When Hamler Test and Analysis (HTA), a consulting firm in Cookeville, Tenn., needed to fatigue test a compressor blade from a gas turbine engine, they used linear dynamic finite element analysis (FEA) software from ALGOR, Inc., Pittsburgh, to simulate the test and determine the optimal setup.
“This program lets me do ‘virtual’ testing,” said Jesse Hamler, President and Chief Technical Officer of HTA. “I can simulate different ideas and hardware configurations without spending time or money to physically make the hardware for each setup, which saves weeks if not months of trial-and-error testing.”
HTA offers testing, design and FEA consulting services. “We specialize in vibration measurement and experimental vibration analysis tools,” said Hamler, “such as tap testing, modal analysis, operating deflection shapes analysis and rotating machinery analysis – particularly for engine vibration. With Algor FEA software, I purchased only the analysis capabilities I really needed – that is, linear static stress and linear dynamics.”
Linear Dynamic Analysis of a Shaker Fatigue Test
HTA was contracted to physically fatigue test a compressor blade from a stationary gas turbine engine used for power generation. “Electro-dynamic shaker testing was required to verify the client’s analytical vibratory high-cycle fatigue life prediction methodology,” said Hamler. “The first phase of this testing involved vibrating several blades to failure at the first bending mode, and the second phase to failure at the first torsion mode.”
Hamler Test and Analysis (HTA) used ALGOR FEA software to analyze the compressor blades of a gas turbine engine like the one shown here. (Image courtesy of The National Energy Technology Laboratory.)
The graph shows the blade tip displacement versus frequency for a shaker sine sweep. Notice the difference in resonance response between the bending and torsion modes.
The left photograph shows the weighted compressor blade test setup for the second phase of shaker testing, where the blade was vibrated at the first torsion mode until it broke (at right).
The primary challenge involved finding an acceptable displacement response of the blade tip at the first bending mode frequency of 2900 Hz. Because displacement is directly proportional to acceleration but inversely proportional to the square of frequency, the target displacement would be difficult to achieve at 2900 Hz, even with the gain in response at resonance. Mass loading the end of the blade with a special investment cast clamp lowered the first bending mode frequency to approximately 850 Hz. Experimental trail and error determined the correct amount of mass.
It was more challenging to find a way to fail a blade at the first torsion mode for the phase two testing. A trial-and-error approach was not feasible due to time constraints, so the FEA program was used to direct the testing in the right direction.
“It is difficult to excite an angular mode shape with linear movement,” said Hamler. “Initial sine sweeps of the phase one mass-loaded test setup indicated that the first torsion mode had dropped from 8400 Hz to 1450 Hz with the addition of the tip mass. It did not appear as though the shaker would enable a good response from the new ‘mass-loaded’ torsion mode.”
The gain in response obtained at a torsion mode is minimal when the excitation is linear motion. A commercially available linear or rotary shaker system would not provide enough excitation to achieve the desired torsion mode response with the phase one test setup. However, the FEA program showed that a sufficient torsion mode response could be attained by substantially increasing the mass moment of inertia about the nodal axis or nodal line of the first torsion mode (axis of rotation with zero displacement).
“An initial analysis predicted that, by making such modifications, the first torsion mode would occur at a lower frequency than the first bending mode, and that the shaker could reach the appropriate acceleration to meet the desired blade stress levels,” continued Hamler. The results also predicted that if the total mass increase was too large, the torsion and bending modes would become coupled. Thus, increasing the mass moment of inertia about the torsion mode nodal axis would require concentrated masses to be applied at a significant radial distance from the nodal axis, while reducing the mass increase near the nodal axis. Designing hardware that could meet these requirements and physically attach to the blade would be challenging. Furthermore, such hardware would have to be manufacturable.”
Using Alibre Design software, Hamler created a CAD model of a clamp that could attach to the
compressor blade and support a weight on each side of the torsion mode nodal axis. The assembly measured 3.5 in. wide by 1.14 in. deep by 0.86 in. high.
Hamler opened the CAD model in the Algor program to set up for linear dynamic analysis. In the FEA model, the surface at the base of the compressor blade was fully constrained. Loads were applied as 17g acceleration in the Z direction with excitation at the first torsion mode and first bending mode natural frequencies of 420 Hz and 622 Hz, respectively. The proper damping amount was determined experimentally and included in the FEA model. Modal and frequency response analyses predicted the proper size and location of each weight, which reduced the number of experiments.
Alibre Design was used to create this CAD model of the weighted compressor blade assembly. The compressor blade is highlighted in orange and the weights and clamps are highlighted in green.
Natural Frequency (Modal) and Frequency Response analyses were performed to simulate a shaker fatigue test. On the left, color-coded contours show the displacement magnitude in the compressor blade. A wireframe of the undisplaced shape illustrates the torsion mode movement. On the right, a display of stress contours indicated the area where a crack would likely initiate. A close-up view (inset) shows that the finite element mesh was made finer in the area of highest stress.
The initial test setup design used a 1.25 oz trailing edge weight and a 0.8 oz leading edge weight. “FEA results indicated that this design produced an acceptable response on the shaker, but each weight was initially made to 1 oz, with the assumption that the resulting experimental response would still be in the vicinity of the FEA prediction,” said Hamler. “If needed, the shaker
excitation level could be adjusted to compensate for any difference. However, the first run with the 1 oz weights indicated that the response was significantly lower than the FEA prediction of the initial weight setup, even at the maximum excitation level capable from the shaker. The next logical step was to tune the test setup to replicate the FEA model. Two pieces of steel flat stock were bolted to the top of the trailing edge weight, giving it a total weight of 1.25 oz. Then the leading edge weight was milled down to 0.8 oz. This small weight adjustment provided a night-and-day difference in shaker response, as predicted by FEA analysis.”
Experimental results closely matched FEA predictions. “Testing was a success, and the blades failed as predicted,” said Hamler. “I was surprised that the FEA model was able to predict the real-world response of a structure so accurately.”
Hamler concluded, “This was a valuable exercise in how FEA can drastically reduce experimentation and troubleshooting involved with non-standard testing objectives. I would say that using FEA cut the testing time in half at the very least.”
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