Abstract
AbstractIn this contribution, we examine the evolution of surface errors during consecutive milling operations. Its description is based on a nonlinear implicit map, which is suitable to investigate the surface quality. It describes the series of consecutive Surface Location Errors (SLE) in roughing operations. As one of the principal results of the paper, bifurcations related to the fixed point of the implicit map are analyzed via normal form theorem. We determined a formula for the criticality of the bifurcation, which allows the approximate computation of the arising period-two solution. The method is demonstrated for the surface error model of milling, and the results are verified by numerical computations. Although the amplitude of the SLE would be negligible, its derivatives has a great influence in the model, which can cause stability problems.
Funder
Hungarian Scientific Research Fund
Nemzeti Kutatási, Fejlesztési és Innovaciós Alap
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering
Reference44 articles.
1. Munoa, J., Beudaert, X., Dombovari, Z., Altintas, Y., Budak, E., Brecher, C., Stepan, G.: Chatter suppression techniques in metal cutting, vol. 65. In: 66th General Assembly of the International-Academy-for-Production-Engineering, Guimaraes (Portugal), 21 Aug 2016–27 Aug 2016, CIRP, pp. 785–808 (2016)
2. Altintas, Y.: Manufacturing Automation—Metal Cutting Mechanics, Machine Tool Vibrations and CNC Design, 2nd edn. Cambridge University Press, Cambridge (2012)
3. Tlusty, J.: Effect of end milling deflections on accuracy. In: Handbook of High-speed Machining Technology, pp. 140–153 (1985)
4. Tlusty, J., Spacek, L.: Self-excited vibrations on machine tools, Nakl. CSAV, Prague, in Czech (1954)
5. Tobias, S.: Machine-Tool Vibration. Blackie, Glasgow (1965)