Shaft flexibility factor (SFF)

Have you heard the expression "L over D", or "L cube over D fourth"? (They are
sometimes written as L/D, or L3/D4.) These expressions refer to what is known
as shaft flexibility factor, or SFF.

Shaft flexibility factor (SFF) is an index that 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 their refinery - those pumps with high
vibration amplitudes, poor reliability, costly maintenance, and short mean-time-
between-failures (MTBF).

They found that “bad actors” have a common denominator - they have small shaft
diameter and long span (between impeller and bearing) 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 (SSF), represented by the
equation:

L^3
SSF  =  ---------

D^4

where:

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 SSF is [ * ]
For between-bearing pumps, the ideal range of SSF is [ * ]
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Shaft flexibility

SFF is used as index to compare the relative “shaft flexibility” of one pump with
another pump of similar size and design. A pump with lower SFF is considered to
have a more robust shaft, less deflection, and 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 SSF 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 SSF 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 data:

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 SSF equation derived from?
• On what conditions is the SSF 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?

[ * ] Some materials are excluded in this beta article.