Calculation Method for Time-Varying Contact Force of the Ball Screw with Nonuniform Surface Waviness

The ball screw mechanism (BSM) is extensively employed in mechanical systems to convert rotational motion into linear motion. Most of the existing studies primarily concentrate on developing time-invariant calculation methods for the BSM, leading to an incomplete understanding of its time-varying contact characteristics. This study establishes a time-varying contact force model that incorporates decomposed circumferential and axial surface waviness of the thread raceways and the ball, aiming to analyze their dynamic effects on load distribution within the BSM. The results reveal that the influence of surface waviness order on load distribution follows an irregular pattern, whereas the influence of waviness magnitude exhibits a systematic correlation. Specifically, parametrically increasing the circumferential and axial waviness amplitudes from 0.5 μm to 2 μm induces a progressive amplification of peak contact forces, accompanied by a synchronized attenuation of valley contact forces over different time instants. This investigation offers fundamental insights into time-variant contact forces arising from machining surface errors, providing valuable guidance for the design and manufacturing of the BSM.