Thermo-mechanical modelling of ball screw preload force variation in different working conditions

Ball screws are robust and economical linear positioning systems widely employed in high-speed and high-precision machines. Due to precision and stability requirements, the preload force is considered one of the main parameters defining the axial stiffness and the maximum axial load of the ball screw feed drives. In high-speed motions, thermal effects are also considerably relevant regarding positioning precision and dynamic stability of the machine. The temperature increase and the thermal gradient between the screw, the balls and the nuts result in geometrical variations and, consequently, variations in the preload force. This paper presents a numerical modelling strategy to predict the preload variation due to temperature increase using a thermo-mechanical 3D finite element method (FEM)-based model for double nut-ball screw drives. Two different thermo-mechanical coupling strategies are compared, and the obtained results are validated with experimental measurements for different initial preload and linear speeds. In the mechanical analysis, the nut-screw ball contact interface, the offset-based preloading and the restrictions of the ball bearings are included in the model, while the thermal analysis considers heat generation and heat diffusion. The causes of the thermal preload variation are discussed considering the ball load distribution and the axial and radial thermal displacements of the contacting points.