Vacuum pumps play an important role in vacuum systems. The method proposed in this article, which uses the extended cycloid curve with a variable trochoid ratio, can be utilized to improve pump performance. The third-order and the fifth-order polynomials are used, and their boundary conditions are designed to generate a smooth trochoid ratio function. Hence, a regular addendum curve for the Roots rotor is generated. The tooth profile for the complete Roots rotor is derived from the addendum curve. Undercutting and carryover analyses are used to verify the feasibility of the designed method. Finally, a design flow on how to achieve high volumetric efficiency for a vacuum system is presented.
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