Research Papers

Mathematical Modeling for Screw Rotor Form Grinding on Vertical Multi-Axis Computerized Numerical Control Form Grinder

[+] Author and Article Information
Yu-Ren Wu

Assistant Professor,
e-mail: yuren@mail.npust.edu.tw

Chung-Wen Fan

Graduate Research Assistant
Department of Mechanical Engineering,
National Pingtung University of
Science and Technology,
Pingtung County,
Taiwan 91201

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received December 19, 2012; final manuscript received August 3, 2013; published online September 23, 2013. Assoc. Editor: Xiaoping Qian.

J. Manuf. Sci. Eng 135(5), 051020 (Sep 23, 2013) (13 pages) Paper No: MANU-12-1369; doi: 10.1115/1.4025339 History: Received December 19, 2012; Revised August 03, 2013

The pair of screw rotors is a key element of a twin-screw compressor, and rotor tooth modification has gradually received attention because it can reduce operating compressor noise. Current rotor machining references are mainly related to forming tool design or abrasion of the “horizontal” grinder, but little attention has been paid to form grinding using a “vertical” grinder and simulating the machining flexibility of each grinder axis. Therefore, this paper established a general coordinate system for the screw rotor form grinding and connected it to a vertical five-axis computerized numerical control form grinder to simulate rotor grinding and tooth modification. Further, the influence of a form grinding wheel contour designed by different declination angles of a rotor tooth profile on a grinding rotor tooth and the influence of the motion parameter of each axis on the machining precision of the rotor and the tooth shape are proposed in this paper.

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J.Sauls, 2008, “Transmission Error in Screw Compressor Rotors,” International Compressor Engineering Conference, Purdue University, West Lafayette, IN, Paper No. 1862.
Shih, Y. P., and Chen, S. D., 2012, “Free-Form Flank Correction in Helical Gear Grinding Using a Five-Axis Computer Numerical Control Gear Profile Grinding Machine,” ASME J. Manuf. Sci. Eng., 134(4), p. 041006. [CrossRef]
Litvin, F. L., and Fuentes, A. F., 2004, Gear Geometry and Applied Theory, 2nd ed., Cambridge University Press, Cambridge, UK.
Litvin, F. L., and Feng, P. H., 1997, “Computerized Design, Generation, and Simulation of Meshing of Rotors of Screw Compressor,” Mech. Mach. Theory, 32(2), pp. 137–160. [CrossRef]
Xing, Z. W., 2000, Screw Compressors: Theory, Design and Application, China Machine Press, Beijing, China (in Chinese).
Stosic, N., Smith, I. K., and Kovacevic, A., 2005, Screw Compressors: Mathematical Modeling and Performance Calculation, Springer, Heidelberg, Germany.
Kovacevic, A., Stosic, N., Mujic, E., and Smith, I. K., 2007, “CFD Integrated Design of Screw Compressors,” Eng. Appl. Comp. Fluid, 1(2), pp. 96–108. Available at: http://jeacfm.cse.polyu.edu.hk/
Wu, Y. R., and Fong, Z. H., 2008, “Rotor Profile Design for the Twin–Screw Compressor Based on the Normal–Rack Generation Method,” ASME J. Mech. Des., 130, p. 042601. [CrossRef]
Guo, C. S., and Tang, Y., 2003, “Screw Rotor Profile Manufacturability,” Mach. Sci. Technol., 7(1), pp. 53–64. [CrossRef]
You, H. Y., Ye, P. Q., Wang, J. S., and Deng, X. Y., 2003, “Design and Application of CBN Shape Grinding Wheel for Gears,” Int. J. Mach. Tools Manuf., 43, pp. 1269–1277. [CrossRef]
Stosic, N., 2006, “A Geometric Approach to Calculating Tool Wear in Screw Rotor Machining,” Int. J. Mach. Tools Manuf., 46, pp. 1961–1965. [CrossRef]
Chiang, C. J., and Fong, Z. H., 2010, “Design of Form Milling Cutters With Multiple Inserts for Screw Rotors,” Mech. Mach. Theory, 45, pp. 1613–1627. [CrossRef]
Wei, J., Zhang, Q., Xu, Z. Z., and Lyu, S. K., 2010, “Study on Precision Grinding of Screw Rotors Using CBN Wheel,” Int. J. Precis. Eng. Manuf., 11(5), pp. 651–658. [CrossRef]
Chen, C. H., 1995, “Screw Compressor With Rotors Having Hyper Profile,” U.S. Patent No. 5454701.


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Fig. 1

Rotor profile declination: (a) male rotor and (b) female rotor

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Fig. 2

General coordinate system for generating rotor with form grinding wheel

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Fig. 3

Instant contact lines between rotor and grinding wheel contours: (a) male rotor and (b) female rotor

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Fig. 4

Coordinate system and structure of vertical form grinding machine

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Fig. 5

Clearance distribution and referenced rotor profiles

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Fig. 6

Form grinding wheels and machined rotor profiles at different cross-sections: (a) male rotor and (b) female rotor

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Fig. 7

Motion curves of each machine axis: (a) male rotor and (b) female rotor

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Fig. 8

Tooth surface error topology: (a) male rotor and (b) female rotor

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Fig. 9

Crowning of male rotor tooth surface: (a) additional motion curve of φb-axis and (b) tooth surface error topology

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Fig. 10

Grinding wheel profiles generated by different rotor profile declination angles: (a) male rotor and (b) female rotor

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Fig. 11

Maximum normal error of screw rotor surfaces with different declination angles

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Fig. 12

Influence of poor tooth profile declination angle on form gear grinding error



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