Research Of Surface Machining Toolpath Planning Technology Based On The Mesh-parameterization Mapping And Its Distortion Compensation

Complex freeform surfaces with high precision and high surface quality are widely used in the fields of aerospace,automobile and medical implants,etc.The machining of complex freeform surfaces is an important and challenging task in the field of manufacturing industry.In the milling and polishing of freeform surfaces,the machining toolpath is one of the most critical factors.When faced with the planning demands of complex iso-scallop toolpath and multidirectional trochoidal toolpath,traditional methods often have some key technical problems,such as complex calculation process,difficult precision control and efficiency optimization,etc.In this paper,based on the mesh-parameterization mapping theory,a new idea is adopted to reduce the complex toolpath planning problem from 3D space to the 2D parametric domain.However,there is a key problem in the toolpath planning based on this dimensionality reduction idea,that is,the geometric distortion of the mesh-parameterization mapping which will affect the accuracy of toolpath planning.Yet this key problem has not been fully studied and solved.Therefore,this paper first studies the mesh-parameterization mapping distortion and its compensation;on the basis of mapping distortion compensation,aiming at the problem of milling toolpath planning for 3D mesh surface,the generation of unidirectional and complex multidirectional polishing toolpath on the mesh surface and the control of material removal distribution,the related investigations are conducted.The main research contents of this paper include:The mesh-parameterization mapping characteristics oriented to machining toolpath planning are studied.In order to solve the problem that the mesh-parameterization mapping distortion affects the accuracy of toolpath planning,the mapping deformation is analyzed from the continuous to discrete point of view,and further the concept of mapping distortion field is proposed and its characteristics are given,which establishes the theoretical foundation for mapping distortion compensation.According to the demands of the toolpath planning for the closed mesh surfaces,the most suitable cutting strategy is selected,which lays a theoretical foundation for further toolpath planning.To address the problem of mapping distortion of mesh parameterization which will affect the accuracy of toolpath planning,the concept and calculation method of mapping distortion compensation(MDC)are proposed.The MDC method includes direction mapping that compensates for angular distortion,and length mapping that compensates for stretch distortion.On this basis,a large span mapping distortion handling(LSMDH)strategy is proposed to solve the problem that different triangle facets have varied mapping distortions.After that,the basic strategy of toolpath planning based on the mesh parameterization technology is proposed.In this way,on the premise of ensuring the accuracy of toolpath planning,one can make full use of the advantages of mesh parameterization technology in dimensionality reduction,and then exploit the rich technical resources in the 2D domain to plan the complex 3D toolpaths.To address the problem of milling toolpath planning for 3D mesh surfaces,the isoparametric and iso-scallop toolpath planning strategies are proposed,which make full use of the advantages of mesh parameterization technology in dimensionality reduction.Based on the idea of transforming the path parameters and using the MDC method,the iso-parametric and iso-scallop toolpaths are directly planned on the parameterized flattened mesh,which can reduce the complexity of geometric calculation and improve the robustness,meanwhile,the problem of self-intersection of path curve can be reduced to the 2D domain.In order to meet the demand of non-uniform offset of path curve,a simple and effective 2D non-uniform offsetting algorithm based on the tracking technology is proposed.Finally,aiming at the undercut and overcut phenomena of the toolpaths on the mesh surface,the paper puts forward a processing strategy that makes full use of the advantages of dimensionality reduction of mesh parameterization,which directly processes the intersection and segmentation of the 2D paths.Aiming at the problem of material removal uniformity caused by curved surface polishing toolpath,a method of scanning line polishing toolpath planning using the dimensionality reduction technology is proposed.Firstly,a simple and effective method is presented to establish the material removal model of tilted elastic polishing disk.Based on the material removal model,the principle of uniform superposition of material removal is given.Based on this principle and using the dimensionality reduction technology,a new method of scanning line polishing toolpath planning is proposed.The key is to use the dual cycling strategy based on dichotomy to solve the adaptive optimal path interval at each polishing path point.In order to address the problem of multidirectional polishing toolpath generation and the control of material removal distribution on 3D mesh surfaces,a strategy of trochoidal polishing toolpath planning based on the dimensionality reduction technology and MDC method is investigated.Firstly,a trochoidal toolpath planning strategy generated along the iso-parametric lines is presented.It does not require any 3D geometric calculation,so the advantage of the mesh parameterization technology in dimensionality reduction is brought into full use.On this basis,using the LSMDH strategy,a trochoidal toolpath planning strategy generated along the equidistant lines is proposed,which can ensure the accuracy of the 3D trochoidal path parameters.In order to obtain a uniform material removal distribution when using trochoidal toolpath polishing,a control method of global material removal distribution is put forward.It first calculates the optimal trochoidal parameters,and then optimizes the polishing feedrate based on the partitioned local regions.