Multi Objective Optimization of Turning Parameters for Low Carbon Steel Using Taguchi Method and Grey Relational Analysis

Abstract

Machining operations, particularly precision turning, are fundamental to determining the service life and functional performance of mechanical components. This study presents a systematic optimization of turning parameters specifically cutting speed (V), depth of cut (D), and feed rate (F) to achieve an optimal balance between surface roughness (Ra) and surface hardness (HRC) in low-carbon steel (0.09% C). Utilizing a Taguchi (L₉) (3³) orthogonal array, nine experimental runs were conducted, reducing experimental overhead by 67% compared to a full factorial design. Signal-to-Noise (S/N) ratio analysis and analysis of variance (ANOVA) at a 95% confidence level were performed after factor pooling to identify statistically significant parameters. The ANOVA results revealed that feed rate exerts a dominant and highly significant impact on surface roughness (P = 0.036), whereas cutting speed governs surface hardness due to strain-hardening mechanisms (P = 0.033). Predictive mathematical equations derived via linear regression yielded high coefficients of determination (R²) of 83.17% for (Ra) and 64.79% for HRC. Due to the conflicting nature of individual optimal configurations, multi-objective optimization was executed using Grey Relational Analysis (GRA). The optimization algorithm successfully identified Experiment No. 8 (V = 275  m/min), (D = 0.75 mm), (F = 0.15 mm/rev) as the absolute optimal manufacturing window, yielding the maximum Grey Relational Grade of 0.992. These findings offer a robust, predictive, and cost-effective framework for enhancing surface integrity and mechanical performance in industrial precision manufacturing.