Dynamic Modeling and Multi-Objective Operating-Parameter Optimization of a Differential Planetary Roller Screw Actuator for an All-Electric Horizontal-Well Downhole Tractor

An all-electric telescopic actuator based on a differential planetary roller screw mechanism (DPRSM) is proposed for a horizontal-well downhole tractor. A theoretical differential-transmission model is established to determine the effective output lead and differential ratio, while an Adams multibody model incorporating contact and friction is developed to investigate the coupled kinematic and mechanical responses under varying screw rotational speeds and axial loads. Based on 42 deterministic simulations, response-specific surrogate models are fitted for the differential ratio, output velocity fluctuation factor, and DPRSM mechanical traction efficiency. The efficiency model is statistically significant, with an R2 of 0.9211, an adjusted R2 of 0.9075, and a predicted R2 of 0.8823. Multi-objective optimization using a desirability function is conducted over a speed–load grid comprising 113,201 points, yielding a maximum overall desirability of 0.693420 at 201 r/min and 25.1 kN. At this operating condition, the predicted differential ratio, output velocity fluctuation factor, and mechanical traction efficiency are 0.267496, 0.013084, and 86.521%, respectively. An additional Adams simulation at the same condition produced corresponding values of 0.267434, 0.012954, and 86.965%. Four additional confirmation cases and six supplementary simulations of the velocity fluctuation factor were used to examine local prediction performance, with the results showing that prediction accuracy varied across operating conditions. The findings provide numerical support for DPRSM design and operating-parameter selection. Experimental testing remains necessary to establish the performance of the proposed actuator under representative downhole conditions.