Shaft flexibility factor (SFF)
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Have you heard of the expression "L over D", or "L cube over D fourth"? (It is
sometimes written as L/D, or L^3/D^4.) This expression refers to what is known
shaft flexibility factor, or SFF.

Shaft flexibility factor (SFF) is an index whose use was popularized by a major
American oil company in the 1970s. The company, now part of a large British
conglomerate, analyzed hundreds of "bad actor” pumps in its refinery - those
pumps with high vibration amplitudes, poor reliability, costly maintenance, and
short mean-time-between-failures (MTBF).

It was found that “bad actors” have a common denominator - they have small
shaft diameter and long span (between impeller and bearing, or between
bearing span) resulting in large shaft deflection and high vibration amplitudes.
These factors often resulted in frequent premature failures of bearings and
mechanical seals.

Analyzing the shaft deflection of thousands of pumps in a refinery was tedious
and time-consuming. (A large-size refinery can easily have up to 5,000 pumps.)
In lieu of doing detailed shaft deflection analysis, the company simplified the
process and came up with an index called shaft flexibility factor (SFF),
represented by the equation:

SFF  =  ---------


L         - span between impeller and radial bearing centerlines (overhang pumps)
or span between centerlines of radial bearings (between-bearing pumps)

D        - shaft diameter under the shaft sleeve at the stuffing box  

^ is an exponential symbol

For overhang pumps, the ideal range of SFF is [ * ]
For between-bearing pumps, the ideal range of SFF is [ * ]

In pumps of similar size and design, the pump with lower SFF is considered to
have a more robust shaft, has less deflection, and has longer MTBF, than a
comparable pump with higher SFF.

Decades ago, the use of smaller pump shaft diameter was strongly influenced
by economics - smaller shaft means smaller and cheaper seals, bearings,
sleeves, etc. It also means less frictional and leakage loss resulting in improved
pump efficiency. In some high suction pressure application, it was even
necessary to reduce the shaft diameter and seal size to reduce the hydraulic
axial thrust in overhang pumps. And in some low NPSHA situations, reducing the
shaft diameter helps reduce the pump NPSHR by reducing the blockage through
the impeller eye.

On the other hand, the longer span design was influenced by the need to
design longer stuffing box that can fit both mechanical seals and packing rings.
Packed pumps typically require several packing rings for effective sealing, thus
requiring longer stuffing box. The need for pump covers to have cooling jacket
also resulted in longer stuffing box, and longer span. (Advances in design have
now allowed mechanical seals to operate at higher temperature without cooling.)
To some extent, the move towards standardization has contributed to longer
span when a common standard shaft, cover, or bearing bracket, is used among
pump of the same design but different sizes.

The smaller shaft diameter and longer span do not imply an inferior design, or
design flaw. Many pumps with high SFF run as good as their counterparts with
low SFF, if selected and used properly.  The situation becomes problematic
when a high SFF pump operates off peak, and/or operates at high suction
specific speed (NSS) conditions. Operating at off peak increases its radial load
that, in turn, increases shaft deflection. On the other hand, the cavitation
occurring in high NSS pump increases its vibration level that, in turn, also
increases shaft deflection. Thus, improving the reliability and MTBF of a pump
oftentimes requires not only a reduction of its SFF, but also a hydraulic re-rate
to ensure that its hydraulics is optimum for the operating conditions.

A pump can be modified to reduce its SFF by increasing its shaft diameter,
decreasing its shaft span, or both. But making these changes is expensive. A
bigger shaft diameter needs bigger mechanical seals and bearings which add
significant cost to the equipment. Therefore, the cost-benefit has to be analyzed
carefully to find an SFF that will yield an optimum value to the added investment.
As the shaft diameter increases more, and as the span is decreases more, there
is a diminishing return on the added costs needed to effect those changes.

Example of using SFF assessment in pump evaluation:

A company received three quotes for a single stage overhang pump. The
pumps have same efficiency and are practically identical except for the following

Option 1 - has SFF of 80 and costs $60,000
Option 2 - has SFF of 90 and costs $55,000
Option 3 - has SFF of 95 and costs $50,000

Based on the SFF assessment used by [ * ], which Option should be selected?
Will a similar pump with SFF of 100 and costs $40,000 only be a better option?

The answers to these questions are available on request. [ * ]

Questions for further discussions: [ * ]

  • Where was the SFF equation derived from?
  • On what conditions is the SFF comparison useful, and when is it not?
  • There are situations where modifying a pump to reduce its SFF can result
    in unintended harm to a pump. Do you know what these instances are?
The EMA Project
Photo of pump shaft - the shaft diameter and span between bearings affect the shaft flexibility