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

doi:10.1007/s40436-025-00563-y

Advances in Manufacturing ›› 2026, Vol. 14 ›› Issue (1): 244-257.doi: 10.1007/s40436-025-00563-y

• • 上一篇

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

Wen-Jun Lyu^1,2,3,4, Zhan-Qiang Liu^1,2,3,5, Bing Wang^1,2,3,4, Yu-Kui Cai^1,2,3,4, Ming Zhao⁶, Hong-Xin Wang⁷

1. School of Mechanical Engineering, Shandong University, Jinan, 250061, People's Republic of China;
2. State Key Laboratory for High-end Equipment and Advanced Technology of Metal Forming, Shandong University, Jinan, 250061, People's Republic of China;
3. Key Laboratory of High-efficiency and Clean Mechanical Manufacture of Ministry of Education, Jinan, 250061, People's Republic of China;
4. Key National Demonstration Center for Experimental Mechanical Engineering Education, Jinan, 250061, People's Republic of China;
5. School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai, 264209, Shandong, People's Republic of China;
6. AECC Shenyang Liming Aero Engine Co. Ltd, Shenyang, 110043, People's Republic of China;
7. Moon Environment Technology Co. Ltd., Yantai, 264001, Shandong, People's Republic of China

收稿日期:2024-04-21 修回日期:2024-06-23 发布日期:2026-03-23
通讯作者: Zhan-Qiang Liu Email:E-mail:melius@sdu.edu.cn E-mail:melius@sdu.edu.cn
作者简介:Wen-Jun Lyu is a doctoral candidate at School of Mechanical Engineering at Shandong University, China. His research interests include high-quality and highefficiency machining as well as intelligent manufacturing.
Zhan-Qiang Liu is a professor and doctoral supervisor at School of Mechanical Engineering, Shandong University, China. His research interests include highspeed machining, surface integrity, and process mechanics.
Bing Wang is a professor and doctoral supervisor at School of Mechanical Engineering, Shandong University, China. His research interests include highquality and high-efficiency cutting technology and intelligent manufacturing.
Yu-Kui Cai is a professor and doctoral supervisor at School of Mechanical Engineering, Shandong University, China. His research interests include bionic microstructures and ultra-precision micromachining technology.
Ming Zhao is a senior engineer at AECC Shenyang Liming Aero Engine Co. Ltd. His research interests include high-quality and high-efficiency machining as well as precision machining.
Hong-Xin Wang is a senior engineer at Moon Environment Technology Co. Ltd. His research interests include the structural optimization and intelligent production of refr igeration equipment.
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. U24B2057, 92360311 and 52275444) and Shandong Province Key Research and Development Plan (Grant No. 2023JMRH0307).

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

Wen-Jun Lyu^1,2,3,4, Zhan-Qiang Liu^1,2,3,5, Bing Wang^1,2,3,4, Yu-Kui Cai^1,2,3,4, Ming Zhao⁶, Hong-Xin Wang⁷

1. School of Mechanical Engineering, Shandong University, Jinan, 250061, People's Republic of China;
2. State Key Laboratory for High-end Equipment and Advanced Technology of Metal Forming, Shandong University, Jinan, 250061, People's Republic of China;
3. Key Laboratory of High-efficiency and Clean Mechanical Manufacture of Ministry of Education, Jinan, 250061, People's Republic of China;
4. Key National Demonstration Center for Experimental Mechanical Engineering Education, Jinan, 250061, People's Republic of China;
5. School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai, 264209, Shandong, People's Republic of China;
6. AECC Shenyang Liming Aero Engine Co. Ltd, Shenyang, 110043, People's Republic of China;
7. Moon Environment Technology Co. Ltd., Yantai, 264001, Shandong, People's Republic of China

Received:2024-04-21 Revised:2024-06-23 Published:2026-03-23
Contact: Zhan-Qiang Liu Email:E-mail:melius@sdu.edu.cn E-mail:melius@sdu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. U24B2057, 92360311 and 52275444) and Shandong Province Key Research and Development Plan (Grant No. 2023JMRH0307).

摘要/Abstract

摘要： 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.

The full text can be downloaded at https://doi.org/10.1007/s40436-025-00563-y

关键词: Removal volume, Point cloud, Time varying, Alpha shape, Tool-edge trajectory

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.

The full text can be downloaded at https://doi.org/10.1007/s40436-025-00563-y

Key words: Removal volume, Point cloud, Time varying, Alpha shape, Tool-edge trajectory

Wen-Jun Lyu, Zhan-Qiang Liu, Bing Wang, Yu-Kui Cai, Ming Zhao, Hong-Xin Wang. Prediction of time-varying instantaneous material removal volume with point cloud contour-filling model in milling process[J]. Advances in Manufacturing, 2026, 14(1): 244-257.

参考文献

[1] Lyu W, Liu Z, Song Q et al (2023) Modelling and prediction of surface topography on machined slot side wall with single-pass end milling. Int J Adv Manuf Tech 124:1095-1113
[2] Abootorabi Zarchi MM, Razfar MR, Abdullah A (2015) Research on the importance of tool-workpiece separation in ultrasonic vibration-assisted milling. P I Mech Eng B-J Eng 231:600-607
[3] Sun Z, Geng D, Guo H et al (2024) Introducing transversal vibration in twist drilling: material removal mechanisms and surface integrity. J Mater Process Tech 325:118296. https://doi.org/10.1016/j.jmatprotec.2024.118296
[4] Li Z, Zhu L, Yang Z et al (2022) Investigation of tool-workpiece contact rate and milling force in elliptical ultrasonic vibration-assisted milling. Int J Adv Manuf Tech 118:585-601
[5] Geng D, Sun Z, Liu Y et al (2024) 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 326:118320. https://doi.org/10.1016/j.jmatprotec.2024.118320
[6] Li Z, Wang X, Zhu L (2016) Arc-surface intersection method to calculate cutter-workpiece engagements for generic cutter in five-axis milling. Comput Aided Design 73:1-10
[7] Ma H, Liu W, Zhou X et al (2021) High efficiency calculation of cutter-workpiece engagement in five-axis milling using distance fields and envelope theory. J Manuf Process 68:1430-1447
[8] Dogrusadik A (2023) An efficient analytical model for the swept volume generation of a flat-end mill in 5-axis CNC milling. Comput Aided Geom D 106:102241. https://doi.org/10.1016/j.cagd.2023.102241
[9] Kiswanto G, Hendriko H, Duc E (2014) An analytical method for obtaining cutter workpiece engagement during a semi-finish in five-axis milling. Comput Aided Design 55:81-93
[10] Xi X, Cai Y, Gao Y et al (2020) An analytical method to calculate cutter-workpiece engagement based on arc-surface intersection method. Int J Adv Manuf Tech 107:935-944
[11] Sai L, Belguith R, Baili M et al (2018) An approach to modeling the chip thickness and cutter workpiece engagement region in 3 and 5 axis ball end milling. J Manuf Process 34:7-17
[12] Ghorbani M, Movahhedy MR (2019) An analytical model for cutter-workpiece engagement calculation in ball-end finish milling of doubly curved surfaces. Int J Adv Manuf Tech 102:1635-1657
[13] Lazoglu I, Boz Y, Erdim H (2011) Five-axis milling mechanics for complex free form surfaces. CIRP Ann-Manuf Techn 60:117-120
[14] Aras E, Albedah A (2014) Extracting cutter/workpiece engagements in five-axis milling using solid modeler. Int J Adv Manuf Tech 73:1351-1362
[15] Boz Y, Erdim H, Lazoglu I (2015) 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 81:811-823
[16] Sullivan A, Erdim H, Perry RN et al (2012) High accuracy NC milling simulation using composite adaptively sampled distance fields. Comput Aided Design 44:522-536
[17] Yang Y, Zhang W, Wan M et al (2013) A solid trimming method to extract cutter-workpiece engagement maps for multi-axis milling. Int J Adv Manuf Tech 68:2801-2813
[18] Li G, Liu Y, Zhao D et al (2021) A general method for instantaneous undeformed chip thickness calculation in five-axis milling based on Boolean operations. Int J Adv Manuf Tech 116:2325-2334
[19] Si H, Wang L, Zhang J et al (2018) A solid-discrete-based method for extracting the cutter-workpiece engagement in five-axis flank milling. Int J Adv Manuf Tech 94:3641-3653
[20] Kim GM, Cho PJ, Chu CN (2000) Cutting force prediction of sculptured surface ball-end milling using Z-map. Int J Mach Tool Manu 40:277-291
[21] Wei ZC, Wang MJ, Zhu JN et al (2011) Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path. Int J Mach Tool Manu 51:428-432
[22] Wei ZC, Wang MJ, Cai YJ et al (2013) Prediction of cutting force in ball-end milling of sculptured surface using improved Z-map. Int J Adv Manuf Tech 68:1167-1177
[23] Wang D, Ren J, Tian W (2020) A method for the prediction of cutting force for 5-axis ball-end milling of workpieces with curved surfaces. Int J Adv Manuf Tech 107:2023-2039
[24] Qin S, Hao Y, Zhu L et al (2023) CWE identification and cutting force prediction in ball-end milling process. Int J Mech Sci 239:107863. https://doi.org/10.1016/j.ijmecsci.2022.107863
[25] Yan B, Xu G, Lu H et al (2023) Identification of milling information and cutter-workpiece engagement in five-axis finishing of turbine blades based on NURBS and NC codes. J Manuf Process 107:43-56
[26] Taner TL, ?mer ?, Erhan B (2015) Generalized cutting force model in multi-axis milling using a new engagement boundary determination approach. Int J Adv Manuf Tech 77:341-355
[27] Luo S, Dong Z, Jun MBG (2017) Chip volume and cutting force calculations in 5-axis CNC machining of free-form surfaces using flat-end mills. Int J Adv Manuf Tech 90:1145-1154
[28] Lotfi M, Amini S, Akbari J (2020) Surface integrity and microstructure changes in 3D elliptical ultrasonic assisted turning of Ti-6Al-4V: FEM and experimental examination. Tribol Int 151:106492. https://doi.org/10.1016/j.triboint.2020.106492
[29] Pei L, Wu H (2019) Effect of ultrasonic vibration on ultra-precision diamond turning of Ti6Al4V. Int J Adv Manuf Tech 103:433-440
[30] Chen G, Zou Y, Qin X et al (2020) Geometrical texture and surface integrity in helical milling and ultrasonic vibration helical milling of Ti-6Al-4V alloy. J Mater Process Tech 278:116494. https://doi.org/10.1016/j.jmatprotec.2019.116494
[31] Zhang J, Ling L, Wang Q et al (2024) Surface quality investigation in high-speed dry milling of Ti-6Al-4V by using 2D ultrasonic-vibration-assisted milling platform. Adv Manuf 12:349-364
[32] Sun Z, Geng D, Meng F et al (2023) High performance drilling of T800 CFRP composites by combining ultrasonic vibration and optimized drill structure. Ultrasonics 134:107097. https://doi.org/10.1016/j.ultras.2023.107097
[33] Zhu Z, Peng F, Yan R et al (2018) High efficiency simulation of five-axis cutting force based on the symbolically solvable cutting contact boundary model. Int J Adv Manuf Tech 94:2435-2455
[34] Lyu W, Liu Z, Cai Y et al (2023) A divide and conquer approach for machined surface topography reconstruction in peripheral milling Inconel 718. Surf Topogr-Metrol 11:15002. https://doi.org/10.1088/2051-672X/acaff8
[35] Chen H, Wang Q (2019) Modelling and simulation of surface topography machined by peripheral milling considering tool radial runout and axial drift. P I Mech Eng B-J Eng 233:2227-2240
[36] Edelsbrunner H, Mücke EP (1994) Three-dimensional alpha shapes. ACM T Graphic 13:43-72

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

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

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