Critical Shaft Speed, Overhung Load
Critical Shaft Speed, Overhung Load
(OP)
I'm doing an analysis for the critical speed of a shaft with overhung load. The overhung load is a small gear, about 8 lb. Load on the gear is 300 lb which is what dictates shaft deflection and stress. Shaft rotation about 13,000 RPM.
Question: Should the load used in the critical speed equation be the weight of the gear or the applied load?
Question: Should the load used in the critical speed equation be the weight of the gear or the applied load?





RE: Critical Shaft Speed, Overhung Load
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RE: Critical Shaft Speed, Overhung Load
Critical speed of single degree of freedom system is related to (k/m)^1/2.
Note there is no force term in there.
The exception would be if an applied load somehow stiffened things up (or down) as in axial force increasing restoring forces in a guitar string or inducing buckling (zero critical speed) in a column or shaft.
The importance and usefulness of static deflection is through its relationship to stiffness (k). If static deflection was "the problem" then space craft at zero gravity would be free of resonant frequencies .
RE: Critical Shaft Speed, Overhung Load
The critical speed of a drive shaft is determined by the deflection, or "sag," of the shaft in a horizontal position under its own weight. The less the sag, the higher the critical speed. ... Knowing the natural deflection of the shaft, it is possible to calculate the first critical speed from the equation:
Ncrit = 187.7 * ( 1/ deflection)^.5
It isn't clear if this 'sag' should take into account loads imposed on the shaft other than the weight. Looking through other literature left this question open. Machinery handbook for example, discusses load and seems to imply weight only, but is equally unclear.
Knowing the vibration is set up because of the mass revolving around the centerline of the shaft, I might think it is only the mass itself that is important, but deflection of the shaft is also a function of imposed loads due to gearing, belt tension, or other loads perpendicular to the shaft axis. Both weight and imposed loads are of course forces and equally capable of deflecting the shaft, so it is unclear to me what loads should be considered for critical speed.
RE: Critical Shaft Speed, Overhung Load
BigInch
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RE: Critical Shaft Speed, Overhung Load
The answer I got was that the load used for the calculation is only the weight of the spinning mass as Tmoose said. Reason is that this mass creates a force which, if we consider it a vector, is rotating 360 degrees. This force will cause the shaft to wobble or gyrate around the shaft axis, and if it wobbles at it's natural frequency, it will induce stress above and beyond what it normally would induce due to a static load.
The applied load from gears or belts is a vector in a constant direction, unchanging. This load will not force the shaft to wobble, so it need not be considered for the critical frequency.
The total bend in the shaft can be seen as a static bend caused by external loads along with another rotating bend superimposed on that one caused by the rotating mass.
Does that sound about right?
RE: Critical Shaft Speed, Overhung Load
BigInch
-born in the trenches.
http://virtualpipeline.spaces.msn.com
RE: Critical Shaft Speed, Overhung Load
Cheers
Greg Locock
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RE: Critical Shaft Speed, Overhung Load
r=e*w^2/[1-(w/wn)^2]=Ze
the classical 1 degree of freedom response.
where k is the spring constant at the shaft end.
m(x+ecoswt)"+kx=0 in x direction
m(y+esinwt)"+kr=0 in y direction
mx"+kx=mw^2coswt
my"+ky=mw^2sinwt
wn=(k/m)^.5
Steady state solutions are
x=eZcoswt
y=eZsinwt
At resonnance w=wn , causind r to blow up.
adding these two vectorially you get
the result above for r
RE: Critical Shaft Speed, Overhung Load
Let me ask you this are you dynamicaly balancing the shaft assembly? I'm working on a miniature system that spins at 90K RPM. After a lot of testing I decided that getting the entire shaft assembly minus bearings balanced was the best thing. I also had a problem with shaft deflection and bearing preloads but have since solved those problems.