Integrating ANOVA and grey synthetic relational degree for energy-efficiency decisions in tangential milling under linear and sinusoidal tool paths

Abstract Energy efficiency in machining is a key dimension of manufacturing sustainability, given the contribution of machine tools to industrial electricity demand. This study proposes and validates a hierarchical decision logic that integrates Analysis of Variance, ANOVA, and Grey Synthetic Relational Degree, GSRD, to interpret and prioritize cutting parameter effects on energy efficiency in tangential side milling of Ti-6Al-4V. A full 2³ factorial design was conducted for two toolpath strategies, linear and sinusoidal, by varying cutting speed, feed per tooth, and radial depth of cut, while electrical energy consumption was monitored using a dedicated power analyzer. The results showed that ANOVA identified radial depth of cut as the structurally dominant factor for both tool paths by exhibiting the largest variance contribution and by remaining statistically significant in the sinusoidal case with a ρ value of 0.001. GSRD refined operational prioritization by ranking parameters according to relational proximity to an ideal energy efficiency response, confirming radial depth of cut as the primary lever for the linear path while prioritizing cutting speed for the sinusoidal path with a relational degree of 0.5686 as the first tuning lever for incremental gains. Across all tested conditions, average improvements of approximately 80 cubic millimeters per watt hour were achieved, corresponding to electricity consumption reductions of up to 15%, indicating that tool path geometry shifts parameter sensitivity through changes in tool workpiece engagement conditions. The proposed framework supports tool path assessment and provides actionable guidance for parameter tuning toward improved energy efficiency in CNC milling.