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. 

The torsional resonant response of a system is an interaction of all the components in the train. Calculation of torsional natural frequencies is based on the entire system and these frequencies are valid only for that given arrangement. If any component of the train is replaced by an item with torsional characteristics different from the original, the system tor sional response must be recalculated and new torsional natural frequencies determined. Occasionally, an original equipment manufacturer is requested to calculate the torsional and lateral critical speeds of the supplied item. Unfortunately, the purchaser is unaware that this request is of limited value since the torsional response of a single item in a train is meaningless. Likewise, a torsional shop test will yield meaningless results if the train is not assembled and tested with every item destined for the field. 

Labyrinth piston, 49 Labyrinth seal leakage, 532 Lantern ring, 74 Lapping block set, 335 Lateral critical speeds, 384 Leakage, seal, 532, 533, 534 Leland-Mueller rule, 26 Lift coefficient, 226 Liquid... 

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

When specified, the vendor shall perform a lateral critical speed analysis for each machine to assure acceptable amphtudes of vibration throughout the anticipated operating speed range. The analysis shall be performed as described in 5.2.4.1. 

Note Lateral critical speeds may be of concern with Type OH6 pumps. Refer to 5.2.4.1 relative to the need for a lateral analysis. Normally pumps of this type are thoroughly investigated during development, and typical rotor dynamics are available and applicable. A lateral analysis should be specified only for unique, new, or critical pumps. 

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. 

A514 Lateral critical speed analysis LAT RESP c 1 Arpump only Brail equipment Nrnone Zr other... 

Lateral critical speed analysis—The required number of lateral critical analysis reports, no laterthan 3 months after the date of order. The reports shall be as required by 1.3.1. 

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. 

This led to the knowledge that extreme high-speed gears, which must be equipped with toothed couplings for lateral critical speed reasons, should have a single helical toothing that is not affected by additional external thrusts. 

The interesting fact is that the two men just mentioned were initially working independently of each other. The initial analysis used infinitely stiff bearings and, while the method improved the results, it did not match the compressor critical speed test results consistently. Later work recognized the existence of a bearing oil film with elastic and damping properties. 

On those compressors where rotor dynamics can be a problem, which is on all but the standard units (even them sometimes) and reciprocaiiiit compressors, this is the point where the acceptance of the compressor for vibration and critical speed criteria should take place. Finding these in the field later is what the user and vendor want to avoid, and this is why ail the elaborate and careful work is done at the running test time,... 

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. 

The topics of critical speed and lateral analysis are covered in each specific pump type section. 

If, on the other hand, the outer cylinder rotates and the inner one is fixed, Taylor s theoretical analysis [125), [126), 127) led to the conclusion that flow should be laminar at all speeds of rotation, and his experiments, at the highest speeds he then attained, were in harmony with this conclusion. In a later study, however, Taylor 125), 126), 127) was able to produce turbulent flow with the outer cylinder rotating, but only at much higher speeds than when the inner cylinder was the rotor. The ratio of the critical speeds was a function of for... 

Another possible deflection mechanism is the occurrence of whirling. Whirling occurs when a shaft reaches a critical speed and becomes dynamically unstable with large lateral amplitudes. This phenomenon is due to the resonance frequency when the rotational speed corresponds to the natural frequencies of lateral vibration of the shaft. For uniform beams vibrating in flexure, the natural frequencies can be expressed as ... 

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. 

Static Analysis for Natural Frequency of an Overhung Shaft. The elements that determine the lateral natural frequency are the magnitudes and locations of concenbated and distributed masses, the tensile modulus of elasticity of the material, and the moment of inertia of the shaft. Ramsey and Zoller (1976) presented the basic elements of natural frequency for a shaft and impeller system like the one shown in Figure 21-32. That method uses a lumped mass, static technique for computing the critical speed of a shaft and impeller system. The mass of the individual impellers and the distributed mass of the shaft is lumped into a single mass at the end of... 

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

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