Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A more accurate analytical formulation of surface roughness in layer-based additive manufacturing to enhance the product’s precision


A theoretical formula for surface roughness of layer-based manufactured parts in additive manufacturing is developed considering a more accurate definition of the centerline by minimizing the total arithmetic deviations of the actual surface profile. The developed model is experimentally validated, and it is compared with those that are used in common practices. Considering the uncontrolled process variables and the complexity of the numerical solutions, the analytical and experimental results show satisfying agreement. A methodology is also developed to decide whether the objective surface slope is feasible with the current number of layers and how the layers need to be laid down to achieve the desired surface accuracy. The methodology yields more accurate small features on the surfaces of the layer-based manufactured products.

This is a preview of subscription content, log in to check access.


  1. 1.

    Turner BN, Gold SA (2015) A review of melt extrusion additive manufacturing processes: II. Materials, dimensional accuracy, and surface roughness. Rapid Prototyp J 21(3):250–261. https://doi.org/10.1108/RPJ-02-2013-0017

  2. 2.

    Agarwala MK, Jamalabad VR, Langrana NA, Safari A, Whalen PJ, Danforth SC (1996) Structural quality of parts processed by fused deposition. Rapid Prototyp J 2(4):4–19. https://doi.org/10.1108/13552549610732034

  3. 3.

    Pandey PM, Reddy NV, Dhande SG (2003) Improvement of surface finish by staircase machining in fused deposition modeling. J Mater Proc Technol 132(1-3):323–331. https://doi.org/10.1016/S0924-0136(02)00953-6

  4. 4.

    Boschetto A, Bottini L (2015) Surface improvement of fused deposition modeling parts by barrel finishing. Rapid Prototyp J 21(6):686–696. https://doi.org/10.1108/RPJ-10-2013-0105

  5. 5.

    Ahn DK, Kim HC, Lee SH (2005) Determination of fabrication direction to minimize post-machining in FDM by prediction of non-linear roughness characteristics. J Mech Sci Technol 19(1):144–155. https://doi.org/10.1007/BF02916113

  6. 6.

    Garg A, Bhattacharya A, Batish A (2017) Chemical vapor treatment of ABS parts built by FDM: analysis of surface finish and mechanical strength. Int J Adv Manuf Technol 89(5-8):2175–2191. https://doi.org/10.1007/s00170-016-9257-1

  7. 7.

    Kuol CC, Wang CW, Lee YF, Liu YL, Qiu QY (2017) A surface quality improvement apparatus for ABS parts fabricated by additive manufacturing. Int J Adv Manuf Technol 89:635–642

  8. 8.

    Ma W, But WC, He P (2004) NURBS-based adaptive slicing for efficient rapid prototyping. Comput Aided Des 36(13):1309–1325. https://doi.org/10.1016/j.cad.2004.02.001

  9. 9.

    Huang B, Singamneni SB (2015) Curved layer adaptive slicing (CLAS) for fused deposition modelling. Rapid Prototyp J 21(4):354–367. https://doi.org/10.1108/RPJ-06-2013-0059

  10. 10.

    Sikder S, Barari A, Kishawy HA (2015) Global adaptive slicing of NURBS based sculptured surface for minimum texture error in rapid prototyping. Rapid Prototyp J 21(6):649–661. https://doi.org/10.1108/RPJ-09-2013-0090

  11. 11.

    Reeves PE, Cobb RC (1997) Reducing the surface deviation of stereolithography using in-process techniques. Rapid Prototyp J 3(1):20–31. https://doi.org/10.1108/13552549710169255

  12. 12.

    Campbell RI, Martorelli M, Lee HS (2002) Surface roughness visualization for rapid prototyping models. Comput Aided Des 34(10):717–725. https://doi.org/10.1016/S0010-4485(01)00201-9

  13. 13.

    Rahmati S, Vahabli E (2015) Evaluation of analytical modeling for improvement of surface roughness of FDM test part using measurement results. Int J Adv Manuf Technol 79(5-8):823–829. https://doi.org/10.1007/s00170-015-6879-7

  14. 14.

    Nourghassemi B (2011) Surface roughness estimation for FDM systems. Master’s Thesis, Ryerson University, Toronto, Ontario, Canada

  15. 15.

    Ahn D, Kim H, Lee S (2009) Surface roughness prediction using measured data and interpolation in layered manufacturing. J Mater Process Technol 209(2):664–671. https://doi.org/10.1016/j.jmatprotec.2008.02.050

  16. 16.

    Byun HS, Lee KH (2006) Determination of optimal build direction in rapid prototyping with variable slicing. Int J Adv Manuf Technol 28(3-4):307–313. https://doi.org/10.1007/s00170-004-2355-5

  17. 17.

    Paul BK, Voorakarnam V (2001) Effect of layer thickness and orientation angle on surface roughness in laminated object manufacturing. J Manuf Process 3(2):94–101. https://doi.org/10.1016/S1526-6125(01)70124-7

  18. 18.

    Pérez Luis CJ, Vivancos CJ, Sebastián Pérez MA (2001) Geometric roughness analysis in solid free-form manufacturing processes. J Mater Process Technol 119(1-3):52–57. https://doi.org/10.1016/S0924-0136(01)00897-4

  19. 19.

    Ahn D, Kweon J, Kwon S, Song J, Lee S (2009) Representation of surface roughness in fused deposition modeling. J Mater Proc Technol 209(15-16):5593–5600. https://doi.org/10.1016/j.jmatprotec.2009.05.016

  20. 20.

    Ahn D, Kweon JH, Choi J, Lee S (2012) Quantification of surface roughness of parts processed by laminated object manufacturing. J Mater Process Technol 212(2):339–346. https://doi.org/10.1016/j.jmatprotec.2011.08.013

  21. 21.

    Boschetto A, Giordano V, Veniali F (2013) 3D roughness profile model in fused deposition modelling. Rapid Prototyp J 19(4):240–252. https://doi.org/10.1108/13552541311323254

  22. 22.

    Barari A, Kishawy HA, Kaji F, Elbestawi MA (2016) On the surface quality of additive manufactured parts. Int J Adv Manuf Technol 89(5-8):1969–1974. https://doi.org/10.1007/s00170-016-9215-y

  23. 23.

    Jamiolahmadi S, Barari A (2014) Surface topography of additive manufacturing parts using a finite difference approach. J Manuf Sci Eng 136(6):61009. https://doi.org/10.1115/1.4028585

  24. 24.

    Kaji F, Barari A (2015) Evaluation of the surface roughness of additive manufacturing parts based on the modelling of cusp geometry. IFAC-PapersOnLine 48(3):658-663. https://doi.org/10.1016/j.ifacol.2015.06.157

  25. 25.

    ANSI/ASME B46.1–2009 standard (2009) Surface texture (surface roughness, waviness, and lay). American Society of Mechanical Engineers, New York

  26. 26.

    Barari A (20013) Inspection of the machined surfaces using manufacturing data. Journal of Manufacturing Systems 32(1):107–113. https://doi.org/10.1016/j.jmsy.2012.07.011

Download references


The research support provided by the Natural Science and Engineering Research Council of Canada (NSERC) is greatly appreciated.

Author information

Correspondence to Ahmad Barari.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lalehpour, A., Barari, A. A more accurate analytical formulation of surface roughness in layer-based additive manufacturing to enhance the product’s precision. Int J Adv Manuf Technol 96, 3793–3804 (2018). https://doi.org/10.1007/s00170-017-1448-x

Download citation


  • Layer-based manufacturing
  • Additive manufacturing
  • Surface roughness
  • Least square method
  • Centerline
  • Total least square, 3D printing, surface metrology