Ultrasonic vibration assisted single point incremental forming (UVaSPIF) is based on localized plastic deformation in a sheet metal blank. It consists of deforming gradually and locally the sheet metal using vibrating hemispherical-head tool controlled by a CNC milling machine. The ultrasonic excitation of the forming tool reduces the vertical component of the forming force. In addition, application of ultrasonic vibration reduces the surface roughness of the specimen. Surface roughness is one of the quantitative and qualitative parameters, which is used to assess the quality of the final product. In the present paper, a statistical analysis and optimization of the effective factors on this parameter are performed in the UVaSPIF process. For this purpose, response surface methodology (RSM) is selected as the experiment design technique. The controllable factors such as vertical step size, sheet thickness, tool diameter, wall inclination angle, and feed rate are specified as input variables of the process. The obtained results from the analysis of variance (ANOVA) and regression analysis of the experimental data confirm the accuracy of the mathematical model. Furthermore, it is shown that the linear, quadratic, and interactional terms of the variables are effective on the surface roughness parameter. To optimize the surface roughness parameter, the most appropriate conditions of the experiment are determined using desirability method, and statistical optimization is subsequently verified by conducting the confirmation test.
