Effect of detector installation error on the measurement accuracy of multi-degree-of-freedom geometric errors of a linear axis

A linear axis is the key component of several mechanical machines, especially of computer numerical control machine tools. The simultaneous measurement of the geometric motion errors of a linear axis is indispensable to compensate the machine errors, which improves the accuracy of machine tools. The principle of laser collimation is widely used for measuring the multi-degree-of-freedom (MDOF) geometric motion errors of a linear axis. However, installation errors of the detectors affect the measurement accuracy. In this study, we have proposed, for the first time, a measurement model for investigating the influence of all detector installation errors on the accuracy of the simultaneous measurement of MDOF geometric motion errors in a linear axis. The effect of detector installation errors on the horizontal straightness, vertical straightness, pitch, and yaw are analyzed using the homogeneous transformation method, which indicates that angular installation errors of detectors along the X0-axis direction can cause a crosstalk between the two straightness errors and between pitch and yaw errors. In addition, translational installation errors of position-sensitive detectors in the X0-axis direction, which is often called the defocusing amount, has a significant effect on the pitch and yaw measurements. To elucidiate the effect of defocusing, a measurement model was verified by both Zemax simulation and experiments. The experimental results indicate that the maximum deviation of the measured results obtained using the proposed model from that obtained using a Renishaw XL-80 interferometer can be greatly reduced by compensating the measurement errors induced by defocusing.