Theoretically Modeling And Experimental Study Of Geometric Errors For CNC Machine Tools In Precision Manufacturing

Optical freeform surfaces have been widely used in various advanced products due to theirimproved performance, lower mass and smaller size. Mathematically, freeform surfacescould not be expressed by certain equations. Besides, the common materials of optics arebrittle materials such as glass. These impose a lot of challenges in the fabrication of theoptical freeform surfaces. Based on CNC machine tools, some ultra-precision manufacturingtechniques such as diamond turning with slow/fast tool servo (STS/FTS), raster milling andprecision grinding have been involved to fulfill the increasing demands for high accuracyand excellent surface quality of optical freeform surfaces. However, there are highrequirements of machine tool accuracy no matter which ultra-precision manufacturingtechnique would be employed.Traditionally, the accuracy of machine tools was improved by the structural optimization ofthe machine tool which always corresponds to better design and manufacturing practices.However, due to physical limitations, production and design techniques can hardly improvethe machine tool accuracy. Therefore, error compensation has become an essential way toimprove manufacturing accuracy with the development of measuring technology andcomputer numerical control technology. The ability and efficiency of error compensationdepend on compensation strategies which lie more on the analysis of machine tool errorsthan error models.Considering the main error source of machine tools in precision manufacturing, which refersto the geometric error, an analysis methodology is established theoretically andexperimentally in the combination of error diagnostic, synthesis error and sensitivityanalysis.Based on the multi-body system theory, a general modeling method of synthesis error whichtakes the interaction of error terms into account is established. Further, a mathematical modelfor error sensitivity analysis is set up by the matrix differential method. After that, thesensitivity matrix which could reveal the relationship between error terms and the synthesiserror is obtained. Circular tests are carried out with the double ball bar followed by the error diagnostic, fromwhich the factors of circular deviation would be found. The error diagnostic results areapplied to adjust machines to better accuracy status.By using the laser interferometer system, the positioning errors, straightness errors andangular errors of both linear axes and rotary axes are illustrated by a large number ofexperiments. For traditional linear axes based on rotary motors-ball screw, the positioningerrors value is much higher than others. For linear axes based on linear motor-air bearing,the magnitude of all error terms are very low, with the linear errors almost at sub-micrometerand nearly all angular errors in±1’’. Besides, the errors of forward and reverse directionsmatch well. Under various feed speeds and loads, the linear axes based on linear motors canstill retain relatively excellent accuracy.The general modeling method of synthesis error established above is applied to a3-axiscommercial CNC machine tool equipped with traditional linear axes based on rotary motors-ball screw in the coordinate system of machine tools. Together with the error terms studiedabove, the distribution and evolution of the synthesis error subjected to the coupling effect ofall axes errors are studied in the workspace further. It is found that the synthesis error in thedirection of a certain axis is close to its positioning error, which proves that the positioningerror is the decisive factor contributing to the synthesis error.The mathematical error sensitivity model for a4-axis ultra-precision polishing machine tooldeveloped with air bearing-linear motor stage is deduced, following the establishment ofsynthesis error model in the coordinate system of workpiece. Then the sensitivity matrixcalculated analyze the effect of error terms on synthesis error in a quantitative level. Itreveals that linear errors mainly have large effect on the synthesis error in the same direction,whereas the linear errors orthogonal to the synthesis error show relative small effect on it.The angular errors have more impact on synthesis error than that of linear errors. The impactof angular errors on each directions of the synthesis error is relatively equal.The analysis methodology of geometric error established in this paper is of theoretical andpractical significance to improve the capability and efficiency of error compensation.