Ranking Factors Affecting FQM First-Stand Rolling Force: Slab Method, FEM, and Grey Relational Analysis

Rolling force critically affects Fine Quality Mill (FQM) continuous rolling precision. The first stand, undergoing the largest reduction, determines subsequent entry conditions, requiring high prediction accuracy. Different from routine engineering-oriented FEM simulation, this study integrates the slab method (SM), finite element method (FEM), and gray relational analysis (GRA) to quantify importance ranking of dynamic yield stress, roll gap, and friction coefficient on first-stand rolling force. This comparative assessment helps process engineers prioritize key variables during on-site rolling force tuning and mitigate unexpected rolling load fluctuations. It uncovers the underlying regularity of rolling-force-related factors and compares the applicability of these methods. Results show that under stable conditions, all methods consistently rank dynamic yield stress as one of the primary influencing factors. These ranking differences reflect distinct response mechanisms to multi-factor coupling. Furthermore, a campaign-clustered ANOVA of 2014 production records independently confirms the importance of dynamic yield stress and roll gap, and response-surface analysis shows that all significant interactions involve the roll gap without reordering the leading factors. This study provides a theoretical basis for force control and modeling of the first stand in retained-mandrel seamless tube continuous rolling.