Research On Profile Error Evaluation And Geometric Error Allocation Of Complex Free-form Surface Turning By Ultra-precision Machining

Complex free-form surfaces have been widely used in industry because of their flexibility in design.However,high precision machining and profile error evaluation of complex freeform surfaces are still regarded as difficult problems in engineering.Ultra-precision machining technology is precisely because it can process complex free-form surfaces with high precision,which has been paid attention to and intensively studied by countries all over the world.During the process of processing complex free-form surfaces with ultra-precision machine tools,geometric errors,as an important error source affecting the precision of machine tools,also play an important role in the profile error of workpiece.In this paper,the profile error of complex free-form surface under the action of geometric error is taken as the starting point,and the following work is carried out:(1)The geometric error model of the four axis ultra-precision lathe is established.Firstly,the relationship between the accuracy of machine tool geometric error and the motion components is analyzed.Then low-sequence body sequence is used to describe the topology of the four-axis ultra-precision lathe on the basis of multi-body system theory,all the motion components of the ultra-precision lathe geometric error and the motion transformation matrix between adjacent components are determined,which deduce the relationship between arbitrary spatial location tool cutting point and the relative position of workpiece forming point;(2)The profile error model of complex free-form surface under the action of geometric error is established.On the basis theory of NURBS modeling,Newton’s method is studied to solve to the shortest distance problem of NURBS surface,profile error evaluation methods and processes are proposed based on the principle of minimum area of NURBS surface.The profile error model of complex free-form surface is established by combining the geometric error model with profile error evaluation methods;(3)The effect of geometric error on the profile error of target surface and the profile distribution characteristics are studied.Based on the geometric error under the action of complex free-form surface profile error model,the target surface profile distribution under each geometric error is studied,and the Sobol sensitivity method is adopted to analyze the sensitivity of geometric errors on target surface profile error.Compared with uncompensated state,the profile error of target surface decreases obviously after sensitive error compensation,which verifies the effectiveness of geometric error sensitivity analysis result;(4)A optimal method of geometric accuracy allocation under the constraint of target surface profile error is proposed.Based on the sensitivity analysis results,the geometric accuracy allocation model of the ultra-precision lathe under the constraint of the target surface profile is established.The optimal solution of the accuracy allocation is obtained by using genetic algorithm and verified by simulation,and the geometric accuracy target of four-axis lathe components under the constraint of profile error is proposed.Finally,the software of geometric error analysis and optimization for ultra-precision four-axis lathe is developed.