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, the installation errors of detectors affect the measurement accuracy. In this study, we have proposed, for the first time, a measurement model for investigating the influence of all installation errors of the detectors on the accuracy of the simultaneous measurement of MDOF geometric motion errors in a linear axis. The effect of the detector installation errors on the horizontal straightness, vertical straightness, pitch, and yaw are analyzed using the homogeneous transformation method, which indicated that the angular installation error of detector along X0-axis direction can cause a crosstalk between the two straightness errors and between pitch and yaw errors. In addition, the translational installation error of position sensitive detector in X0-axis direction, which is often called the defocusing amount, has a significant effect on the pitch and yaw measurements. For elucidating the effect of defocusing, the 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.

中文翻译：

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探测器安装误差对线性轴多自由度几何误差测量精度的影响

直线轴是多种机械设备，尤其是计算机数控机床的关键部件。线性轴几何运动误差的同步测量对于补偿机床误差是必不可少的，它提高了机床的精度。激光准直原理广泛用于测量线性轴的多自由度（MDOF）几何运动误差。但是，探测器的安装误差会影响测量精度。在这项研究中，我们首次提出了一种测量模型，用于研究探测器的所有安装误差对线性轴上 MDOF 几何运动误差的同时测量精度的影响。探测器安装误差对水平直线度的影响，采用齐次变换方法对垂直直线度、俯仰和偏航进行了分析，表明探测器沿X0轴方向的角度安装误差会引起两个直线度误差之间以及俯仰和偏航误差之间的串扰。此外，位敏探测器在X0轴方向的平移安装误差，通常称为散焦量，对俯仰和偏航测量有显着影响。为了阐明散焦的影响，通过 Zemax 模拟和实验验证了测量模型。