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以双轴转台的精度0.4″为目标值,采用MATLAB反向求解全误差方程的误差项,双轴转台各项误差最大极值见表1。
Error Max Error Max Error Max $ \Delta {\varepsilon _{x0}} $ 0.721″ $ \Delta {\varepsilon _{x1}} $ 0.825″ $ \Delta {\tau _{x0}} $ 0.025 mm $ \Delta {\varepsilon _{y0}} $ 0.952″ $ \Delta {\varepsilon _{y1}} $ 0.986″ $ \Delta {\tau _{y0}} $ 0.025 mm $ \Delta {\tau _{z1}} $ $ \infty $ $ \Delta {\tau _{z2}} $ $ \infty $ $ \Delta {\tau _{z3}} $ $ \infty $ $ \Delta {\sigma _{x1}} $ $ \infty $ $ \Delta {\sigma _{x2}} $ $ \infty $ $ \Delta {\tau _{x3}} $ 0.050 mm $ \Delta {\sigma _{y1}} $ $ \infty $ $ \Delta {\sigma _{y2}} $ $ \infty $ $ \Delta {\tau _{y3}} $ 0.050 mm Table 1. Extreme error of turntable simulation
利用各项误差极值,估计双轴回转精度为:
通过双轴转台仿真分析:内、外轴(双轴)倾角回转误差
$ \Delta {\sigma _{x1}} $ 、$ \Delta {\sigma _{y1}} $ 、$ \Delta {\sigma _{x2}} $ 、$ \Delta {\sigma _{y2}} $ 和双轴及待检编码器主轴(主轴)零位误差$ \Delta {\tau _{z1}} $ 、$ \Delta {\tau _{z2}} $ 、$ \Delta {\tau _{z3}} $ 的最大值均趋于$ \infty $ ,可知双轴及主轴倾角回转误差、零位误差对系统回转精度影响较小;内轴及主轴相对转台安装误差$ \Delta {\tau _{x0}} $ 、$ \Delta {\tau _{y0}} $ 、$ \Delta {\tau _{x3}} $ 、$ \Delta {\tau _{y3}} $ 的最大值为常数,可知双轴及主轴的安装误差不随转台角度变化而发生改变;双轴同轴度误差$ \Delta {\varepsilon _{x0}} $ 、$ \Delta {\varepsilon _{y0}} $ 、$ \Delta {\varepsilon _{x1}} $ 、$ \Delta {\varepsilon _{y1}} $ 的最大值为变量,可知双轴的同轴度误差随转台角度变化而改变。为保证双轴转台精度小于0.4″的设计要求,采用精密机械加工及装配工艺,控制安装误差位移量小于0.025 mm,通过精确控制双轴同轴度误差,保证双轴转角回转精度,实现高精度误差检测。
Error detection system of photoelectric encoder based on optical continuous closed-loop
doi: 10.3788/IRLA20210715
- Received Date: 2022-01-20
- Rev Recd Date: 2022-02-25
- Publish Date: 2022-08-05
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Key words:
- photoelectric encoder /
- error measurement /
- photoelectric autocollimator /
- error modeling /
- turntable
Abstract: In order to solve the problems of low accuracy, complex optical machine structure, and long detection cycle in the error detection of the photoelectric encoder, the optical small-angle measurement principle of an autocollimator and a polyhedral prism, and the continuous error detection method of the reciprocal rotation angle of the dual-axis turntable were combined to establish an error detection system for photoelectric encoder based on optical continuous closed-loop. By using the multi-body system theory and the relative pose matrix transformation method, a full error model of the dual-axis turntable was established, and the influence of the fixed error and variable error of the full error model on the system was analyzed. The detection system was calibrated with a calibrated autocollimator and a 23-sided polyhedral prism, and a high-precision photoelectric encoder was used to compare the detection accuracy with the system. The test results show that the rotation accuracy of the dual-axis had met the requirements of the numerical simulation calculations, the system detection accuracy had reached 0.38″, and the measurement uncertainty is 0.2″ (k=2). And for the encoder actually produced, the detection accuracy of the system is basically the same as the accuracy of the factory calibration. Which had been verified the feasibility of the optical continuous closed-loop system to achieve high precision and circumference continuous error detection.