Research of a novel eccentric involute rotor and its performance analysis for twin-screw vacuum pumps
Introduction
As a kind of positive-displacement pump, the twin-screw vacuum pump has many advantages of simple structure, smooth operation and dry-running mode. Therefore, it can be used in many fields, such as semiconductor, chemical, electronic, nuclear and medicine applications. The twin-screw vacuum pump mainly consists of a pair of intermeshing screw rotors rotating in opposite direction about parallel axes in a casing, so that a series of periodically varying closed volumes, called working chambers, are formed by two intermeshing screw rotors and casing. Thus, the suction, compression and discharge processes of gases can be achieved.
As the requirements for dry vacuum pumps, the twin-screw pumps have been widely concerned. Many published literatures of studying this pump exist. Ohbayashi et al. [1] proposed two cycloid curves for forming cross-sectional profile to solve the problem of root cutting of screw rotors, and, however, its area utilization is low. Stosic et al. [2] proposed a series of profiles for twin-screw vacuum pump, and calculated performances on the profiles. Furthermore, the calculations were compared with experimental data. Akutsu et al. [3] proposed a gradational lead screw dry vacuum pump, in which the transmission ratio of two rotors is 5:6. The gradational lead screw dry vacuum pump has a wide working pressure range. Pfaller et al. [4] studied the influence of rotor pitch distribution on the performance of screw spindle vacuum pumps. An optimized distribution of rotor pitch was presented. The underlying physical dependencies were given. In other respects, Zhang et al. [5] proposed a novel tilt form grinding method to overcome the problem of concave profile grinding. Moreover, the mathematical models and numerical simulations were used to analyze the performance of screw machinery in literatures [[6], [7], [8], [9], [10], [11]].
The screw rotors and their cross-sectional profiles directly affect the pumping speed, inter-stage seal and ultimate vacuum degree of the twin-screw vacuum pump. At present, the conventionally used cross-sectional profile, the cycloid-involute profile consists of four curves: a dedendum circular arc, an addendum circular arc, a cycloid curve and a circular involute. The screw rotor generated by the cycloid-involute profile has the problem that discontinuous spatial contact curves during operations exist, and this problem will lead to obvious gas leakages between adjacent working chambers. Many studies on screw rotors focused on the modification and improvement on this conventional cross-sectional profile and its forming screw rotor.
Lu et al. [12] analyzed the trapezoidal tooth profile from its angle-radius and special shape, proposed a method to correct the interferential phenomenon of the trapezoidal profile, and designed a smooth profile. Hsieh et al. [13] pointed out drawbacks of the cross-sectional profiles, which is unfavourable to the gas sealing, and proposed two types of profiles to reduce the carryover and improve the gas sealing. Wang et al. [14] put forward a method to eliminate the carryover of the conventional cycloid-involute profile of screw rotors by using cycloid, and proposed a novel screw rotor with variable cross-sectional profiles by this method. The performance and deformation of the rotor was analyzed. Wang et al. [15] also proposed a novel cross-sectional profile of screw rotors, which using circular arc and an equidistant curve of an epicycloid to eliminate the carryovers, and then studied the influence of geometric parameters.
As regards to researches on other aspects of screw rotor of twin-screw vacuum pumps, Zhang et al. [16] proposed a cavitary structure locating in screw rotors for the dynamic balance, and analyzed geometries of the cavity. Lu et al. [17] analyzed the working process and leakage of the twin-screw vacuum pump, and derived the basic control equations by using the energy conservation equation and the fundamental of variable mass thermodynamics. The study will be helpful to predict the performance of twin-screw vacuum pumps. Fan et al. [18] studied the performance of rotors with different gradational lead screw, and compared the gradational lead screw rotor with the constant lead screw rotor. It is truly a trend that screw rotors are designed in variable lead, because the gradational lead screw rotor is high efficiency and energy-saving. The results indicate that the gradational lead screw rotors are superior to the constant lead screw rotors.
The conventional the screw rotor, whose cross-sectional profile is the cycloid-involute profile, contains a carryover and discontinuous spatial contact curves. This problem will lead to serious gas leakages. The previous studies on this cross-sectional profile have improved the continuity of the spatial contact curve of the screw rotor by adding special curves [14], which, however, will lead to a more complicated composition of the cross-sectional profile. The purpose of this study was to solve the above problem of the conventional cycloid-involute screw rotor, and propose a new more advanced one. In this study, an eccentric involute and its conjugate curve were used to smoothly connect the dedendum and addendum circular arcs, and then a novel eccentric involute screw rotor (EIR) with continous spatial contact curves was constructed. Equations of all constituent curves of the cross-sectional profile of the proposed EIR were derived, and influences of parameters on the shape and performance of the EIR were studied.
Section snippets
Calculations of the conjugate profile of an eccentric involute
In this section, the problem of the conventional screw rotor, whose cross-sectional profile was cycloid-involute profile, was analyzed. A method was proposed to smoothly connect the addendum and dedendum circular arcs by using an eccentric involute. Meanwhile, the conjugate curve of the eccentric involute was derived, and its equation was obtained.
A geometric model of novel screw rotors
In this section a geometric model of the left and right cross-sectional profiles of novel screw rotors, eccentric involute rotor (EIR), was established.
Analysis of the proposed EIRs
Effects of independent geometric parameters including the pitch circle R2 and involute central angle θ on the shapes, area-utilizing ratio and spatial contact curves of the proposed EIR were analyzed.
Conclusion
An eccentric involute and its conjugate curve are used to smoothly connect the addendum and dedendum circular arcs, so that a novel cross-sectional profile consisting of only four profiles is proposed, and its corresponding screw rotor, a novel eccentric involute screw rotor (EIR), whose spatial contact curves are continuous and short, are constructed. The proposed EIRs and its cross-sectional profiles can achieve complete meshing in operation. The proposed EIR is suitable for the design of the
Declaration of competing interest
No conflict of interest.
Acknowledgements
The work was supported by National Natural Science Foundation of China 50806082, 51706247; The work was supported by Natural Science Foundation of Shandong Province, China (ZR2019MEE079).
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