A double circular arc fitting algorithm for CNC machining of non-uniform scroll components

  • Zaixin Wu
  • Tao LiuEmail author


Scroll compressors have been widely used in refrigeration and air conditioners. The manufacturing of scroll components with complex shape and of high precision constitutes a very important task in guaranteeing the performance of a scroll compressor. Uniform scrolls with constant wrap thickness may be availably machined by generating method. However, for the machining of non-uniform scrolls with variable wrap thickness, the generating method is no longer applicable. The current practice in the machining of non-uniform scrolls is to apply a numerical method using CAD/CAM software in a CNC milling machine. This process is data-intensive and the machining quality is not reliable as the tool path generated does not have G1 continuity. In this paper, the authors present a double circular arc (DCA) fitting algorithm for high-precision manufacturing of non-uniform scroll components. The proposed algorithm is validated by cutting experiments on a CNC milling machine, which incorporates the DCA fitting algorithm–based finishing machining and NC tool path code generation. Test results have shown that the application of DCA fitting algorithm to non-uniform scroll machining is effective, not only in decreasing the number of generated tool path points, but also with satisfied machining precision.


Scroll compressor Non-uniform scroll profile Double circular arc Finish machining Precision 


Funding information

This study is supported by the National Natural Science Foundation of China (Grant No. 51665035) and the fundamental research funds for the universities in Gansu Province (Grant No. 1302ZTC034).


  1. 1.
    Morishita E, Sugihara M (1986) Some design problems of scroll compressors. Bull JSME 29(258):4139–4146CrossRefGoogle Scholar
  2. 2.
    Ivlev VI, Bozrov VM, Voronov VA (2015) Testing a scroll machine in pneumatic motor-expander modes. J Machin Manuf Reliabil 44(2):120–124. CrossRefGoogle Scholar
  3. 3.
    Cui MM (2006) Numerical study of unsteady flows in a scroll compressor. J Fluids Eng 128(5):947–955. CrossRefGoogle Scholar
  4. 4.
    Winandy EO, Saavedra C, Jean L (2002) Experimental analysis and simplified modeling of a hermetic scroll refrigeration compressor. Appl Therm Eng 22:107–120. CrossRefGoogle Scholar
  5. 5.
    Dong AC, Oh KK, Myung DO (2014) An experimental study on semiconductor process chiller using the digital scroll compressor. J Mech Sci Technol 28(8):3345–3352. CrossRefGoogle Scholar
  6. 6.
    Blunier B, Cirrincione G, Herve Y, Miraoui A (2008) A new analytical and dynamical model of a scroll compressor with experimental validation. Int J Refrig 32(5):874–891. CrossRefGoogle Scholar
  7. 7.
    Wang H, Tian J, Du Y, Hou X (2018) Numerical simulation of CO2 scroll compressor in transcritical compression cycle. Heat Mass Transfer 54:1395–1403. CrossRefGoogle Scholar
  8. 8.
    Sun H, Hu H, Wu J, Ding G, Li G (2018) A theory-based explicit calculation model for variable speed scroll compressors with vapor injection. Int J Refrig 188:402–412. CrossRefGoogle Scholar
  9. 9.
    Wang BL, Han LJ, Shi WX, Li XT (2012) Modulation method of scroll compressor based on suction gas bypass. Appl Therm Eng 37:183–189. CrossRefGoogle Scholar
  10. 10.
    Kim D, Jeon Y, Jang D (2018) Performance comparison among two-phase liquid and vapor injection heat pumps with a scroll compressor using R410A. Appl Therm Eng 137:193–202. CrossRefGoogle Scholar
  11. 11.
    Rak J, Pietrowicz S, Gnutek Z (2017) 3D numerical calculations of tangent leakages in scroll compressor during unsteady process. Prog Comput Fluid Dyn 17(6):344–351. MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kato K, Takeuchi Y, Maeda Y, Yamanaka T (2005) High-precision and high-efficiency machining of scroll compressor components bottom machining of orbiting and fixed scrolls in low wear. Int J Adv Manuf Technol 27(3–4):260–267. CrossRefGoogle Scholar
  13. 13.
    Bell IH, Groll EA, Braun JE, Horton WT, Lemort V (2014) Comprehensive analytic solutions for the geometry of symmetric constant-wall-thickness scroll machines. Int J Refrig 45:223–242. CrossRefGoogle Scholar
  14. 14.
    Peng B, Lemort V, Legros A, Zhang HS (2017) Variable thickness scroll compressor performance analysis-Part I: geometric and thermodynamic modeling. Proc Inst Mech Eng, Part E 231(4):633–640. CrossRefGoogle Scholar
  15. 15.
    Liu Y, Tang Y, Chang Y, Yang Y (2012) Optimum design of scroll profiles created from involute of circle with variable radii by using finite element analysis. Mech Mach Theory 55:1–17. CrossRefGoogle Scholar
  16. 16.
    Wang XR, Wang ZQ, Wang YS, Lin TS, He P (2017) A bisection method for the milling of NURBS mapping projection curves by CNC machines. Int J Adv Manuf Technol 91(1–4):155–164. CrossRefGoogle Scholar
  17. 17.
    Chen Y, Yao L (2018) Study on a method of CNC form milling for the concave convex arc line gear. Int J Adv Manuf Technol 99(9–12):2327–2339. CrossRefGoogle Scholar
  18. 18.
    Sprott K (2016) Surface normal interpolation for five axis CNC milling. Int J Adv Manuf Technol 84(9–12):2319–2329. CrossRefGoogle Scholar
  19. 19.
    Pi SW, Liu Q, Liu QT (2018) A novel dynamic contour error estimation and control in high-speed CNC. Int J Adv Manuf Technol 96(1–4):547–560. CrossRefGoogle Scholar
  20. 20.
    Jiang Z, Cheng K, Harrison DK (2000) A concurrent engineering approach to the development of a scroll compressor. J Mater Process Technol 107:194–200. CrossRefGoogle Scholar
  21. 21.
    Jiang Z, Harrison DK, Cheng K (2003) Computer-aided design and manufacturing of scroll compressors. J Mater Process Technol 138:145–151. CrossRefGoogle Scholar
  22. 22.
    Meek DS, Walton DJ (1995) Approximating smooth planar curves by arc splines. J Comput Appl Math 59(2):221–231. MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Šír Z, Feichtinger R, Jüttler B (2006) Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics. Comput Aided Des 38(6):608–618. CrossRefGoogle Scholar
  24. 24.
    Yang J, Wu A, Liu Y (2018) Kinematics model and trajectory interpolation algorithm for CNC turning of non-circular profiles. Precis Eng. 54:212–221. CrossRefGoogle Scholar
  25. 25.
    Knez M, Žagar E (2018) Interpolation of circular arcs by parametric polynomials of maximal geometric smoothness. Comput Aided Geom Des 63:66–77. MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Chen H, Zhao WS, Xi XC, Chen M (2017) Non-circular parametric curve and curved surface interpolation and tool compensation for WEDM based on unit arc length increment method. Int J Adv Manuf Technol 88(5–8):1257–1266. CrossRefGoogle Scholar
  27. 27.
    Lee JN, Li CN (2010) The CAM system for scroll profile with three CNC interpolations. Adv Mater Res 83–86:696–703. CrossRefGoogle Scholar
  28. 28.
    Qiu H, Kubo A, Li ZY, Lin C (2008) Optimal Archimedes’ spiral interpolation for cutter path generation in NC machining of noncircular contours. Int J Adv Manuf Technol 36(1–2):69–82. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical and Electronical EngineeringLanzhou University of TechnologyLanzhouPeople’s Republic of China

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