Accurate Modeling and Measurement for Preload in Double-Nut Ball Screws

Abstract Accurate measurement of ball screw preload, critical for performance optimization, remains a persistent challenge due to the limitations inherent in conventional methods. Based on the validated applicability of Stribeck theory to screw friction behavior, this study establishes a direct relationship between dynamic preload drag torque (DPDT) and preload force through the coefficient of friction (COF), thereby developing a comprehensive methodology for preload calculation. A novel Stribeck-based COF model was established through synchronous measurements under various conditions as a benchmark case. Decomposition of the total DPDT into Coulomb, viscous, and Stribeck-effect components reveals distinct regimes. Simplified empirical equations for preload were further derived through Taylor expansion. Validation demonstrates a mean error below 5% across operating conditions, outperforming traditional formulas (an error of more than 30%). It provides a robust methodology for high-accuracy preload measurement in double-nut ball screws, advancing the fundamental understanding of friction behavior in precision transmission systems and laying the foundation for developing universal models in subsequent research.