Building a Mathematical Equation for Describing Volume Changes in Suction and Pumping Chambers of an Improved Type of the Roots Blower
Main Article Content
Abstract
The volume change in suction and pumping chambers of the roots type of hydraulic devices is an important factor deciding machine performance. This volume change creates suction and pumping pressures when the machine is working. Therefore, when designing and optimizing design of the machine, it is necessary to build a mathematical model for describing those changes in relation with rotation angle of the driving shaft. To reach this goal, the authors carry out volume modelling process by building mathematical model for calculating the volume changes of the area of the suction/pumping chambers in relation with rotation angle of the driving shaft of the specific type of Roots pump, which has been proposed by the authors. In addition, this study also points out that when the designing parameter such as the ratio parameter between ellipse's shorter axis and its larger axis changes from 1 to 0.5, the volume change gradually increases and reaches 26.77% when the design parameter equals to 0.5.
Keywords
Roots Blower, Hydraulic machinery, Elliptical gears
Article Details
References
[1] Philander Higley Roots, Francis Marion Roots Patent. Rotary blower, US2369 Patent (1860).
[2] Wang, P. Y., Fong, Z. H., and Fang, H. S., Design constraints of five-arc Roots vacuum pumps, Proc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 216(C2) (2002) 225–234.
[3] Yaw-Hong Kang, Ha-Hai Vu, A newly developed rotor profile for lobe pumps: Generation and numerical performance assessment, Journal of Mechanical Science and Technology 28 (3) (2014) 915-926.
[4] Ucer, S. and Celik, I., Analysis of Flow Trough Roots Blower Systems, International Compressor Engineering Conference, (1980) 126-132.
[5] Faydor. L. Litvin, Pin Hao Feng, Computerized design and generation of cycloidal gearings, Mech. Mach. Theory Vol. 31, No. 7 (1996) 891-911.
[6] Daniel C.H. Yang, Shih-Hsi Tong, the specific flowrate of deviation function based lobe pumps–derivation and analysis, Mechanism and Machine Theory 37 (2002) 1025-1042.
[7] Shih-Hsi Tong, Daniel C. H. Yang, Rotor Profiles Synthesis for Lobe Pumps with Given Flow Rate Functions, J. Mech. Des 127 (2) (2005) 287-294.
[8] Nguyễn Hồng Thái, Trần Ngọc Tiên, Đề xuất một biên dạng mới trong thiết kế quạt thổi cao áp dạng Roots, Hội nghị khoa học cơ học Thủy khí toàn quốc lần thứ 20, (2017) 692-698.
[9] Tran Ngoc Tien, Nguyen Hong Thai, A novel design of the Roots blower, Journal of Science and Technology 57 (2) (2019) 249-260.
[10] Libardo V. Vanegas-Useche, Magd M. Abdel-Wahab, Graham A. Parker, A New Noncircular Gear Pair to Reduce Shaft Accelerations: A Comparison with Sinusoidal and Elliptical Gears, Dyna 83 (198) (2016) 220-228.
[11] Wales L. Palmer and Israel W. Knox, Improvement in rotary pressure-blowers, US166295A Patent (1875).
[2] Wang, P. Y., Fong, Z. H., and Fang, H. S., Design constraints of five-arc Roots vacuum pumps, Proc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 216(C2) (2002) 225–234.
[3] Yaw-Hong Kang, Ha-Hai Vu, A newly developed rotor profile for lobe pumps: Generation and numerical performance assessment, Journal of Mechanical Science and Technology 28 (3) (2014) 915-926.
[4] Ucer, S. and Celik, I., Analysis of Flow Trough Roots Blower Systems, International Compressor Engineering Conference, (1980) 126-132.
[5] Faydor. L. Litvin, Pin Hao Feng, Computerized design and generation of cycloidal gearings, Mech. Mach. Theory Vol. 31, No. 7 (1996) 891-911.
[6] Daniel C.H. Yang, Shih-Hsi Tong, the specific flowrate of deviation function based lobe pumps–derivation and analysis, Mechanism and Machine Theory 37 (2002) 1025-1042.
[7] Shih-Hsi Tong, Daniel C. H. Yang, Rotor Profiles Synthesis for Lobe Pumps with Given Flow Rate Functions, J. Mech. Des 127 (2) (2005) 287-294.
[8] Nguyễn Hồng Thái, Trần Ngọc Tiên, Đề xuất một biên dạng mới trong thiết kế quạt thổi cao áp dạng Roots, Hội nghị khoa học cơ học Thủy khí toàn quốc lần thứ 20, (2017) 692-698.
[9] Tran Ngoc Tien, Nguyen Hong Thai, A novel design of the Roots blower, Journal of Science and Technology 57 (2) (2019) 249-260.
[10] Libardo V. Vanegas-Useche, Magd M. Abdel-Wahab, Graham A. Parker, A New Noncircular Gear Pair to Reduce Shaft Accelerations: A Comparison with Sinusoidal and Elliptical Gears, Dyna 83 (198) (2016) 220-228.
[11] Wales L. Palmer and Israel W. Knox, Improvement in rotary pressure-blowers, US166295A Patent (1875).