Design of experiments for statistical modeling and multi-response optimization of nickel electroplating process

Abstract

The central composite experimental design and response surface methodology have been employed for statistical modeling and analysis of the results dealing with nickel electroplating process. The empirical models developed in terms of design variables (current density J (A/dm 2), temperature T (°C) and pH) have been found statistically adequate to describe the process responses, i.e. cathode efficiency Y (%), coating thickness U (μm), brightness V (%) and hardness W (HV). The graphical representations consisted of 2D contour plots and 3D surface plots have been used for exploring and analysis of response surfaces in order to identify the main, quadratic and interaction effects. The multi-response optimization of nickel electroplating process has been carried out by means of desirability function approach. To this end, a genetic algorithm has been used for mathematical optimization of the multi-response problem. The optimization algorithm has conducted to a set of equivalent solutions named Pareto optimal set. The confirmation runs have been employed in order to make a decision about the optimal solution approved by experiment. Thus, the optimum conditions of nickel electroplating has been defined in this work as J* = 5.35 (A/dm 2), T* = 33.44 (°C) and pH* = 6.22 and respectively the responses confirmed by experiment were Y = 79.12 ± 0.18 (%), U = 52.77 ± 0.48 (μm), V = 26.12 ± 0.45 (%) and W = 371.6 ± 1.77 (HV). In such conditions the quality of nickel electroplating deposit was the best one in accordance with experimental results.