Geometrical Simulation and Analysis of Ball-End Milling Surface Topography


Ball-end milling cutter has a strong adaptability and widely used in machining complex surface of parts. However, the geometry of ball-end milling cutter tooth is complex, and contact points between cutter tooth and part are varying constantly during milling process, which lead that it is difficult to study the surface topography by the traditional experimental method. Based on the time-step method, this paper proposes an improved Z-MAP algorithm to simulate the part surface topography after ball-end milling. On the basis of the cutter tooth movement equation established by homogeneous matrix transformation, the improved Z-MAP algorithm combines servo rectangular encirclement and the angle summation method to quickly obtain the instantaneous swept points that belong to the part, and introduce Newton iterative method to calculate the height of swept points. Comparing to traditional Z-MAP algorithm which discrete segments of cutter tooth can only sweep one discrete point of part during a unit time step, the proposed algorithm need not to disperse cutter tooth, accomplishes higher precision and efficiency. The influence of processing parameters, such as step over, feed per tooth, cutter posture, and cutter tooth initial phase angle difference, upon the surface topography and roughness are analyzed. The experiments are conducted to validate the availability of the proposed algorithm, and the results show that surface topographies simulated by the improved Z-MAP algorithm have a higher consistency with the experiments and costs less time than by the traditional Z-MAP algorithm under the same simulation conditions. Therefore, the proposed algorithm is effective for simulating the machined surface quality in practical production and rational selection of machining parameters.


Mechanical and Aerospace Engineering


The authors wish to thank the financial support for this work from the National Natural Science Foundation of China (51575442), the Shaanxi Natural Science Foundation of China (2016JZ011), the Shaanxi Province Education Department (2014SZS10-Z01), and the Intelligent Systems Center at the Missouri University of Science and Technology.

Keywords and Phrases

Ball-end milling; Improved Z-MAP algorithm; Simulation analysis; Surface topography

International Standard Serial Number (ISSN)

0268-3768; 1433-3015

Document Type

Article - Journal

Document Version


File Type





© 2019 Springer London, All rights reserved.

Publication Date

01 Jun 2019