A Stochastic Model of Abrasive Processing. The Kinematics of Flat Grinding

The authors propose a mathematical model of flat grinding by a tool modeled as a disc with abrasive grains distributed on the cylindrical surface, with random geometric characteristics. The cutting process is modeled by each grain separately at kinematically defined motion of the tool. A system of equations is obtained that describes the relations between the coordinates of the surface machined by the currently used grain, and the coordinates of the surface formed by the previous grain. The solution for a single grain is analyzed; the configuration of the workpiece surface after multiple subsequent passes is determined. A variable-length array is used to store the variation of all the grains’ cutting thickness in the grinding process. The chip thickness of abrasive grains located in the zone of contact between the grinding wheel and the material is calculated. The texture of the surface formed after passes by the abrasive grains of the grinding wheel under pre-defined cutting conditions is evaluated. Based on the data obtained, waviness of the surface is calculated. The results of the simulation can be used to predict accuracy and quality of the surfaces when grinding.

References

[1] Voronov S.A., Ma Veidun. Matematicheskoe modelirovanie protsessa ploskogo shlifovaniia [Mathematical modeling of the process of flat grinding]. Problemy mashinostroeniia i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability]. 2017, no. 4, pp. 85–94.

[2] Komanduri R. Machining and Grinding: a Historical Review of the Classical Papers. Applied Mechanics Reviews, 1993, vol. 46, pp. 80–132.

[3] Malkin S., Guo C. Grinding Technology: Theory and Applications of Machining with Abrasives. New York, Industrial Press publ., 2008. 320 p.

[4] Hou Z.B., Komanduri R. On the mechanics of the grinding process – Part I. Stochastic nature of the grinding process. International journal of machine tools & manufacture, 2003, vol. 43, pp. 1579–1593.

[5] Maslov E.N. Teoriia shlifovaniia materialov [Theory of grinding of materials]. Moscow, Mashinostroenie publ., 1974. 318 p.

[6] Kashcheev V.N. Abrazivnoe razrushenie tverdykh tel [Abrasive destruction of solid bodies]. Moscow, Nauka publ., 1970. 245 p.

[7] Kremen’ Z.I., Iur’ev V.G., Baboshkin A.F. Tekhnologiia shlifovaniia v mashinostroenii [Grinding technology in mechanical engineering]. Sankt-Petersburg, Politekhnika publ., 2007. 423 p.

[8] Crandall S.H. Random Vibration. Moscow, Mir publ., 1967. 356 p.

[9] Hecker R., Liang S.Y. Predictive modeling of surface roughness in grinding. International journal of machine tools & manufacture, 2003, vol. 43, pp. 755–761.

[10] Holtermann R., Schumann S., Menzel A., Biermann D. Modelling, Simulation and experimental investigation of chip formation in internal traverse grinding. Production Engineering Research and Development, 2013, vol. 7(2–3), pp. 251–263.

[11] Stepien P. A probabilistic model of the grinding process. Applied Mathematical Modelling, 2009, vol. 33(10), pp. 3863–3884.

[12] GOST 2789–73. Sherokhovatost’ poverkhnosti. Parametry, kharakteristiki i oboznacheniia [State Standard 2789–73. The roughness of the surface. Parameters, characteristics and identification]. Moscow, Standartinform publ., 1970. 10 p.