An invariant method updating Abbe principle for accuracy test and error calibration of rotary pairs in machine tools

Abstract

Abstract A new invariant method is presented to update the Abbe principle for accuracy test and error calibration of the rotary pairs in machine tools. According to the kinematic properties, the error motion of a rotor is decomposed into the angular error motion and the translational error motion; the Abbe principle to test and calibrate these two types of error motion is stated to avoid the deviations caused by different measuring positions or reduce the interpolation errors related to the coordinate systems. To meet the updated Abbe principle, the minimal spherical image curve and the minimal striction curve are respectively deduced to represent the angular error motion and the translational one of the rotor exactly. Then, the invariant errors, including the spherical circle area covered by the minimal spherical image curve and the cylindrical volume occupied by the minimal striction curve, are used to evaluate the accuracy of a rotary pair in accuracy test. The quasi-moving axis and the quasi-fixed axis of a rotary pair are defined respectively. The former is a line of the rotor, whose trajectory has both the minimal spherical image curve and the minimal striction curve; the latter is the proximate geometric axis of the trajectory traced by the former. They are used to locate the coordinate systems for error calibration. Some relative tests are given; the results show the invariant method reduces the deviations caused by different measuring positions in accuracy test of a spindle and decreases the interpolation errors in error calibration of a rotary table.