How does the Roots pump work?

LC type Roots oil pump works:

The LC type Roots oil pump is a rotary variable displacement vacuum pump. It was evolved from the Roots blower. According to the different working range of the Roots vacuum pump, it is divided into a low-vacuum LC type Roots oil pump with a straight exhaust atmosphere;
The working principle of the LC type Roots oil pump: The working principle of the Roots oil pump - I know that in the pump chamber, two "8" shaped rotors are mounted perpendicular to each other on a pair of parallel shafts, with a transmission ratio of 1. A pair of gear belts rotate in synchronism with each other in opposite directions. Between the rotors, there is a certain gap between the rotor and the inner wall of the pump casing to achieve high speed operation. Since the Roots oil pump is a vacuum pump without internal compression, the compression ratio is usually low, so the high and medium vacuum pumps require a foreline pump. The ultimate vacuum of the Roots pump depends on the structure and manufacturing accuracy of the pump itself and on the ultimate vacuum of the foreline pump. In order to increase the ultimate vacuum of the pump, the Roots oil pump can be used in series. The Roots oil pump works like a Roots blower. Due to the continuous rotation of the rotor, the pumped gas is sucked from the intake port into the space v0 between the rotor and the pump casing, and then discharged through the exhaust port. Since the v0 space is fully closed after inhalation, the gas is not compressed and expanded in the pump chamber. However, when the top of the rotor turns over the edge of the exhaust port and the v0 space communicates with the exhaust side, since the gas pressure on the exhaust side is high, a part of the gas is returned to the space v0, so that the gas pressure suddenly increases. When the rotor continues to rotate, the gas exits the pump.

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