| Ultra-precision diamond turning(UPDT)has unique advantages,such as high precision and good repeatability,in the processing of metal materials,and is widely used in the production of precision components in precision instruments,aerospace,nuclear fusion and other fields.The geometric error caused by the inaccurate manufacturing and assembly of key parts in machine tools are the main sources of error in the turning process and have a great influence on the workpiece dimensional accuracy.This paper investigates the mechanism how geometric error of ultra-precision lathe affect the machining accuracy of complex surfaces.The turning simulation model of complex surfaces and importance analysis method of geometric error are proposed to reveal the laws of geometric error to workpiece topography and identify the crucial geometric error,which provides some theoretical guidance to the improvement of workpiece dimensional accuracy and design of machine tool’s guideways.The studies in this thesis can be summarized as follows:(1)A geometric error model of three-axis ultra-precision lathe is established to describe the mapping between geometric error and tool position error.Firstly,the error source of the machine tool is analyzed,and the geometric error term and motion transformation matrix of each feed axis are determined.Then,the topological structure of ultra-precision lathe is described by using the low-sequence body sequence,and on the basis of multi-body system theory,the geometric error model of ultra-precision lathe is derived by calculating the actual position of the tool in the workpiece coordinate system under the influence of geometric error.(2)The effect of geometric error on the workpiece dimensional precision is studied.First of all,according to the characteristics of motion transformation matrix of feed axis,a matrix decomposition method is put forward.The original matrix transformation matrix is decomposed into the sum of a unit and an error characteristic matrix.Combining with the geometric error model,this method can be used to calculate the tool position error caused by its own geometric error of each feed shaft,and reflect the accumulation process of geometric error in machining.Then,a simulation model of UPDT considering geometric error is proposed based on the geometric error model and ultra-precision turning process,and the relationship between geometric error and surface morphology of curved workpiece is established.Finally,a feature surface containing annular microarray and planar structure is designed.The change of its surface topography reflects the affecting mechanism of geometric error on the feature surface.The influence of geometric error on the workpiece dimensional accuracy is studied by the simulation model of the surface topography and the feature surface.(3)An importance analysis method of geometric error is proposed to quantify the influence degree of geometric error on the workpiece dimensional precision,and identify sensitive geometric error of curved surface workpiece in ultra-precision turning.Firstly,the problem of sensitive geometric error identification in ultra-precision turning is transformed into a feature screening problem based on random forest algorithm,and then the importance coefficient of geometric error is defined and calculated.Then,sensitive geometric errors of four typical surfaces,such as radial sinusoidal surface,angle sinusoidal surface,optical aspheric surface and sinusoidal grid surface,are identified by the proposed method.Finally,the rationality of analysis results is verified by compensating the sensitive geometric error.On the one hand,the sensitive geometric error of four typical surfaces are compensated by means of simulation.On the other hand,two sinusoidal grid surfaces are machined by a three-axis ultra-precision lathe,one of which compensates the sensitive geometric error and the other one is not. |
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