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Three-dimensional chatter stability prediction of milling based on the linear and exponential cutting force model

  • Yiqing YangEmail author
  • Qiang Liu
  • Bin Zhang
ORIGINAL ARTICLE

Abstract

Stability lobes are widely used to avoid chatter which restricts the machining quality and productivity. A lot of work has been done to predict the stability lobes fast and accurately. However, most of them are based on the linear force model, and the chatter stability limit is formulated as independent on the feed rate, which is inconsistent with the machining practice. By referencing with the zero-order solution, this paper investigates the chatter stability prediction based on the exponential force model. Focusing on the cutters with a lead angle (i.e., inserted face mill, the ball-end mill, and bull-nose end mill) where chatter is likely to be brought up in Z direction, the stability model is extended to three-dimensional. Taylor equation is utilized to linearize the exponential expressions when computing the directional coefficients in order to solve the stability limit analytically as the linear force model. Simulation results show that the exponential force model agrees with the measurements as well as the linear force model in the cutting force prediction, and it is able to demonstrate the feed rate effect on the stability limit. The stability limit is found to be increased as the feed rate increases, which is evidenced by the time domain simulation. Cutting tests are performed in the end to verify the stability model. The proposed model could be reduced to either X/Y dimensional or linear force model-based stability model by further simplifications.

Keywords

Milling Chatter stability Three-dimensional Exponential force model Face mill 

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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationBeihang UniversityBeijingChina

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