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Improved precise integration method for chatter stability prediction of two-DOF milling system

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Abstract

The motivation of this paper is to update the precise integration method (PIM) by a second-order Taylor formula and make detailed contrasts with the existing PIM, the semi-discretization method (SDM) to exhibit the necessity of developing this improved PIM (IPIM). The dynamics of two-degree of freedom (DOF) milling process with consideration of regeneration effect is first governed by a time periodic delay differential equation (DDE). With time period being evenly divided into a limited set of intervals, the integral non-homogeneous element is approximated by the second-order Taylor formula in every small time segment. After decomposing the exponential factor into a real term with 2N order algorithm, the transition matrix representing the specific machining system state is established in one whole tooth passing period to search for the chatter-free borderline. To investigate the characteristics of the proposed method in convergence rate, prediction accuracy, and computational efficiency, the benchmark example used in the literatures is introduced to develop a battery of comparisons with PIM and SDM. Finally, the experimental verification is also conducted in a CNC machine tool to further confirm the operability of the proposed IPIM, and the results indicate the method is of availability.

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Funding

This work received financial support from the National Natural Science Foundation of China (51575075) and Collaborative Innovation Center of Major Machine Manufacturing in Liaoning.

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Authors and Affiliations

  1. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Hongkun Li, Yuebang Dai & Zhenfang Fan

Authors
  1. Hongkun Li
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  2. Yuebang Dai
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  3. Zhenfang Fan
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Corresponding author

Correspondence to Yuebang Dai.

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Li, H., Dai, Y. & Fan, Z. Improved precise integration method for chatter stability prediction of two-DOF milling system. Int J Adv Manuf Technol 101, 1235–1246 (2019). https://doi.org/10.1007/s00170-018-2981-y

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  • DOI: https://doi.org/10.1007/s00170-018-2981-y

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