Thermal error compensation of linear axis with fixed-fixed installation

To improve the machining accuracy of machine tool, thermal error modeling and compensation methods are proposed from the view of formation mechanism of thermally-induced error of ball-screw linear axis with fixed-fixed installation. The relationships among such factors as heat generation, heat dissipation, thermal stress, temperature rise, thermal expansion, and the resulting thermal error are explored. The thermal error is formulated as the product of an amplitude function with temperature of screw shaft as its independent variable and a cosine function with axial position as its independent variable. The independent variables of thermal error model are temperature of screw shaft, axial position, and the running time. The closed-loop iterative thermal behavior modeling method is proposed to determine accurate temperature of screw shaft by updating rate of heat generation, convective coefficient, thermal contact resistance (TCR), lubricant viscosity, and preload in each sub-step. To demonstrate the modeling method, the thermal errors are predicted and compensated at different working conditions. The results show that the repetitive positioning error is reduced by more than 45%, 36%, and 19% compared to that without the compensation, with pitch compensation and multivariate linear regression analysis (MLRA) compensation, respectively.