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In order to analyze the error sources of circular gratings angle-measuring system, a series of coordinate systems were established on the gratings angle-measuring system through taking many mechanical errors into account, such as rotary errors of the axis system, installing eccentricity and tilt of circular gratings disc, graduation errors, readhead installation errors and etc. Then position and attitude relationships between two adjacent coordinate systems were established, thus the displacement error of gratings’ graduation in the readhead coordinate system was calculated by homogeneous transformation method, so an angle-measuring error model was established, the relationship between the mechanical error sources and the angle-measuring errors under the condition of the different number of used readheads was expounded. According to the established error model and theoretical analysis, some conclusions were drawn, that is, adopting single readhead can not eliminate first harmonic errors resulted from the installation eccentricity error; using twin readheads not installed centrosymmetrically can not totally eliminate first harmonic errors, and some residual first order harmonic errors retained; applying four readheads can eliminate mechanical installation errors, but can not completely eliminate the graduation errors. Finally, an experiment was carried out on the circular gratings angle-measuring system mounted on an aerostatic bearings, some conclusions were verified, and it provided a theoretical basis for raising the angular position accuracy of the angle-measuring system. Keywords-circular gratings; graduation errors; homogeneous transformation; angle-measuring system; rotary error

Error Analysis of Circular Gratings Angle-Measuring System