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Error measurement of a rotary axis is the key to error compensation and to improving motion accuracy. However, only a few instruments can measure all the motion errors of a rotary axis. In this paper, a device based on laser collimation and laser interferometry was introduced for simultaneous measurement of all six degrees-of-freedom motion errors of a rotary axis. Synchronous rotation of the target and reference rotary axes was achieved by developing a proportional&ndash, integral&ndash, derivative algorithm. An error model for the measuring device was established using a homogeneous transformation matrix. The influences of installation errors, manufacturing errors, and error crosstalk were studied in detail, and compensation methods for them were proposed. After compensation, the repeatability of axial and radial motion errors was significantly improved. The repeatability values of angular positioning error and of tilt motion error around the y axis and x axis were 28.0&Prime, 2.8&Prime, and 3.9&Prime, The repeatability values of translational motion errors were less than 2.8 &mu, m. The comparison experiments show that the comparison errors of angular positioning error and tilt motion error around the y axis were 2.3&Prime, and 2.9&Prime, respectively. These results demonstrate the effectiveness of our method and the error compensation model.

The rotary axis is the basis for rotational motion. Its motion errors have critical effects on the accuracy of the related equipment, such as a five-axis computer numerical control machine tool. There are several difficult problems in the implementation of high-precision and fast measurement of the multi-degree-of-freedom motion errors of a rotary axis. In this paper, a novel method for the simultaneous measurement of five-degree-of-freedom motion errors of a rotary axis is proposed, which uses a single-mode fiber-coupled laser with a full-circle measuring range. It has the advantages of high efficiency, low cost, and it requires no decoupling calculation. An experimental system was built and a series of experiments were performed. The standard deviation of stability for 60 min of the five-degree-of-freedom measurement is 0.05 arcsec, 0.06 arcsec, 0.04 μm, 0.03 μm, and 0.19 arcsec, respectively. The repeatability deviation of measuring an indexing table is ± 3.4 arcsec, ± 4.6 arcsec, ± 2.6 μm, ± 2.4 μm, and ± 3.2 arcsec. The maximum deviation of comparison is 3.9 arcsec and 3.2 arcsec. These results demonstrate the effectiveness of the proposed method; thus, a new approach of simultaneous measurement of the multi-degree-of-freedom motion errors of a rotary axis is provided.

This paper introduces an error-compensation model for our measurement method to measure five motion errors of a rotary axis based on fibre laser collimation. The error-compensation model is established in a matrix form using the homogeneous coordinate transformation theory. The influences of the installation errors, error crosstalk, and manufacturing errors are analysed. The model is verified by both ZEMAX simulation and measurement experiments. The repeatability values of the radial and axial motion errors are significantly suppressed by more than 50% after compensation. The repeatability experiments of five degrees of freedom motion errors and the comparison experiments of two degrees of freedom motion errors of an indexing table were performed by our measuring device and a standard instrument. The results show that the repeatability values of the angular positioning error e z and tilt motion error around the Y axis e y are 1.2'' and 4.4'', and the comparison deviations of the two motion errors are 4.0'' and 4.4'', respectively. The repeatability values of the radial and axial motion errors, δ y and δ z , are 1.3 and 0.6 µm, respectively. The repeatability value of the tilt motion error around the X axis e x is 3.8''.

Base on three wave coupled equations and energy conservation law, the frequency doubling properties of CsBe2BO3F2 (CBBF) are analyzed theoretically at the first time. The phase matching angle, effective nonlinear coefficient, walk-off angle and permitted parameters are simulated in type I and type II phase matching. The difference of the CBBF optical properties between type-I and type-II are elucidated.: a wider phase matching range, a larger effective NLO coefficient and a smaller walk-off angle in range of 693.9~2730 nm in type-I were obtained. The properties of CBBF have been compared with the KBe2BO3F2 (KBBF) crystal. The larger lowest wavelength limit, smaller walk-off angles, a broader permitted angle and a larger peak value of the permitted wavelength of CBBF were proved.

For the first time, the SHG efficiency of RBBF crystal in type-I and type-II phase matching has been simulated. RBBF crystal is pumped by the fundamental radiation of a Q-switched Nd:YAG laser with the wavelength of 1064nm and the shape of plane wave or Gaussian beam. When the pumped radiation is of plane wave, the conversion efficiency of RBBF in type-I and type-II could be as high as 100% and 78%. When the pumped radiation is of Gaussian beam, the conversion efficiency shows a monotonically increasing trend in the type-I phase matching, and in the type-II phase matching the conversion efficiency varies periodically.