First lateral critical speed

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. 

Critical Speed. The first lateral critical speed of the rotating assembly shall be at least 120% of die maximum operating speed. A dry critical speed calculation (see HI 9.6.4) is adequate to verify compliance. HI 9.6.4 shall be used to calculate static deflections used for the critical speed calculation. 

Type OH2 pnmps shall be designed such that their first dry lateral critical speed is at least 20 percent above maximnm continnons operating speed. 

Note Depending on pump design, the first or second wet lateral critical speed of multistage and high-speed pumps may coincide with the operating speed, particularly as internal clearances increase with wear. A lateral analysis can predict when this coincidence is likely and whether the resulting vibration will be acceptable. 

Critical speed the mixer shaft speed which matches the first lateral natural frequency of the shaft and impeller system. Excessive vibrations and shaft deflections are present at this speed. 

Large mixers running at less than 150 rpm usually operate below the first critical speed. Small mixers operating above 250 rpm usually operate between first and second critical, 1.2Nc to 0.8Nc2, where Nc2 is the second lateral natural frequency. Other frequencies, such as a blade-passing frequency, four times the operating speed for a four-blade impeller with four baffles, can cause mechanical excitations. Structural vibrations at certain fractions of operating speed can also contribute to natural frequency problems. 

Let us recall the micellar aqueous system, as this procedure is actually the basic one. The chemistry is based on fatty acids, that build micelles in higher pH ranges and vesicles at pH c. 8.0-8.5 (Hargreaves and Deamer, 1978a). The interest in fatty acids lies also in the fact that they are considered possible candidates for the first prebiotic membranes, as will be seen later on. The experimental apparatus is particularly simple, also a reminder of a possible prebiotic situation the water-insoluble ethyl caprylate is overlaid on an aqueous alkaline solution, so that at the macroscopic interphase there is an hydrolysis reaction that produces caprylate ions. The reaction is very slow, as shown in Figure 7.15, but eventually the critical micelle concentration (cmc) is reached in solution, and thus the first caprylate micelles are formed. Aqueous micelles can actually be seen as lipophylic spherical surfaces, to which the lipophylic ethyl caprylate (EC) avidly binds. The efficient molecular dispersion of EC on the micellar surface speeds up its hydrolysis, (a kind of physical micellar catalysis) and caprylate ions are rapidly formed. This results in the formation of more micelles. However, more micelles determine more binding of the water-insoluble EC, with the formation of more and more micelles a typical autocatalytic behavior. The increase in micelle population was directly monitored by fluorescence quenching techniques, as already used in the case of the... 

Regardless of the care taken in measuring a variable, the measurement is subject to uncertainty or errors. The reliability of an instrument is a critical factor in its selection and in the interpretation of collected data. There are few quantities that are known or can be measured precisely. One exception is the speed of light in a vacuum that is exactly 299 792 458 ms . For other quantities, the uncertainty in the value is expressed in two ways the first is to define the value with a limited number of digits (or figures) and the second is to include a second number indicating the probability that the measured value lies within a defined interval—its uncertainty, which is discussed in detail later in this chapter. It represents an interval in which the true value of a measurement lies. If the uncertainty of the measured volume in a graduated cylinder equals 1 ml. 

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