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 operation.24
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 results.
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 Publications, 2006.
2 Sofronas, A., Case 44: Cracking due to sudden temperature changes in piping, Hydrocarbon Processing, May 2008, p. 135.
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, p. 83.
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.