Modeling and multi-response optimization of milling characteristics based on Taguchi and gray relational analysis

This article focuses on experimental investigation and effective approach to optimize the milling characteristics with mono and multiple response outputs such as vibration signals, cutting force, and surface roughness. To achieve this goal, experiments were designed based on Taguchi’s L18 (21 × 33) orthogonal array. During the milling of AISI 1050 steel, process performance indicators such as vibration signals (RMS), cutting force (Fx), and surface roughness (Ra) were measured. The effect of process parameters such as depth of cut, feed rate, cutting speed, and number of insert on RMS, Fx, and Ra were investigated and parameters were simultaneously optimized by taking into consideration the multi-response outputs using Taguchi-based gray relational analysis. Taguchi’s signal-to-noise ratio was employed to obtain the best combination with smaller-the-better and larger-the-better approaches for mono- and multi-optimization, respectively. Analysis of variance was conducted to determine the importance of process parameters on responses. Mathematical models were created, namely, RMSpre, Rapre, and Fxpre, using regression analysis. According to the multi-response optimization results, which were obtained from the largest signal-to-noise ratio of the gray relational grade, it was found out that the optimum combination was depth of cut of 1 mm, feed rate of 0.05 mm/rev, cutting speed of 308 m/min, and number of insert of 1 to minimize simultaneously RMS, Fx, and Ra. It was obtained that the percentage improvement in gray relational grade with the multiple responses is 42.9%. It is clearly shown that the performance indicators are significantly improved using this approach in milling of AISI 1050 steel. Moreover, analysis of variance for gray relational grade proved that the feed rate is the most influential factor as the minimization of all responses is concurrently considered.