Analysis of kinematics of tool and work piece contact during lens processing

Using the first axiom of statics for equilibrium of a two forces system applied to points of a solid body, it was verified, that the pressure in the zone of contact of a tool with a lens during its abrasive processing by the grinding-free method is unevenly distributed. With this in mind, the nature of the distribution of the pressure profile has been presented graphically, showing the equilibrium condition when the tool is rotated around the center of the spherical surface of the lens relative to its axis of symmetry and the clamping force of the unions that are grinded has been recorded. On that base an expression is proposed for determining the current pressure at an arbitrarily chosen point on the surface of the lens. An expression for determining the continuously changing contact area of the instrument and the lens during its processing by grinding-free method is obtained. The calculation of current pressure at different points of the diametrical cross-section of the contact zone of the lapping surfaces of the tool, performing oscillatory motion, and the lens is performed. As a result, the uneven distribution of pressure in the area under study was revealed, with the minimum value of this indicator taking place in the zone of contact of the tool edge with the lens, and the maximum in the zone of contact of the lens edge with the tool. The observed non-uniformity increases with an increase in the angle of deviation of the tool from the axis of symmetry of the lens. Theoretical and experimental studies of the influence of the tool diameter on the polishing process of the lens under conditions of free grinding, which prevents the occurrence of local error in the marginal zone of the latter due to the pressure drop between the grinding surfaces during the instrument movement, are carried out. At the same time it was found that in order to avoid a “blockage of the edge”, it is necessary to use a tool with diameter of at least 0.8 of the diameter of the lens (in case it is the lower link). The obtained results allow assigning the optimal diameter of the tool depending on the size of the processed lens without preliminary laborious experiments and can be used in optical and optoelectronic instrument making.

lens, grinding-free method, pressure profile, interface zone, return-rotational movement, angle of inclination, local error

1. Preston E. W. The Theory and Design of Plate Glass Polishing Machines. Journal of the Society of Glass Technology, 1927, no. 11, pp. 214–256.

2. Artobolevskii I. I. Theory of Mechanisms and Machines. Mosсow, Nauka Publ., 1988. 640 p. (in Russian).

3. Abramov Yu. T., Perets M. I. Influence of the “overrun” on the distribution of contact pressure between the tool and the disk-shaped product. Voprosy mekhaniki i mashinostroeniya [Questions of Mechanics and Mechanical Engineering]. Riga, 1973, vol. 4, pp. 42–52 (in Russian).

4. Minyuk S. A., Berezkina N. S., Goncharova M. N., Metel'skii A. V. Mikulik N. A. (ed.). Mathematics for Engineers. Vol. 2. Minsk, Elaida Publ., 2006. 496 p. (in Russian).

5. Zubakov, V. G. Zubakov V. G., Semibratov M. N., Shtandel S. K., Semibratov M. N. (ed.). Optical Parts Technology., Mashinostroenie Publ., 1985. 368 p. (in Russian).

6. Kozeruk A. S. Controlling the formation of precision surfaces of machine parts and devices based on mathematical modeling. Minsk, 1997. 317 sheets. (in Russian).