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

In this work, a dynamic model of flat grinding by a tool with a given distribution of abrasive grains owning random geometric characteristics is introduced. It is assumed that the tool is mounted on an elastically-supported suspension, oscillating in the plane under the action of the cutting forces that are determined by the resulting interaction of separate abrasive grains with the treated material. Equations for the tool oscillations, relationships for the calculation of the cut layer thickness, and equations for the formation of new surfaces are obtained. Cutting forces are calculated taking into account the tool’s dynamical displacements. The surface texture formed after passes by abrasive grains of the grinding wheel is evaluated. An estimation of the machined surface quality is carried out through the statistical processing of parameters of the formed texture taking into consideration the dynamical influence of the grinding process. The results of simulation of the machined surface characteristics with and without the consideration of dynamics are compared. The influence of the tool attachment stiffness and rotation speed on the tool’s dynamical displacement during the grinding process is investigated. It is shown that there are various vibration excitation sources in the system, characteristic both of the forced oscillations at the frequency of teeth passing, and the regenerative oscillations at the dynamic system natural frequencies.

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. 3, pp. 12–22.

[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] Voronov S.A., Kiselev I.A., Ma V., Shirshov A.A. Imitatsionnaia dinamicheskaia model’ protsessa shlifovaniia slozhnoprofil’nykh detalei. Razvitie metodov modelirovaniia [Numerical Simulation of a Grinding Process Model for the Spatial Work-pieces: Development of Modeling Techniques]. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science and Education. Bauman MSTU]. 2015, no. 5, pp. 40–58. Available at: http://technomag.edu.ru/jour/article/view/283/285 (accessed 09 September 2017).

[5] 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.

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

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

[8] Voronov S.A., Ma V. Stokhasticheskaia model’ protsessa abrazivnoi obrabotki. Kinematika ploskogo shlifovaniia [A Stochastic Model of Abrasive Processing. The Kinematics of Flat Grinding]. Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building]. 2017, no. 11, pp. 69–79.

[9] Voronov S.A., Ma V. Vliianie geometrii abrazivnogo zerna na sily rezaniia pri shlifovanii [Effect of Abrasive Grain Geometry on Cutting Forces in Grinding]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie [Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering]. 2017, no. 5, pp. 52–63.

[10] Zherebtsov S., Salishchev G., Galeyev R., Maekawa K. Mechanical Properties of Ti–6Al–4V Titanium Alloy with Submicrocrystalline Structure Produced by Severe Plastic Deformation. Materials Transactions, 2005, vol. 46, no. 9, pp. 2020–2025.