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

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).

Abstract

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.

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

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