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radius, many smaller portions of the work surface are ground in series of varying spherical radii of performed spherical lens surface (Figure 432) The connection of these varying spherical radii along the workpiece surface forms the desired parabolic shape, and the mathematical expression can be found in the work of Tan [54] and Russell [60] However, it is necessary to have some explanation of the operation of the FORTRAN programs, which were used to calculate the tool path and write the CNC program Two main FORTRAN programs make all the computations necessary to supply the CNC machining centre with a tool path: The first program calculates the tool coordinates that give the maximum line contact with the desired parabolic profile A data file supplies this program with the desired parabolic profile focal length, F, grinding tool tip radius, R, and the grinding wheel pitch diameter, D The second program generates the CNC code for machining The desired output values are the X and Y-axis movement and the inclination angle of the grinding tool, Fig 432: Formation of the parabolic profile by the best-fit computed by this program arc method within zones [62] Metal-bonded wheels were initially used as these do not wear easily on radius work or on small areas of contact Subsequently, resinoidbonded wheels were used quite successfully Metal-bonded wheels gave a better surface roughness and form accuracy Resin-bonded wheels produced brighter surfaces and form accuracy with more ductile streaks [61] The finest grinding wheel parameters were chosen to get a better surface quality The grinding wheel used was of a 1030 m grit size The grinding operation started from the periphery of the workpiece and ended at the apex, or the centre The thermal imaging materials used were monocrystalline germanium and silicon Both blanks were polished after grinding A special aluminium tool was developed A felt cloth was glued to the spherical surface of this tool, and a polishing paste of 1 m alpha alumina was applied to it during polishing The same set-up was used for polishing on the CNC machine Fig 433: Zone-by-zone grinding [62]
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Tan s work [54] showed that the resinoid-bonded wheel worked well for both Ge and Si It could easily be redressed and trued, and the existing commercial sizes are available Better surface roughness
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Fig 434: The aspheric surface generation process [63]
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values were obtained using both wheels for Si Si, however, was more difficult to polish, and a lighter pressure had to be applied to prevent the felt from coming off Thus, for the same time interval, Ge had a much better surface finish Polishing improved the form accuracy for Ge but not for Si Both ductile and fracture modes of material removal were observed in the case of both Si and Ge [55] Figure 435 shows a number of ductile streaks on silicon and Figure 436 a large number of ductile streaks on Ge A better surface roughness, form accuracy, and smoothness can be obtained with a five-axis CNC jig grinder, and also by dressing the grinding wheel for the ductile mode as suggested by Rusell [60] The same type of work has been done by Kapoor [48], which suggests that resinoid-bonded wheels give more ductile streaks than do metal-bonded wheels, the latter giving a better form accuracy The main idea to use a general purpose machine such as VMC for aspherizing arising is to reduce the cost of the final product Extensive experimental work was done by Venkatesh et al [62] [64] to establish optimum grinding parameters for economical machining A resin-bonded wheel with a smaller grit size was recommended to facilitate ductile machining with little expense in the form accuracy as compared with the metal-bonded wheel Research work that is reported shows that in addition to ductile mode grinding and conventional fracture mode grinding, the intermediate mode of grinding, microcrack grinding can also yield good results at a low cost Microcrack grinding can also be described as partial ductile grinding The curves of surface roughness versus polishing time are shown in Figure 437 Parks and Evans have reported the knee points in the polishing curves
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