Page 369 - Centrifugal Pumps 2E

334 Centrifugal Pumps: Design and Application

Shaft Sizing Based on Peak Torsional Stress

The stress produced in the shaft as a result of transmitting driver en-
ergy to the impellers is torsional. A simple technique for sizing pump
shafts is based on limiting the maximum torsional stress to a semi-empiri-
cal value. The limiting-stress value is based on the shaft material, operat-
ing temperature, and certain design controls on key way geometry, diam-
eter transitions, and type of application. Since only one stress value is
calculated due to one type of load, the limiting stress is obviously kept
low. Typical values range from 4,000 psi to 8,500 psi. With this method
of shaft sizing, no attempt is made to calculate the effects of stress con-
centration factors, combined stresses resulting from radial and axial
loads, or stresses due to start-up and off-design conditions.
The peak torsional stress is equal to the following;

The torque is calculated from the maximum anticipated operating
horsepower. Special attention should be given to pumps operating with
products having a low specific gravity. Shop performance testing will
generally be conducted with water as the fluid, and overloading the shaft
may occur; hence, performance testing at reduced speed may be re-
quired. The shaft diameter used for calculating the stress should be the
smallest diameter of the shaft that carries torsional load. For most cen-
trifugal pumps the shaft diameters gradually increase toward the center
of the shaft span. This is necessary to facilitate mounting the impellers.
As a result the coupling diameter tends to be the smallest diameter carry-
ing torsional load. It is a good design practice to ensure that all reliefs
and grooves are not less than the coupling diameter. On some designs,
such as single-stage overhung pumps, the smallest shaft diameter is un-
der the impeller, in which case, this diameter shall be used for calculating
shaft stress. Reliefs and groove should not be less than this diameter,
Example
Determine the minimum shaft diameter at the coupling for a 4-stage
pump operating at 3,560 RPM where the maximum horsepower at the
end of the curve is 850 bhp. Use 4140 shaft material with a limiting
stress value of 6,500 psi.

Solution