A Graphical Analysis of Regenerative Machine Tool Instability

1962 ◽  
Vol 84 (1) ◽  
pp. 103-111 ◽  
Author(s):  
J. P. Gurney ◽  
S. A. Tobias
Keyword(s):  
Machine Tool ◽  
Penetration Rate ◽  
Cutting Speed ◽  
Chip Thickness ◽  
Graphical Analysis ◽  
Mode Interaction ◽  
Thickness Variation ◽  
Machine Tool Structure ◽  
The Stability ◽  
Radial Drilling

A graphical method for the investigation of regenerative machine tool chatter is presented. The method is based on the harmonic response locus of the machine tool structure and allows the determination of the stable and unstable cutting speed ranges. The chip thickness variation effect as well as the penetration rate effect are taken into consideration. The method is illustrated by a number of examples relating to drilling or spot facing chatter arising on a radial drilling machine. The effects of mode interaction and of the penetration rate on the stability and on the variation of the chatter frequency are discussed. A critical assessment of the method is presented, in comparison with other methods available.

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.

An Analysis and Modeling of the Dynamic Stability of the Cutting Process Against Self-Excited Vibration

2020 ◽  
Vol 22 (4) ◽  
pp. 1287-1300
Author(s):  
A. Motallebia ◽  
A. Doniavi ◽  
Y. Sahebi
Keyword(s):  
Machine Tool ◽  
Removal Rate ◽  
Dimensional Accuracy ◽  
Modal Testing ◽  
Cutting Process ◽  
Work Piece ◽  
Stability Diagrams ◽  
Machine Tool Structure ◽  
Excited Vibration ◽  
The Stability

AbstractChatter is a self-excited vibration which depends on several parameters such as the dynamic characteristics of the machine tool structure, the material of the work piece, the material removal rate, and the geometry of tools. Chatter has an undesirable effect on dimensional accuracy, smoothness of the work piece surface, and the lifetime of tools and the machine tool. Thus, it is useful to understand this phenomenon in order to improve the economic aspect of machining. In the present article, first the theoretical study and mathematical modeling of chatter in the cutting process were carried out, and then by performing modal testing on a milling machine and drawing chatter stability diagrams, we determined the stability regions of the machine tool operation and recognized that witch parameter has a most important effect on chatter.

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.

In-Process Analysis of Machine Tool Structure Dynamics and Prediction of Machining Chatter

1976 ◽  
Vol 98 (1) ◽  
pp. 301-305 ◽  
Author(s):  
Toshimichi Moriwaki ◽  
Kazuaki Iwata
Keyword(s):  
Machine Tool ◽  
Structural Model ◽  
Process Analysis ◽  
Stability Limit ◽  
Shear Plane ◽  
Experimental Investigations ◽  
Machine Tool Structure ◽  
The Stability ◽  
Cutting Experiments ◽  
Theoretical Analyses

Theoretical and experimental investigations were carried out to identify the dynamics of a machine tool structure during cutting to predict the borderline of stability against the self-excited regenerative chatter. The validity of theoretical analyses in calculating the stability limit for conventional machining was confirmed by cutting experiments using a structural model. The model dynamics were identified during cutting under stable (non-chattering) cutting conditions by applying a technique of system identification based on time series analysis of the small random cutting force variations measured by a specially designed tool dynamometer and the corresponding minute vibrations. The experimentally obtained borderline of stability had a fairly good agreement with that calculated from the identified dynamics of the structure and the cutting dynamics, the latter being estimated from the static cutting data based on the so-called shear plane model.

scholarly journals An Analysis and Modeling of the Dynamic Stability of the Cutting Process Against Self-Excited Vibration

2019 ◽  
Vol 23 (1) ◽  
pp. 28-35
Author(s):  
A. Motallebia ◽  
A. Doniavi ◽  
Y. Sahebi
Keyword(s):  
Machine Tool ◽  
Removal Rate ◽  
Dimensional Accuracy ◽  
Modal Testing ◽  
Cutting Process ◽  
Work Piece ◽  
Stability Diagrams ◽  
Machine Tool Structure ◽  
Excited Vibration ◽  
The Stability

Abstract Chatter is a self-excited vibration that depends on several parameters such as the dynamic characteristics of a machine tool structure, the material of work piece, the material removal rate, and the geometry of tools. Chatter has an undesirable effect on dimensional accuracy, smoothness of work piece surface, lifetime of tools and machine tools. Thus, it is useful to understand this phenomenon in order to improve the economic aspect of machining. In the present article, firstly, the theoretical study and mathematical modeling of chatter in the cutting process were carried out. Then, by performing modal testing on a milling machine and drawing chatter stability diagrams, we determined the stability regions of the machine tool operation and recognized the parameter that had the most important effect on chatter.

Mode-Coupled Regenerative Machine Tool Vibrations

2003 ◽  
Author(s):  
Tama´s Kalma´r-Nagy ◽  
Francis C. Moon
Keyword(s):  
Machine Tool ◽  
Cutting Tool ◽  
Chip Thickness ◽  
The Other ◽  
Lumped Parameter Model ◽  
Regenerative Effect ◽  
Lumped Parameter ◽  
Tool Vibrations ◽  
The Stability ◽  
Effect Time

In this paper a new 3 degree-of-freedom lumped-parameter model for machine tool vibrations is developed and analyzed. One mode is shown to be stable and decoupled from the other two, and thus the stability of the system can be determined by analyzing the remaining two modes. It is shown that this mode-coupled nonconservative cutting tool model including the regenerative effect (time delay) can produce an instability criteria that admits low-level or zero chip thickness chatter.

Improved Methods for the Prediction of Chatter in Turning, Part 3: A Generalized Linear Theory

1990 ◽  
Vol 112 (1) ◽  
pp. 28-35 ◽  
Author(s):  
I. E. Minis ◽  
E. B. Magrab ◽  
I. O. Pandelidis
Keyword(s):  
Machine Tool ◽  
Linear Theory ◽  
A Priori ◽  
Cutting Conditions ◽  
Depth Of Cut ◽  
Orthogonal Turning ◽  
Machine Tool Structure ◽  
Wide Range ◽  
Machining System ◽  
The Stability

The linear theory of chatter has been generalized to any machining configuration without a priori assumptions on either the direction of the cutting force or the modal directions of the machine tool structure. Furthermore, the effects of the tool’s orientation on the stability of the machining system are directly expressed by its closed loop characteristic equation. Using experimental measurements for the dynamics of both the machine tool structure and the cutting process obtained previously under actual cutting conditions, the proposed theory is applied to two cases of orthogonal turning. The resulting predictions of the critical depth of cut are in excellent agreement with the measurements of actual chatter for a wide range of cutting conditions.

A New Approach to the Analysis of Machine-Tool System Stability Under Working Conditions

1977 ◽  
Vol 99 (3) ◽  
pp. 585-590 ◽  
Author(s):  
F. A. Burney ◽  
S. M. Pandit ◽  
S. M. Wu
Keyword(s):  
Machine Tool ◽  
Working Conditions ◽  
Cutting Speed ◽  
Stochastic Approach ◽  
Static Stability ◽  
Face Milling ◽  
System Stability ◽  
New Approach ◽  
Characteristic Roots ◽  
The Stability

A new stochastic approach is developed in this paper for analyzing the machine-tool system stability under working conditions. Mathematical models are fitted to the relative longitudinal cutter-workpiece displacement data recorded under different cutting conditions during the face-milling operation on a milling machine. The stability of the system is judged from the characteristic roots of these models. The variation in stability is examined versus both the cutting speed and the feed, and good results are obtained. It is shown that not only the dynamic but also the static stability can be ascertained. Furthermore, the stability of subsystems can also be determined. The significance of these results is discussed with special reference to on-line chatter control. The analysis of vibration signals produced by similar but evenly and unevenly spaced face milling cutters is presented as a vindication of the new approach.

Chatter When Machining Aluminium Alloy: An Investigation Using a Structural Model

1968 ◽  
Vol 183 (1) ◽  
pp. 17-29 ◽  
Author(s):  
B. M. Johnson ◽  
C. Andrew
Keyword(s):  
Machine Tool ◽  
Aluminium Alloy ◽  
Orthogonal Cutting ◽  
Cutting Speed ◽  
Chip Thickness ◽  
Regenerative Chatter ◽  
Tool Vibration ◽  
Undeformed Chip Thickness ◽  
Machining Force ◽  
Conventional Tool

This paper describes an experimental investigation of machine tool chatter, in which the machine tool structure was replaced by a model, two-degrees-of-freedom structure with adjustable and consistent vibration characteristics. Primarily non-regenerative chatter, and secondarily regenerative chatter, were investigated for orthogonal cutting of an aluminium alloy with both conventional and restricted-contact cutting tools. The results are presented in the form of stability charts; these show the limiting widths of cut which can be machined without chatter, for given sets of machining and structural conditions. For non-regenerative chatter, it was found that the limiting width of cut: increases with a decrease in the structure's cross-receptance between the directions normal and tangential to the cut surface; increases with a decrease in cutting speed, but in a manner depending on the structural characteristics; is substantially independent of the mean undeformed chip thickness; increases by at least 25 per cent if contact is restricted to a length approximately equal to the undeformed chip thickness. For regenerative chatter it was found that the limiting width of cut: was approximately one half of the limiting width for non-regenerative chatter, for the otherwise similar machining and structural conditions investigated; increases with a decrease in cutting speed; increases by at least 25 per cent if contact is restricted to a length approximately equal to the undeformed chip thickness. Theoretical predictions of non-regenerative chatter with a conventional tool, based on independent measurements of machining force oscillations during tool vibration, agree well with experimental results. For regenerative chatter with a conventional tool, the theory was based on the superposition of machining force oscillations arising from tool vibration and from removing a wavy surface. The predictions were in error at low cutting speeds, indicating that the force oscillations are not superposable at this condition.

Suppression of Machine Tool Chatter Using Nonlinear Energy Sink

2011 ◽  
Author(s):  
Amir Nankali ◽  
Harsheeta Surampalli ◽  
Young S. Lee ◽  
Tama´s Kalma´r-Nagy
Keyword(s):  
Hopf Bifurcation ◽  
Machine Tool ◽  
Stability Boundary ◽  
Chip Thickness ◽  
Nonlinear Energy Sink ◽  
Mass Ratio ◽  
Energy Transfers ◽  
Energy Sink ◽  
The Stability ◽  
Nonlinear Energy

Suppression of regenerative instability in a single-degree-of-freedom (SDOF) machine tool model was studied by means of targeted energy transfers (TETs). The regenerative cutting force generates time-delay effects in the tool equation of motion, which retained the nonlinear terms up to the third order in this work. Then, an ungrounded nonlinear energy sink (NES) was coupled to the SDOF tool, by which biased energy transfers from the tool to the NES and efficient dissipation can be realized whenever regenerative effects invoke instability in the tool. Shifts of the stability boundary (i.e., Hopf bifurcation point) with respect to chip thickness were examined for various NES parameters. There seems to exist an optimal value of damping for a fixed mass ratio to shift the stability boundary for stably cutting more material off by increasing chip thickness; on the other hand, the larger the mass ratio becomes, the further the occurrence of Hopf bifurcation is delayed. The limit cycle oscillation (LCO) due to the regenerative instability appears as being subcritical, which can be (locally) eliminated or attenuated at a fixed rotational speed of a workpiece by the nonlinear modal interactions with an NES (i.e., by means of TETs). Three suppression mechanisms have been identified; that is, recurrent burstouts and suppressions, partial and complete suppressions of regenerative instabilities in a machine tool model. Each suppression mechanism was characterized numerically by time histories of displacements, and wavelet transforms and instantaneous energies. Furthermore, analytical study was performed by employing the complexification-averaging technique to yield a time-delayed slow-flow model. Finally, regenerative instability suppression in a more practical machine tool model was examined by considering contact-loss conditions.

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