# Progress in mechanical strength calculations

A turbine diaphragm, due to its complex structure and harsh operating conditions, is a very difficult subject for mechanical strength calculations. Structural complexity of the diaphragm is characterized by the following features:

- It is a complicated 360 degree plate, composed of three major components (an outer ring, a set of vanes with complex geometry, and an inner ring) made from different materials;

- A diaphragm is always split in two halves;

- The outer ring is supported by its outer diameter;

- The inner ring is supported only by vanes.

In addition to this complexity, a diaphragm is subjected to complex loading, consisting of the following forces:

- Uniformly distributed steam pressure across the entire inlet face;

- Bending moment on vanes from high velocity steam flow;

- Thermal gradients in radial direction and between diaphragm halves;

- Vibration.

The combination of two diaphragm halves (instead of a solid continuous plate), and the plurality of vanes with complex geometry presents the main problem for stress and deflection calculations. Therefore, mechanical strength calculations progressed very slowly and went through a long and painful process - from the original simplified mathematical model up to the current computerized Finite Element Analysis (Table 1).

The mechanical strength of the original Saudi Armco diaphragms was calculated using the "Modified Smith Method".  Mechanical strength of all the "current design" diaphragms were calculated by FEA. Since the majority of Saudi Aramco turbine failures occurred in stage #4 area, the original diaphragm was also carefully re-calculated by FEA at the current operating conditions.

The results of these calculations are presented in Figures 1 and 2. Figure 1 shows the calculated deflections and equivalent stresses in the original and current diaphragm halves. Figure 2 demonstrates the distribution of vane stresses (as percentage above yield strength) in a diaphragm half for all known diaphragms that failed during 40+ years of operation. The "0" and "180" degree locations are representative of the vanes at the horizontal joint. Based upon the accumulated experience, the acceptable allowance has been set at 2% of vane nodes above yield strength for the diaphragms designed and manufactured at the authors’ company (it can be different for diaphragms designed and manufactured by other facilities).

The results of these calculations showed the following:

1) The original diaphragm is unsuitable for the current operating conditions due to high calculated     deflections and very high calculated stresses in the vanes at the horizontal joint;

2) The original vanes are not strong enough; even with 100% main weld penetration they still have, although reduced, but still unacceptably high stresses;

3) The mechanical strength of the current diaphragm (which is made using the latest achievements in design and manufacturing) is substantially higher compared to the original diaphragm: calculated stresses and deflections are well within design limits for current operating conditions.

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