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Surface quality evaluation in meso-scale end-milling operation based on fractal theory and the Taguchi method

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This paper presents a study of the Taguchi application to optimize surface quality based on fractal theory in meso-scale end-milling operation. Usually, the surface quality is characterized by roughness, but in the meso-scale area, the size of the workpiece will be difficult to meet the requirements of the sampling length, which will have a huge influence on the characterization results. Although there are many algorithms for adjusting, the operation process is very cumbersome; for this reason, characterization method based on fractal theory is introduced and applied to evaluate the machined surface in the research. Also, the Taguchi method is applied to search the optimal parameters combination, during which spindle speed, depth of cut, and feed rate are considered as the control factors. Specifically, firstly, the machining surface characterization method based on fractal theory is introduced in details; then, an orthogonal array of L25(53) is used for the experimental study; through ANOVA analyses, the significant factors which affect surface quality are established, and the optimal cutting parameter combination is determined; later, confirmation tests are carried out to verify the applicability of the characterization methods for the meso-scale cutting surface. Research shows that fractal characterization method is better to evaluate the surface quality in the meso-scale.

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  1. 1.

    Lee TS, Lin YJ (2000) A 3D predictive cutting force model for end milling of parts having sculptured surfaces. Int J Adv Manuf Technol 16(11):773–783

  2. 2.

    Altintas Y (1994) Direct adaptive control of end milling process. Int J Mach Tools Manuf 34(4):461–472

  3. 3.

    Tsai YH, Chen JC, Lou SJ (1999) An in-process surface recognition system based on neural networks in end milling cutting operations. Int J Mach Tools Manuf 39(4):583–605

  4. 4.

    Blunt L, Jiang X (2003) Advanced techniques for assessment surface topography: development of a basis for 3D surface texture standards “surfstand”. Kogan Page, London

  5. 5.

    Dong WP, Sulivan PJ, Stout KJ (1994) Comprehensive study of parameters for characterising 3D surface topography. III: parameters for characterising amplitude and some functional properties. Wear 178(1):45–60

  6. 6.

    Shi Z, Liu L, Liu Z (2015) Influence of dynamic effects on surface roughness for face milling process. Int J Adv Manuf Technol 80(9–12):1823–1831

  7. 7.

    Wojciechowski S, Chwalczuk T, Twardowski P, Krolczyk GM (2015) Modeling of cutter displacements during ball end milling of inclined surfaces. Arch Civil Mechan Eng 15(4):798–805

  8. 8.

    Wojciechowski S, Twardowski P, Pelic M, Maruda RW, Barrans S, Krolczyk GM (2016) Precision surface characterization for finish cylindrical milling with dynamic tool displacements model. Precision Eng 46:158–165

  9. 9.

    Shi K, Zhang D, Ren J (2015) Optimization of process parameters for surface roughness and microhardness in dry milling of magnesium alloy using Taguchi with grey relational analysis. Int J Adv Manuf Technol 81:1–7

  10. 10.

    Elhami S, Razfar MR, Farahnakian M, Rasti A (2013) Application of GONNS to predict constrained optimum surface roughness in face milling of high-silicon austenitic stainless steel. Int J Adv Manuf Technol 66(5–8):975–986

  11. 11.

    Luo G, Ming W, Zhang Z, Liu M, Li H, Li Y, Yin L (2014) Investigating the effect of WEDM process parameters on 3d micron-scale surface topography related to fractal dimension. J Adv Manuf Technol 75(9–12):1773–1786

  12. 12.

    Zhang JZ, Chen JC, Kirby ED (2007) Surface roughness optimization in an end-milling operation using the Taguchi design method. J Mater Process Technol 184(1–3):233–239

  13. 13.

    Mandelbrot BB (1982) The fractal geometry of nature. Freeman, San Francisco

  14. 14.

    Majumdar A, Tien CL (1990) Fractal characterization and simulation of rough surfaces. Wear 136(2):313–327

  15. 15.

    Sayles RS, Thomas TR (1978) Surface topography as a nonstationary random process. Nature 271(5644):431–434

  16. 16.

    Durst PJ, Mason GL, Mckinley B, Baylot A (2011) Predicting RMS surface roughness using fractal dimension and PSD parameters. J TERRAMECHANICS 48(2):105–111

  17. 17.

    Constantoudis V, Patsis GP, Gogolides E (2012) Fractals and device performance variability: the key role of roughness in micro and nanofabrication. Microelectron Eng 90(2):121–125

  18. 18.

    Goedecke A, Jackson RL, Mock R (2012) A fractal expansion of a three dimensional elastic-plastic multi-scale rough surface contact model. Tribol Int 59:230–239

  19. 19.

    Wang QY, Liang ZQ, Wang XB, Zhao WX, Wu YB, Zhou TF (2015) Fractal analysis of surface topography in ground monocrystal sapphire. Appl Surf Sci 327:182–189

  20. 20.

    Yang D, Liu Z (2015) Surface topography analysis and cutting parameters optimization for peripheral milling titanium alloy Ti–6Al–4V. Int J Refract Met Hard Mater 51:192–200

  21. 21.

    Philip Selvaraj D, Chandramohan P, Mohanraj M (2014) Optimization of surface roughness, cutting force and tool wear of nitrogen alloyed duplex stainless steel in a dry turning process using Taguchi method. Measurement 49(11):205–215

  22. 22.

    Asiltürk I, Akkus H (2011) Determining the effect of cutting parameters on surface roughness in hard turning using the Taguchi method. Meas 44(9):1697–1704

  23. 23.

    Canakci A, Erdemir F, Varol T, Patir A (2013) Determining the effect of process parameters on particle size in mechanical milling using the Taguchi method: measurement and analysis. Measurement 46(9):3532–3540

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Correspondence to Li Jiao.

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Mao, H., Jiao, L., Gao, S. et al. Surface quality evaluation in meso-scale end-milling operation based on fractal theory and the Taguchi method. Int J Adv Manuf Technol 91, 657–665 (2017).

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  • Fractal theory
  • Taguchi design
  • End-milling operations
  • Meso-scale