Robust compensation of elastic deformations in ball screw drives

Elastic deformations occur in ball screw drives typically due to inertial forces, guideway friction, and cutting forces. This results in elongation and compression of the ball screw, which deteriorates the dynamic linear positioning accuracy. Closing the control loop with a linear encoder helps to alleviate this problem to a certain extent. However, linear scales cost significantly more than rotary encoders and their installation also brings about additional costs. This paper presents a new strategy for mitigating the detrimental effect of elastic deformations, in order to improve the translational accuracy of ball screw drives when only rotational feedback is available. A simple and physically intuitive model is developed, which is used to offset the position commands that are fed to the servo control law. Compensation is proposed using a closed-loop scheme, which is found to be robust against cutting forces, as well as variations in the table mass and guideway friction. These effects are detected as equivalent disturbances that cause an elastic deformation. The proposed closed-loop compensation strategy has been validated in machining and high-speed tracking experiments, as well as simulations, which demonstrate its effectiveness in terms of improving the ball screw drive’s final translational accuracy.