Research on prediction models for limiting vacuum degree and its pre-pumping time of Roots pump

Aiming at the problems of high complexity, poor universality and insufficient precision in the models for the limiting vacuum degree and its pre-pumping time of Roots pumps, a high-precision, concise and universal prediction model was constructed, so as to provide theoretical support for the performance optimization and precise evaluation of Roots pumps. A fully parametric rotor profile model based on shape coefficients was established to achieve an accurate description of the rotor's geometric characteristics. The swept area method was used to analyze the theoretical flow, and the calculation formulas for instantaneous flow, average flow and flow pulsation coefficient were derived. Based on the laminar flow theory, combined with the geometric characteristics of radial, meshing and end face clearances, leakage models for the three clearances were established. Among them, an innovative equivalent parallel rectangular plate model with equal end-leakage area was adopted for end face leakage. Based on the principle of balance between pumping flow and leakage flow, as well as the isothermal conversion theory of pre-pumping baseline volume, models for the limiting vacuum degree and its pre-pumping time were established respectively. Moreover, CFD (computational fluid dynamics) simulation was used to conduct multi-dimensional verification on flow characteristics, leakage flow, limiting vacuum degree and its pre-pumping time. The results showed that the maximum error between the theoretical value and the simulation value of the flow characteristic parameters under the involute profile was 3.84%, the consistency error between the theoretical value and the simulation value of the leakage flow was within 4.72%, the error between the theoretical value and the simulation value of the limiting vacuum degree was 4.03%, the error of the pre-pumping time was 1.88%, and the rationality of each model and equivalent method had been verified. The analytical error is within the acceptable range for engineering. The fully parameterized design method improves the correlation between the rotor profile and performance parameters, and has good operability and repeatability. It can be directly applied to the performance optimization and rapid design of Roots pumps, thereby providing reliable theoretical support for the engineering application of Roots pumps in medium and high vacuum systems.