Article #40: Bearing Forces Due
to Shafts Misalignment
Dear Dr.
Regarding your analysis of the force created by misalignment of a coupling between the motor and pump, I believe you are using an incorrect assumption. The 20# rotor unbalance at 0.020” is not the same as misalignment. Each coupling half would be machined and for all intention purposes balanced on the shaft. Misalignment of the two coupling halves does not equate to an eccentric out of balance load as you have shown in the February article in Pumps and Systems. I would expect that the coupling has some type of misalignment capability with a grid or elastomer to accommodate misalignment and shaft run-out. The only force transmitted through the coupling to the shaft would be by the grid or elastomer which would be significantly less than the weight of the coupling. Therefore, the life of the bearing would not be significantly impacted by “minor” coupling misalignment. That is also why you did not see a larger vibration magnitude between the two different alignments. Hopefully my explanation makes sense to you.
Regards,
Rick
Vice President Engineering
Littleford Day, Inc
Dr. Nelik,
In
response to the question of how shaft alignment affects mechanical seal life it
is my thought that the bearings are taking most of the negative effects of
the misalignment and the seal really is not affected until the bearings
start to fail. Assuming no severe pipe strain or soft foot
conditions exist, I would think that the seal should last until the
bearings begin to fail. From this point it depends on how much vibration can be
tolerated by the seal in question before it fails. Thank you very much for a
consistently great column. Keep up the good work.
Sincerely,
George M. Gates
Millwright
I have received
several great comments on the recently published article on rotor misalignment.
Below are two most representative, as they relate to bearings and seals, and
thus I wanted to reply on both issues at the same time. First of all, thank you
for your insightful and thoughtful questions, and I was impressed that there
still a lot of “thinking gun powder” out there! Let’s keep the challenge!
First, let’s talk
about the bearing loads, Rick. You are correct – misalignment is not the same
as unbalance. But the effect on bearing loads is similar, although in my
original article I did not elaborate on the exact details of the mechanism of
the load transmission. You are also right about the effect on these loads by
the type of coupling, but unfortunately the problem with misalignment remains
for either rigid, or soft coupling cases.
Let’s consider a
very simplified example of the flexible coupling, as sown on Figure 1. Imagine
the rotors being offset by eccentricity “e”, with simple disks (hubs) at the
shafts ends. Imagine there is a thin rubber band connecting the hubs – an
extremely simplified example of a flexible coupling:
Fig. 1 Exaggerated simplified examples of a
flexible coupling connection with a single rubber spoke
As motor shaft
rotates, the rubber spoke deforms by x=2e, and its center deflects by the
eccentricity “e”. The elastic force of deformation is then F=kxe, and is small,
because of the spring constant of the rubber spoke (k) is very small. In this
case, bearing forces Ra and Rb are indeed small, but the rubber spokes will not
last very long, as they flex until, accumulating enough revolutions, fail.
Now consider
another extreme, by replacing the rubber spoke by a huge stiff metallic spoke:
Fig. 2 A single
large metal spoke is too stiff to deflect, so the entire driven rotor deflects.
Now, the entire
rotor is too flimsy in comparison to the metal spoke, and it deflects like a
worm, as shown on Fig. 2. Due to rotation, the deflected mass “M” exerts
centrifugal force on the rotor. True, the mass “M” is not the entire rotor, bit
a portion of it, plus the mass of the metal spoke. Thus mass “M” is some
portion of the rotor mass, and would depend on each design under consideration,
rotor geometry, as well as the geometry of the motor rotor as well, plus their
stiffness.
The exact fraction
of rotor mass “M” can be evaluated in each case, but, in the extreme, to
simplify, the entire rotor mass can be assumed as involved into deflection, and
thus, given the offset “e”, the force can be calculated, which would then allow
to calculate bearing reactions.
For a rough rule
of thumb, this normally is good enough, as it tells the story: misalignment can
hurt, and so just do alignment right, and never mind calculations. However,
should such calculation indeed be of interest (perhaps in academic sense), a
lot of research on this subject is available, with details, sophistication of
modeling, FEA application, and testing. For example, a good paper on this
subject is “Study Shows Shaft Misalignment Reduces bearing Life”, by
Your point to why
my test did not detect much difference in vibration is a good one. However, the
pump I tried this on was a small one, and thus perhaps not enough energy level
to show the difference. Also, come to think of it, I think the pumps had a
flexible coupling, thus, it would seem per either mine or your theory, its
flexibility was the reason for low loading.
Now, to answer
In conclusion, -
your questions are very important and refreshingly challenging, and your
interest in understanding the basics is commendable. And – true to the promise
– a free coupon to attend our next
Keep on pumping!
Lev