A normal section plane method for profile error analysis of five-axis machine tools based on the ideal tool flank milling surface

The existing studies on profile error analysis and machining accuracy measurement do not consider the impact of the theoretical errors on the machine tool accuracy measurement. Therefore, this study proposes an estimation method of the surface profile error based on the normal section plane, using the theoretical flank milled surface for comparison. This effectively improves the accuracy of profile error estimation. The theoretical flank milled surface is the surface machined by flank milling under ideal conditions. Hence, compared to the traditional analysis method based on the designed three-dimensional model of S-shaped test pieces, the calculated profile error of this method does not include theoretical errors, thereby eliminating the impact of theoretical errors on machine tool accuracy measurement and evaluation. First, an improved method for continuous parameterized dual spline interpolation was proposed. It simplifies the solution of the singular problem of the coefficient matrix of the spline basis function and obtains a continuous ideal machining tool axis trajectory surface with complete geometric characteristics. Next, a method for constructing the theoretical flank milled surface machined with a cylindrical milling tool using equidistant mapping characteristics was proposed; then, the differential transformation relationship at the cutting contact point of the curved surface under the influence of tool path errors was established. Furthermore, the normal section plane method based on the differentiation of the cutting contact point was proposed. The problem of solving the distance from a point to a surface is converted to the problem of solving the distance from a point to a curve in the normal section plane. This improves the accuracy of profile error estimation. The effectiveness of the method was verified by comparing the analysis results of the profile errors of a typical cylindrical surface with the point to surface and the point to curve methods.