MATHEMATICAL SIMULATION OF CONCURRENT TWO-SIDED LENS PROCESSING

The purpose of the paper is to modernize technology for obtaining high-accuracy lenses with fine centre. Presently their operating surfaces are fixed  to an accessory with the help of adhesive substance that leads to elastic deformation in glass and causes local errors in lens parts.

A mathematical model for concurrent two-sided processing of high-accuracy optical parts with spherical surfaces has been developed in the paper. The paper presents analytical expressions that permit to calculate sliding speed at any point on the processed spherical surface depending on type and value of technological equipment settings. Calculation of parameter Q = Pv in a diametric section of the convexo-concave lens has been carried out while using these expressions together with functional dependence of pressure on contact zone еarea of tool and part bedding surfaces.

Theoretical and experimental investigations have been carried out with the purpose to study changes in Q parameter according to the processed lens surface for various setting parameters of the technological equipment and their optimum values ensuring preferential stock removal in the central or boundary part zone or uniform distribution of the removal along the whole processed surface have been determined in the paper.

The paper proposes a machine tool scheme for concurrent two-sided grinding and polishing of lenses while fixing their side (cylindrical) surface. Machine tool kinematics makes it possible flexibly and within wide limits to change its setting parameters  that significantly facilitates the control of form-building process of parts with highly-precise spherical surfaces.

Methodology for investigations presupposes the following: mathematical simulation of highly-precise spherical surface form-building process under conditions of forced closing, execution of numerical and experimental studies.  

1. Kozeruk, A. S., Klimovich, V. F., Sukhotsky, A. A. (2007). Stanok dlia odnovremennoi dvustoronnei obrabotki linzy s pologimi vognutymi poverkhnostiami [Machine tool for concurrent two-sided processing of lenses with shallow and concave surfaces. Patent. Republic of Belarus, no 10724 (in Russian).

2. Preston, F. W. (1927). The Theory and Design of Plate Glass Polishing Machines. Journal of the Society of Glass Technology, 11, 214–256.

3. Filonov, I. P., Klimovich, F. F., Kozeruk, A. S. (1995). Control over precision surface form-building of machine parts and devices. Minsk, DesignPRO. 208 p. (in Russian).

4. Artobolevsky, I. I. (1988). Theory of mechanisms and machines. Moscow, Nauka. 639 p. (in Russian).

5. Kozeruk, A. S. (1997). Upravlenie formoobrazovaniem pretsizionnykh poverkhnostei detalei mashin i priborov na osnove matematicheskogo modelirovaniia. Diss. dokt. tekhnicheskikh nauk [Control over precision surface form-building of machine parts and devices on the basis of mathematical simulation. Doctoral dissertation Engineering]. Minsk. 317 p. (in Russian).

6. Klimovich, F. F., Kozeruk, A. S., Filonov, I. P. (1997). Mathematical simulation of spherical surface wearing process. Optichesky Zhournal [Optical Journal], 64 (2), 111–112 (in Russian).

7. Kozeruk, A. S. (1997). Precision surface form-building. Minsk, VUZ-IuNITI. 176 p. (in Russian).

8. Kozeruk, A. S., Sukhotskii, A. A., Klimovich, V. F., Kuznechik, V. O. (2009). Quality and productivity investigation of highly-precise spherical surfaces of optical parts. Vests? Natsyianal'nai akademii navuk. Belarus?. Ser. f?zika-tekhnichnykh navuk [Proceedings of National Academy of Science of Belarus. Series of Physical and Technical Sciences], 2, 40–44 (in Russian).

9. Zubakov, V. G., Semibratov, M. N., Shtandel, S. K. (1985). Technology of optical parts. Moscow, Mashinostroenie. 368 p. (in Russian).

10. Kozeruk, A. S., Sukhotskii, A. A., Klimovich, V. F., Filonova, M. I. (2008). Investigation of kinematics regularities in two-sided processing of concavo-convex optical parts. Vests? Natsyianal'nai akademii navuk. Belarus?. Ser. f?zika-tekhnichnykh navuk [Proceedings of National Academy of Science of Belarus. Series of Physical and Technical Sciences], 2, 26–31 (in Russian).