Stability of Random Vibrations With Special Reference to Machine Tool Chatter

1975 ◽  
Vol 97 (1) ◽  
pp. 216-219 ◽  
Author(s):  
S. M. Pandit ◽  
T. L. Subramanian ◽  
S. M. Wu
Keyword(s):  
Time Series ◽  
Machine Tool ◽  
Cutting Tool ◽  
Time Series Model ◽  
Random Vibrations ◽  
Vibrational Signal ◽  
Vibration Data ◽  
Machine Tool Chatter ◽  
The Stability ◽  
Tool Chatter

Static and dynamic stabilities of self-excited random vibrations are investigated in terms of the differential equation and time series model for the vibrational signal. Various instabilities are demarcated in the parameter space of the time series model, so that the stability of random vibrations can be ascertained by locating the parameters obtained from the vibration data. These results are applied to machine tool chatter by analyzing tool point vibrations in a turning operation under different degrees of chatter. This analysis substantiates the theoretical investigation, which is further confirmed by resonance curves obtained for the workpiece and cutting tool.

Structural Dynamics in Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research—2

1965 ◽  
Vol 87 (4) ◽  
pp. 455-463 ◽  
Author(s):  
G. W. Long ◽  
J. R. Lemon
Keyword(s):  
Transfer Function ◽  
Machine Tool ◽  
Stability Theory ◽  
Transfer Functions ◽  
Phase Relationship ◽  
Structure Response ◽  
Machine Tool Structure ◽  
Machine Tool Chatter ◽  
The Stability ◽  
Tool Chatter

This paper is one of four being presented simultaneously on the subject of self-excited machine-tool chatter. Transfer-function theory is applied to obtain a representation of the dynamics of a machine-tool structure. The stability theory developed to investigate self-excited machine-tool chatter requires such a representation. Transfer functions of simple symmetric systems are derived and compared with measurements. When measured frequency-response data of more complex structures are obtained, it provides a very convenient means of data interpretation and enables one to develop the significant equations of motion that define the structure response throughout a specified frequency range. The transfer function presents the phase relationship between structure response and exciting force at all frequencies in the specified range. This knowledge of phase is essential to the proper application of the stability theory and explains the “digging-in” type of instability that is often encountered in machine-tool operation. The instrumentation used throughout these tests is discussed and evaluated. The concept of developing dynamic expressions for machine-tool components and joining these together through properly defined boundary conditions, thereby building up the transfer function of the complete machine-tool structure, is suggested as an area for further study.

Modeling Machine Tool Chatter by Time Series

1975 ◽  
Vol 97 (1) ◽  
pp. 211-215 ◽  
Author(s):  
S. M. Pandit ◽  
T. L. Subramanian ◽  
S. M. Wu
Keyword(s):  
Time Series ◽  
Machine Tool ◽  
Random Vibration ◽  
Vibration Signals ◽  
Forcing Function ◽  
Machine Tool Chatter ◽  
Random Disturbances ◽  
Noise Forcing ◽  
Modeling Data ◽  
Tool Chatter

Machine tool chatter is formulated as self-excited random vibration with white noise forcing function. The formulation takes into account the unknown factors and random disturbances present in the cutting process when chatter occurs. Based on this formulation, a procedure for modeling chatter using the time series of sampled observations on vibration signals is developed. Feasibility of this procedure is established by modeling data obtained from a turning operation under conditions of severe chatter.

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

Improvement of forecasting robustness of time series model for thermal error on CNC machine tool

2016 ◽  
Vol 24 (10) ◽  
pp. 2480-2489 ◽  
Author(s):  
苗恩铭 MIAO En-ming ◽  
刘 义 LIU Yi ◽  
董云飞 DONG Yun-fei ◽  
陈维康 CHEN Wei-kang
Keyword(s):  
Time Series ◽  
Machine Tool ◽  
Thermal Error ◽  
Time Series Model ◽  
Cnc Machine Tool ◽  
Cnc Machine

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

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 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
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