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.

On Chatter Vibrations of Machine Tool or Work Due to Regenerative Effect and Time Lag

1974 ◽  
Vol 96 (4) ◽  
pp. 1337-1346 ◽  
Author(s):  
H. O¯ta ◽  
K. Ko¯no
Keyword(s):  
Machine Tool ◽  
Thrust Force ◽  
Time Lag ◽  
Chip Thickness ◽  
Regenerative Effect ◽  
Equivalent Time ◽  
Chatter Vibrations ◽  
Cutting Effect ◽  
Overlap Factor ◽  
Effect Time

This paper treats the most general chatter vibrations of machine tool or work originating by regenerative effect having an arbitrary overlap factor, by wave cutting effect (time lag of thrust force upon chip thickness fluctuation as varied by relative motion between tool and work), and by wave removing effect (time lead of shearing area upon chip thickness fluctuation through a previous cut). The new concept of “equivalent time lag of thrust force,” containing both any overlap factor and time lag of thrust force, is introduced, and by it, the cutting limit of absolute stability free from chatter can be obtained very easily. Moreover, this concept is verified to be very effective as a stability criterion for regenerative chatter with an unsymmetrical boring bar.

Regenerative Chatter Vibration Occurring in Turning With Different Side Cutting Edge Angles

1995 ◽  
Vol 117 (4) ◽  
pp. 551-558 ◽  
Author(s):  
E. Marui ◽  
M. Hashimoto ◽  
S. Kato
Keyword(s):  
Energy Supply ◽  
Cutting Tool ◽  
Cutting Tools ◽  
Cutting Edge ◽  
The Other ◽  
Chatter Vibration ◽  
Regenerative Chatter ◽  
Edge Angle ◽  
Regenerative Effect ◽  
Two Factors

This paper deals with the regenerative chatter vibration occurring in cutting tools with different side cutting edge angles. The occurrence of regenerative chatter vibration of the cutting tool is influenced by two factors, which are closely related to the vibratory energy supply or consumption. One factor is the interference effect between the tool flank and the workpiece. Of course, this factor exists in the primary chatter, too. The other is the regenerative effect. The influence of both factors on the regenerative chatter vibration of cutting tools with different side cutting edge angles is examined experimentally. The vibratory energy supply is simulated, considering the dynamic cutting process. As a result, the property of the regenerative chatter vibration and the influence of the side cutting edge angle on the regenerative chatter vibration are clarified.

Period-1 Motions in a Periodically Forced, Nonlinear, Machine-Tool System

2019 ◽  
Author(s):  
Siyuan Xing ◽  
Albert C. J. Luo
Keyword(s):  
Machine Tool ◽  
Numerical Simulations ◽  
Analytical Method ◽  
Degree Of Freedom ◽  
Eigenvalue Analysis ◽  
Tool Vibrations ◽  
Stability And Bifurcations ◽  
The Stability ◽  
Two Degree Of Freedom

Abstract In this paper, period-1 motions in a two-degree-of-freedom, nonlinear, machine-tool system are investigated by a semi-analytical method. The stability and bifurcations of the period-1 motions are discussed from the eigenvalue analysis. A condition is presented for the tool-and-workpiece separation in period-1 motions. Machine-tool vibrations varying with displacement disturbance from a workpiece are discussed. Numerical simulations of period-1 motions are completed from analytical predictions.

scholarly journals Characterization of Giant Magnetostrictive Materials Using Three Complex Material Parameters by Particle Swarm Optimization

Micromachines ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1416
Author(s):  
Yukai Chen ◽  
Xin Yang ◽  
Mingzhi Yang ◽  
Yanfei Wei ◽  
Haobin Zheng
Keyword(s):  
Classical Method ◽  
Lumped Parameter Model ◽  
Complex Material ◽  
Material Parameters ◽  
Magnetostrictive Materials ◽  
Lumped Parameter ◽  
Giant Magnetostrictive Materials ◽  
Power Transducer ◽  
And Performance ◽  
The Stability

Complex material parameters that can represent the losses of giant magnetostrictive materials (GMMs) are the key parameters for high-power transducer design and performance analysis. Since the GMMs work under pre-stress conditions and their performance is highly sensitive to pre-stress, the complex parameters of a GMM are preferably characterized in a specific pre-stress condition. In this study, an optimized characterization method for GMMs is proposed using three complex material parameters. Firstly, a lumped parameter model is improved for a longitudinal transducer by incorporating three material losses. Then, the structural damping and contact damping are experimentally measured and applied to confine the parametric variance ranges. Using the improved lumped parameter model, the real parts of the three key material parameters are characterized by fitting the experimental impedance data while the imaginary parts are separately extracted by the phase data. The global sensitivity analysis that accounts for the interaction effects of the multiple parameter variances shows that the proposed method outperforms the classical method as the sensitivities of all the six key parameters to both impedance and phase fitness functions are all high, which implies that the extracted material complex parameters are credible. In addition, the stability and credibility of the proposed parameter characterization is further corroborated by the results of ten random characterizations.

Dynamic Response of a Cam-Actuated Mechanism With Pneumatic Coupling

1977 ◽  
Vol 99 (3) ◽  
pp. 598-603 ◽  
Author(s):  
F. Y. Chen
Keyword(s):  
Dynamic Response ◽  
Dynamic Characteristics ◽  
Lumped Parameter Model ◽  
System Equation ◽  
Variation Of Parameters ◽  
Lumped Parameter ◽  
Cam Follower ◽  
The Stability

The dynamic characteristics of a cam-actuated system whose follower mass is coupled with a nonlinear pneumatic mechanism of hysteretic type are investigated using a lumped-parameter model. The dynamic response of the cam follower is obtained from the solution of the formulated system equation by the Krylov-Bogoliubov method of variation of parameters. The stability of the system is also investigated.

scholarly journals Disturbance of the Regenerative Effect by Use of Milling Tools Modified with Asymmetric Dynamic Properties

2020 ◽  
Vol 4 (3) ◽  
pp. 67
Author(s):  
Jonas Baumann ◽  
Andreas Wirtz ◽  
Tobias Siebrecht ◽  
Dirk Biermann
Keyword(s):  
Dynamic Properties ◽  
Constant Width ◽  
Chip Thickness ◽  
Stability Limit ◽  
Dynamic Compliance ◽  
Depth Of Cut ◽  
Regenerative Effect ◽  
The Stability ◽  
Tool Shank ◽  
Milling Tools

Milling processes are often limited by self-excited vibrations of the tool or workpiece, generated by the regenerative effect, especially when using long cantilevered tools or machining thin-walled workpieces. The regenerative effect arises from a periodic modulation of the uncut chip thickness within the frequencies of the eigenmodes, which results in a critical excitation in the consecutive cuts or tooth engagements. This paper presents a new approach for disturbing the regenerative effect by using milling tools which are modified with asymmetric dynamic properties. A four-fluted milling tool was modified with parallel slots in the tool shank in order to establish asymmetric dynamic characteristics or different eigenfrequencies for consecutive tooth engagements, respectively. Measurements of the frequency response functions at the tool tip showed a decrease in the eigenfrequencies as well as an increase in the dynamic compliance in the direction of the grooves. Milling experiments with a constant width of cut and constantly increasing axial depth of cut indicated a significant increase in the stability limit for the specific preparations of up to 69%.

On the Effects of Turning Process Asymmetry on Process Dynamics

1989 ◽  
Vol 111 (3) ◽  
pp. 193-198 ◽  
Author(s):  
B. E. Klamecki
Keyword(s):  
Cutting Tool ◽  
Lumped Parameter Model ◽  
Tool Support ◽  
Turning Process ◽  
Complex Dynamic ◽  
Periodic Forcing ◽  
Process Dynamics ◽  
Lumped Parameter ◽  
Tool Edge ◽  
Edge Displacement

The implications of a fundamental asymmetry in the lathe turning process are considered. The asymmetry is the directional dependence of system stiffness that exists at the cutting tool edge. Depending on tool edge displacement, the system stiffness is determined by the workpiece stiffness or the relatively much stiffer tool support structure. A one degree-of-freedom, lumped parameter model with nonlinear stiffness is constructed and subjected to a periodic forcing. Time and frequency domain analyses show that extremely complex dynamic behavior can occur in this simple system.

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.

EFFECT OF SURFACE LAYER ON ELECTROMECHANICAL STABILITY OF TWEEZERS AND CANTILEVERS FABRICATED FROM CONDUCTIVE CYLINDRICAL NANOWIRES

2016 ◽  
Vol 23 (02) ◽  
pp. 1550101 ◽  
Author(s):  
MARYAM KEIVANI ◽  
ALI KOOCHI ◽  
HAMID M. SEDIGHI ◽  
MOHAMADREZA ABADYAN ◽  
AMIN FARROKHABADI ◽  
...  
Keyword(s):  
Surface Layer ◽  
Homotopy Perturbation Method ◽  
Differential Quadrature Method ◽  
Surface Elasticity ◽  
Lumped Parameter Model ◽  
Governing Equations ◽  
Lumped Parameter ◽  
The Stability ◽  
The Impact ◽  
Effect Of Surface

Herein, the impact of surface layer on the stability of nanoscale tweezers and cantilevers fabricated from nanowires with cylindrical cross section is studied. A modified continuum based on the Gurtin–Murdoch surface elasticity is applied for incorporating the presence of surface layer. Considering the cylindrical geometry of the nanowire, the presence of the Coulomb attraction and dispersion forces are incorporated in the derived formulations. Three different approaches, i.e. numerical differential quadrature method (DQM), an approximated homotopy perturbation method (HPM) and developing lumped parameter model (LPM) have been employed to solve the governing equations. The impact of surface layer on the instability of the system is demonstrated.

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.

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