Geometric deviation evaluation for a five-axis flank milling tool path using the tool swept envelope

  • Yao-An LuEmail author
  • Cheng-Yong Wang
  • Li Zhou


The geometric deviation is a fundamental concern of five-axis flank milling tool path planning. The determination of the tool swept envelope (TSE) is a very important issue for geometric deviation evaluation because the machined surface is formed by the TSE. Envelope condition is usually utilized to calculate the swept profiles on the cutter surfaces to construct the TSE. The envelope condition presumes the velocity of any point on the tool axis trajectory surface does not vanish. However, it will vanish if the tool axis trajectory surface is not regular. If the swept profiles are still integrated directly to form the TSE when the tool axis trajectory surface is not regular, a wrong result is returned and it will affect the geometric deviation evaluation as well. Kinds of research have largely overlooked this problem. This research presents a robust TSE modeling method and an efficient geometric deviation evaluation method using the TSE. First, the two rotary axes movements are considered to define the tool axis trajectory surface. Then, based on the tool axis trajectory surface and the cutter geometry, cutter’s swept profiles are determined by using the envelope theory of sphere congruence. By utilizing the proposed method to detect outlier tool positions, the TSE is decomposed into multiple surface patches according to the outlier tool positions. To deal with the tool path self-intersection issue, surface patches of the TSE and the cutting tools at the outlier tool positions are represented as triangular facets. Finally, the geometric deviation for a flank milling tool path is calculated via the discrete vector model of the design surface. Examples are given to demonstrate the validity of the proposed methods.


Geometric deviation Tool swept envelope Flank milling Self-intersection tool path 



This work was supported by the Science and Technology Planning Project of Guangdong Province (Grant Number 2017B090913006), the National Natural Science Foundation of China (Grant Number 51805094), and the China Postdoctoral Science Foundation (Grant Number 2018M633009).


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electromechanical EngineeringGuangdong University of TechnologyGuangzhouChina
  2. 2.School of Mechatronic EngineeringGuangdong Polytechnic Normal UniversityGuangzhouChina

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