Determining Shaft Diameter

 One day I stumbled to the question of material selection of a pump shaft, as already well known by rotating engineer, reference to API 610 material tabulation is the quick way to determine.

However, arrive challenge from pump manufacturer to not respect to API 610 tabulation, that have risk to be corroded due to environmental condition suitability and pumped liquid. Instead of superduplex SS (D-2) pump manufacturer propose AISI 4140 (Carbon Steel).

Expected corrosion rate is provided by pump manufacturer, to define acceptance criteria, it refer to; how much safety factor or extra diameter given on the pump shaft itself.

Reference made to Maintenance Fundamental - R. Keith Mobley 2nd ed.

There is a practical equation that defined min. shaft diameter as shown below

Quick formula to determine shaft diameter (eq.1)

shaft dia

shaft stress formula

CASE SAMPLE

AISI 4140 shaft, yield at 60.000psi, use for pump with power 498kW =668HP, spin at 1800RPM, shaft data shown in datasheet 90mm, define whether the shaft size is acceptable?

Using above equation, we will get diameter min = 32mm, the real shaft diameter use by pump manufacturer is 90mm, which is 3x the diameter minimum. This is considered as acceptable, we must respect that in calculation it not yet considering manufacturing defect, microscopic material defect, temperature factor. So for quick check, this able to use.

However, further check shall be done, and the best way is to performance test is, whether there will be fail, and do a reference check of previous successful application also can be use as method to verify the design.

CURIOUSITY OF FORMULA SOURCE

In accordance with that I'm curious on how above quick formula derivate from.

Reference made to Standard Handbook of Machine Design by Joseph E. Shigley, Charles R. Mischke

Based on this book that used during my college, when checking shaft performance adequacy, below item to look into.

1. Distortion due to bending
2. Distortion due to transverse shear
3. Distortion due to torsion
4. Load Induced Stress

However, after checking, above practical formula is derivate from Load Induced Stress equation as below. Standard Handbook of Machine Design by Joseph E. Shigley, Charles R. Mischke

load induce stress formula derivation

The shear is function of Torque divided by diameter^3, so we able to conclude that eq.1 comes from equation (37.20) where conversion from Torque = Power / RPM. Those formula able to give quick justification whether the shaft diameter is adequate or not. Very Handy!