## 1 Introduction  
As the main equipment used for obtaining a clean and high vacuum, molecular pumps are widely used in precision instruments and industrial production [1]. The development of molecular pump technology has promoted the improvement and innovation of high vacuum leak detection technology. The helium mass spectrometer leak detector, which is a mass spectrometer analyzer that relies on a vacuum environment to detect leaks or gaps, determines the leak rate by detecting the amount of helium gas entering the mass spectrometer chamber. Additionally, the helium mass spectrometer leak detector, which has stable performance and high sensitivity, is extensively utilized. The pumping characteristics of the molecular pump can affect the detection performance of the helium mass spectrometer. In 1970, the world's first hybrid molecular pump was successfully developed by Alpha in France. [PERSON] studied the leakage of turbomolecular pumps in detail, analyzedthe effect of leakage on the compression ratio and proposed a specific way to implement improved spacer rings to reduce leakage [2]. [PERSON] found that the structure of the turbine stage and the traction stage of the hybrid molecular pump affected pumping performance and proposed two options, changing several stages of blades at the turbine-stage articulation and adding a disc transition structure, to improve the pumping performance [3]. [PERSON] proposed a conceptual molecular pump with the ability to pump over a wide range; although not successfully applied, this concept provides a guiding direction for the development of molecular pumps [4]. [PERSON] proposed solutions to problems arising from the practical application of hybrid molecular pumps [5]. [PERSON] improved the structure of the hybrid molecular pump by reducing the height of the traction stage by changing the groove structure of the disc pump and decreasing the occupied space of the hybrid molecular pump by applying turbine vanes for pumping [6]. With the continuous optimization and improvement of hybrid molecular pumps, research methods have gradually improved and become more diverse. In 1960, [PERSON] established the extraction theory of turbine blade trains based on the transmission probability, which is still widely utilized [7]. Through experimental research, [PERSON] and [PERSON] obtained the main parameters that affect the pumping performance of a composite molecular pump. In the turbine stage, the main parameters are the rotor speed, blade row inclination and pitch chord ratio [8; 9]. The research scope of compound molecular pumps has gradually expanded from the molecular flow state to the transition and continuous flow states. The calculation method is no longer limited to analytical methods, and a statistical method based on random numbers is being thoroughly developed and tested. [PERSON] obtained the pumping performance of the transitional flow state of the molecular pump by considering both intermolecular collisions and molecule-wall collisions in the turbine channel [10]. [PERSON] et al. optimized the statistical calculation method through a direct Monte Carlo simulation method [11]. [PERSON] et al. established a multidisciplinary design platform to study the design method of a magnetic levitation turbomolecular pump system [12]. [PERSON] et al. established a new modeling method of rows of rotors and stators for turbine blade and established differentiated combined blade rows according to flow field characteristics [13]. [PERSON], [PERSON], and [PERSON] et al. have performed much research on a method to calculate pumping characteristics of high vacuum system of turbomolecular vacuum pumps and optimize molecular pump parameters [14; 15; 16]. Currently, there are many new molecular pumps with specific functions, and the development of various new structural forms of molecular pumps expands their application range.