Lateral Analysis

Lateral analysis is a critical speed analysis performed on a rotor by modelling its
shaft as a series of elements of specific length and diameter, and with constant
modulus of elasticity.

The intent of lateral analysis is to calculate the critical speeds (1st, 2nd, and 3rd)
of a rotor to find out if there are sufficient margins of separation between those
critical speeds and the rotor operating speed. Lateral resonant frequencies can
excite the rotor and result in high and damaging rotor vibration.

If the analysis indicated that there were no sufficient margin of separation, a
change in the rotor design could be made early on in the design stage to get an
acceptable amount of separation. In many application, mostly low energy,  a 10%
separation is acceptable. Some standards, such as API 610, specify the required
minimum amount of separation.

Standard pumps running at standard RPM are presumed to have been designed
with no resonant frequencies at their normal running speeds. Hence a lateral
analysis is typically required in highly specialized service, such as in high speed
application, in critical service, in train arrangement that include another major
piece of equipment, such as a  turbine, or a gearbox, or in newly designed
equipment.

In an undamped analysis (dry critical speed), the damping effects of the process
liquid, or the film damping at the bearings, are not included in the analysis. In a
damped analysis (wet critical speed), the damping effects are included.

In a typical critical speed analysis, a model drawing of the rotor is made. The
static loads consisting of impeller/s, shaft, coupling, and other rotating parts such
as wear rings and sleeves, are considered lumped masses located at their
respective centerlines. The following calculations are then performed:

• Support stiffness.
• Hydrostatic stiffness, of wear parts, which is a function of the rotor rotative
speed and the differential pressure across those parts, but independent of
• Hydrodynamic stiffness of bearings which is a function of the bearing load
due to static and dynamic reaction forces.
• Static and dynamic reaction forces.
• Polar mass moment of inertia.
• The eigenvalues and resonant frequencies of the rotor.

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