**Author’s Note**: *My October 2017 *Pumps & Systems* column (read it here) on shaft deflection due to internal loads ended with a challenge to the readers to do their own calculations to compare radial load on the shaft due to an impeller weight versus internally induced hydraulic load. Below is one of the responses provided by our readers:*

## Questions for Dr. Pump

**Hello Dr. Nelik,**

Your recent article addressed various reasons for mechanical seal failures including off-best efficiency point (BEP) operation of an end-suction pump. The following is an estimate of impeller shaft deflections at various operating points in a single-volute end-suction pump.

The performance curve, shown in Figure 4 of the October article, indicates a 3,000-gallons per minute (gpm) BEP. Using this flow rate and the Hydraulic Institute (HI) expected-efficiency chart, a pump with an approximate specific speed of 1,500 was chosen. So, at a BEP operation of 3,000 gpm, 250 feet (ft) and 1,750 rotations per minute (rpm), the following results were obtained by using a 2 3/16-inch diameter impeller shaft extending 12 inches from the closest bearing. Using the expected efficiency estimator program, the impeller diameter, D2, was determined to be about 17 ¼ inches (in.). An estimated impeller weight of 75 pounds was used.

The calculated L3D4 ratio of 76 is about midway in the American National Standards Institute (ANSI) range of 20 to 120.

The cantilever beam, Equation 1, shown in the article, was used for calculating deflections at the end of the impeller shaft due to applied impeller weight or radial thrust load at that point.

*Pumps & Systems*, October 2017). It is the high hydraulic radial thrust and not the weight of the impeller that causes excessive deflection and seal failures.

The equation, y=(Fr*X^2)/(6*E*I) (3*L-X), was used to estimate shaft deflection, y, elsewhere, X from nearest bearing, due to a radial load, Fr, at the free end, L.

The equation, θ=(Fr*X)/(2*E*I) (2*L-X), was used to estimate the shaft deflection angle, θ, at a location, X from nearest bearing, due to a radial load, Fr, at the free end, L.

The center of the impeller and the seal face locations were assumed to be X=L=12-in and X=6-1/2-in respectively from the closest bearing.

The shaft deflection due to impeller weight alone was calculated to be about 0.0013-in at the end, L, and about 0.0005-in at the seal, X.

Radial thrust, Fr, at various percentages of BEP operation were determined by using K factors from a curve for single-volute pumps. These factors were then used in the equation, Fr=K*(H*sg/2.31)*D2*B2, where D2= impeller OD and B2= impeller exit width (≈1.33-in).

Shaft deflections due radial thrust are about 1.3 times those due to the impeller weight alone at BEP operation, about 5.8 times greater at 50 percent of BEP and about 9.3 times greater at shut off.

Regards,

Lee Ruiz,

Oceanside, California

## Feedback From the Author:

Good work, Lee! Your calculations are excellent.

I plotted your results (for a single volute pump) and added a diagram showing “classical” understanding and comparison of such deflection for various pump volute design. Your calculations follow very closely to the “classics.”It is also interesting to compare the drop in load (and thus in deflections) when the casing design is modified.

What is not usually known is the effect on efficiency due to such casing changes.

Obviously, from a reliability standpoint any reduction in load (deflection) is good news. But at the same time, a reduction in efficiency follows, which is the price that’s paid for the reduced load.

## Next Challenge

Here is a next question to challenge the readers: Can you quantify such efficiency degradation due to casing modifications for better reliability? Obviously, a balance needs to be evaluated for each case, depending on a pump type, size and energy level.

Our International Pump Research and Development Center conducts such testing, and we welcome those of you interested in those results and data to contact us: www.pumpingmachinery.com/consulting/consulting.htm