It is essential to obtain the 5-DOF errors motion of the rotary table for reconstruct-ing the real trajectory of the rotating shaft, but there are many error coupling prob-lems when measuring the error motions of the rotary table. In order to improve the measurement accuracy of the 5-DOF error motion of the rotary table, a method of measuring 5-DOF error motions based on BMPES (Bidirectional Multi-Point Error Separation ) is proposed. Firstly, by analyzing the motion characteristics of the ro-tary table with multiple degrees of freedom error during the rotation, a detection system with double-layer structure probe arrangement is designed. Then, the three-point method is used in the radial direction to separate the roundness error of the measuring disk, which improves the measurement accuracy of radial error. Finally, the coupling relationship between the mixing errors collected by the axial probes is researched, and a face-four-point error separation method is proposed, which can separate the flatness error of the lower surface of the measuring disk complete the decoupling of the tilt error and the axial runout error. Simulation results show that for the measurement of radial, tilt and axial errors, the measurement errors of the BMPES method proposed in this paper are reduced by 97.89%, 68.40% and 99.99%, respectively, compared with the five-point method, and when eccentricity errors exist, the measurement errors of radial and tilt errors are reduced by 99.06% and 85.67%, which verifies that the method can accurately obtain the five degrees of freedom motion of the rotary table errors.

Piezoelectric ceramic actuators exhibit nonlinear hysteresis characteristics owing to their material properties. To modify the inverse piezoelectric effect as an ideal linear execution, the classical Prandtl–Ishlinskii (PI) model is usually used for compensation by feedforward control. The PI model compensates well on simple hysteresis characteristics. However, when the output requirements are complex, the PI model demonstrates uneven compensation accuracy on the complex hysteresis characteristics and cannot achieve an accuracy similar to that of simple hysteresis. This paper proposes a simplification of complex hysteresis: Separated Level-loop PI (SLPI) model. First, we use a loop-separation logic algorithm to simplify the complex hysteresis characteristics to obtain hysteresis in the form of single loops with loop levels and vertexes. Second, the hysteresis characteristics of each loop are independently modeled using the PI model. Finally, the inverse model is reconstructed using a rollback method to restore a positive sequence of the feedforward voltage; then, the feedforward voltage is input as a compensation value to achieve higher and more uniform accuracy. Experiments and discussions show that the SLPI model can effectively improve the compensation results of complex hysteresis characteristics; moreover, the average compensation accuracy difference between single hysteresis loops was reduced.