Three dimension free curves find wide applications in engineering. There is no problem to express them exactly mathematically, but th e reportage has not been done on the investigation of precision analysis of thre e-...Three dimension free curves find wide applications in engineering. There is no problem to express them exactly mathematically, but th e reportage has not been done on the investigation of precision analysis of thre e-dimension free curves nanofabrication. Nanofabrication Precision includes the geometrical precision and the precision of driving system (below simply cal led the system precision). This paper submits the precision analysis method of c urve normal vector to analyze geometrical precision. Take an aspherical surf ace for example, it can be fitted and constructed by tensor product parameter cu rves, such as linear drawing curves, straight veins curves, rotating curves, swe eping curves, DUCT curves and Geomap curves. Then the curves of the aspherical s urface is iterated and modified to select the best fitted curves of the aspheric al surface. Finally, the geometrical precision of perfect approximate aspherical surface fitting has been sought. This kind of geometrical fitting construction is very important. Another is the system precision, which contains axial position precision, line p recision, and twisting and swinging precision, etc. The paper adopts the theory of precision optimum match (Prof. Wang Er-qi first put forward in 19 83) to allocate precision optimumly. The minimum cost is used as an objective fu nction, and weight method matches the precision. To obtain the optimum match combination of the minimum cost design parameters and every composing element t olerance, the precision is iterated and sought optimumly to design the system op timumly. The theoretical analysis shows that it’s feasible to control three dim ension free curves nanofabrication within nanometer scale precision.展开更多
文摘Three dimension free curves find wide applications in engineering. There is no problem to express them exactly mathematically, but th e reportage has not been done on the investigation of precision analysis of thre e-dimension free curves nanofabrication. Nanofabrication Precision includes the geometrical precision and the precision of driving system (below simply cal led the system precision). This paper submits the precision analysis method of c urve normal vector to analyze geometrical precision. Take an aspherical surf ace for example, it can be fitted and constructed by tensor product parameter cu rves, such as linear drawing curves, straight veins curves, rotating curves, swe eping curves, DUCT curves and Geomap curves. Then the curves of the aspherical s urface is iterated and modified to select the best fitted curves of the aspheric al surface. Finally, the geometrical precision of perfect approximate aspherical surface fitting has been sought. This kind of geometrical fitting construction is very important. Another is the system precision, which contains axial position precision, line p recision, and twisting and swinging precision, etc. The paper adopts the theory of precision optimum match (Prof. Wang Er-qi first put forward in 19 83) to allocate precision optimumly. The minimum cost is used as an objective fu nction, and weight method matches the precision. To obtain the optimum match combination of the minimum cost design parameters and every composing element t olerance, the precision is iterated and sought optimumly to design the system op timumly. The theoretical analysis shows that it’s feasible to control three dim ension free curves nanofabrication within nanometer scale precision.
