Regenerative Cutting Dynamics for a Periodically Forced Machine-Tool System

2019 ◽  
Author(s):  
Siyuan Xing ◽  
Albert C. J. Luo
Keyword(s):  
Machine Tool ◽  
Numerical Simulations ◽  
Analytical Method ◽  
Orthogonal Cutting ◽  
Periodic Oscillation ◽  
Eigenvalue Analysis ◽  
Stable Period ◽  
Machine Tool Chatter ◽  
Stability And Bifurcations ◽  
Cutting System

Abstract In this paper, a nonlinear, regenerative, orthogonal cutting system with a weak periodic oscillation of workpiece is considered. Period-1 motions in such a system are studied through a semi-analytical method, and the corresponding stability and bifurcations of the period-1 motions are analyzed via the eigenvalue analysis. The vibration of machine-tool varying with excitation is studied, and excitation effects on machine-tool chatters are discussed. Numerical simulations of unstable and stable period-1 motions are completed from analytical predictions. The machine-tool chatter can emerge from the saddle-node or Neimark bifurcation of period-1 motions.

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.

Period-1 and Period-2 Motions in a Brusselator With a Harmonic Diffusion

2017 ◽  
Author(s):  
Albert C. J. Luo ◽  
Siyu Guo
Keyword(s):  
Numerical Simulations ◽  
Analytical Solutions ◽  
Eigenvalue Analysis ◽  
Harmonic Amplitude ◽  
Periodic Motions ◽  
Stable Period ◽  
Period 2 ◽  
Approximate Analytical Solutions ◽  
Stability And Bifurcations

In this paper, the analytical solutions of periodic evolution of Brusselator are investigated through the general harmonic balanced method. Both stable and unstable, period-1 and period-2 solutions of the Brussellator are presented. Stability and bifurcations of the periodic evolution are determined by the eigenvalue analysis. Numerical simulations of stable period-1 and period-2 motions of Brusselator are completed. The harmonic amplitude spectrums show harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions can be prescribed specifically.

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

DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
Author(s):  
LINNING QIAN ◽  
QISHAO LU ◽  
JIARU BAI ◽  
ZHAOSHENG FENG
Keyword(s):  
Numerical Simulations ◽  
Analytical Method ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Lambert W Function ◽  
Impulsive Effect ◽  
State Dependent ◽  
Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

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

scholarly journals Numerical Simulations of Advective Flows Around Black Holes

1997 ◽  
Vol 163 ◽  
pp. 690-691
Author(s):  
Sandip K. Chakrabarti ◽  
D. Ryu ◽  
D. Molteni ◽  
H. Sponholz ◽  
G. Lanzafame ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Periodic Oscillation ◽  
Compact Objects ◽  
Advective Flow ◽  
Sonic Point ◽  
Quasi Periodic Oscillation ◽  
Accretion Flows ◽  
Advective Flows ◽  
Cooling Effects ◽  
Implicit Code

Observational results of compact objects are best understood using advective accretion flows (Chakrabarti, 1996, 1997). We present here the results of numerical simulations of all possible types of such flows.Two parameter (specific energy ε and specific angular momentum λ) space of solutions of inviscid advective flow is classified into ‘SA’ (shocks in accretion), ‘NSA’ (no shock in accretion), ‘I’ (inner sonic point only), ‘O’ (outer sonic point only) etc. (Fig. 1 of Chakrabarti, 1997 and references therein). Fig. 1a shows examples of solutions (Molteni, Ryu & Chakrabarti, 1996; Eggum, in preparation) from ‘SA’, ‘I’ and ‘O’ regions where we superpose analytical (solid) and numerical simulations (short dashed curve is with SPH code and medium dashed curve is with TVD code; very long dashed curve is with explicit/implicit code). The agreement is excellent. In presence of cooling effects, shocks from ‘SA’ oscillate (Fig. 1b) when the cooling timescale roughly agrees with postshock infall time scale (Molteni, Sponholz & Chakrabarti, 1996). The solid, long dashed and short dashed curves are drawn for T1/2 (bremsstrahlung), T0.4 and T0.75 cooling laws respectively. In the absence of steady shock solutions, shocks for parameters from ‘NSA’ oscillate (Fig. 2) even in the absence of viscosity (Ryu et al. 1997). The oscillation frequency and amplitude roughly agree with those of quasi-periodic oscillation of black hole candidates. When the flow starts from a cool Keplerian disk, it simply becomes sub-Keplerian before it enters through the horizon. Fig. 3a shows this behaviour where the ratio of λ/λKeplerian is plotted. When the flow deviates from a hot Keplerian disk, it may develop a standing shock as well (Fig. 3b) (Molteni et al. 1996).

A New Approach to Blade Design With Constant Rake and Relief Angles for Face-Hobbing of Bevel Gears

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Mohsen Habibi ◽  
Zezhong Chevy Chen
Keyword(s):  
Tool Wear ◽  
Machine Tool ◽  
Computer Aided Design ◽  
Cutting Edge ◽  
Wear Characteristics ◽  
Bevel Gears ◽  
Cutting Velocity ◽  
Productive Process ◽  
Aided Design ◽  
Cutting System

Face-hobbing is a productive process to manufacture bevel and hypoid gears. Due to the complexity of face-hobbing, few research works have been conducted on this process. In face-hobbing, the cutting velocity along the cutting edge varies because of the intricate geometry of the cutting system and the machine tool kinematics. Due to the varying cutting velocity and the specific cutting system geometry, working relief and rake angles change along the cutting edge and have large variations at the corner which cause the local tool wear. In this paper, a new method to design cutting blades is proposed by changing the geometry of the rake and relief surfaces to avoid those large variations while the cutting edge is kept unchanged. In the proposed method, the working rake and relief angles are kept constant along the cutting edge by considering the varying cutting velocity and the machine tool kinematics. By applying the proposed method to design the blades, the tool wear characteristics are improved especially at the corner. In addition, in this paper, complete mathematical representations of the cutting system are presented. The working rake and relief angles are measured on the computer-aided design (CAD) model of the proposed and conventional blades and compared with each other. The results show that, unlike the conventional blade, in case of the proposed blade, the working rake and relief angles remain constant along the cutting edge. In addition, in order to validate the better tool wear characteristics of the proposed blade, finite element (FE) machining simulations are conducted on both the proposed and conventional blades. The results show improvements in the tool wear characteristics of the proposed blade in comparison with the conventional one.

Analysis of Chatter Vibration Through Step-Function Response

1972 ◽  
Vol 94 (4) ◽  
pp. 985-990
Author(s):  
H. Takeyama ◽  
O. Sakata
Keyword(s):  
Machine Tool ◽  
Step Function ◽  
Response Analysis ◽  
Chatter Vibration ◽  
First Approximation ◽  
Machine Tool Structure ◽  
On Line ◽  
Cutting Zone ◽  
Simple Evaluation ◽  
Cutting System

This paper deals with a challenge to apply the method of indicial response analysis for obtaining the frequency characteristics of total cutting system, tool system, and cutting zone. The feasibility of this method has been verified by simulation tests. Furthermore, linearity in cutting zone has been demonstrated to a first approximation by utilizing the proposed method. As examples of its application, on-line prediction or prevention of chatter vibration and simple evaluation of machine tool structure have been proposed.

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