An analytical method for calculating forces and torques in oil-free scroll vacuum pumps and compressors

Oil-free scroll vacuum pumps are finding increasing use in high-tech industries. Scroll vacuum pumps have never been in mass production in Russia, and they are currently being researched and developed. The geometry of spiral elements and bearing units, as well as the drive power, can be evaluated in terms of the gas forces acting on the spiral elements. To calculate these forces, the pressure in the cavities of the scroll mechanism is first determined. Then, axial and radial gas forces are calculated using a numerical method. In this paper, simple analytical expressions for calculating the gas forces acting on spiral elements and the corresponding shaft torque are obtained for the most common case of involute profiles. The formulas are presented for the special cases of adiabatic and isothermal compression. The influence of the compression type and the size of a gap between spirals on the gas forces and the shaft torque is demonstrated by the example of a scroll pump at a flow rate of 5 m³/h. The proposed relationships can be recommended for the calculation of scroll pumps and compressors.

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