PC-BASED FINITE ELEMENT ANALYSIS SAVES CLOSE TO $500,000 IN DESIGN OF TURBINE

Cut-away view of one of the turbines manufactured by Tiernay Turbines, which clearly shows the fan and its blades.

Algor finite element analysis (FEA) software on a personal computer helped Tiernay Turbines reduce thermal stress and correct a rubbing problem in a turbine backshroud while the turbine was still in the design phase. Algor software also helped eliminate resonance in a turbofan blade of an existing product.

Since design iterations of the turbine backshroud were made without the time- and cost-consuming construction of a physical prototype, Tiernay Turbines, Inc. (Phoenix, Arizona), saved up to $500,000 according to Dr. Quan B. Li, dynamic stress specialist for Tiernay. It took Dr. Li, in collaboration with Master Engine Designer Carl Warner, only three weeks, rather than approximately five years, to complete this whole study.

Says Dr. Li, "In the past, the complete design-testing-modification process for a satisfactory turbine took about 10 - 20 years, actually occurring in a series of four or five five-year cycles. Each cycle consists of design, testing and modification. Algor FEA software helped Tiernay compress one of these five-year cycles into just three weeks!

"In particular, it would take many years to fix a rubbing problem in the backshroud," he adds. "Usually when this type of rubbing occurs, engineers try to correct it by applying shims to adjust the gap between the backshroud and the wheel. But they have no exact idea how the backshroud moves against the wheel, or how the wheel moves against the backshroud - they go by trial-and-error."

At its Phoenix facility, Tiernay Turbines designs and manufactures turbo machines for military and commercial applications, such as 10 KW generators and aircycle refrigeration systems for the US Air Force. Tiernay uses the Algor FEA System on an upgraded IBM XT with color monitor and EGA graphics. Algor's system incorporates detailed graphics into the modeling, meshing, analysis, and post-processing phases for visual verification of data. The Supersap full stress/dynamic analysis programs and Thermosap heat transfer analysis modules were used for this particular problem.

"The Algor FEA System very quickly showed me where the maximum stresses and deformations were occurring, and what critical parameters were affecting the stress and deformation," Dr. Li points out. "It gave me a graphic display of the deformations resulting from stresses on the part. Hand calculations are not only much more tedious, but they can't give you that kind of visual insight into the behavior either."

Dr. Quan B. Li using SuperDraw II to view the backshroud model.

Details of the Turbine Backshroud Analysis

The Tiernay backshroud has a 6.5" ID and a 25" OD; it is made of IN-718, a specialized nickel-based aerospace steel. It encloses the 23" diameter, 360-pound turbine wheel, keeping in pressurized hot air to give the turbine power. On the other side of the backshroud is insulation. Thermal stress on the backshroud, explains Dr. Li, was caused by differential thermal growth due to nonuniform temperature distribution. The large temperature differential led to severe incompatibility of the material, causing the inner edge of the backshroud to swing toward the turbine wheel so much that the backshroud would hit the turbine wheel, causing the rubbing problem.

As a first step in the preparation for the stress and thermal analyses, Dr. Li employed Algor's own full-featured drawing program, SuperDraw II, to graphically create the model geometry on-screen. He delineated the model's outline by entering lines whose endpoints define points in space called keynodes. Algor's Superlink allowed him to quickly translate this basic model geometry into a file consisting of nodes and elements for FEA. Dr. Li chose to model the backshroud with two-dimensional axisymmetric linear elements.

Dr. Li used Algor's MSHGEN to subdivide the model for finer pieces. He divided the model into polygons, called keynode regions. For each region, Dr. Li specified the number of mesh divisions on two adjacent sides and the locations of intermediate nodes. MSHGEN automatically generated a mesh of 54-elements using this information, storing two files - one for heat transfer analysis and the other for stress analysis. TDraw displayed a graphic representation of the model on the computer monitor, allowing Dr. Li to visually verify the accuracy of the mesh construction.

The thermal boundary conditions, material properties, and temperature input information were established by editing the MSHGEN heat transfer output file with Algor's TEdit. Dr. Li utilized a Thermosap processor module to perform the heat transfer analysis; it calculated the temperatures and heat flux distribution. These output results were then applied to the stress analysis model through Algor's Advance. "It is a very handy tool," comments Dr. Li. "Updating nodal temperatures of the model for stress analysis took me only a few minutes. The fact that Advance lets you overlay heat transfer analysis results onto a model explains why I was able to construct the heat transfer and stress analysis files from the same Superlink file." To establish the input file for stress analysis, Dr. Li used AEdit to set the boundary conditions, define the temperature-dependent material properties, and input other loads (e.g., pressure load).

Since there was such critical loading, Dr. Li wanted to determine tri-axial stresses - combinations of six numerical values for the three-dimensional state of stress. Three of the values are normal stresses in the X, Y, and Z direction, the other three are shear stresses on three orthogonal XY, YZ, and ZX planes. Nearly one dozen yield criteria can be used to determine tri-axial stresses and the beginning of material yield. Algor's FEA System will give the results from several major criteria, including the von Mises Failure Criterion, the Tresca Criterion, and the Principal Stress Criterion. The von Mises Criterion, also called the Maximum Distortional Energy Theory, is the most widely accepted theory for ductile materials, mainly because it has been validated by experimental tests.

Dr. Li ran another analysis, this time using a Supersap processor to determine stresses and deflections caused by the heat which was previously ascertained. TDraw was used after the stress analysis to examine the results, enabling Dr. Li to view both the original and deformed models simultaneously, but in different colors. "With the deformed model overlaid on the original, it becomes very apparent where the deflection occurs. TDraw also allows you to magnify the deflections to make minuscule deformations more obvious." The analysis using the von Mises Criterion revealed that the greatest thermal stress was occurring at the highest inside diameter corner closest to the turbine wheel. The displayed deflections showed that the heat was causing the inner edge of the backshroud to swing toward the wheel and hit it.

Based on the outcome of this analysis, Dr. Li built a second model, enlarging the ID of the backshroud and adding insulation to reduce the temperature gradient. The new model was constructed on-screen by making modifications to the original with SuperDraw II, again, without the time- and cost-consumption required to build a physical prototype.

By using the procedures described above, Dr. Li applied Algor's FEA System again to study the modified component, using the same boundary conditions. "This model yielded much better thermal stress levels," he says. "The thermal stress was reduced from 106,000 psi to 77,000 psi - safely below the allowable stress of 110,000 psi with a 30 percent margin." A final design modification was made to accommodate the thermal deformation; the gap between the turbine wheel and backshroud was adjusted so that the wheel and backshroud will not rub against each other when the engine is in operation.

Analysis of the Turbofan Blade

The Algor FEA System was also vital in performing dynamic stress analysis on the Tiernay blade in an aircycle machine's turbofan. "The blade comes into very strong vibration and would break," relates Dr. Li. "The whole machine would fail if a blade came off, because the whole rotor loses balance." The blade is made of 17-4 stainless steel; the double-curved and twisted shape measures approximately 1?quot; tall, tapering from a 2" width at the root to 1?quot; at the tip.

A structure like the blade is "dynamically weak" - it may be easily excited at or near its resonant frequencies. If the structure's dynamic properties can be characterized, the behavior of the structure can be predicted; then controlled and optimized. Dynamic stress analysis, which identifies a structure's modes of vibration, is the method by which this characterization can be made. Each mode has a specific natural frequency and a characteristic mode shape, which defines the resonance spatially over the entire structure.

Dr. Li with a laser holographic interferometry set-up used in verification of the dynamic analysis.

By performing dynamic analysis on the blade, Dr. Li could predict how it would behave at each of its resonant frequencies, ascertain the forced response correlated to the source of the disturbance, pinpoint the critical area, and predict its fatigue life.

Dr. Li constructed the 3-D model from 2-D outlines using Algor's Layergen program to connect the 2-D slices in 3-D space. He assumed that the blade root was fixed, since it was cast to the hub, a large solid cylinder. Dr. Li used an integration order of four to get a more accurate stiffness matrix than a lower order would have given.

An additional factor in the analysis was assumed forcing function provided by a Tiernay aerodynamic specialist, Dr. Sanjay Sherikar. The force was due to turbulence, which hits the blade like a hammer. From this analysis, a 3-D Campbell diagram was established. Dr. Li also entered the static stress due to centrifugal loading. With the static stress and dynamic stress analyses performed, Dr. Li could establish a Goodman diagram for fatigue analysis.

After the analysis, Algor's POST and POSTD, which creates stress output files from the processed model, gave Dr. Li a listing of the stresses and deflections. Since the turbulence is random in nature, it gave him a wide range of frequencies of excitation, each of which was an integral number multiplied by the rpm of the rotor.

For an additional source of verification of the dynamic analysis, Dr. Li used laser holographic interferometry to measure the surface deformation. "In the gas turbine industry," Dr. Li relates, "holographic interferometry has become an important tool for identifying the natural frequencies and the corresponding modes of turbine blades and disks." This technique, he explains, serves to accurately measure very small deformations and takes advantage of a whole-field holographic fringe pattern in collecting measurement data. The great number of data points is a significant advantage of holographic interferometry over other methods for a comprehensive comparison of analysis and test. The natural frequencies predicted by the Algor FEA System and those measured by holographic interferometry were in good agreement. The maximum difference in a range of three modes was only 5.8 percent.

The combined analyses showed that the excitation force was too strong. Based on that, Tiernay modified the fan inlet housing. "Afterward, the engine ran smoothly," Dr. Li says.

Algor's FEA System, Dr. Li concludes, facilitates Tiernay's design work by providing a wide variety of analysis tools, from static and dynamic stress analysis to heat transfer analysis. It also enables Tiernay to make design-analysis iterations without the time- and cost-consuming construction of physical prototypes, "The roughly five years and half of a million dollars saved by using Algor's FEA System can now be devoted to other Tiernay research and development projects."