Research On Ultra-Precision Turning Of High-Steep Free-Form Surfaces And The Effect Mechanism Of Machine Tool Error On Surface Machining Quality

Freeform surfaces have superior performance in realizing special optical properties and carrying out special precision physical experiments.The rapid development of ultraprecision turning processing technology provides a solution for the high-precision manufacturing of complex free-form surfaces.However,the machining quality of complex free-form surfaces is affected by many factors,including tool path,machine tool geometric error,motion axis following error,dynamic performance of key components,etc.The interaction mechanism is very complex.Firstly,the non-uniform B-spline global surface interpolation is an important method for the representation of free-form surfaces.However,in the radial Cartesian coordinate system,the free-form surface interpolation boundary has poor accuracy,the distribution of surface parameters is not clear,and there is a lack of active control methods for surface parameter distribution.Secondly,reasonable tool path planning is the basic requirement of ultra-precision turning of complex free-form surfaces.However,there is a lack of efficient tool path generation methods for parametric complex free-form surfaces,and the distribution of parameters on the surface is not clear,which makes it impossible to directly use the surface parameters to generate the desired tool path.Thirdly,various errors of the machine tool will affect the tool position and posture and cause the micro-topography error and contour error of the free-form surface.However,there is a lack of a complete numerical calculation method for the topographic error and contour error of the free-form surfaces under the influence of various errors.Finally,the sensitivity of freeform surface contour error with respect to machine tool error has important theoretical guiding significance in error compensation,machine tool design and manufacturing,and machine tool inspection tool design.However,there is a lack of sensitivity analysis methods for free-form surface contour error with respect to machine tool error.This paper takes the high-steep and complex free-form surface parts required for special precision physical experiments as the research object.Carry out research on the key technologies of the free-form surface non-uniform B-spline global interpolation method,tool path planning,machine tool multi-error action mechanism,and error sensitivity analysis involved in ultra-precision turning of this type of parts.Specifically:For non-uniform B-spline global surface interpolation,based on the strong linear correlation between the arc length and the parameters of the non-uniform B-spline curve,the non-uniform B-spline curve cutting and re-discretization method are used to make the arc length of the radial curve of the free-form surface consistent.The trimmed non-uniform B-spline curve is discretized at equal intervals,and the equal arc length distribution of discrete points with equal parameter intervals on the radial curve of the surface is realized.Based on the iterative interpolation method,the high-precision calculation of the derivative of the surface boundary is realized.By calculating the interpolation accuracy of the surface instance,the validity of the boundary-constrained global interpolation in the radial Cartesian coordinate system is verified.The radial arc length of the improved non-uniform B-spline interpolation surface constrained by the boundary vector is calculated,and the strong linear correlation between the radial parameters of the surface and the arc length of the radial curve is verified.It lays a theoretical foundation for the tool path planning based on non-uniform B-spline parameters.For the tool path planning of parametric free-form surfaces,based on the calculation idea of Archimedes’ spiral line,the spiral tool path is directly generated by using equally spaced surface parameters on the improved non-uniform B-spline global interpolation surface.The parametric spiral tool path inherits the strong linear correlation between the radial parameters of the surface and the arc length of the radial curve,and the equal spatial pitch is ensured,thereby achieving the consistency of the residual height of the tool on the free-form surface.Based on the strong linear correlation between the arc length and the parameters of the non-uniform B-spline curve,the equal arc length dispersion of the spatial spiral line is realized,and the chord height error of the machining trajectory is efficiently controlled.Based on the non-uniform B-spline global surface interpolation theory,the tool position surface during the machining process is accurately calculated,which provides a new idea for tool radius compensation.By using the partial derivative solution method and vector projection calculation method of non-uniform B-spline surfaces,combined with the surface base plane solution method in the turning process,a general clearance angle interference verification method based on non-uniform B-spline surfaces is formed.For the machining quality of free-form surfaces caused by machine tool errors and the sensitivity of surface contour errors to machine tool errors,on the basis of the calculation method of turning micro-topography of unobstructed flat surface-like surfaces,the accurate calculation of the micro-topography of complex free-form surfaces with high steepness is realized,and the completeness of the numerical calculation method of turning topography is improved.The kinematic error modeling method based on dual quaternion theory is studied.On the basis of clarifying the specific meaning of geometric error measurement data,an accurate error model is constructed,which simplifies the calculation and expression process.The re-discretization of the spiral tool path under the influence of error is realized,and a complete numerical calculation method for the micro-topography of complex freeform surface under the influence of error is formed.Based on the projection calculation method of the non-uniform B-spline surface outer point,the influence of various errors on the contour error of the free-form surface is accurately calculated.The sensitivity analysis method based on variance is used to evaluate the sensitivity of free-form surface contour error relative to geometric error,and the scientificity of correcting sensitive error in error compensation is analyzed.The relationship between different types of free-form surfaces and sensitive error terms is studied.The results show that the radial steepness of the surface and the complexity of the surface will affect the sensitive error term,which provides a theoretical basis for the design of special machine tools and machine tool inspection tools.Overall,this study clarifies the formation mechanism of the ultra-precision turning accuracy of complex free-form surfaces while realizing the ultra-precision turning of complex free-form surfaces.Through the in-depth research on the related technologies of ultra-precision turning of complex free-form surfaces,the experience and conclusions with regularity and universality are extracted and summarized,so as to provide useful reference for the development and progress of ultra-precision machining technology.