SUBJECT: Shaft deflection and the pump best efficiency point. 10-8

We all know that L3/D4 is a convenient method of talking about shaft deflection and this number has proven to be an accurate method of predicting premature seal and bearing failure. In another section of this Technical Series I gave you the formula we use to calculate the force on the end of the shaft of a single stage centrifugal pump with an overhung impeller. This is the most popular pump being used in the process industry today. Here again is the formula we use to calculate the hydraulic force on the end of the pump shaft:

As I have in my other papers I will be working the numbers in both the imperial and metric systems. First we will work the numbers in the imperial system and at the end of this paper we will make the same calculations in the metric system.

I will use a direct conversion to metric to show you that the conversion works. In reality we would not be using these exact numbers, but it is important to develop confidence in your ability to work in either system. Because I am working with a direct conversion I will continue to use 1750 rpm or the numbers will come out differently. I am well aware that your calculations will probably be at 1450 or 2900 rpm.

We are now going to use this formula to make an actual calculation of the shaft deflection on a typical ANSI standard pump at shut off. This is a common starting method for centrifugal pumps of this type. The following information would have been read off the pump curve that came with the pump and a radial thrust factor chart (K) that is shown in paper 1-6

Putting these numbers into the formula we get:

= 383 pounds

If we add the weight of the impeller estimated to be ten pounds, the total force on the end of the shaft becomes 393 pounds.

Now that we have the total force, we will use this information to calculate how much the overhung shaft will bend. To make the calculation we will use the following bending formula:

Substituting this term into the bending formula we get:

If we simplify the formula we would get:

Thirteen thousands of an inch bending is enough deflection to cause problems with the impeller, wear rings, mechanical seals and bearings.

Here is the metric force formula:

Here are the numbers converted to metric:

Putting these numbers into the formula we get:

If we add the weight of the impeller estimated to be 4.54 kg., the total force on the end of the shaft becomes 182.12 kg..

Now that we have the total force, we will use this information to calculate how much the overhung shaft will bend. To make the calculation we will use the following bending formula:

Now lets put in the actual numbers and see how much the shaft will bend with 182.12 kilograms force on the end of it:

F = 182.12 kilograms

L = 22.86 centimeters

D = 3.75 centimeters.

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