Nonlinear Delay Equations With Fluctuating Delay: Application to Regenerative Chatter

2002 ◽  
Author(s):  
Ali Demir ◽  
N. Sri Namachchivaya ◽  
W. F. Langford
Keyword(s):  
Differential Equations ◽  
Machine Tool ◽  
Periodic Solutions ◽  
Stability Boundary ◽  
Spindle Speed ◽  
Regenerative Chatter ◽  
Machine Tool Chatter ◽  
Tool Motion ◽  
Nonlinear Delay ◽  
Tool Chatter

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. We make use of Lyapunov-Schmidt Reduction method to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.

Machine tool chatter reduction via active structural control

1994 ◽  
Author(s):  
Stephen D. O'Regan ◽  
J. Miesner ◽  
R. Aiken ◽  
A. Packman ◽  
Erdal A. Unver ◽  
...  
Keyword(s):  
Machine Tool ◽  
Structural Control ◽  
Active Structural Control ◽  
Machine Tool Chatter ◽  
Tool Chatter

scholarly journals Prediction of Self-excited Machine Tool Chatter

1977 ◽  
Vol 43 (506) ◽  
pp. 205-210 ◽  
Author(s):  
Toshimichi MORIWAKI ◽  
Tetsuzo HARIGAI ◽  
Kazuaki IWATA
Keyword(s):  
Machine Tool ◽  
Machine Tool Chatter ◽  
Tool Chatter

scholarly journals Machine tool chatter test and analysis

2019 ◽  
Vol 2019 (23) ◽  
pp. 8880-8883
Author(s):  
Linxi Li ◽  
Jianlin Zhong ◽  
Hongjun Wang ◽  
Yangjie Gao
Keyword(s):  
Machine Tool ◽  
Machine Tool Chatter ◽  
Tool Chatter

Machine tool chatter monitoring by coherence analysis

1992 ◽  
Vol 30 (8) ◽  
pp. 1901-1924 ◽  
Author(s):  
W. DONG ◽  
Y. H. JOE AU ◽  
A. MARDAPITTAS
Keyword(s):  
Machine Tool ◽  
Coherence Analysis ◽  
Machine Tool Chatter ◽  
Tool Chatter

Application of Self-Excited Machine-Tool Chatter Theory: Contribution to Machine-Tool Chatter Research—4

1965 ◽  
Vol 87 (4) ◽  
pp. 471-479 ◽  
Author(s):  
J. R. Lemon ◽  
P. C. Ackermann
Keyword(s):  
Machine Tool ◽  
Stability Region ◽  
High Stability ◽  
Closed Loop ◽  
Measured Data ◽  
Cutting Conditions ◽  
Machine Tool Chatter ◽  
The Subject ◽  
Cutting Speeds ◽  
Tool Chatter

This paper is one of a series of four being presented simultaneously on the subject of self-excited machine-tool chatter. It deals primarily with the applications of the closed-loop chatter theory to several actual machine-tool systems. In all cases the predicted chatter performance is compared with measured data and the correlation discussed. The predicted and measured onset of chatter compare reasonably well, in each example, when the complexities of the test setups are considered. The most serious discrepancy between experiments and the simplified chatter theory is the high-stability region at low cutting speeds. Dynamic specifications to assure the chatter-free performance of a machine tool for a given set of cutting conditions are discussed. The difficulties in arriving at such specifications are also pointed out.

Cutting Dynamics in Machine Tool Chatter: Contribution to Machine-Tool Chatter Research—3

1965 ◽  
Vol 87 (4) ◽  
pp. 464-470 ◽  
Author(s):  
R. L. Kegg
Keyword(s):  
Machine Tool ◽  
Metal Cutting ◽  
Chip Thickness ◽  
Cutting Process ◽  
Dynamic Force ◽  
General Technique ◽  
Cross Sensitivity ◽  
Machine Tool Chatter ◽  
Measuring Techniques ◽  
Tool Chatter

This is one of four papers presented simultaneously on the general subject of chatter. This work is concerned with finding a representation of the dynamic metal-cutting process which is suitable for use in a linear closed-loop theory of stability of the system composed of the machine tool structure, the cutting process, and their means of combining. Measuring techniques for experimentally determining this behavior are discussed and some problems in the dynamic measurement of forces are explored. It is found that it is not at all sufficient to simply build a dynamometer whose lowest natural frequency is well beyond the range of interest. It is also shown that dynamic cross sensitivity can far exceed static cross sensitivity so that a more general technique for data correction developed in the present work must be used to calibrate dynamic force data. Results obtained to date with an oscillating tool and a flat uncut surface show that some phase, increasing with frequency, is always present between the dynamic cutting forces and the oscillatory uncut chip thickness. This phase is different for the two components of the resultant cutting force. It is felt that two mechanisms, both associated with the tool clearance flank, can explain most of the dynamic cutting effects found in testing.

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