Testing and quality

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TESTING AND QUALITY 0.00 100.00 (mm) 50.00 5 Results of the FEM calculation for the two-diameter and three-diameter natural modes. verified that the mode shape with two nodal diameters is actually excited during operation. Figure 4 depicts an instantaneous deflection state of the particular vibration mode. • Example 2 : Zero-diameter mode at f=900 Hz excited by the 21st order: From the frequency response function for the resonant vibration at f = 900 Hz, it is evident that all three acceleration signals are in phase and have the same amplitude. This is clearly an axisymmetric mode with zero nodal diameters; in this case, verification by a synchronous animation of the measured signals and the computed mode shape is unnecessary. Comparison with results of the FEM calculation Finally, the measurement results were compared with the FEM calculations carried out by Sulzer Pumps 5. A rotor surrounded by water was used as boundary condition. The impeller was modeled as non-rotating, since stiffening due to centrifugal forces has only a negligible influence on the natural frequencies. Figure 6 shows a comparison of the measured and the computed natural frequencies. 6 Comparison of the measured and computed natural frequencies. 16 | Sulzer Technical Review 1/2011 The frequencies are in good agreement, except for the «umbrella»-mode with a measured natural frequency of approx. 900 Hz, vs. the FEM calculation resulting in a frequency of 701 Hz. This deviation could be due to a truncated shaft stub, which is included in the finite element model. Note that the forces induced by the 12 diffuser guide vanes and acting on the impeller have lowest relevant excitation orders of 12 and 24; the corresponding excitation frequencies lie just below the matching natural modes of the impeller: • 12th order of the maximum pump speed: 1135 Hz ↔ natural frequency of two-diameter mode: 1150Hz • 24th order of the maximum pump speed: 2250 Hz ↔ nat. frequency of four-diameter mode: 2500Hz. Spatial aliasing With seven sensors that are equally spaced around the circumference, theoretically, only the vibration modes with zero to three nodal diameters can be detected positively. For vibration modes with four or more nodal diameters, spatial undersampling occurs due to the sensor arrangement, which has an insuf- Number of f [Hz] f [Hz] Remarks Excitation order nodal diameters approx. reading computed by FEM from spectrogram 0 900 701 «umbrella»-mode 21 1 750 757 «rocker»-mode 22 2 1150 1199 23 3 1900 1846 24 4 2500 not computed by FEM 38 Max. 5 2800 not computed by FEM Min. 50.00 0.00 100.00 (mm) 25.00 75.00 ficient sensor density. For instance, mode shapes with 1 or 6 nodal diameters cannot be differentiated, since both modes would result in identical vibrations at the sensor positions. With the additional knowledge of the FEM results, the vibration mode shapes can usually be unambiguously identified, even with only three sensors. Without the combination with FEM results, a considerably denser sensor arrangement would be necessary in order to avoid spatial aliasing. Interpretation The vibrations measured during operation indicate that the natural frequencies of the impeller are near the predictions by the FEM. However, the resonances have sufficient damping so that the corresponding vibration levels remain well within acceptable limits and the integrity of the impeller is not at risk. Literature • Berten, S., Thesis EPFL No. 4642, http://library.epfl.ch/en/theses/?nr=4642 • Tanaka, H., “Vibration behaviour and dynamic stress of runners of very high head reversible pump-turbines,” IAHR Symposium 1990, special session, Belgrade Ulrich Moser Sulzer Markets and Technology AG Sulzer Innotec Sulzer-Allee 25 8404 Winterthur Switzerland Phone +41 52 262 82 61 ulrich.moser@sulzer.com Hans Rudolf Graf Sulzer Markets and Technology AG Sulzer Innotec Sulzer-Allee 25 8404 Winterthur Switzerland Phone +41 52 262 82 40 hansrudolf.graf@sulzer.com
SULZER ANALOGY Testing poisons In the plant world, there are numerous poisons, which, when consumed, can lead to serious problems or even death for human beings. People always have to try something out first in order to determine whether it is poisonous or not. So how do animals know which plants to beware of and which are beneficial? Structural formula of the alkaloid morphine, which Friedrich Wilhelm Sertürner extracted from the opium poppy in pure form in 1806. The struggle for survival in the natural world takes place not only between hunting lions and fleeing gazelles. Even the apparently peaceful coexistence between plants and animals is an incessant battle with the aim of surviving long enough to pass on one’s own genes to the next generation. As plants are unable to flee their predators, they have to defend themselves from the hungry mouths of animals in other ways. Spines, thorns, and bristly hairs offer mechanical protection. Unpleasant odors may also discourage consumption. The most effective defenses, however, are plant toxins that punish the “attacker” with physical problems or even death. It’s purely the dosage that makes the poison The plant world has developed an incredible wealth of chemical defenses. Tannins are very astringent. They cause the tongue to contract, dry out the mouth and throat, and disturb digestion. The greatest poison arsenal, however, are the alkaloids, which can be found © Smellme | Dreamstime.com in 20 percent of all flowering plants. Anyone who does not regard the bitter taste as a warning will have to experience on this own body how these nerve agents work. Humans also know about these poisons—from the atropine in the deadly nightshade and the quinine in cinchona bark to the nicotine in tobacco and the caffeine in coffee. Like almost any poison, alkaloids are digestible in small dosages, and they can have a stimulating or intoxicating effect. Both humans and animals have learned that low quantities of alkaloids only damage microbes and insects, and thereby provide the body with some protection against certain infections and pests. How do animals know what is poisonous? In order to avoid risks, the panda bear restricts itself to harmless bamboo plants—with the disadvantage that it has to consume enormous quantities of this plant, which is low in nutrition. The rat has a very different strategy. It is an omnivore and has conquered the entire world thanks to its flexibility. As poisons lurk everywhere, the rat is very mistrustful of new things. If it finds an unfamiliar food source, it only eats a mini-portion at first. Only if it does not suffer any adverse reaction does it consume the new discovery in larger quantities. Moreover, if it sees that other rats are eating a new food without any Black howler monkey: Consumes unknown plant material only in small quantities in order to avoid a possible poisoning. problem, the rat knows that it can also eat the new food. Poison training course for rat embryos The poison training course for rats starts in the womb, where the embryo develops aversions to noxious smells and a preference for safe tastes. In mammals, young animals learn with their mother’s milk how good food smells and tastes. Moreover, when the baby animal takes its food from its mother’s mouth, this is not simply convenience, but vital training of the highest quality. Anyone who is mainly surrounded by poisonous leaves, such as the howler monkeys in the coastal forest of Costa Rica, has to come up with a particularly subtle feeding strategy. The more abundant a type of tree, the more is it avoided by the apes—because the only plants that can thrive are those that are inedible for herbivores. If a tree is judged acceptable, the animals seek out the youngest and smallest leaves—and if the plant nevertheless produces toxins, these would initially only be present in small amounts in fresh plant material. Furthermore, the howler monkeys only eat the stem of the leaf, thereby keeping to the part of the plant with the lowest toxic content. Herbert Cerutti 4331 Sulzer Technical Review 1/2011 | 17
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