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.

Statistical Analysis of the Dynamic Cutting Coefficients and Machine Tool Stability

1993 ◽  
Vol 115 (2) ◽  
pp. 205-215 ◽  
Author(s):  
M. A. El Baradie
Keyword(s):  
Machine Tool ◽  
Confidence Level ◽  
Cutting Process ◽  
Structure Dynamics ◽  
Cutting Coefficients ◽  
Statistical Variations ◽  
Machine Tool Structure ◽  
Machine Tool Chatter ◽  
Machine Structure ◽  
Tool Chatter

Machine tool chatter is a statistical phenomenon since it is dependent on the interaction of two statistical quantities, these being the dynamic characteristics of the machine tool structure and the transfer function of the cutting process. In this paper, a generalized statistical theory of machine tool chatter has been developed. This takes into consideration the scatter of the dynamic data of the machine structure and/or that of the cutting process. The dynamics of the cutting process have been represented by a mathematical model which derives the cutting coefficients from steady state cutting data, based on a nondimensional analysis of the cutting process. The dynamics of the machine tool structure and the cutting process, being the input data to the theory, were determined experimentally. The predicted stability charts were plotted to take into consideration the scatter in the machine structure dynamics and/or the cutting process. At the threshold of stability, the statistical variations due to the dynamic cutting coefficients amount to ±29.5 percent at 99 percent confidence level, while the statistical variations due to the structure dynamics amount to ±4.5 percent only, at the same confidence level. Therefore, the threshold of stability can be specified only in terms of mean values with confidence limits.

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.

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

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

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.

scholarly journals On the Essential Instabilities Caused by Fractional-Order Transfer Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Farshad Merrikh-Bayat ◽  
Masoud Karimi-Ghartemani
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Characteristic Equation ◽  
Stability Condition ◽  
Transfer Functions ◽  
Branch Points ◽  
The Stability ◽  
Unstable Branch

The exact stability condition for certain class of fractional-order (multivalued) transfer functions is presented. Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities. It is shown that a multivalued transfer function can behave unstably because of the numerator term while it has no unstable poles. So, in this case, not only the characteristic equation but the numerator term is of significant importance. In this manner, a family of unstable fractional-order transfer functions is introduced which exhibit essential instabilities, that is, those which cannot be removed by feedback. Two illustrative examples are presented; the transfer function of which has no unstable poles but the instability occurred because of the unstable branch points of the numerator term. The effect of unstable branch points is studied and simulations are presented.

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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