Real-time thermal error prediction and compensation of ball screw feed systems via model order reduction and hybrid boundary condition update

Thermal deformation of a ball screw is a quasi-static process and incurs positioning error. To obtain a rapid prediction model to compensate for this deformation error, a reduced-order finite element (FE) model is required. For updating the boundary conditions (BCs) of such a reduced-order model (ROM), a hybrid BC update process composed of the response surface method (RSM) and 3-point temperature measurement is devised in this paper. We develop an adaptive reduced-order model (AROM) for real-time prediction and compensation of the error in a time-varying environment under any operating conditions. This system solves not only the heat generation rate (HGR) and nut movement effects on the lubricant temperature variation, but also the convective heat transfer coefficient (CHTC) and thermal resistance (TR) effects at joint interfaces. High prediction accuracy has been verified via a test-bed with a precision linear scale. An AROM server application is also proposed for a thermal error free smart factory.