The Dynamics of Lead-Screw Drives: Low-Order Modeling and Experiments

The closed-loop performance of a lead-screw drive is usually limited by a resonance in which the carriage oscillates in the direction of motion as the screw undergoes longitudinal and torsional deformation. In this paper, we develop a model of lead-screw system dynamics that accounts for the distributed inertia of the screw and the compliance and damping of the thrust bearings, nut, and coupling. The distributed-parameter model of the lead-screw drive system is reduced to a low-order model using a Galerkin procedure and verified by experiments performed on a pair of ball-screw systems. The model is found to accurately predict the presence of a finite right-half plane zero in the transfer function from motor torque to carriage position. A viscoelastic damper incorporated into one of the lead-screw support bearings is shown to give rise to significant, deterministic damping in the system transfer functions.