Critical speed, shaft design

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 standards define terms used in the industry and describe the basic design of the unit. It deals with the casing, rotors and shafts, wheels and blades, combustors, seals, bearings, critical speeds, pipe connections and auxiliary piping, mounting plates, weather-proofing, and acoustical treatment. 

The mixer manufacturer should always be consulted for proper mechanical features design and strength characteristics, such as horsepower, gear rating AGA, shaft diameter, shaft deflection, critical speeds, bottom steady bearing, and side shaft bearings. 

The shaft is a forging and may he designed as a stiff shaft or flexible shaft. A stiff shaft design means that the shaft will operate helow any of its critical speeds. Usual practice limits design operation to 60% of the first critical speed. This requires a heavier shaft than the flexible design that allows the shaft to pass through its first critical speed at 40-60% of normal and maximum operating speeds. 

A complete mechanical design should include a calculation of the critical speed. When the operating speed is close to or exceeds the critical shaft speed, vibrations can lead to mechanical instabilities and severe equipment damage. For more information, see the chapter by King [6] in Mixing in the Process Industries or the chapter by Dickey and Fasano in the Handbook of Industrial Mixing [1]. 

This equation shows how the shaft deflection is related to speed of rotation. For low speeds (w o) the radius of whirl (r = BS) is practically zero at the critical speed, when a> = o> , r = BS becomes infinite whilst for very much higher speeds B coincides with G. Thus at very high speeds the centre of mass remains at rest and the shaft rotates about this point, i.e. the shaft is selfcentring. This explains why high-speed shafts are usually designed for operation at speeds above the critical whirling speed in order to achieve stability. 

The calculations in sections 13.3 and 13.5 are based on avoidance of the shaft critical speed or sudden failure due to jamming. This section allows the basic designs in those sections to be assessed for the probability of failure due to fatigue. This is expressed in terms of a factor of safety for fatigue, Ff. 

Table 13.4 The importance of conducting a fatigue check for shafts design according to the EEUA critical speed methods...

Each shaft is designed for mechanical loads and critical shaft speed. Motor size and shaft design are related. A larger shaft to take the torque will re[Pg.329]

The general rule used to design a mixer shaft and impeller systems is to keep operating speed 20% away from a critical speed ... 

The transfer matrix (Pestel and Leckie, 1995) method can be used to calculate the critical speed and dynamic response of the shaft design. The matrix is composed of the mass and elastic characteristics of each span. The matrix is then multiplied by the deflection, slope, bending moment, and shear force at the position on one end of the span to calculate the deflection, slope, bending moment, and shear force at the position on the other end of the span. This calculation for each span is shown below in matrix form. Each span i has position i-1 on one end of the span and position i on the other end. 

The method for calculating the critical speed is first to multiply each transfer matrix for each span by the previous matrix. In other words, if n positions are present, the transfer matrix for the shaft design would be as follows ... 

Mechanical design considerations seals, dynamic loads, rotating shafts, and critical speed... 

Near top speed, a fan may operate at a speed that is near or above the natural frequency of the wheel and shaft. Under such conditions, the fan can vibrate badly even when the wheel is clean and properly balanced. Whereas manufacturers often do not check the natural frequency of the wheel and shaft ia standard designs, many have suitable computer programs for such calculations. Frequency calculations should be made on large high speed fans. The first critical wheel and shaft speed of a fan that is subject to wheel deposits or out-of-balance wear should be about 25—50% above the normal operating speed. 

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