Article #40: Bearing Forces Due to Shafts Misalignment


Dear Dr. Nelik,

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.



Rick Kesig, PE

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. 



 George M. Gates 




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 Wesley Hines, et al, from University of Tennessee, published in Maintenance Technology magazine. It calculates the loads for different types of couplings, and relates these loads to bearing life L10. It contains an interesting tabulation of L10 bearing life as a function of misalignment. For example, for a grid type coupling, 5 mils misalignment reduces bearing life by 50%, according to the authors’ findings.


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 George Gates’ question on the effect of misalignment on mechanical seal, - consider the illustrations above. Since the rotary seal part sits on the shaft, which is deflected due to misalignment, it will deflect away from the stationary seal face, and thus a leak. Seal manufacturers generally state the 0.002” being a maximum allowable misalignment of the seal faces, i.e. it does not take much misalignment to cause seal problems.


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 Pump School is awaiting for you!


Keep on pumping!


Lev Nelik