mrjonadam
Aerospace
- Mar 25, 2009
- 1
I have a rotating hollow shaft and I'm assuming a fixed end condition. I'm looking for the critical(whirling) speed. Right now I'm using the following equation:
Nc = (3.57*sqrt(EI/m))/L^2
where, E = Young's modulus (lb/in^2)
I = second moment of area (in^4)
m = mass per unit length (lb/in)
L = length (in)
Nc = critical speed (rpm) or (Hz)?
I have attached a PDF with the derivation of the calculation and the equation I'm using. This equation is for a shaft between long bearings and can be found on the last page of the document.
I'm having trouble understanding the units that result from this critical speed calculation. I get the output to be in units of in^(-1/2) and I'm pretty sure it should be either rpm or Hz.
Also, I followed the derivation noted in the PDF for critical speed and agree that it should be:
w = sqrt(KEI/mL^3)
where, K = is a constant depending on the mass and the end fixing conditions.
But I don't know how to find or what units K might be in for my problem.
I greatly appreciate anyone's help in figuring out what I'm doing wrong, or a suggestion on another equation to use.
Nc = (3.57*sqrt(EI/m))/L^2
where, E = Young's modulus (lb/in^2)
I = second moment of area (in^4)
m = mass per unit length (lb/in)
L = length (in)
Nc = critical speed (rpm) or (Hz)?
I have attached a PDF with the derivation of the calculation and the equation I'm using. This equation is for a shaft between long bearings and can be found on the last page of the document.
I'm having trouble understanding the units that result from this critical speed calculation. I get the output to be in units of in^(-1/2) and I'm pretty sure it should be either rpm or Hz.
Also, I followed the derivation noted in the PDF for critical speed and agree that it should be:
w = sqrt(KEI/mL^3)
where, K = is a constant depending on the mass and the end fixing conditions.
But I don't know how to find or what units K might be in for my problem.
I greatly appreciate anyone's help in figuring out what I'm doing wrong, or a suggestion on another equation to use.