Vibration avoidance

Other limitation for the spatial resolution can be found in the detector. A limited number of pixels in the camera array can be a reason for pure resolution in the case of a big field of view. For example, if field of view should be 10 by 10 nun with camera division 512x512 pixels the pixel size will be approximately 20 microns. To improve the relation of the field of view and the spatial resolution a mega-pixel sensor can be used. One more limitation for the spatial resolution is in mechanical movement (rotation) of the object, camera and source. In the case of a mechanical movement all displacements and rotations should be done with accuracy better than the spatial resolution in any tested place of the object. In the case of big-size assemblies and PCB s it is difficult to avoid vibrations, axle play and object non-planarity during testing. 

CAHRS and CSHRS) [145, 146 and 147]. These 6WM spectroscopies depend on (Im for HRS) and obey the tlnee-photon selection rules. Their signals are always to the blue of the incident beam(s), thus avoiding fluorescence problems. The selection ndes allow one to probe, with optical frequencies, the usual IR spectrum (one photon), not the conventional Raman active vibrations (two photon), but also new vibrations that are synnnetry forbidden in both IR and conventional Raman methods. 

Figure B3.4.12. A schematic ID vibrational pre-dissociation potential curve (wide flill line) with a superimposed plot of the two bound fimctions and the resonance fimction. Note that the resonance wavefiinction is associated with a complex wavevector and is slowly increasing at very large values of R. In practice this increase is avoided by iismg absorbing potentials, complex scaling, or stabilization.

The gain in stability can now be interpreted as resulting from the direct midpoint discretization of the rapidly vibrating, local variable r, thus avoiding the potentially damaging discrete decoupling transformation. 

This is a check on the reasonableness of the method chosen. For example, it would not be reasonable to select a method to investigate vibrational motions that are very anharmonic with a calculation that uses a harmonic oscillator approximation. To avoid such mistakes, it is important the researcher understand the method s underlying theory. 

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

However, because of the avoided crossing of the potential energy curves the wave functions of Vq and Fi are mixed, very strongly at r = 6.93 A and less strongly on either side. Consequently, when the wave packet reaches the high r limit of the vibrational level there is a chance that the wave function will take on sufficient of the character of Na + 1 that neutral sodium (or iodine) atoms may be detected. 

A fan blade is continuously vibrating millions of cycles up and down ia operatioa over a short period of time. Each time a blade tip moves past an obstmction it is loaded and then unloaded. If forced by virtue of tip speed and number of blades to vibrate at its natural frequency, the ampHtude is greatly iacreased and internal stresses result. It is very important when selecting or rating a fan to avoid operation near the natural frequency. The most common method of checking for a resonance problem is by usiag the relatioa ... 

Supports. The spaciag of supports is governed by the hot allowable stress of the piping materials stabiUty, ia the case of large-diameter thin-wall pipe deflection to avoid sagging or pocketing and the natural frequency of the unsupported length to avoid susceptibiUty to undesirable vibration. 

Bellows can vibrate, both from internal fluid flow and externally imposed mechanical vibrations. Internal flow liner sleeves prevent flow-induced resonance, which produces bellows fatigue failure in minutes at high flow velocities. Mechanically induced resonant vibration is avoided by a bellows with a natural frequency far away from the forcing frequency, if known. Multiple-ply bellows are less susceptible to vibration failure because of the damping effect of interply friction. 

To avoid maintenance problems, the location of pressure measurement devices must be carefully considered to protect against vibration, freezing, corrosion, temperature, overpressure, etc. For example, in the case of a hard-to-handle fluid, an inert gas is sometimes used to isolate the sensing device from direct contact with the fluid. 

Flow-induced tube vibration occurs at critical fluid velocities through tube banks, and is to be avoided because of the severe damage that can result. Methods to predict and correct vibration problems may be found in Eisinger Trans. ASME J. Pressure Vessel Tech., 102, 138-145 [May 1980]) and Chen J. Sound Vibration, 93, 439-455 [1984]). 

Suction Limitations of a Pump Whenever the pressure in a liquid drops below the vapor pressure corresponding to its temperature, the liquid will vaporize. When this happens within an operating pump, the vapor bubbles will be carried along to a point of higher pressure, where they suddenly collapse. This phenomenon is known as cavitation. Cavitation in a pump should be avoided, as it is accompanied by metal removal, vibration, reduced flow, loss in efficiency, and noise. When the absolute suction pressure is low, cavitation may occur in the pump inlet and damage result in the pump suction and on the impeller vanes near the inlet edges. To avoid this phenomenon, it is necessary to maintain a required net positive suction head (NPSH)r, which is the equivalent total head of liquid at the pump centerline less the vapor pressure p. Each pump manufacturer publishes curves relating (NPSH)r to capacity and speed for each pump. 

To avoid operating difficulties, the torsional critical frequencies of the combined engine and driven equipment should be calculated or measured to assure that operating speeds are removed from these criticals or that vibration dampers are provided or that the equipment is designed for the resulting cyclic stresses. 

Vibration is both a cause of problems and an effect of equipment problems. The potential destructive force of an out-of-balance load has led to setting lower shutdown limits on the magnitude of vibration than other rotating equipment. Flexible connections for process and utility lines become a must so these vibration problems are not transmitted to connected equipment. Flexible hoses with liners having concentric convolutions (bellows type) avoid the sharp points inherent with spiral metallic liners. By avoiding the sharp point the liner is less likely to cut the exterior covering. 

Vibration during Check plow and linkage for loose compo-plowing out—can nents/wear lead to premature. sharpen plow or use serrated blade for hardened equipment failure heels and a potential ignition source— Manually remove heel more frequently see above. Plow at lower bowl speed Advance plow more slowly Make sure plow system is well damped Avoid air actuated plows Avoid use of full depth plows with hard cakes Use nitrogen knife to scrape centrifuge ... 

At certain speeds, rotating masses become dynamicatty unstable and cause deflection and vibration in the rotor w hich may damage the motor. The speed at w hich such instability occurs is known as critical speed and occurs at different multiples of the rated speed. The masses must therefore rotate within 20T beknv or above the critical speeds to avoid such a situation. These vibrations settle down again at higher speeds above critical and recur at the next higher critical speed. 

Note The level of vibration at site may be higher than that mentioned above, perhaps due to the foundation or the coupling of the load. This must be checked and adequate precautions taken to avoid excessive vibrations. 

Expander-compressor shafts are preferably designed to operate below the first lateral critical speed and torsional resonance. A flame-plated band of aluminum alloy or similarly suitable material is generally applied to the shaft in the area sensed by the vibration probes to preclude erroneous electrical runout readings. This technique has been used on hundreds of expanders, steam turbines, and other turbomachines with complete success. Unless integral with the shaft, expander wheels (disks) are often attached to the shaft on a special tapered profile, with dowel-type keys and keyways. The latter design attempts to avoid the stress concentrations occasionally associated with splines and conventional keyways. It also reduces the cost of manufacture. When used, wheels are sometimes secured to the tapered ends of the shaft by a common center stretch rod which is pre-stressed during assembly. This results in a constant preload on each wheel to ensure proper contact between wheels and shaft at the anticipated extremes of temperature and speed. 

Of all vibration frequeneies, the most dangerous are the synehronous vibrations, where an externally foreed vibration exeites one of the natural (resonant) frequeneies in the maehine. Campbell diagrams eonstrueted by the manufaeturers will help the operator avoid these frequeneies during run-up or eoimuissioning of tlie maehine in question. 

---