An invariant approach replacing Abbe principle for motion accuracy test and motion error identification of linear axes

Abstract The motion accuracy of a linear axis is represented by the geometric errors defined in the current standards. However, the geometric errors are the local properties for the error-included motion of the moving component and their values are related to the position of the measured function point or line. This will cause uncertainties for the results of an accuracy test. Thus, a new invariant approach is presented for the motion accuracy test and motion error identification of a linear axis. The translational and angular error motions of the moving component are identified definitively according to the global kinematic properties of the error-included motion. The invariant errors, including the range of translational error motion, the range of tilting error motion and the range of rolling error motion, are defined to evaluate the motion accuracy. The relationships between the geometric errors of the trajectory traced by an arbitrary point or line and the motion errors of the moving component are established to replace the Abbe principle and the Bryan principle for accuracy test in a rigorous mathematical way. The motion of a linear axis in a machine tool is tested as the experiments to illustrate the advantages of the invariant approach. The results show that the invariant errors are independent of the measured function point or line. The geometric errors of the trajectory traced by an arbitrary point or line can be calculated, and the deviations caused by the translational and angular error motions are distinguished using the invariant approach.