Re: Kilian's mount: Parts are getting p
Bob Luffel (bobl@hpgrla.gr.hp.com)
Mon, 1 May 95 10:38:00 MDT
>
> >
> >
> > Somehow I keep forgetting my structures lectures. It is true that
> > stiffness is a function of ^4, but isnt the moment of inertia a function
> > of the OD minus the ID which will make a tubular section be less stiff
> > than a solid. It is just for stiffness to weight ratio that hollow sections
> > become much better. I somehow have a feeling that this thread is
> > implying hollow is the answer. There is a trade where hollow becomes
> > best, but I have a difficulty with small diameters.
> >
> > Bob
> >
> >
> > >
> > >
> > >
> > > The polar moment of inertia of a shaft (or tube) is also to the 4th power,
> > > so torsional stiffness is increased to the same degree as
> > > transverse bending.
> > >
> > > I have always wanted to drill out the center of my German Equatorial's
> > > stainless dec. shaft to lighten it, but drilling long straight holes
>can be
> > > a challenge (though gun-makers solved this one long ago...).
> > >
> > >
> > >
> > > Bob
> > >
> >
> >
> I am no engineer but from I have read if a solid shaft of diameter D has
> stiffness 100% and a weight of 100% then a hollow shaft of diameter D with
> D/16 wall thickness will have a stiffness of 41% and a weight of 23%. A shaft
> of 1.32D with D/16 wall thickness will have stiffness of 100% and weight of
> 31% of a solid shaft D.
>
> So yes a solid shaft of given diameter is stiffer then a tube but a 1/3 larger
> tube at 1/3 the weight will give us the same stiffness.
> This info was from Gleaning For ATM Sky and Tel June 1976. The artical
> is Structural Considerations for Telescope Makers.
> Bob Pfaff
>
Right on the money.
It all comes down to design goals and your ability
to make the tradeoffs - if you want to minimize weight and still achieve
a given stiffness, then a larger hollow structure will move you in the
right direction (assuming you can accomodate the larger member). Remember
the old Byers 812? It had a large/hollow conical RA axis (very stiff and
it had a large diameter surface for mating the dec axis to).
Hollowing out existing shafts will of course lower their stiffness
(in bending and torsion to the same degree). Also, since small shafts
weigh less than large ones anyways, you won't get much lightening
effect for small shafts!
Here are some simple formulas to calculate relative stiffnesses/weights:
Do = Outer Diameter
Di = Inner Diameter
(Do^4 - Di^4)/Do^4 = Ratio of hollow shaft stiffness to same dia solid stiffness
(Do^2 - Di^2)/Do^2 = Ratio of hollow shaft weight to same dia solid weight
To compare a hollow shaft to a different dia solid, just substitute the
solid shaft's diameter into the Do of the denominator.
Aluminum is .343 times as stiff as steel and .348 times as heavy as
steel (carbon steel).
Bob Luffel (there are a lot of Bob's around here, aren't there?)