Comprehensive error modelling and error compensation for complex optical free-form surface polishing platform

Four-axis polishing platform plays an important role in machining a complex optical free-form surface and the kinematic error generally determine the accuracy of the optical free-form surface fabricated by this platform. This paper analyses kinematics of the polishing platform based on the homogeneous coordinate transformation theory and the error of kinematics synthesis model is established. Based on minimum error assumption, transition matrix is obtained from machine tool coordinate system to the cutting tool coordinate system and changing rule of comprehensive error in different position and direction is gained in two-axis motion worktable. Laser interferometer is used to measure the geometric error of polishing platform, it is found that different feed rate and measured spacing had no significant effect on the positioning error of moving axis and positioning error rather than the straightness and angle error has more significant influence on the accuracy of machine tool. Compensation experiment was conducted based on integrated error model, the x-axis and z-axis positioning error was reduced by 87.37% and 90.32% after compensation and the compensation result is remarkable.