Prediction of time-varying instantaneous material removal volume with point cloud contour-filling model in milling process

Abstract

Instantaneous material removal volume (IMRV) is a key parameter for predicting the cutting power, cutting force, and machining process. This paper presents a novel approach, known as the point cloud contour-filling method, for calculating the IMRV for each cutting tool edge at any instantaneous moment. Firstly, the kinematics during milling operations are analyzed to capture the exact motion trajectory envelope point cloud of the cutting tool edge. Secondly, the Z-map algorithm and Boolean operations are utilized to calculate the point cloud of the intersection between the workpiece and tool-edge trajectory envelope within unit time steps Δt (known as the IMRV point cloud). Finally, the 3D alpha method and Delaunay triangulation are employed to calculate the shape and volume of the IMRV. The proposed model considers the real tool-edge trajectory and tool installation errors, and introduces the variable of tool-workpiece engagement time t for the first time. The model is verified using milling tests. The proposed method provides a visualization of instantaneous complex engagement between the tool and workpiece during the milling process and can be further used for simulating milling forces and cutting power.

Keywords

Removal volume / Point cloud / Time varying / Alpha shape / Tool-edge trajectory

References

[1] Lyu W, Liu Z, Song Qet al.. Modelling and prediction of surface topography on machined slot side wall with single-pass end milling. Int J Adv Manuf Tech, 2023, 124: 1095-1113

[2] Abootorabi Zarchi MM, Razfar MR, Abdullah A. Research on the importance of tool-workpiece separation in ultrasonic vibration-assisted milling. P I Mech Eng B-J Eng, 2015, 231: 600-607

[3] Sun Z, Geng D, Guo Het al.. Introducing transversal vibration in twist drilling: material removal mechanisms and surface integrity. J Mater Process Tech, 2024, 325: 118296

[4] Li Z, Zhu L, Yang Zet al.. Investigation of tool-workpiece contact rate and milling force in elliptical ultrasonic vibration-assisted milling. Int J Adv Manuf Tech, 2022, 118: 585-601

[5] Geng D, Sun Z, Liu Yet al.. Unravelling the influence of vibration on material removal and microstructure evolution in ultrasonic transversal vibration-assisted helical milling of Ti-6Al-4V holes. J Mater Process Tech, 2024, 326: 118320

[6] Li Z, Wang X, Zhu L. Arc-surface intersection method to calculate cutter-workpiece engagements for generic cutter in five-axis milling. Comput Aided Design, 2016, 73: 1-10

[7] Ma H, Liu W, Zhou Xet al.. High efficiency calculation of cutter-workpiece engagement in five-axis milling using distance fields and envelope theory. J Manuf Process, 2021, 68: 1430-1447

[8] Dogrusadik A. An efficient analytical model for the swept volume generation of a flat-end mill in 5-axis CNC milling. Comput Aided Geom D, 2023, 106: 102241

[9] Kiswanto G, Hendriko H, Duc E. An analytical method for obtaining cutter workpiece engagement during a semi-finish in five-axis milling. Comput Aided Design, 2014, 55: 81-93

[10] Xi X, Cai Y, Gao Yet al.. An analytical method to calculate cutter-workpiece engagement based on arc-surface intersection method. Int J Adv Manuf Tech, 2020, 107: 935-944

[11] Sai L, Belguith R, Baili Met al.. An approach to modeling the chip thickness and cutter workpiece engagement region in 3 and 5 axis ball end milling. J Manuf Process, 2018, 34: 7-17

[12] Ghorbani M, Movahhedy MR. An analytical model for cutter-workpiece engagement calculation in ball-end finish milling of doubly curved surfaces. Int J Adv Manuf Tech, 2019, 102: 1635-1657

[13] Lazoglu I, Boz Y, Erdim H. Five-axis milling mechanics for complex free form surfaces. CIRP Ann-Manuf Techn, 2011, 60: 117-120

[14] Aras E, Albedah A. Extracting cutter/workpiece engagements in five-axis milling using solid modeler. Int J Adv Manuf Tech, 2014, 73: 1351-1362

[15] Boz Y, Erdim H, Lazoglu I. A comparison of solid model and three-orthogonal dexelfield methods for cutter-workpiece engagement calculations in three- and five-axis virtual milling. Int J Adv Manuf Tech, 2015, 81: 811-823

[16] Sullivan A, Erdim H, Perry RNet al.. High accuracy NC milling simulation using composite adaptively sampled distance fields. Comput Aided Design, 2012, 44: 522-536

[17] Yang Y, Zhang W, Wan Met al.. A solid trimming method to extract cutter-workpiece engagement maps for multi-axis milling. Int J Adv Manuf Tech, 2013, 68: 2801-2813

[18] Li G, Liu Y, Zhao Det al.. A general method for instantaneous undeformed chip thickness calculation in five-axis milling based on Boolean operations. Int J Adv Manuf Tech, 2021, 116: 2325-2334

[19] Si H, Wang L, Zhang Jet al.. A solid-discrete-based method for extracting the cutter-workpiece engagement in five-axis flank milling. Int J Adv Manuf Tech, 2018, 94: 3641-3653

[20] Kim GM, Cho PJ, Chu CN. Cutting force prediction of sculptured surface ball-end milling using Z-map. Int J Mach Tool Manu, 2000, 40: 277-291

[21] Wei ZC, Wang MJ, Zhu JNet al.. Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path. Int J Mach Tool Manu, 2011, 51: 428-432

[22] Wei ZC, Wang MJ, Cai YJet al.. Prediction of cutting force in ball-end milling of sculptured surface using improved Z-map. Int J Adv Manuf Tech, 2013, 68: 1167-1177

[23] Wang D, Ren J, Tian W. A method for the prediction of cutting force for 5-axis ball-end milling of workpieces with curved surfaces. Int J Adv Manuf Tech, 2020, 107: 2023-2039

[24] Qin S, Hao Y, Zhu Let al.. CWE identification and cutting force prediction in ball-end milling process. Int J Mech Sci, 2023, 239: 107863

[25] Yan B, Xu G, Lu Het al.. Identification of milling information and cutter-workpiece engagement in five-axis finishing of turbine blades based on NURBS and NC codes. J Manuf Process, 2023, 107: 43-56

[26] Taner TL, Ömer Ö, Erhan B. Generalized cutting force model in multi-axis milling using a new engagement boundary determination approach. Int J Adv Manuf Tech, 2015, 77: 341-355

[27] Luo S, Dong Z, Jun MBG. Chip volume and cutting force calculations in 5-axis CNC machining of free-form surfaces using flat-end mills. Int J Adv Manuf Tech, 2017, 90: 1145-1154

[28] Lotfi M, Amini S, Akbari J. Surface integrity and microstructure changes in 3D elliptical ultrasonic assisted turning of Ti-6Al-4V: FEM and experimental examination. Tribol Int, 2020, 151: 106492

[29] Pei L, Wu H. Effect of ultrasonic vibration on ultra-precision diamond turning of Ti6Al4V. Int J Adv Manuf Tech, 2019, 103: 433-440

[30] Chen G, Zou Y, Qin Xet al.. Geometrical texture and surface integrity in helical milling and ultrasonic vibration helical milling of Ti-6Al-4V alloy. J Mater Process Tech, 2020, 278: 116494

[31] Zhang J, Ling L, Wang Qet al.. Surface quality investigation in high-speed dry milling of Ti-6Al-4V by using 2D ultrasonic-vibration-assisted milling platform. Adv Manuf, 2024, 12: 349-364

[32] Sun Z, Geng D, Meng Fet al.. High performance drilling of T800 CFRP composites by combining ultrasonic vibration and optimized drill structure. Ultrasonics, 2023, 134: 107097

[33] Zhu Z, Peng F, Yan Ret al.. High efficiency simulation of five-axis cutting force based on the symbolically solvable cutting contact boundary model. Int J Adv Manuf Tech, 2018, 94: 2435-2455

[34] Lyu W, Liu Z, Cai Yet al.. A divide and conquer approach for machined surface topography reconstruction in peripheral milling Inconel 718. Surf Topogr-Metrol, 2023, 11: 15002

[35] Chen H, Wang Q. Modelling and simulation of surface topography machined by peripheral milling considering tool radial runout and axial drift. P I Mech Eng B-J Eng, 2019, 233: 2227-2240

[36] Edelsbrunner H, Mücke EP. Three-dimensional alpha shapes. ACM T Graphic, 1994, 13: 43-72

Funding

National Natural Science Foundation of China(92360311)

Key Technology Research and Development Program of Shandong Province(2023JMRH0307)

RIGHTS & PERMISSIONS

Shanghai University and Periodicals Agency of Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature