Geometric Modelling and Analysis of Superelliptic Rotor Profile for Roots Vacuum Pump

Binglin Li; Ping Luo; Manzhu Jiang

doi:10.54691/d9ge8v89

Authors

Binglin Li
Ping Luo
Manzhu Jiang

DOI:

https://doi.org/10.54691/d9ge8v89

Keywords:

Roots Vacuum Pump; Superelliptic Rotor; Numerical Simulations; Area Utilization Rate; Flow Fluctuation; Volumetric Efficiency.

Abstract

The rotor profile has a significant influence on the performance of Roots vacuum pump. This paper proposes a novel profile which consists of a superellipse at the top and a conjugate curve at the waist. The mathematical model for the superelliptic rotor profile is established, and the constraint equations of superelliptic parameters are derived to avoid undercutting, carryover, and interference. It is found that the area utilization rate increases with the axis ratio increases when the superelliptic index is constant. In order to evaluate the pumping performance of the superelliptic rotor, three-dimensional numerical simulations are performed to analyze the pressure distribution and flow rate, and the flow fluctuation coefficient and volumetric efficiency are calculated. The results show that as the superelliptic index increases, the flow rate of the Roots pump increases, the flow fluctuation coefficient decreases, and the volumetric efficiency increases up to 88% for constant axis ratio.

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References

[1] F.L. Litvin, P. H. Feng, Computerized design and generation of cycloidal gearings. Mech. and Mach. Theory 31(7) (1996) 891-911.

[2] P.Y. Wang, Z.H. Fong, H.S. Fang. Design constraints of five-arc Roots vacuum pumps. Proc. Instit. Mech. Eng. Part C 216(2) (2002) 225-234.

[3] C.F. Hsieh, Y.W. Hwang. Tooth profile of a Roots rotor with a variable trochoid ratio. Math. Comput. Model. 48(1-2) (2008) 19-33.

[4] Y.W. Hwang, C.F. Hsieh. Study on high volumetric efficiency of the Roots rotor profile with variable trochoid ratio. Proc. Instit. Mech. Eng. Part C 220(9) (2006) 1375-1384.

[5] C.F. Hsieh. A new curve for application to the rotor profile of rotary lobe pumps. Mech. Mach. Theory 87 (2015) 70-81.

[6] J. Wang, R. Liu, S. Yang, et al. Geometric study and simulation of an elliptical rotor profile for Roots vacuum pumps. Vacuum. 153 (2018) 168-175.

[7] J. Wang, S. Yang, R. Sha, et al. Geometric design and analysis of novel asymmetrical rotors for Roots vacuum pumps. J. Mech. Des. 142(6) (2020) 064501.

[8] Z. Li, X. Wang, X. Han, et al. Geometric design of two novel rotor profiles for Roots vacuum pumps with elliptical curve. Results Eng. 25 (2025) 104170.

[9] Y.H. Kang, H.H. Vu. A newly developed rotor profile for lobe pumps: Generation and numerical performance assessment, J. Mech. Sci. Technol. 28 (2014) 915-926.

[10] Y.H. Kang, H.H. Vu, C.H. Hsu. Factors impacting on performance of lobe pumps: A numerical evaluation, J. Mech. 28(2) (2012) 229-238.

[11] Y.R. Wu, V.T. Tran. Generation method for a novel Roots rotor profile to improve performance of dry multi-stage vacuum pumps. Mech. Mach. Theory 128 (2018) 475-491.

[12] V.T. Tran, B.T. Thanh, B.T. Long, et al. Study on the effects of tooth profile design parameters of rotor to performance of vacuum pump. Int. J. Mod. Phys. 34(22n24) (2020) 2040141.

[13] Z.Q. Li, X.J. Wang. New cycloid rotor profiles design under different rolling circle radii for Roots vacuum pumps. SN Appl. Sci. 4(10) (2022) 280.

[14] L. Liu, P. Chen, J. Du. Design of rotor profile of a new roots vacuum pump. J. Phys: Conf. Ser 1676(1) (2020) 012078.

[15] S. Zhou, X. Jia, X. Peng, et al. The effects of design parameters on performance of a novel roots profile. Int. J. Hydrog. Energy 48(6) (2023) 2368-2384.

[16] G. Houzeaux, R. Codina. A finite element method for the solution of rotary pumps. Comput. Fluids 36(4) (2007) 667-679.

[17] S.K. Sun, B. Zhao, X.H. Jia, et al. Three-dimensional numerical simulation and experimental validation of flows in working chambers and inlet/outlet pockets of Roots pump. Vacuum 137 (2017) 195-204.

[18] Y. Liu, L. Wang, Z. Zhu. Numerical study on flow characteristics of rotor pumps including cavitation. Proc. Instit. Mech. Eng. Part C 229(14) (2015) 2626-2638.

[19] F.L. Litvin, A. Fuentes. Gear geometry and applied theory. Cambridge university press, 2004.