Periodic Motions of the Machine Tools in Cutting Process

2007 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve S. Suh ◽  
Albert C. J. Luo
Keyword(s):  
Mechanical Model ◽  
Machine Tools ◽  
Degree Of Freedom ◽  
Cutting Process ◽  
Force Distribution ◽  
Periodic Motions ◽  
Numerical Predictions ◽  
Discontinuous Boundary ◽  
Mapping Structures ◽  
Two Degree Of Freedom

In this paper, a two-degree of freedom dynamical system with discontinuity is developed to describe the vibration in the cutting process. The analytical solutions for the switchability of motion on the discontinuous boundary are presented. the switching sets based on the discontinuous boundary is introduced and the basic mappings are introduced to investigate periodic motion in such a mechanical model. The mapping structures for the stick and non-stick motions are discussed. Numerical predictions of motions of the machine tool in the cutting process are presented through the two-degree of freedom system with discontinuity. The phase trajectory and velocity and force responses are presented and the switchability of motion on the discontinuous boundary is illustrated through force distribution and force product on the boundary.

On Motion Switchability in a Two Degree of Freedom, Friction-Induced Oscillator Traveling on Constant Speed Belts

2009 ◽  
Author(s):  
Albert C. J. Luo ◽  
Tingting Mao
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Constant Speed ◽  
Periodic Motions ◽  
Mapping Structures ◽  
Two Degree Of Freedom ◽  
Motion Complexity

In this paper, all possible stick and non-stick motions in such a friction-induced oscillator are discussed and the corresponding analytical conditions for the stick and non-stick motions to the traveling belts are presented. The mapping structures are introduced and the periodic motions of the two oscillators are presented through the corresponding mapping structure. Velocity and force responses for stick and non-stick, periodic motions in the 2-DOF friction-induced system are illustrated for a better understanding of the motion complexity in such many degrees of freedom systems.

Galloping Vibration of Nonlinear Cables Through a Two Degree-of-Freedom Oscillator

2016 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Transmission Line ◽  
Analytical Solutions ◽  
Transmission Lines ◽  
Nonlinear Oscillator ◽  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Two Degree Of Freedom

In this paper, galloping vibrations of a lightly iced transmission line are investigated through a two-degree-of-freedom (2-DOF) nonlinear oscillator. The 2-DOF nonlinear oscillator is used to describe the transverse and torsional motions of the galloping cables. The analytical solutions of periodic motions of galloping cables are presented through generalized harmonic balanced method. The analytical solutions of periodic motions for the galloping cable are compared with the numerical solutions, and the corresponding stability and bifurcation of periodic motions are analyzed by the eigenvalues analysis. To demonstrate the accuracy of the analytical solutions of periodic motions, the harmonic amplitudes are presented. This investigation will help one better understand galloping mechanism of iced transmission lines.

The Research of Damping Adjustable Isolators Control Method

2013 ◽  
Vol 774-776 ◽  
pp. 44-47
Author(s):  
Bo Jiang
Keyword(s):  
Fuzzy Control ◽  
Mechanical Model ◽  
Control Method ◽  
Simulation Analysis ◽  
Degree Of Freedom ◽  
Matlab Software ◽  
Fluid Damping ◽  
Two Degree Of Freedom

The mechanical model of the electro-rheological fluid damping adjustable isolator is established. Then the two degree of freedom vibration adjusting system of engine and car frame is built. The PD fuzzy control method is used to control the damping characteristic of the damping adjustable isolator. Simulation analysis is executed by using Matlab software. The datum of simulation analysis indicates that the isolation capability of the PD fuzzy control electro-rheological fluid damping adjustable isolator is well.

Bifurcation Trees of Period-1 Motions to Chaos in a Two-Degree-of-Freedom, Nonlinear Oscillator

2015 ◽  
Vol 25 (13) ◽  
pp. 1550179 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Dynamical System ◽  
Fourier Series ◽  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Degree Of Freedom ◽  
Harmonic Amplitude ◽  
Periodic Motions ◽  
Series Transformation ◽  
Two Degree Of Freedom ◽  
Analytical Bifurcation Trees

In this paper, analytical solutions for period-[Formula: see text] motions in a two-degree-of-freedom (2-DOF) nonlinear oscillator are developed through the finite Fourier series. From the finite Fourier series transformation, the dynamical system of coefficients of the finite Fourier series is developed. From such a dynamical system, the solutions of period-[Formula: see text] motions are obtained and the corresponding stability and bifurcation analyses of period-[Formula: see text] motions are carried out. Analytical bifurcation trees of period-1 motions to chaos are presented. Displacements, velocities and trajectories of periodic motions in the 2-DOF nonlinear oscillator are used to illustrate motion complexity, and harmonic amplitude spectrums give harmonic effects on periodic motions of the 2-DOF nonlinear oscillator.

Bifurcation Trees of a Periodically Forced, Two-Degree-of-Freedom Oscillator With a Nonlinear Hardening Spring

2015 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Analytical Solutions ◽  
Degree Of Freedom ◽  
Harmonic Amplitude ◽  
Periodic Motions ◽  
Stable Period ◽  
Period 2 ◽  
Approximate Analytical Solutions ◽  
The Stability ◽  
Nonlinear Hardening ◽  
Two Degree Of Freedom

In this paper, analytical solutions of periodic motions in a periodically forced, damped, two-degree-of-freedom oscillator with a nonlinear hardening spring are obtained. The bifurcation trees of periodic motions are presented, and the stability and bifurcation of the periodic motion are determined through the eigenvalue analysis. Numerical simulations of stable period-1 and period-2 motions in the two-degree-of-freedom systems are presented, and the harmonic amplitude spectrums are presented to show the harmonic effects on periodic motions, and the accuracy of approximate analytical solutions can be estimated through the harmonic amplitudes.

Analytical Prediction of Periodic Motions in a Machine Tool With Loss of Effective Chip Contact

2008 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steven C. S. Suh ◽  
Albert C. J. Luo
Keyword(s):  
Machine Tool ◽  
Closed Form ◽  
Systems Theory ◽  
Phase Trajectory ◽  
Degree Of Freedom ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Discontinuous Systems ◽  
Closed Form Solutions ◽  
Two Degree Of Freedom

This study applies a discontinuous systems theory by Luo (2005) to an approximate machine-tool model. The machine-tool is modeled by a two-degree of freedom forced switching oscillator. The switching of the model emulates the various types of dynamics in a machine-tool system. The main focus of this study is the loss of effective chip contact and boundaries of this motion. The periodic motions will be studied through the mappings developed for this machine-tool. The periodic motions will be numerically and analytically predicted via closed form solutions. The phase trajectory, velocity, and force responses are presented.

scholarly journals MECHANICAL MODEL FOR HUMAN BALANCING ON ROLLING BALANCE BOARD

2018 ◽  
Vol 18 ◽  
pp. 32 ◽  
Author(s):  
Csenge A. Molnar ◽  
Ambrus Zelei ◽  
Tamas Insperger
Keyword(s):  
Mechanical Model ◽  
Frontal Plane ◽  
Degree Of Freedom ◽  
Upper Body ◽  
Feedback Delay ◽  
Human Balancing ◽  
Simulation Results ◽  
Two Degree Of Freedom ◽  
Balance Board ◽  
Human Nervous System

A two-degree-of-freedom mechanical model was developed to analyze human balancing on rolling balance board in the frontal plane. The human nervous system is modeled as a proportionalderivative controller with constant feedback delay. The radius R of the wheels and the board distance h measured from the center of the wheel are adjustable parameters. Simulation results using the mechanical model were compared with real balancing trials recorded by an OptiTrack motion capture system. The goal of the paper is to investigate whether the two-degree-of-freedom model is accurate enough to model the balancing task and to introduce a stabilometry parameter in order to characterize balancing skill in case of different set of R and h. The conclusion is that the angle of the upper body and the angle of the head also play an important role in the balancing process therefore a three- or four-degree-of-freedom model is more appropriate.

scholarly journals Dynamics and Stability of a Two Degree of Freedom Oscillator With an Elastic Stop

2005 ◽  
Vol 1 (1) ◽  
pp. 94-102 ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Periodic Solutions ◽  
Analytical Form ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
External Excitation ◽  
Time Duration ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Two Degree Of Freedom

A two degree of freedom oscillator with a colliding component is considered. The aim of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes to a finite value to an infinite one. Several cases are considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are found in analytical form. In the case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases.

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