Motion Error Prediction of Linear Axis Considering Tolerance Coupling and Worktable Elastic Deformation

The linear axis is a core motion module in precision equipment and directly affects assembly and machining accuracy. Inaccurate prediction of motion error may lead to failure in aerospace manufacturing and assembly. Most existing methods typically assume rigid components and neglect tolerance coupling, yielding inaccurate predictions. Therefore, a method considering both tolerance coupling and worktable elastic deformation is developed. First, the variation ranges of geometric errors under the coupled tolerances were characterized using Small Displacement Torsor theory. Second, a two-stage error propagation model is established: errors were initially propagated from the base to four sliders by Homogeneous Transformation Matrices, and subsequently mapped to the worktable utilizing transfer coefficients derived from finite element analysis. Finally, Monte Carlo Simulation was employed to obtain the error variation intervals and their statistical distributions. A case study demonstrated that neglecting worktable elastic deformation underestimates translational errors by up to 40%. Meanwhile, neglecting tolerance coupling would underestimate rotational and translational errors by up to 43% and 25%, respectively. Furthermore, applying the proposed model to tolerance allocation proved that the schemes guided by simplified models would cause critical design failures. Therefore, incorporating both factors is important for obtaining physically grounded error predictions and for improving the reliability of tolerance allocation.