Chatter stability analysis for milling with single-delay and multi-delay using combined high-order full-discretization method

2020 ◽  
Vol 111 (5-6) ◽  
pp. 1401-1413
Author(s):  
Zhenghu Yan ◽  
Changfu Zhang ◽  
Xingguang Jiang ◽  
Baoji Ma
Keyword(s):  
Stability Analysis ◽  
High Order ◽  
Discretization Method ◽  
Chatter Stability ◽  
Full Discretization

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 An Efficient Third-Order Full-Discretization Method for Prediction of Regenerative Chatter Stability in Milling

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Chao Huang ◽  
Wen-An Yang ◽  
Xulin Cai ◽  
Weichao Liu ◽  
YouPeng You
Keyword(s):  
Metal Removal ◽  
Removal Rate ◽  
Discretization Method ◽  
Chatter Stability ◽  
Computationally Efficient ◽  
Third Order ◽  
Regenerative Chatter ◽  
Full Discretization ◽  
Milling Operations ◽  
Comparison Results

The prediction of regenerative chatter stability has long been recognized as an important issue of concern in the field of machining community because it limits metal removal rate below the machine’s capacity and hence reduces the productivity of the machine. Various full-discretization methods have been designed for predicting regenerative chatter stability. The main problem of such methods is that they can predict the regenerative chatter stability but do not efficiently determine stability lobe diagrams (SLDs). Using third-order Newton interpolation and third-order Hermite interpolation techniques, this study proposes a straightforward and effective third-order full-discretization method (called NI-HI-3rdFDM) to predict the regenerative chatter stability in milling operations. Experimental results using simulation show that the proposed NI-HI-3rdFDM can not only efficiently predict the regenerative chatter stability but also accurately identify the SLD. The comparison results also indicate that the proposed NI-HI-3rdFDM is very much more accurate than that of other existing methods for predicting the regenerative chatter stability in milling operations. A demonstrative experimental verification is provided to illustrate the usage of the proposed NI-HI-3rdFDM to regenerative chatter stability prediction. The feature of accurate computing makes the proposed NI-HI-3rdFDM more adaptable to a dynamic milling scenario, in which a computationally efficient and accurate chatter stability method is required.

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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