First critical rotor speed

Some initial impulse unbalance is often required to start the whirl motion. Newkirk has suggested that the effect is caused by interfaces of joints in a rotor (shrink fits) rather than defects in rotor material. This type of whirl phenomenon occurs only at rotational speeds above the first critical. The phenomenon may disappear and then reappear at a higher speed. Some success has been achieved in reducing this type of whirl by reducing the number of separate parts, restricting the shrink fits, and providing some lockup of assembled elements. 

All turbines are variable-speed drivers and operate near or above one of the rotor s critical speeds. Narrowbands should be established that track each of the critical speeds defined for the turbine s rotor. In most applications, steam turbines operate above the first critical speed and in some cases above the second. A movable narrowband window should be established to track the fundamental (1 x), second (2x), and third (3x) harmonics of actual shaft speed. The best method is to use orders analysis and a tachometer to adjust the window location. 

In most cases, running speed is the forcing function that excites the natural frequency of the dynamic component. As a result, rotating equipment is designed to operate at primary rotor speeds that do not coincide with the rotor assembly s natural frequencies. Most low- to moderate-speed machines are designed to operate below the first critical speed of the rotor assembly. 

Rotors that are shorter than the first critical length are said to be subcriticaL Such rotors do not need special means to avoid resonant speeds. Rotors that are longer than the first critical length are called supercritical. They must be operated at speeds away from resonance... 

The important critical speed for a decanter is the lowest speed at which there is significant flexible deformation of the rotor. This speed is called the first rotor critical speed. Decanters will always have a certain unbalance, both due to the handling of solids from the process and due to wear on the rotor. Operating the decanter close to, or just above, the flexible critical speed of the rotor will result in high vibration levels and very high stresses in the rotor components. The critical value of the rotor speed will therefore be an upper limit for the operating speed, and the decanter must be operated below this speed with a safe margin. 

In order to increase the critical speed of the rotor a number of different modifications can be made to the rotor system. By supporting one or both main bearings in a flexible pillow block the first critical speed of the rotor can be turned into a low speed rigid-body motion for the rotor. It can then be operated supercritically with respect to this critical speed. Other modifications are the floating conveyor and the separately supported gearbox. 

The first or free-free rotor bending mode frequency (based on the required margin for operation below the critical speed)... 

Appears suddenly at or above rotor critical speed when critical is below one-half operating speed. Increasing speed increases vibration amplitude, blit whirl frequency remains constant. When speed IS decreased, vibration disappears below where it first appeared. Fnction-indnced rotor whirl Encountered m bnilt-np rotors or rotors with shrink fits or rotor disassembly to inspect fits, increase shrink fits Coupling friction has been known to induce whirl... 

Flexible rotors are designed to operate at speeds above those corresponding to their first natural frequencies of transverse vibrations. The phase relation of the maximum amplitude of vibration experiences a significant shift as the rotor operates above a different critical speed. Hence, the unbalance in a flexible rotor cannot simply be considered in terms of a force and moment when the response of the vibration system is in-line (or in-phase) with the generating force (the unbalance). Consequently, the two-plane dynamic balancing usually applied to a rigid rotor is inadequate to assure the rotor is balanced in its flexible mode. 

The determination of the first bending critical speed is well established however, there is also concern with regard to the rotor support system s sensitivity to exciting forces. These come from unbalance and/or gas dynamic forces arising during operation in service. Operation with dirty corrosive gas will soon cause rotor unbalance. The rotor dynamics verification test is concerned with synchronous excitaticm, namely unbalance. The test must also verify that the separation margins are to specification. 

Higher-speed machines may be designed to operate between the first and second, or second and third, critical speeds of the rotor assembly. As these machines accelerate through the resonant zones or critical speeds, their natural frequency is momentarily excited. As long as the ramp rate limits the duration of excitation, this mode of operation is acceptable. However, care must be taken to ensure that the transient time through the resonant zone is as short as possible. 

Pump rotors shall be designed such that their first dry critical speed is the following percentage above their maximum allowable continuous speed ... 

The rotor of one- and two-stage pumps shall be designed so its first dry bending critical speed is at least 20 % above the pump s maximum continuous operating speed. 

The high rotational speeds in a centrifugal compressor demand attention to the critical speed of the assembly, sonic velocity in the gas being compressed, and vibration of the rotor. In the normal case of a flexible-shaft machine, operating speeds should be between the first and second critical speeds. These usually differ by a factor of at least two to five or higher, and it should he possible to operate a compressor with comfortable margins on both sides. 

In general the bowl strength, the first rotor critical speed, and the maximum permissible speed of the main bearings control the maximum speed at which a decanter can be operated. 

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