Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations

By T. Kalmár-Nagy, Gábor Stépán, F. Moon. 2001

268 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Materials Chemistry, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d953aaa26c30eac7df83ec7c783249a74c31fa51

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Ali H. Nayfeh
2. Sun Yi
3. David Gilsinn
4. Zoltan Dombovari
5. Gábor Stépán
6. Yusuf Altintas

In Materials Chemistry

1. Sun Yi
2. Ali H. Nayfeh
3. David Gilsinn

In Numerical Analysis

1. Sun Yi
2. Ali H. Nayfeh
3. David Gilsinn
4. Zoltan Dombovari
5. Yusuf Altintas
6. Gábor Stépán
7. Brian P. Mann
8. Qizhi Xie

Citations in the corpus

• The effect of serration on mechanics and stability of milling cutters (2010, background): “The effect of nonlinearities can be further studied analytically [9,10] or using continuation algorithms such as [11–13].”
• Estimates of the bistable region in metal cutting (2008, unknown): “A rigorous analytical investigation of the nature of the loss of stability of stationary cutting was performed only much later only by means of the Centre Manifold reduction and Normal Form calculations ( Stepan 1997; Kalmár-Nagy et al. 2001).”
• Time-Delay Systems: Analysis and Control Using the Lambert W Function (2010, methodology): “3.1, can be expressed as (Kalmar-Nagy et al., 2001) ẍ(t) + 2ζωnẋ(t) + ( ω2n + kc m ) x(t) − kc m x(t − T ) = kc 8f0m ( (x(t) − x(t − T ))2 − 5 12f0 (x(t) − x(t − T ))3 ) , (3.1) wherex(t) is the general coordinate of tool edge position and the delay, T = 2π/Ω, is the time period for one…”
• Estimating Critical Hopf Bifurcation Parameters for a Second-Order Delay Differential Equation with Application to Machine Tool Chatter (2002, methodology): “The results obtained for the model considered in this paper have also been obtained by Kalmar-Nagy and co-workers [12, 18, 26 , 27].”
• Calculating Centre Manifolds for Delay Differential Equations Using Maple (2009, unknown): “…construction by hand, e.g., Faria and Magalhães (1995a,b); Gilsinn (2002); Guo and Huang (2003); Guo et al. (2004); Guo (2005); Jiang et al. (2006); Kalmár-Nagy et al. (1999, 2001); Liu and Yuan (2005); Nayfeh (2008); Orosz and Stépán (2004, 2006); Sri Namachchivaya and van Roessel (2003);…”
• Order reduction of retarded nonlinear systems – the method of multiple scales versus center-manifold reduction (2008, methodology): “Then, we represent Equation (82) as an operator differential equation. The result is [ 23 , 24]”