Friction Torque Modeling and Experimental Investigation of a Four-Point-Contact Ball Screw Preloaded by Increasing Ball Diameter

Most existing friction torque models for ball screws mainly address two-point contact and are difficult to apply to four-point contact configurations preloaded by increasing ball diameter. This study develops a differentiated model based on the distinct kinematics of the two contact pairs in four-point contact: one is rolling-dominated with slight sliding, whereas the other is additionally generated by the enlarged ball diameter and is sliding-dominated. First, Hertz theory is used to determine the normal load at each contact point. Then, for the rolling-dominated pair, elastic hysteresis rolling friction, differential microslip friction, and elastohydrodynamic oil-film shear friction are considered; for the sliding-dominated pair, sliding friction and oil-film shear friction are included. By combining the Hamrock–Dowson film-thickness formula, Roelands pressure-viscosity relationship, and Eyring shear model, friction torque models for the two contact pairs under mixed lubrication are established and superposed to obtain the total torque, thereby relating ball diameter increment, rotational speed, and friction torque. Friction torque tests conducted on the 4010 ball screw showed that the MAPE between theoretical calculations and experimental results on the internal validation set was 8.55%. The model also reflects the characteristics of a significant increase in friction torque with rotational speed under low preload and its tendency to stabilize under high preload.