Comparison of the full-discretization methods for milling stability analysis by using different high-order polynomials to interpolate both state term and delayed term

2020 ◽  
Vol 108 (1-2) ◽  
pp. 571-588 ◽  
Author(s):  
Zhenghu Yan ◽  
Changfu Zhang ◽  
Xinguang Jiang ◽  
Baoji Ma
Keyword(s):  
Stability Analysis ◽  
High Order ◽  
Full Discretization ◽  
Milling Stability ◽  
Discretization Methods

scholarly journals Stability Analysis of Multi-Discrete Delay Milling with Helix Effects Using a General Order Full-Discretization Method Updated with a Generalized Integral Quadrature

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1003
Author(s):  
Chigbogu Ozoegwu ◽  
Peter Eberhard
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
High Order ◽  
Discretization Method ◽  
High Order Methods ◽  
Full Discretization ◽  
Low Speed ◽  
Automated Algorithm ◽  
Stability Lobes ◽  
General Order

A tensor-based general order full-discretization method is enhanced with the capacity to handle multiple discrete delays and helix effects leading to a unique automated algorithm in the stability analysis of milling process chatter. The automated algorithm is then exploited in investigating the effects of interpolation order of chatter states and helix-induced terms on the convergence of milling stability lobes. The enhanced capacity to handle the distributed helix effects is based on a general order formulation of the Newton-Coates integral quadrature method. Application to benchmark milling models showed that high order methods are necessary for convergence of the low speed domain of stability lobes while all the numerically stable orders converge in the high speed domain where the ultra-high order methods are prone to numerical instability. Also, composite numerical integration of the helix-induced integrand beyond the usual zero-th order method leads to higher accuracy of stability lobes especially in the low speed domain.

scholarly journals High-order semi-discretization methods for stability analysis in milling based on precise integration

2021 ◽  
Author(s):  
Zhenghu Yan ◽  
Changfu Zhang ◽  
Jianli Jia ◽  
Baoji Ma ◽  
Xinguang Jiang ◽  
...  
Keyword(s):  
Stability Analysis ◽  
High Order ◽  
Precise Integration ◽  
Discretization Methods

Stability analysis of high order neural networks with proportional delays

2020 ◽  
Vol 372 ◽  
pp. 33-39 ◽  
Author(s):  
Wenqi Shen ◽  
Xian Zhang ◽  
Yantao Wang
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
High Order ◽  
Proportional Delays
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