Linear dynamic finite-element analysis was used to optimize testing.
Hamler Test and Analysis (HTA) provides testing, design, and finite-element analysis (FEA) consulting services, specializing in vibration measurement and experimental vibration analysis tools such as tap testing, modal analysis, operating deflection shapes analysis, and rotating machinery analysis. HTA was contracted to perform physical fatigue testing of a compressor blade from a stationary gas turbine engine used for power generation. Electrodynamic shaker testing was required to verify the client’s analytical vibratory high-cycle fatigue life prediction methodology. The first phase of the shaker testing involved vibrating several blades to failure at the first bending mode, and the second phase involved testing several blades to failure at the first torsion mode.
The primary challenge involved attaining an acceptable blade tip response displacement at the first bending mode frequency of 2,900 Hz. The target response was dictated by blade stress levels required by the customer during testing. Because displacement is directly proportional to acceleration, but inversely proportional to the square of frequency, the target displacement would be difficult to achieve at 2,900 Hz, even with the gain in response at resonance. This challenge was overcome by mass-loading the end of the blade with a special investment cast clamp, which lowered the first bending mode frequency to approximately 850 Hz. This change made it possible to achieve the desired bending mode tip displacement and, consequently, the required blade stress levels. The optimization of the correct amount of mass was determined by experimental trial and error.
It is difficult to excite an angular mode shape with linear movement. Initial sine sweeps of the mass-loaded test setup from phase one indicated that the first torsion mode had dropped from 8,400 Hz to 1,450 Hz with the addition of the tip mass, and an adequate response from the new mass-loaded torsion mode did not appear to be attainable on the shaker. The gain in response obtained at a torsion mode is minimal when the excitation is linear motion. There was not a commercially available linear or rotary shaker system that could provide enough excitation to achieve the desired torsion mode response with the test setup from Phase One. Using ALGOR FEA software, sufficient torsion mode response could be attained with reasonable levels of linear excitation 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 finite-element analysis predicted that, by making such modifications, the first torsion mode would occur at a lower frequency than the first bending mode, and the desired blade stress levels could be obtained with acceleration levels that were attainable from the shaker. However, the FEA results also predicted that if the total mass increase was too large, the torsion and bending modes would become coupled. Hence, 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 also minimizing the mass increase near the nodal axis. Designing hardware that could meet these requirements and physically attach to the blade would be challenging, and such hardware would have to be feasible to manufacture.
Using Alibre Design computer-aided design software, HTA 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 blade-weights- clamps assembly measured 3.5 × 1.14 × 0.86". The CAD model was opened in ALGOR 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. Damping was determined experimentally and included in the FEA model. Modal and frequency response analyses were performed to predict the proper size and location of each weight, minimizing shaker experiments and the fabrication of weight assemblies.
The initial test setup design incorporated a 1.25-ounce trailing edge weight and a 0.8-ounce leading edge weight. FEA results indicated that this design would produce an acceptable response on the shaker, but each weight was initially made to have a weight of 1 ounce, with the assumption that the resulting experimental response would still be in the vicinity of the FEA prediction. Therefore, if needed, the shaker excitation level could be adjusted to compensate for any difference. However, the first run with the 1-ounce weights indicated that the response was significantly lower than the FEA prediction of the 1.25-ounce and 0.8-ounce 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 ounces. Then the leading edge weight was milled down to 0.8 ounce. This small weight adjustment provided a night-and-day difference in response on the shaker, as predicted by FEA.
This work was done by Jesse Hamler, President and Chief Technical Officer at Hamler Test and Analysis, using ALGOR software. For more information, click here.