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Rotational speed and dependence of pump performance on rotational speed
The frequency of rotation of the pump is the number of revolutions of the pump shaft per unit of time, denoted by the letter n and measured in revolutions per minute (rpm). The frequency of rotation of the pumps, driven by induction motors with a frequency of supply voltage of 50 Hz, is 2750 – 2950 revolutions per minute for a 2-pole motor and 1375 – 1475 revolutions per minute for a 4-pole motor. Other rotational speeds of the motor shaft are also allowed for the operation of pumping equipment subject to and within the limits of design restrictions.
From the course of electrical engineering it is well known that the frequency of rotation of the magnetic field in an electric motor is proportional to the voltage of the supply circuit. When the frequency of the mains voltage is 50 Hz, the synchronous frequency n1 of the rotation of the magnetic field is 3000 revolutions per minute. Since the pumps are driven in the overwhelming majority of cases by asynchronous motors, the rotational speed of the induction motor shaft will always be lower than the synchronous rotational speed of the magnetic field, taking into account the slip value. The rotation of the rotor of the induction motor is connected by the formula with the number of pole pairs, slip and frequency of the supply voltage:
The formula shows that to change the rotational speed of an induction motor, it is enough to make changes in the number of pole pairs (p), rotor slip (s) or change the frequency of the supply voltage (f1).
Regulation of motor speed by changing the number of pairs of poles allows you to get only a step change in the speed of rotation, which is often unacceptable to ensure the required parameters of the electric pump. The exception is a series of circulation pumps that allow stepwise regulation. For asynchronous motors of squirrel cage pumps, the regulation of the engine speed by glide does not apply. The change in the frequency of the supply voltage is the most acceptable, effective and perfect method of regulation, allowing to provide a stepless, smooth change in the hydraulic, electrical and mechanical characteristics of the electric pump. But today this method of regulation requires the use of additional control equipment – an asynchronous motor frequency converter.
In the absence of the influence of cavitation on the pump operation, a change in the rotational speed of the electric motor will be accompanied by a change in the pump characteristics in accordance with the laws of similarity
1. Performance Q is proportional to the ratio of the rotational speed:
2. The manometric head H is proportional to the ratio of the rotational speed in the square:
3. The power consumption N is proportional to the ratio of the rotational speed in the cube:
As can be seen from the similarity formulas, a slight change in the shaft speed is accompanied by significant changes in the power consumption. For example, a centrifugal pump operating with a 50 Hz mains supply, with an engine speed of 2950 rpm, while reducing the mains frequency to 40 Hz, will reduce the number of revolutions, respectively, to 2360 rpm and performance by 20%. In this case, in accordance with the laws of similarity, energy consumption will be reduced by 50%.