Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

336 Centrifugal Pumps: Design and Application
Substituting and solving for N:
Shaft Sizing Based on Fatigue Evaluation
Pump shafts are subjected to reversing or fluctuating stresses and can
fail even though the actual maximum stresses are much less than the yield
strength of the material. A pump shaft is subject to alternating or varying
stresses as a result of the static weight and radial load of impellers, pressure
pulses as impeller vanes pass diffuser vanes or cutwater lips, driver
start-stop cycles, flow anomalies due to pump/driver/system interaction,
driver torque variations, and other factors. In order to perform a fatigue
analysis, it is first necessary to quantify the various alternating and
steady-state loads and establish the number of cycles for the design life.
In most cases, the design life is for an infinite number of cycles; however,
in the case of start-stop cycles, the design life might be 500 or 1,000
cycles depending on the application.
Once the loads have been defined and the stresses have been calculated,
it is necessary to establish what the acceptable stress values are.
The use of the maximum-shear-stress theory of failure in conjunction
with the Soderberg diagram provides one of the easier methods of determining
the acceptable stress level for infinite life (Peterson; Shigley;
Roark). Since the primary loads on pump shafts are generally torsion and
bending loads, the equation for acceptable loading becomes: