Mode-Coupled Regenerative Machine Tool Vibrations

2005 ◽  
pp. 129-151 ◽  
Author(s):  
T. Kalmár-Nagy ◽  
F.C. Moon
Keyword(s):  
Machine Tool ◽  
Tool Vibrations

scholarly journals Influence of machine tool vibrations on geometric specifications of balls

2021 ◽  
Vol 55 ◽  
pp. 568-575
Author(s):  
Michal Richtarik ◽  
Martin Gavlas ◽  
Mário Drbúl ◽  
Andrej Czán ◽  
Milan Sága
Keyword(s):  
Machine Tool ◽  
Tool Vibrations

scholarly journals Targeted Energy Transfers for Suppressing Regenerative Machine Tool Vibrations

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Amir Nankali ◽  
Young S. Lee ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Machine Tool ◽  
Passive Control ◽  
Stability Margin ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Transition Curve ◽  
Hopf Bifurcation Point ◽  
Energy Transfers ◽  
Tool Vibrations ◽  
Nonlinear Energy

We study the dynamics of targeted energy transfers in suppressing chatter instability in a single-degree-of-freedom (SDOF) machine tool system. The nonlinear regenerative (time-delayed) cutting force is a main source of machine tool vibrations (chatter). We introduce an ungrounded nonlinear energy sink (NES) coupled to the tool, by which energy transfers from the tool to the NES and efficient dissipation can be realized during chatter. Studying variations of a transition curve with respect to the NES parameters, we analytically show that the location of the Hopf bifurcation point is influenced only by the NES mass and damping coefficient. We demonstrate that application of a well-designed NES renders the subcritical limit cycle oscillations (LCOs) into supercritical ones, followed by Neimark–Sacker and saddle-node bifurcations, which help to increase the stability margin in machining. Numerical and asymptotic bifurcation analyses are performed and three suppression mechanisms are identified. The asymptotic stability analysis is performed to study the domains of attraction for these suppression mechanisms which exhibit good agreement with the bifurcations sets obtained from the numerical continuation methods. The results will help to design nonlinear energy sinks for passive control of regenerative instabilities in machining.

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 Computational and experimental analysis of machine tool vibrations in micro-milling

2017 ◽  
Vol 112 ◽  
pp. 01022 ◽  
Author(s):  
Dimitrios Sagris ◽  
Constantine Davids ◽  
Evlampia Stergianni ◽  
Christos Tsiafis ◽  
Ioannis Tsiafis
Keyword(s):  
Machine Tool ◽  
Experimental Analysis ◽  
Micro Milling ◽  
Tool Vibrations

EXPERIMENTAL CHARACTERIZATION OF QUASIPERIODICITY AND CHAOS IN A MECHANICAL SYSTEM WITH DELAY

1999 ◽  
Vol 09 (01) ◽  
pp. 49-65 ◽  
Author(s):  
M. A. JOHNSON ◽  
F. C. MOON
Keyword(s):  
Machine Tool ◽  
Mechanical System ◽  
Experimental Technique ◽  
Poincaré Sections ◽  
Chaotic Vibrations ◽  
Tool Vibrations ◽  
Delay Differential ◽  
Poincare Sections ◽  
Equation With Delay

We present an electro-mechanical system with finite delay whose construction was motivated by delay differential equations used to describe machine tool vibrations [Johnson, 1996; Moon & Johnson, 1998]. We show that the electro-mechanical system is capable of exhibiting periodic, quasiperiodic and chaotic vibrations. We provide a novel experimental technique for creating real-time Poincaré sections for systems with delay. This experimental technique was also applied to machine tool vibrations [Johnson, 1996]. Experimental Poincaré sections clearly show the existence of tori, and reveal the tori bifurcation sequence which leads to chaotic vibrations. The electro-mechanical system can be modeled by a single second-order differential equation with delay and a cubic nonlinearity. We show that the simple mathematical model fully replicates the bifurcation sequence seen in the electro-mechanical system.

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