Deriving the functional relation of input parameters in single-point incremental forming through dimensional analysis

The system is designed with the basics of fundamental units termed dimensional analysis (DA). The fundamental units are modeled to figure out some quantitative measures without the knowledge of the system behavior. Subsequently, the dimension analysis-based modeling helps to develop the functional relation of input parameters for the set objectives. The generalized model is validated with the output of experiments with an agreement to adopt the model within a certain range of error. Single-point incremental forming (SPIF) is an innovative sheet metal forming technique in which the metal sheets are shaped as desired without using dedicated dies. The SPIF investigations and declared results are desperately waiting for its industrial acceptability, but the optimization of the process is absent. The current study is to develop the functional relation of input parameters of SPIF through dimensional analysis. The investigation included statistical, ANN, and DA results for R in SPIF. Statistically, the step-down size (Δz; p = 0.005), area of tool end (A; p = 0.048), and wall angle (θ; p = 0.014) are found significant. The modified R-values are lower than the true and ANN modeled R, and its mean error is noted as 6.136. The functional relation confirmed that the step-down size and area of tool end are prominent factors for surface roughness and its influences on output are 150% and 100%, respectively.