Modeling of formation regularities of conical surfaces

The scheme of processing conical surfaces by grinding them to a flat tool is considered and a technical solution for the implementation of such processing is proposed. Using the created device allows implementing the group method of forming conical parts with a deviation of the generatrix of the cone from straightness of not more than ± 0.00012 mm. A mathematical model of the patterns of removal of stock from a conical part with a flat tool is developed. A formula is obtained for calculating the modulus of the sliding velocity at any point on the processed conical surface, which implements engineering methods for controlling the shaping of conical parts without conducting preliminary labor-intensive experimental studies. An optimization technique for the adjustment parameters of technological equipment was proposed. The most effective axicon processing modes were revealed at the stages of preliminary, medium and fine grinding, as well as at the polishing stage, depending on the technological heredity of the workpiece from the point of view of distribution of the stock to be removed over its surface. It has been established that changes in the eccentricity between the axes of rotation of the tool and the faceplate as well as the amplitudes of the reciprocating rotational movements of the latter practically do not affect both accuracy and processing productivity, therefore, in practice, these parameters can not be optimized, but their average values can be assigned. The operating modes of the basic lever grinding and polishing machine are established, at which the required accuracy of the working surface of the tool is provided, which directly affects the straightness of the generatrix of the cone. Studies of the regularities of the shaping of the side surface of a conical lens in the conditions of free grinding are carried out and the adjustment parameters of technological equipment that affect the quality and productivity of the processing process are determined.

1. Karasik V. E., Orlov V. M. Laser Vision Systems. Moscow, Bauman Moscow State Technical University, 2001. 352 p. (in Russian)

2. Seredovich V. A., Komissarov A. V., Komissarov D. V., Shirokova T. A. Ground Laser Scanning. Novosibirsk, Siberian State Geodetic Academy, 2009. 261 p. (in Russian).

3. Kozeruk A. S. Shaping Precision Surfaces. Minsk, VUZ-UNITI Publ., 1997. 176 p. (in Russian).

4. Kozeruk A. S., Diaz Gonzalez R. O., Sukhotsky A. A., Philonova M. I. Simulation of axicon processing area on technological equipment. Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya fizika-technichnych navuk = Proceedings of the National Academy of Sciences of Belarus. Physical-technical series, 2020, vol. 65, no. 3, pp. 365–374 (in Russian). https://doi.org/10.29235/1561-8358-2020-65-3-365-374

5. Kozeruk A. S. Managing the Shaping of Precision Surfaces of Machine Parts and Devices Based on Mathematical Modeling. Minsk, 1997. 317 p. (in Russian).

6. Filonov I. P., Kozeruk A. S., Malpika D. L., Filonova M. I., Kuznechik V. O., Dias Gonsalez R. O. Mathematical modeling of technological equipment for processing optical parts. Nauka i t ekhnika = S cience & Technique, 2017, vol. 16, no. 5, pp. 367–375 (in Russian). https://doi.org/10.21122/2227-1031-2017-16-5-367-375

7. Zubakov V. G., Semybratov M. N., Standel S. K. Optical Parts Technology. Moscow, Mashinostroenie Publ., 1985. 368 p. (in Russian).

8. Semibratov M. N., Zubakov V. G., Shtandel’ S. K., Kuznetsov S. M. Technology of Optical Parts. Moscow, Mashinostroenie Publ., 1978. 415 p. (in Russian).