论文部分内容阅读
针对二维位移测量系统中光栅制作与装配非理想所引起的几何误差,基于多普勒频移理论和坐标变换方法,建立了同时包含光栅非正交角与装配角在内的通用几何误差模型,定量研究了各误差角对系统性能的影响程度,仿真分析了X与Y方向余弦误差和耦合误差随误差参数的变化规律。结果表明,光栅制作和装配误差与系统所用衍射级次、衍射次数和光学细分倍数无关,只与各误差角和被测位移有关。与此同时,四个误差角都会导致余弦误差的产生,而耦合误差则主要受光栅非正交角和偏航角的影响。此外,相同误差角所引起的耦合误差要明显严重于余弦误差,是系统几何误差的主要构成成分。通过搭建基于二维交叉光栅的平面位移测量系统,利用10 mm方形运动轨迹实验验证了理论分析与数值仿真的正确性。
Aiming at the geometrical error caused by non-ideal grating production and assembly in two-dimensional displacement measurement system, a general geometric error model including both grating non-orthogonal angle and assembly angle was established based on Doppler frequency shift theory and coordinate transformation method , Quantitatively studied the influence degree of each error angle on the system performance, and analyzed the variation law of the cosine error and the coupling error with the error parameters in X and Y directions. The results show that the error of grating fabrication and assembly has nothing to do with the order of diffraction, the number of diffraction and the optical subdivision multiples used in the system. It is only related to the error angle and measured displacement. At the same time, the four error angles will lead to the generation of cosine error, while the coupling error is mainly affected by the grating non-orthogonal angle and yaw angle. In addition, the coupling error caused by the same error angle is obviously more serious than the cosine error, which is the main component of the system geometric error. By setting up a plane displacement measurement system based on two-dimensional crossed grating, the correctness of the theoretical analysis and numerical simulation is verified by experiments on a 10 mm square trajectory.