This column has suggested using simple analytical models to
troubleshoot equipment. However, in some cases, a more detailed
solution may be required. The following case histories examine the heat up of
a steam turbine and the thermal growth of the rotor assembly
and stationary case. The finite element analysis (FEA) is used
here to identify root causes for failure events.
The outline of a simplified model for a four-stage steam
turbine is shown in Fig. 1. It is an
axis-symmetric model, which means that if you rotate the area
about the Y axis, it will be a solid three- dimensional model.
This greatly simplifies the FE modeling, and this information
is all that is needed for this problem. The results are easily
explained to management.
In this case, a rotor disk had rubbed against a case
diaphragm. The investigation team developed a list of possible
root causes. One of the many potential sources for the incident
was that, since the insulation was left off the machine, the
rotor shaft expanded more than in the cold case. Under these
conditions, the rotor would make contact with the diaphragm for
an instant. Management requested an analysis to confirm that
the touching event was possible.
This axis-symmetric model contains steam temperatures and
film coefficients; it can then calculate the thermal
displacements of the machine as it heats up from the cold
condition.1 This condition is called a
transient coupled heat-transfer-stress problem
because the nodal temperatures are determined from startup, and
they are automatically inputted into the stress model to
calculate displacements at any time.
Previous articles have illustrated the benefits of
simplified FE models when an in-house answer to a problem is
required quickly. It should be done by an engineer who also
understands the equipments
This analysis determines if the growth difference between
the rotor and case at the rub point, meaning (b-a), as shown in
Fig. 1, exceeds the cold-assembly clearance.
If it does, then there will be a potential interference and rub
incidence. Since a rub never occurred when the insulation was
in place, the same rub-point displacements will be compared
with the insulation on and off.
Fig. 1. Axis-symmetric
view of a steam turbine.
The analysis indicated that, although the case was cooler
without the insulation, so was the rotor assembly, and the
growth difference (b-a) was essentially the same. This is not
unreasonable since the gas temperature at each stage stays
about the same as it warms up the rotor and case. The rub
problem was attributed to other causes. However, the insulation
was reinstalled for safety and efficiency reasons.
Case 2. An analysis was
also done on a 12-stage 40,000-hp steam turbine with similar
The presented examples with FE show that an analysis can be
useful in determining what isnt the cause, as
well as what is the true cause. By eliminating a
possible cause, the investigation can proceed in reviewing
other potential concern areas. HP
1 Lawrence, K. L., ANSYS Tutorial Release 10, SDC
2 Sofronas, A., Case 44: Cracking due to
sudden temperature changes in piping, Hydrocarbon Processing, May 2008, p.
3 Sofronas, A., Case 46: Rotary screw
compressor failure, Hydrocarbon Processing, September
2008, p. 168.
4 Sofronas, A., Case 61: Pressure loss in a
reactor, Hydrocarbon Processing, March 2010,
Dr. Tony Sofronas, P.E., was
worldwide lead mechanical engineer for ExxonMobil
Chemicals before retiring. He now owns Engineered
Products, which provides consulting and engineering
seminars on machinery and pressure vessels. Dr.
Sofronas has authored two engineering books and
numerous technical articles on analytical methods.
Early in his career, he worked for General Electric
and Bendix and has extensive knowledge of design and
failure analysis for various types of equipment.