Analysis the influence of pyramidal error on the encoder accuracy test by using coordinate transformation

In order to realize the high precision measurement of encoder accuracy, the principle and method to measure encoder accuracy by using polyhedron and autocollimator are introduced. The polyhedron coordinate system and autocollimator measurement coordinate system are established, and the precise mathematical model is established, which is relation with the measurement error of the encoder accuracy and pyramidal error. The simulation results show that the encoder shaft tilt angle and tilt direction will affect the measurement results of the encoder accuracy. Measurement error of encoder accuracy increases with encoder shaft tilt angle, and approximately proportional to the square. Measurement error of encoder accuracy changes with encoder shaft tilt direction. When encoder shaft tilt direction is 0° or 180°, measurement error is the smallest; When encoder shaft tilt direction is 90° or 270°, measurement error is the maximum. As encoder shaft tilt angle is 5′, the measurement errors can reach 0.11″~0.48″, which cannot be ignored for encoder with 1~3 levels of precision grade. Pyramidal error should be cotrolled in the appropriate range based on the precision grade of measured encoder. Specific requirements on pyramidal error are given for encoders with different precision grades. ©, 2015, Chinese Optical Society. All right reserved.