Three-dimensional Elliptical Vibration Cutting For Optical Freeform Surfaces: Tool Path Generation And Effects To The Surface Quality

There is an increasing use of optical parts on difficult-to-cut materials in a range ofapplication areas, including optical engineering, biomedical and semiconductor products etc.However, most of these optical materials and the mold materials of processing these opticalparts are difficult-to-cut materials, which have poor machinability. Diamond turning hasbeen reviewed as a high efficient method to machine the surfaces with complex shapes,while the diamond turning method is used to fabricate the nonferrous materials for the poormachinability of the difficult-to-cut materials. In order to expand the range of the diamondmachineable materials and improve the surface quality, this paper focuses on the tool pathgeneration and the effects of the parameters to the surface quality of three-dimensionalellipse vibration cutting optical freeform surfaces under the support of National NaturalScience Foundation of China. The followings works are researched in this paper.Firstly, the three-dimensional (3D) ellipse driven equation (EDE) Ⅰ is introduced,which can’t represent the shape and space location of the3D ellipse. So the3D EDE Ⅰcan’t be used to research the influence of the ellipse parameters to the surface quality. The3D EDE Ⅱ is defined which can represent the shape and space location of the3D ellipsein this paper. It includes4shape parameters and3space location parameters. Because theparameters are different between these two ellipse driven equations, harmonic analysis isused to match the ellipse parameters of these two ellipse driven equations. This research canprovide the theory basis for revealing the laws of the ellipse parameters to the surfacequality.Secondly, the changes of the3D EDE Ⅱ parameters will affect the parameters of the3D EDE Ⅰ. So the relationships of the parameters are researched between these two typesof equations. The laws of the changes of3D EDE Ⅱ parameters to the the parameters of3D EDE Ⅰ have been revealed.Thirdly, the algorithm of the tool path generation is proposed, considering the tool geometry parameters, the cutting process parameters,3D ellipse vibration, tool arc radiuscompensation and the position between the cutter-contact point and the cutter-location point.At the same time, how to use the tool path to machine the optical freeform surfaces has beendescribed clearly. The examples of the toric surface and sinusoidal surface are used toverify the tool path.Fourthly, the machined surface residual height topography is analysed according to thetoric surface and sinusoidal surface. The laws of the ellipse parameters, cutting parametersand tool parameters to the surface quality have been revealed. This research can telldesigners how to choose the ellipse parameters, cutting parameters and tool parameters tomachine optical parts.Fifthly, genetic algorithm is proposed to solve the optimum ellipse parameters whichare the shape and position parameters. This research can provide theory basis for thedesigners to use optimum elliptical vibration parameters to machine optical freeformsurfaces of difficult-to-machine materials in the cutting experiments.This research can provide theory basis for three-dimensional ellipse vibration cuttingoptical freeform surfaces.