Ultrasonic Vibration assisted Single Point Incremental Forming (UVaSPIF) process is an attractive and adaptive method in which a sheet metal is gradually and locally formed by a vibrating hemispherical-head tool. The ultrasonic excitation of forming tool reduces the average of vertical component of forming force and spring-back rate of the formed sample. The spring-back phenomenon is one of the most important geometrical errors in SPIF process, which appear in the formed sample after the process execution. In the present article, a statistical analysis and optimization of effective factors on this phenomenon is performed in the UVaSPIF process based on DOE (Design of Experiments) principles. For this purpose, RSM (Response Surface Methodology) 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 is specified as input variables of the process. The obtained results from ANOVA (Analysis of Variance) and regression analysis of experimental data, confirm the accuracy of mathematical model. Furthermore, it is shown that the linear, quadratic, and interactional terms of the variables are effective on the spring-back phenomenon. To optimize the spring-back phenomenon, the finest conditions of the experiment are determined using desirability method, and statistical optimization is subsequently verified by conducting the confirmation test.
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