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To remove material quickly, and end up with the desired surface, the contact area between the grinding tool and the workpiece should be as large as possible As only spheres and toroids permit the condition of a full-area contact, partial-area contact, or line contact will be the best alternative The use of a machine with a rotating tool suggests that the contact surface must be symmetrically rotational In general, the shape of the workpiece is not predictable; hence, the condition of having a large contact area is put in jeopardy Thus, the method was chosen based on a long line contact between the tool and the workpiece during the first step of rough grinding During the subsequent steps of polishing, the use of a flexible tool allows conformity between the workpiece and the tool, approaching the original condition of the contact area Two cup-shaped identical sized diamond-grinding wheels with metallic (D20/30 MICL50M1/4) and resinoid (SD240-R1OO B69-6 mm) bonding were used The profile of the grinding edge is circular in this case, but not restricted to this shape, thus, forming a toroid The important feature is that the grinding surface shape is axially symmetrical It is now possible to programme the path of this tool on the CNC machine such that it is in line (or arc) contact with the workpiece as it cuts the desired shape on the glass To illustrate this, the grinding of a paraboloid is shown The cup tool can be thought of as consisting of a collection of circles whose planes are perpendicular to the axis of rotation of the tool When a plane, as shown in Figure 431, intersects the paraboloid the common line is an ellipse To cut a concave paraboloid, the tool must fit inside the paraboloid Hence, the tool must have a diameter smaller than the shortest radius found on the ellipse of intersection of any plane intersecting the paraboloid In the case of a paraboloid, the shortest radius of curvature on the eclipse of intersection is found when the plane contains the axis of symmetry of the paraboloid Any circle at the outer side of the tool can be contained in one of the planes intersecting the paraboloid The angle that this plane makes with the axis of the paraboloid can be adjusted such that I the arc of the circle and that of the ellipse (Figure 431) at d differs in the sag height by no more than a preset tolerance This condition sets a certain common arc length over which the difference in sag does not exceed a certain value, say 05 m B d Subsequently, the tool axis can be programmed to Plane take a slightly different position relative to the axis of rotation of the workpiece, as well as relative to Zone the apex P, of the paraboloid The sequence is then Paraboloid P repeated to form a neighbouring zone of the one indicated in Figure 431 The principle of the process is somewhat similar Fig 431: The basic principle of zone-based to the one used in producing spherical lenses Instead grinding [60] of making the whole lens surface with a spherical.

Inclusions Ways in which the system will help the business or its customers. Business functions that users will perform on the system, or consumer use of the system. Functionality for the customer. Is this a new system or an upgrade, or an addition of a component or an enhancement What old systems are being upgraded Is any new hardware being acquired Are any components or licenses being upgraded What telephony, data, and wireless systems and equipment, including platforms, operating systems, data bases and data management tools, and networks, are being a ected or replaced What data will the system work with What system(s) currently hold this data How frequently is the data updated, backed up, or archived Who will use the system Identify both business units or departments, and also speci c users. Who will support the system Who will support the users What documentation and training will the project need to deliver to these people so they can do their job What do these people know that could improve the quality of the project

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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].

Exclusions Value some users might expect which is not realized by implementation of this system. Activities that the system will not support. De ne what system (computerized or manual) will be used to perform those functions. What related systems are not being changed

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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