A mathematical model of the deposition rate and layer height during electrochemical additive manufacturing

  • Abishek B. Kamaraj
  • Murali SundaramEmail author


Electrochemical additive manufacturing (ECAM) is a novel non-thermal metal additive manufacturing technology. The layer height is an important parameter in additive manufacturing processes which determines the resolution and quality of the parts manufactured. The modeling of the rate of deposition enables the prediction of the layer size and time of deposition for a particular feature. The developed model takes the electrical process parameters and the horizontal scan speed as inputs and gives the rate of deposition and deposited layer height as the output. The current density was calculated based on an existing model considering ion transport and electrode kinetics. The predicted deposition rates were validated with experimental findings. It was found that the pulsed voltage with a 75% duty cycle had the highest deposition rate. While the deposition rates varied between 1 and 3 μm/s, the scan speed was found to be between 0.1 to 2 mm/s for a diameter 250-μm tool. The scan speed had a lower limit for each interelectrode gap below which a possibility of short-circuiting exists. The influence of the pulse duty cycle on the layer height reduces at larger interelectrode gaps.


Additive manufacturing Electrochemical deposition Layer height Model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Funding information

This material is based upon work supported by the National Science Foundation under Grant Nos. CMMI-1400800 and CMMI-1454181.


  1. 1.
    Vaezi M, Seitz H, Yang S (2012) A review on 3D micro-additive manufacturing technologies. Int J Adv Manuf Technol 67:1721–1754CrossRefGoogle Scholar
  2. 2.
    Stansbury J, Idacavage M (2016) 3D printing with polymers: challenges among expanding options and opportunities. Dent Mater 32:54–64CrossRefGoogle Scholar
  3. 3.
    Shapiro A, Borgonia J, Chen Q, Dillon R, McEnerney B, Polit-Casillas R, Soloway L (2016) Additive manufacturing for aerospace flight applications. J Spacecr Rocket 53:952–959CrossRefGoogle Scholar
  4. 4.
    MacDonald E, Wicker R (2016) Multiprocess 3D printing for increasing component functionality. Science 353:aaf2093CrossRefGoogle Scholar
  5. 5.
    Chabok H, Zhou C, Chen Y, Eskandarinazhad A, Zhou Q, Shung K (2012) Ultrasound Transducer Array Fabrication Based on Additive Manufacturing of Piezocomposites. ASME. International Symposium on Flexible Automation, ASME/ISCIE 2012 International Symposium on Flexible Automation pp. 433–444.
  6. 6.
    Kruth JP, Froyen L, Van Vaerenbergh J, Mercelis P, Rombouts M, Lauwers B (2004) Selective laser melting of iron-based powder. J Mater Process Technol 149:616–622CrossRefGoogle Scholar
  7. 7.
    Roberts IA, Wang CJ, Esterlein R, Stanford M, Mynors DJ (2009) A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing. Int J Mach Tools Manuf 49:916–923CrossRefGoogle Scholar
  8. 8.
    Cabrini M, Lorenzi S, Pastore T, Pellegrini S, Ambrosio P, Calignano F, Manfredi D, Pavese M, Fino P (2016) Effect of heat treatment on corrosion resistance of DMLS AlSi10Mg alloy. Electrochim Acta 206:346–355CrossRefGoogle Scholar
  9. 9.
    Sundaram MM, Kamaraj AB, Kumar VS (2015) Mask-less electrochemical additive manufacturing: a feasibility study. J Manuf Sci Eng 137:021006–021015CrossRefGoogle Scholar
  10. 10.
    Brant A, Sundaram M (2016) A novel electrochemical micro additive manufacturing method of overhanging metal parts without reliance on support structures. Proc Manuf 5:928–943Google Scholar
  11. 11.
    Shailendar S, Sundaram M (2016) A feasibility study of localized electrochemical deposition using liquid marbles. Mater Manuf Process 31:81–86CrossRefGoogle Scholar
  12. 12.
    Brant AM, Sundaram MM, Kamaraj AB (2015) Finite element simulation of localized electrochemical deposition for maskless electrochemical additive manufacturing. J Manuf Sci Eng 137:011018–011018CrossRefGoogle Scholar
  13. 13.
    Madden JD, Hunter IW (1996) Three-dimensional microfabrication by localized electrochemical deposition. J Microelectromech Syst 5:24–32CrossRefGoogle Scholar
  14. 14.
    Yeo S, Choo JH, Yip KS (2000) Localized electrochemical deposition: the growth behavior of nickel microcolumns. In Micromachining and Microfabrication Process Technology VI. International Society for Optics and Photonics. 4174:30–40.
  15. 15.
    Wang F, Sun J, Liu D, Wang Y, Zhu W (2017) Effect of voltage and gap on micro-nickel-column growth patterns in localized electrochemical deposition. J Electrochem Soc 164:D297–D301CrossRefGoogle Scholar
  16. 16.
    Said RA (2004) Adaptive tip-withdrawal control for reliable microfabrication by localized electrodeposition. J Microelectromech Syst 13:822–832CrossRefGoogle Scholar
  17. 17.
    Yeo SH, Choo JH (2001) Effects of rotor electrode in the fabrication of high aspect ratio microstructures by localized electrochemical deposition. J Micromech Microeng 11:435–442CrossRefGoogle Scholar
  18. 18.
    Daryadel S, Behroozfar A, Morsali SR, Moreno S, Baniasadi M, Bykova J, Bernal RA, Minary-Jolandan M (2018) Localized pulsed electrodeposition process for three-dimensional printing of Nanotwinned metallic nanostructures. Nano Lett 18:208–214CrossRefGoogle Scholar
  19. 19.
    Kamaraj AB, Sundaram M (2018) A study on the effect of inter-electrode gap and pulse voltage on current density in electrochemical additive manufacturing. J Appl Electrochem 48:463–469CrossRefGoogle Scholar
  20. 20.
    Said RA (2003) Microfabrication by localized electrochemical deposition: experimental investigation and theoretical modelling. Nanotechnology 14:523–531CrossRefGoogle Scholar
  21. 21.
    Kamaraj A, Lewis S, Sundaram M (2016) Numerical study of localized electrochemical deposition for micro electrochemical additive manufacturing. Procedia CIRP 42:788–792CrossRefGoogle Scholar
  22. 22.
    Said RA (2003) Shape formation of microstructures fabricated by localized electrochemical deposition. J Electrochem Soc 150:C549–C557CrossRefGoogle Scholar
  23. 23.
    Wang F, Wang F, He H (2016) Parametric electrochemical deposition of controllable morphology of copper micro-columns. J Electrochem Soc 163:E322–E327CrossRefGoogle Scholar
  24. 24.
    Volgin VM, Kabanova TB, Davydov AD (2018) Modeling of local maskless electrochemical deposition of metal microcolumns. Chem Eng Sci 183:123–135CrossRefGoogle Scholar
  25. 25.
    Volgin VM, Lyubimov VV, Gnidina IV, Davydov AD, Kabanova TB (2018) Simulation of localized electrodeposition of microwires and microtubes. Procedia CIRP 68:242–247CrossRefGoogle Scholar
  26. 26.
    Wang F, Bian H, Wang F, Sun J, Zhu W (2017) Fabrication of micro copper walls by localized electrochemical deposition through the layer by layer movement of a micro anode. J Electrochem Soc 164:D758–D763CrossRefGoogle Scholar
  27. 27.
    Cui CQ, Lee JY (1994) Effects of oxygen reduction on nickel deposition from unbuffered aqueous solutions: I. Deposition Process Deposit Struct J Electrochem Soc 141:2030–2035Google Scholar
  28. 28.
    Ibrahim MAM (2006) Black nickel electrodeposition from a modified Watts bath. J Appl Electrochem 36:295–301CrossRefGoogle Scholar
  29. 29.
    Popov K, Keča D, Vidojković S, Lazarević B, Milojković V (1976) Mathematical model and digital simulation of pulsating overpotential copper electrodeposition. J Appl Electrochem 6:365–370CrossRefGoogle Scholar
  30. 30.
    Abdel-Hamid Z (1998) Improving the throwing power of nickel electroplating baths. Mater Chem Phys 53:235–238CrossRefGoogle Scholar
  31. 31.
    Wesley WA, Carey JW (1939) The electrodeposition of nickel from nickel chloride solutions. Trans Electrochem Soc 75:209–236CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringUniversity of CincinnatiCincinnatiUSA

Personalised recommendations