The evaluation models of circumference diameter, area diameter, and volume diameter were established based on the cylindrical coordinate measuring method, respectively. Many groups of roundness profiles of cylindrical specimens were extracted, and their pseudo and actual circumference diameters, area diameters, and volume diameters were evaluated according to the established evaluation models and the sampling data of the extracted roundness profiles. The relationship models between the pseudo calculated sizes and the actual calculated sizes were built through a series of training based on the neural network regression. The checked experiments for the training models showed that the evaluation of the calculated sizes can meet their measurement accuracy requirement through the pseudo calculated sizes, which were evaluated based on the roundness profiles by using the cylindricity or roundness measuring instrument.

This paper presents a method to improve the alignment accuracy of a mask in linear scale projection lithography, in which the adjacent pixel gray square variance method is applied to a charge-coupled device (CCD) image to obtain the best position of the focal length of the motherboard and then realize the alignment of the focal plane. Two image positions in the focal plane of the CCD are compared with the traits overlap according to the image splicing principle, and four typical errors are corrected on the basis of the total grating errors. Simultaneously, the rotation error of the mask is used to summarize the grayscale variation function of the CCD image. Threshold functions are employed to express the factors including the wave crests of the amplitude, period error, and phase error, which govern the rotation accuracy and weight alignment accuracy expression of the established four error factors. Finally, in the experiment, the slope of the mask is corrected and adjusted to the same direction as the slide plate with the assistance of a dual-frequency laser interferometer. The effect of the alignment error on the lithography accuracy is discussed and verified in the static case, and it is found that the CCD maximum resolution pixel is 0.1 μm and accuracy of the scale is 0.79 μm in only a 200-mm-measurement range.

The extraction simulation method and theory of cylindrical components were promoted in this paper. According to the manufacturing principle of the cylindrical components, the main influence factors of their precision manufacturing were analyzed, and their extraction models of cylindrical features were built under the analysis of the errors of the slideway and the spindle as well as the parallelism error between the slideway and the spindle rotary axis. The determination principle of modeling parameters of cylindrical features was studied. According to the extraction strategies of the roundness profiles, generatrix profiles, birdcage profile, and single spiral profile, some cylindrical features were simulated by using the established models, and their corresponding global sizes, calculated sizes, and form errors were evaluated and compared. The simulation experiments showed that the simulation models can meet the needs for the research of the relationship among the size tolerance, the form tolerance, the waviness, and the roughness, and can be taken as the theoretic base for the error budgets of the slideway and the rotation spindle in the design of precision machine tools.

Large-diameter aspheric mirrors made of hard and brittle materials suffer from low efficiency in the grinding stage, making them difficult to process. In this study, a nonuniform rational basis spline (NURBS) interpolation method is proposed and developed based on the grinding wheel path planning. The characteristic parameters of NURBS machining program are calculated to ensure the accuracy of curve interpolation path planning, and a series of control points are selected according to the normal vector points of the grinding wheel path. The control points were determined by the distance between the aspheric tangent and the next type value point at a fixed distance d. We then established a mathematical model for the knot point and simulated the relationship between the knot point and d. This indicated that d must be optimized according to the number of points to reduce the number of control points. According to this established model, a comparison experiment was conducted using an off-axis aspheric mirror, with a 280mm diameter. Straight line and NURBS grinding were compared, and the NURBS interpolation method was shown to effectively improve grinding accuracy and efficiency by about 30.