A novel Chebyshev-Gauss pseudospectral method for accurate milling stability prediction

2021 ◽  
Author(s):  
Ding Chen ◽  
XiaoJian Zhang ◽  
Han Ding
Keyword(s):  
Pseudospectral Method ◽  
Stability Prediction ◽  
Milling Stability ◽  
Gauss Pseudospectral Method

scholarly journals Optimal Path-Following Guidance with Generalized Weighting Functions Based on Indirect Gauss Pseudospectral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Qi Chen ◽  
Xugang Wang ◽  
Jing Yang
Keyword(s):  
Degrees Of Freedom ◽  
Optimal Path ◽  
Pseudospectral Method ◽  
Path Following ◽  
Control Cost ◽  
Weighting Functions ◽  
Guidance Law ◽  
Computational Performance ◽  
Gauss Pseudospectral Method ◽  
Virtual Target

An indirect Gauss pseudospectral method based path-following guidance law is presented in this paper. A virtual target moving along the desired path with explicitly specified speed is introduced to formulate the guidance problem. By establishing a virtual target-fixed coordinate system, the path-following guidance is transformed into a terminal guidance with impact angle constraints, which is then solved by using indirect Gauss pseudospectral method. Meanwhile, the acceleration dynamics are modeled as the first-order lag to the command. Using the receding horizon technique a closed-loop guidance law, which considers generalized weighting functions (even discontinuous) of both the states and the control cost, is derived. The accuracy and effectiveness of the proposed guidance law are validated by numerical comparisons. A STM32 Nucleo board based on the ARM Cortex-M7 processor is used to evaluate the real-time computational performance of the proposed indirect Gauss pseudospectral method. Simulations for various types of desired paths are presented to show that the proposed guidance law has better performance when compared with the existing results for pure pursuit, a nonlinear guidance law, and trajectory shaping path-following guidance and provides more degrees of freedom in path-following guidance design applications.

Third-order updated full-discretization method for milling stability prediction

2017 ◽  
Vol 92 (5-8) ◽  
pp. 2299-2309 ◽  
Author(s):  
Zhenghu Yan ◽  
Xibin Wang ◽  
Zhibing Liu ◽  
Dongqian Wang ◽  
Li Jiao ◽  
...  
Keyword(s):  
Discretization Method ◽  
Stability Prediction ◽  
Third Order ◽  
Full Discretization ◽  
Milling Stability
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