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| Prediction of Chatter Stability for Milling Process Using Semi-Analytical Approach Based on Three-Order Runge-Kutta Method |
| LI Zhongqun, PENG Yuerong, XIA Lei, ZHU Fan |
| (School of Mechanical Engineering, Hunan University of Technology, Zhuzhou 412007, China) |
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Abstract In order to solve the dynamic model of milling process set up using regenerative chatter theory, a new
semi-analytical approach based on three-order Runge-Kutta method was proposed in the paper. Firstly, the dynamic differential
equation was represented by the form of the state space equation. Secondly, the state transition matrix was deduced
using the three-order Runge-Kutta method. Lastly, the stability under current cutting condition was determined according
to the Floquet theory, and as a result, the stability lobe diagram (SLD) of milling process can be obtained. It was shown that
the proposed semi-analytical approach based on three-order Runge-Kutta method has higher convergence rate and computation
accuracy, when compared with the simulation results of the classical semi-discretization method.
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2016, 
