Prediction of tool tip dynamics for generalized milling cutters using the 3D model of the tool body

Lutfi Taner Tunc1,2
1Nuclear Advanced Manufacturing Research Centre, University of Sheffield, Sheffield, UK
2Composite Technologies Centre of Excellence, Sabanci University, Istanbul, Turkey

Tóm tắt

In general, chatter is the main limitation to proper material removal in milling operations. Stability lobes are good tools to determine chatter-free cutting conditions in terms of spindle speed and cutting depth, which require the frequency response function (FRF) at the tool tip to be known. There are experimental methods to measure the tool tip FRF but this may be time consuming or even impossible for each tool and tool holder combination. Receptance coupling substructure analysis (RCSA) is a widely used approach to predict tool tip dynamics. This paper proposes the use of the RCSA approach with a stereolithographic (STL) slicing algorithm to enable the exact calculation of cross sectional properties such as area and area moment of inertia of the cutting tool from its 3D model opposed to the approximation methods. So that, the effect of flutes on cutting tool structure introduced in an exact manner and the RCSA approach becomes feasible for more complicated tool geometries with varying cross-sectional properties, i.e., tapered ball end mills, end mills with variable flute geometries, and so on. The solid model of the tool can be available by either the tool manufacturer or 3D measurement. Although, at the presence of 3D models, finite element methods (FEM) offer accurate simulation of the dynamic response for solid bodies, they suffer from the compromise between accuracy and computation time, as high number of elements is needed for accuracy. Thus, the use of analytical methods where possible improves the simulation time significantly. The proposed STL slicing algorithm is integrated with a previously developed RCSA method. The experimental results show that the proposed algorithm works more accurate in calculation of the cross-sectional properties and hence free-free response of the tool compared to the existing arc approximation methods. It is also shown that the proposed approach performs better than FEM solutions in terms of the computation time and the compromise between accuracy and computation performance. Finally, the proposed approach in prediction of tool tip dynamics for a robotic machining platform.

Tài liệu tham khảo

Altintas Y, Budak E (1995) Analytical prediction of stability lobes in milling. Ann CIRP 44:357–362 Insperger T, Stepan G (2002) Semi-discretization method for delayed systems. Int J Numer Methods Eng 55(5):503–518 Schmitz TL, Donaldson R (2000) Predicting high-speed machining dynamics by substructure analysis. Ann CIRP 49(1):303–308 Aristizabal-Ochoa JD (2004) Timoshenko beam column with generalized end conditions and non-classical modes of vibration of shear beams. J Eng Mech 130:1151–1159 Schmitz TL, Davies M, Medicus K, Snyder J (2001) Improving high speed machining material removal rates by rapid dynamic analysis. Annals of the CIRP 50(1):263–268 Park SS, Altintas Y, Movahhedy M (2003) Receptance coupling for end mills. Int J Mach Tools Manuf 43(9):889–896 Schmitz TL, Powell K, Won D, Duncan GS, Sawyer WG, Ziegert JC (2007) Shrink fit tool holder connection stiffness/damping modelling for frequency response prediction in milling. Int J Mach Tools Manuf 47:1368–1380 Namazi M, Altintas Y, Abe T, Rajapakse N (2007) Modeling and identification of tool holder–spindle interface dynamics. Int J Mach Tools Manuf 47(9):1333–1341 Yang Y, Wan M, Ma YC, Zhang WH (2016) An improved method for tool point dynamics analysis using a bi-distributed joint interface model. Int J Mech Sci 105:239–252 Özşahin O, Ertürk A, Özgüven HN, Budak E (2009) A closed-form approach for identification of dynamical contact parameters in spindle–holder–tool assemblies. Int J Mach Tools Manuf 49:25–35 Ertürk A, Özgüven HN, Budak E (2006) Analytical modelling of spindle–tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF. Int J Mach Tools Manuf 46:1901–1912 Ertürk A, Özgüven HN, Budak E (2007) Effect analysis of bearing and interface dynamics on tool point FRF for chatter stability in machine tools by using a new analytical model for spindle–tool assemblies. Int J Mach Tools Manuf 47:23–32 Arbertelli P, Goletti M, Monno M (2013) A new receptance coupling substructure analysis methodology to improve chatter free cutting conditions prediction. Int J Mach Tools Manuf 72:16–24 Kivanc EB, Budak E (2004) Structural modeling of end mills for form error and stability analysis. Int J Mach Tools Manuf 44:1151–1161 Mancisidor I, Urkiola A, Barcena R, Munoa J, Dombovari Z, Zatarain M (2014) Receptance coupling for tool point dynamic prediction by fixed boundaries approach. Int J Mach Tools Manuf 78:18–29 Özşahin O, Altintas Y (2015) Prediction of frequency response function (FRF) of asymmetric tools from the analytical coupling of spindle and beam models of holder and tool. Int J Mach Tools Manuf 92:31–40 Yang Y, Zhang WH, Ma YC, Wan M (2015) Generalized method for the analysis of bending, torsional and axial receptances of tool–holder–spindle assembly. Int J Mach Tools Manuf 99:48–67 Altintas, Y., Kersting, P., Biermann, D., Budak, E., Denkena, B., Lazoglu, I (2014) Virtual process systems for part machining operations. CIRP Ann – Manuf Technol 585–605 Lefebvre PP, Lauwers B (2004) STL model segmentation for multi-axis machining operations planning. Computer-Aided Design and Applications 1:277–284 Timoshenko SP (1922) On the transverse vibrations of bars of uniform cross-section. Philos Mag 43:125–131 Blevins R (1979) Formulas for natural frequency and mode shape. Van Nostrand Reinhold Co., NY