Drafting systems in ring spinning convert rove or sliver into a finely attenuated strand through a series of roller pairs, each imposing controlled draft ratios on the fibre bundle. The mechanical performance of such systems is governed not only by draft ratio and fibre characteristics but fundamentally by the tribological interactions at the roller–fibre–surface interface. Despite extensive research on process parameters and fibre behaviour, a rigorous, multi-dimensional framework quantifying how surface geometry compatibility drives tribological outcomes has remained absent from the scholarly literature.This paper presents a novel theoretical framework — the Geometric Matching Framework (GMF) — for the multi-objective optimisation of tribological interactions in drafting systems. The framework introduces six interdependent indices: the Geometric Matching Index (GMI), Contact Ratio (CR), Slip Model (SM), Traction Efficiency Index (TEI), Wear Penalty Index (WPI), and Thermal Penalty Index (TPI), integrated through a weighted composite Overall Drafting Optimisation Index (ODI). A dedicated section on Surface Geometry Conjugation Theory further analyses the four interface geometry combinations that arise when knurled or plain apron surfaces interact with knurled middle rollers and flat nose bars, formally characterising the dual-interface geometric compromise inherent in conventional apron drafting systems.Parametric analyses demonstrate that geometric surface matching significantly elevates traction efficiency while reducing wear and thermal penalties. The conjugate knurled interface achieves ΔODI ≈ +0.48 over the mismatched knurled–flat combination. A Pareto-optimal trade-off analysis validates the multi-objective character of the framework. The GMF is offered as a theoretical foundation for future experimental validation, surface engineering decisions, and machine design innovation in high-speed textile drafting systems.