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.

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.

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.

Cutting Process Stability of a Boring Bar With Active Dynamic Absorber

1991 ◽  
Author(s):  
Sanjiv G. Tewani ◽  
Keith E. Rouch ◽  
Bruce L. Walcott
Keyword(s):  
Machine Tool ◽  
Vibration Control ◽  
Active Vibration Control ◽  
Cutting Process ◽  
Process Stability ◽  
Boring Bar ◽  
Machine Tool Chatter ◽  
Active Vibration ◽  
Dynamic Absorber ◽  
Tool Chatter

Abstract Active vibration control has been considered in the past as a viable means of controlling machine tool chatter in the boring bar. Theoretically, it has been shown that the amplitude of vibrations of the machine tool can be substantially reduced using such an active control system. This paper looks into the cutting process stability of a boring bar equipped with an active vibration control device. An equivalent lumped mass model of the boring bar is considered. A cutting process model that considers the dynamic variation of shear and friction angle responsible for the self-excited vibration during machine tool chatter is considered. The model also considers the regeneration effect during the cutting process. Stability charts have been obtained in the form of maximum allowable width of cut as a function of cutting speed. A comparison of the stability boundaries of the boring bar with no control, with passive dynamic absorber and with active dynamic absorber is made. A substantial increase in the region of stable operation of the boring bar with active dynamic absorber is observed.

Theory of Self-Excited Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research—1

1965 ◽  
Vol 87 (4) ◽  
pp. 447-454 ◽  
Author(s):  
H. E. Merritt
Keyword(s):  
Machine Tool ◽  
Cutting Force ◽  
Degrees Of Freedom ◽  
Structural Characteristics ◽  
Dynamic Stiffness ◽  
Cutting Process ◽  
Design Stage ◽  
Structural Dynamic ◽  
Machine Tool Chatter ◽  
Tool Chatter

Self-excited chatter, an instability of the cutting process in combination with the machine structure, is a basic performance limitation of a machine tool. A theory is developed which permits calculation of borderlines of stability for a structure having n-degrees of freedom and assuming no dynamics in the cutting process. Harmonic solutions of the system characteristic equation are found using a special chart, and the resulting data are used to plot a stability chart. However, an infinite number of such stability charts exists for a given machine because the structure dynamics vary with cutting-force orientation. This fact makes a simpler index of chatter performance desirable. A simple stability criterion is proposed which states that the directional cutting stiffness must be less than one half the minimum directional dynamic stiffness of the structure for each force orientation to assure chatter-free performance at all spindle speeds. Thus chatter-free performance can be fundamentally identified with adequate structural dynamic stiffness for all cutting-force orientations. Such a broad requirement for dynamic stiffness is difficult to meet in the design stage since structural characteristics are not easily predicted and controlled. Machine testing with continual improvements in the structure to increase dynamic stiffness is currently the best way to combat 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

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.

Vibration Analysis of Radial Drilling Machine Structure Using Finite Element Method

2012 ◽  
Vol 472-475 ◽  
pp. 2717-2721 ◽  
Author(s):  
Rajiv Kumar ◽  
Mohinder Pal Garg ◽  
Rakesh C. Sharma
Keyword(s):  
Machine Tool ◽  
Natural Frequency ◽  
Mode Shapes ◽  
Drilling Machine ◽  
Element Analysis ◽  
Stiffness Matrices ◽  
Machine Tool Structure ◽  
Radial Drilling ◽  
Machine Structure

Manufacturing industries now a days have stringent expectation from the machine tools in terms of productivity as well as quality of products.Vibration plays an important role in determining the quality of product.If the pattern of vibration prevailing in the machine tool during cutting is known,then machine tool structure can be designed in such a way so that natural frequency of machine tool structure can be isolated from the forced frequency.So, this study is focused on finding the natural frequency and mode shapes of radial drilling machine structure.Finite element analysis has been done to find out the natural frequencies and mode shapes of radial drilling machine structure.Assembled mass and stiffness matrices are obtained for each element and solved by using inverse iteration technique.

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