius, and if the middle length is long enough, they will attain your full calc’d. angular stiffness k=JG/l, or corresponding stresses ? and ? for some distance. In this transition length they will be influenced by the material outside the transition zone. I would spend pages and pages and hours too, of Theory of Elasticity clacs. and verbiage to try to prove this. From the stress and stiffness standpoint, I dare-say, you could run a line from the 300mm dia. to the 400mm dia. and have a fair approx. for the stiffness, given the lengths.
Most of you have probably read my standard harangue about FEA (access to a FEA program) does not an engineer make. But, here it seems to me, you have a good application for FEA biting you in the butt and instead you pulled 450mm out of your butt; which I think might still be a pretty good first guess, given the 300mm length. Model this shaft and apply a unit torque or a unit rotation and develop your own stiffness; much better than any guess. For at least a dia. on either side of the transitions you want a fairly tight mesh; I guess that means the whole shaft, given the dia’s. and lengths.
Remember, your stiffness (k=JG/l) is an idealized stiffness which only gives correct results at points somewhat removed from transitions and points of torque application, etc. (Saint-Venant’s Principle, et.al.) An old rule of thumb is shaft dia. or beam depth, plus. Thus, it’s probably somewhat nebulous given the dimensions of your shaft. But, you should be able develop a more meaningful stiffness and stress distribution with good FEA modeling and proper interpretation of the results. You must still pay attention to stress concentrations, and total system balancing. You must include the total mass distribution in your dynamic analysis.
For all this free advice, I want a copy of your work and results, for my own edification. I am awaiting the results. Good Luck, prove me right, please.
